0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n059.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:52:24 CST 2018
50.61/50.85	% done 15174 iterations in 50.642s
50.61/50.85	% SZS status Theorem for 'stdin'
50.61/50.85	% SZS output start Refutation
50.61/50.85	tff(zf_stmt_4, conjecture,
50.61/50.85	  (![Xr:app_encode_fun(a,app_encode_fun(a,$o))]:
50.61/50.85	     ((![Xx:a,Xy:a]:
50.61/50.85	         (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xr,Xx),Xy) =>
50.61/50.85	          (![Xq:app_encode_fun(a,$o)]:
50.61/50.85	             (((![Xw:a]:
50.61/50.85	                  (app_encode_app(a,$o,
50.61/50.85	                                  app_encode_app(a,app_encode_fun(a,$o),Xr,Xx),
50.61/50.85	                                  Xw) =>
50.61/50.85	                   app_encode_app(a,$o,Xq,Xw))) & 
50.61/50.85	               (![Xv:a,Xw:a]:
50.61/50.85	                  ((app_encode_app(a,$o,Xq,Xv) & 
50.61/50.85	                    app_encode_app(a,$o,
50.61/50.85	                                   app_encode_app(a,app_encode_fun(a,$o),Xr,
50.61/50.85	                                                  Xv),
50.61/50.85	                                   Xw)) =>
50.61/50.85	                   app_encode_app(a,$o,Xq,Xw)))) =>
50.61/50.85	              app_encode_app(a,$o,Xq,Xy))))) & 
50.61/50.85	      (![Xx:a,Xy:a,Xz:a]:
50.61/50.85	         (((![Xq:app_encode_fun(a,$o)]:
50.61/50.85	              (((![Xw:a]:
50.61/50.85	                   (app_encode_app(a,$o,
50.61/50.85	                                   app_encode_app(a,app_encode_fun(a,$o),Xr,
50.61/50.85	                                                  Xx),
50.61/50.85	                                   Xw) =>
50.61/50.85	                    app_encode_app(a,$o,Xq,Xw))) & 
50.61/50.85	                (![Xv:a,Xw:a]:
50.61/50.85	                   ((app_encode_app(a,$o,Xq,Xv) & 
50.61/50.85	                     app_encode_app(a,$o,
50.61/50.85	                                    app_encode_app(a,app_encode_fun(a,$o),Xr,
50.61/50.85	                                                   Xv),
50.61/50.85	                                    Xw)) =>
50.61/50.85	                    app_encode_app(a,$o,Xq,Xw)))) =>
50.61/50.85	               app_encode_app(a,$o,Xq,Xy))) & 
50.61/50.85	           (![Xq:app_encode_fun(a,$o)]:
50.61/50.85	              (((![Xw:a]:
50.61/50.85	                   (app_encode_app(a,$o,
50.61/50.85	                                   app_encode_app(a,app_encode_fun(a,$o),Xr,
50.61/50.85	                                                  Xy),
50.61/50.85	                                   Xw) =>
50.61/50.85	                    app_encode_app(a,$o,Xq,Xw))) & 
50.61/50.85	                (![Xv:a,Xw:a]:
50.61/50.85	                   ((app_encode_app(a,$o,Xq,Xv) & 
50.61/50.85	                     app_encode_app(a,$o,
50.61/50.85	                                    app_encode_app(a,app_encode_fun(a,$o),Xr,
50.61/50.85	                                                   Xv),
50.61/50.85	                                    Xw)) =>
50.61/50.85	                    app_encode_app(a,$o,Xq,Xw)))) =>
50.61/50.85	               app_encode_app(a,$o,Xq,Xz)))) =>
50.61/50.85	          (![Xq:app_encode_fun(a,$o)]:
50.61/50.85	             (((![Xw:a]:
50.61/50.85	                  (app_encode_app(a,$o,
50.61/50.85	                                  app_encode_app(a,app_encode_fun(a,$o),Xr,Xx),
50.61/50.85	                                  Xw) =>
50.61/50.85	                   app_encode_app(a,$o,Xq,Xw))) & 
50.61/50.85	               (![Xv:a,Xw:a]:
50.61/50.85	                  ((app_encode_app(a,$o,Xq,Xv) & 
50.61/50.85	                    app_encode_app(a,$o,
50.61/50.85	                                   app_encode_app(a,app_encode_fun(a,$o),Xr,
50.61/50.85	                                                  Xv),
50.61/50.85	                                   Xw)) =>
50.61/50.85	                   app_encode_app(a,$o,Xq,Xw)))) =>
50.61/50.85	              app_encode_app(a,$o,Xq,Xz)))))))).
50.61/50.85	tff(zf_stmt_0, negated_conjecture,
50.61/50.85	  (~
50.61/50.85	    (![Xr:app_encode_fun(a,app_encode_fun(a,$o))]:
50.61/50.85	       ((![Xx:a,Xy:a]:
50.61/50.85	           (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xr,Xx),
50.61/50.85	                           Xy) =>
50.61/50.85	            (![Xq:app_encode_fun(a,$o)]:
50.61/50.85	               (((![Xw:a]:
50.61/50.85	                    (app_encode_app(a,$o,
50.61/50.85	                                    app_encode_app(a,app_encode_fun(a,$o),Xr,
50.61/50.85	                                                   Xx),
50.61/50.85	                                    Xw) =>
50.61/50.85	                     app_encode_app(a,$o,Xq,Xw))) & 
50.61/50.85	                 (![Xv:a,Xw:a]:
50.61/50.85	                    ((app_encode_app(a,$o,Xq,Xv) & 
50.61/50.85	                      app_encode_app(a,$o,
50.61/50.85	                                     app_encode_app(a,app_encode_fun(a,$o),
50.61/50.85	                                                    Xr,Xv),
50.61/50.85	                                     Xw)) =>
50.61/50.85	                     app_encode_app(a,$o,Xq,Xw)))) =>
50.61/50.85	                app_encode_app(a,$o,Xq,Xy))))) & 
50.61/50.85	        (![Xx:a,Xy:a,Xz:a]:
50.61/50.85	           (((![Xq:app_encode_fun(a,$o)]:
50.61/50.85	                (((![Xw:a]:
50.61/50.85	                     (app_encode_app(a,$o,
50.61/50.85	                                     app_encode_app(a,app_encode_fun(a,$o),
50.61/50.85	                                                    Xr,Xx),
50.61/50.85	                                     Xw) =>
50.61/50.85	                      app_encode_app(a,$o,Xq,Xw))) & 
50.61/50.85	                  (![Xv:a,Xw:a]:
50.61/50.85	                     ((app_encode_app(a,$o,Xq,Xv) & 
50.61/50.85	                       app_encode_app(a,$o,
50.61/50.85	                                      app_encode_app(a,app_encode_fun(a,$o),
50.61/50.85	                                                     Xr,Xv),
50.61/50.85	                                      Xw)) =>
50.61/50.85	                      app_encode_app(a,$o,Xq,Xw)))) =>
50.61/50.85	                 app_encode_app(a,$o,Xq,Xy))) & 
50.61/50.85	             (![Xq:app_encode_fun(a,$o)]:
50.61/50.85	                (((![Xw:a]:
50.61/50.85	                     (app_encode_app(a,$o,
50.61/50.85	                                     app_encode_app(a,app_encode_fun(a,$o),
50.61/50.85	                                                    Xr,Xy),
50.61/50.85	                                     Xw) =>
50.61/50.85	                      app_encode_app(a,$o,Xq,Xw))) & 
50.61/50.85	                  (![Xv:a,Xw:a]:
50.61/50.85	                     ((app_encode_app(a,$o,Xq,Xv) & 
50.61/50.85	                       app_encode_app(a,$o,
50.61/50.85	                                      app_encode_app(a,app_encode_fun(a,$o),
50.61/50.85	                                                     Xr,Xv),
50.61/50.85	                                      Xw)) =>
50.61/50.85	                      app_encode_app(a,$o,Xq,Xw)))) =>
50.61/50.85	                 app_encode_app(a,$o,Xq,Xz)))) =>
50.61/50.85	            (![Xq:app_encode_fun(a,$o)]:
50.61/50.85	               (((![Xw:a]:
50.61/50.85	                    (app_encode_app(a,$o,
50.61/50.85	                                    app_encode_app(a,app_encode_fun(a,$o),Xr,
50.61/50.85	                                                   Xx),
50.61/50.85	                                    Xw) =>
50.61/50.85	                     app_encode_app(a,$o,Xq,Xw))) & 
50.61/50.85	                 (![Xv:a,Xw:a]:
50.61/50.85	                    ((app_encode_app(a,$o,Xq,Xv) & 
50.61/50.85	                      app_encode_app(a,$o,
50.61/50.85	                                     app_encode_app(a,app_encode_fun(a,$o),
50.61/50.85	                                                    Xr,Xv),
50.61/50.85	                                     Xw)) =>
50.61/50.85	                     app_encode_app(a,$o,Xq,Xw)))) =>
50.61/50.85	                app_encode_app(a,$o,Xq,Xz))))))))).
50.61/50.85	tff('0', plain,
50.61/50.85	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.85	      (app_encode_app(a, $o, 
50.61/50.85	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, X6, sk_Xv1(X6))
50.61/50.85	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.85	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.85	tff('1', plain,
50.61/50.85	    ![X4 : a, X6 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.85	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, X6, sk_Xv1(X6))
50.61/50.85	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.85	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.85	tff('2', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ $true
50.61/50.85	       | ~ app_encode_app(a, $o, X1, sk_Xw3(X1))
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.85	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.85	    inference('sup-', [status(thm)], ['0', '1'])).
50.61/50.85	tff('3', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.85	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.85	       | ~ app_encode_app(a, $o, X1, sk_Xw3(X1))),
50.61/50.85	    inference('simplify', [status(thm)], ['2'])).
50.61/50.85	tff('4', plain,
50.61/50.85	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, X6, sk_Xv1(X6))
50.61/50.85	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.85	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.85	tff('5', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, X1, sk_Xw3(X1))
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.85	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.85	    inference('clc', [status(thm)], ['3', '4'])).
50.61/50.85	tff('6', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ $true
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
50.61/50.85	    inference('eq_fact', [status(thm)], ['5'])).
50.61/50.85	tff('7', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.85	    inference('simplify', [status(thm)], ['6'])).
50.61/50.85	tff('8', plain,
50.61/50.85	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.85	      (app_encode_app(a, $o, 
50.61/50.85	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X6)), 
50.61/50.85	           sk_Xw2(X6))
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.85	           sk_Xw3(X6))),
50.61/50.85	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.85	tff('9', plain,
50.61/50.85	    ![X7 : a, X8 : a]:
50.61/50.85	      (app_encode_app(a, $o, 
50.61/50.85	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, X7)
50.61/50.85	       | ~ app_encode_app(a, $o, 
50.61/50.85	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X7), X8)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, X8)),
50.61/50.85	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.85	tff('10', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ $true
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.85	           sk_Xw3(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.85	    inference('sup-', [status(thm)], ['8', '9'])).
50.61/50.85	tff('11', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.85	           sk_Xw3(X0))),
50.61/50.85	    inference('simplify', [status(thm)], ['10'])).
50.61/50.85	tff('12', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ $true
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.85	    inference('sup-', [status(thm)], ['11', '9'])).
50.61/50.85	tff('13', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.85	    inference('simplify', [status(thm)], ['12'])).
50.61/50.85	tff('14', plain,
50.61/50.85	    ![X4 : a, X6 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.85	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X6)), 
50.61/50.85	           sk_Xw2(X6))
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.85	           sk_Xw3(X6))),
50.61/50.85	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.85	tff('15', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ $true
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.85	           sk_Xw3(X0))
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
50.61/50.85	           sk_Xw2(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.85	    inference('sup-', [status(thm)], ['13', '14'])).
50.61/50.85	tff('16', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.85	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
50.61/50.85	           sk_Xw2(X0))
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.85	           sk_Xw3(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xz)),
50.61/50.85	    inference('simplify', [status(thm)], ['15'])).
50.61/50.85	tff('17', plain,
50.61/50.85	    ![X4 : a, X7 : a, X8 : a]:
50.61/50.85	      (~ app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, X7)
50.61/50.85	       | ~ app_encode_app(a, $o, 
50.61/50.85	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X7), X8)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, X8)),
50.61/50.85	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.85	tff('18', plain,
50.61/50.85	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ $true
50.61/50.85	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.85	       | ~ app_encode_app(a, $o, 
50.61/50.85	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.85	    inference('sup-', [status(thm)], ['13', '17'])).
50.61/50.85	tff('19', plain,
50.61/50.85	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.85	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.85	       | ~ app_encode_app(a, $o, 
50.61/50.85	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.85	       | app_encode_app(a, $o, X2, sk_Xz)),
50.61/50.85	    inference('simplify', [status(thm)], ['18'])).
50.61/50.85	tff('20', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.85	      X2 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ $true
50.61/50.85	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.85	           sk_Xw3(X0))
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.85	    inference('sup-', [status(thm)], ['16', '19'])).
50.61/50.85	tff('21', plain,
50.61/50.85	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.85	      X2 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.85	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.85	       | app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.85	           sk_Xw3(X0))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.85	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.85	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.85	       | app_encode_app(a, $o, X2, sk_Xz)),
50.61/50.85	    inference('simplify', [status(thm)], ['20'])).
50.61/50.85	tff('22', plain,
50.61/50.85	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.85	      (app_encode_app(a, $o, 
50.61/50.85	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.85	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.85	       | app_encode_app(a, $o, X5, sk_Xv(X5))
50.61/50.85	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.85	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.85	tff('23', plain,
50.61/50.85	    ![X4 : a, X5 : app_encode_fun(a, $o)]:
50.61/50.85	      (~ app_encode_app(a, $o, 
50.61/50.85	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.85	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.85	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xv(X5))
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('24', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['22', '23'])).
50.61/50.86	tff('25', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
50.61/50.86	    inference('simplify', [status(thm)], ['24'])).
50.61/50.86	tff('26', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xv(X5))
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('27', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, X1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['25', '26'])).
50.61/50.86	tff('28', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))),
50.61/50.86	    inference('eq_fact', [status(thm)], ['27'])).
50.61/50.86	tff('29', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['28'])).
50.61/50.86	tff('30', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X5)), 
50.61/50.86	           sk_Xw(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('31', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['30', '9'])).
50.61/50.86	tff('32', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['31'])).
50.61/50.86	tff('33', plain,
50.61/50.86	    ![X9 : a]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X9)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X9)),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('34', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['32', '33'])).
50.61/50.86	tff('35', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['34'])).
50.61/50.86	tff('36', plain,
50.61/50.86	    ![X4 : a, X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X5)), 
50.61/50.86	           sk_Xw(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('37', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
50.61/50.86	           sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['35', '36'])).
50.61/50.86	tff('38', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
50.61/50.86	           sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['37'])).
50.61/50.86	tff('39', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X5)), 
50.61/50.86	           sk_Xw(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('40', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
50.61/50.86	           sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['38', '39'])).
50.61/50.86	tff('41', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['35', '17'])).
50.61/50.86	tff('42', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['41'])).
50.61/50.86	tff('43', plain,
50.61/50.86	    ![X7 : a, X8 : a]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X7)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X7), X8)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X8)),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('44', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X2, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)),
50.61/50.86	    inference('clc', [status(thm)], ['42', '43'])).
50.61/50.86	tff('45', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['40', '44'])).
50.61/50.86	tff('46', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X2))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['45'])).
50.61/50.86	tff('47', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['46'])).
50.61/50.86	tff('48', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['47'])).
50.61/50.86	tff('49', plain,
50.61/50.86	    ![X4 : a, X9 : a]:
50.61/50.86	      (~ app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X9)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X9)),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('50', plain,
50.61/50.86	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['35', '49'])).
50.61/50.86	tff('51', plain,
50.61/50.86	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['50'])).
50.61/50.86	tff('52', plain,
50.61/50.86	    ![X9 : a]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X9)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X9)),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('53', plain,
50.61/50.86	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)),
50.61/50.86	    inference('clc', [status(thm)], ['51', '52'])).
50.61/50.86	tff('54', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['48', '53'])).
50.61/50.86	tff('55', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X2))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['54'])).
50.61/50.86	tff('56', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['55'])).
50.61/50.86	tff('57', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['56'])).
50.61/50.86	tff('58', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))),
50.61/50.86	    inference('eq_fact', [status(thm)], ['57'])).
50.61/50.86	tff('59', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['58'])).
50.61/50.86	tff('60', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('61', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	         sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['59', '60'])).
50.61/50.86	tff('62', plain,
50.61/50.86	    (app_encode_app(a, $o, 
50.61/50.86	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	         sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['61'])).
50.61/50.86	tff('63', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('clc', [status(thm)], ['62', '33'])).
50.61/50.86	tff('64', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xv(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('65', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['64', '33'])).
50.61/50.86	tff('66', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['65'])).
50.61/50.86	tff('67', plain,
50.61/50.86	    ![X4 : a, X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xv(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('68', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['66', '67'])).
50.61/50.86	tff('69', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv(X1))),
50.61/50.86	    inference('simplify', [status(thm)], ['68'])).
50.61/50.86	tff('70', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xv(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('71', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['70', '52'])).
50.61/50.86	tff('72', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['71'])).
50.61/50.86	tff('73', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['69', '72'])).
50.61/50.86	tff('74', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['73'])).
50.61/50.86	tff('75', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['74'])).
50.61/50.86	tff('76', plain,
50.61/50.86	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['66', '49'])).
50.61/50.86	tff('77', plain,
50.61/50.86	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv(X1))),
50.61/50.86	    inference('simplify', [status(thm)], ['76'])).
50.61/50.86	tff('78', plain,
50.61/50.86	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)),
50.61/50.86	    inference('clc', [status(thm)], ['77', '52'])).
50.61/50.86	tff('79', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv(X1))),
50.61/50.86	    inference('sup-', [status(thm)], ['75', '78'])).
50.61/50.86	tff('80', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xv(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['79'])).
50.61/50.86	tff('81', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['80'])).
50.61/50.86	tff('82', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['81'])).
50.61/50.86	tff('83', plain,
50.61/50.86	    (app_encode_app(a, $o, 
50.61/50.86	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['63', '82'])).
50.61/50.86	tff('84', plain,
50.61/50.86	    ![X4 : a, X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('85', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['83', '84'])).
50.61/50.86	tff('86', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['85'])).
50.61/50.86	tff('87', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['39', '43'])).
50.61/50.86	tff('88', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['87'])).
50.61/50.86	tff('89', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['88', '52'])).
50.61/50.86	tff('90', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['89'])).
50.61/50.86	tff('91', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw(X5))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('92', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	         sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['90', '91'])).
50.61/50.86	tff('93', plain,
50.61/50.86	    (app_encode_app(a, $o, 
50.61/50.86	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	       sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['92'])).
50.61/50.86	tff('94', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
50.61/50.86	    inference('clc', [status(thm)], ['93', '52'])).
50.61/50.86	tff('95', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['94', '72'])).
50.61/50.86	tff('96', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	           sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['86', '95'])).
50.61/50.86	tff('97', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	         sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['59', '96'])).
50.61/50.86	tff('98', plain,
50.61/50.86	    (app_encode_app(a, $o, 
50.61/50.86	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	       sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['97'])).
50.61/50.86	tff('99', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
50.61/50.86	         sk_Xw1(sk_Xq1))),
50.61/50.86	    inference('clc', [status(thm)], ['98', '82'])).
50.61/50.86	tff('100', plain,
50.61/50.86	    ![X0 : a]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['83', '49'])).
50.61/50.86	tff('101', plain,
50.61/50.86	    ![X0 : a]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['100'])).
50.61/50.86	tff('102', plain,
50.61/50.86	    ![X0 : a]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)),
50.61/50.86	    inference('clc', [status(thm)], ['101', '52'])).
50.61/50.86	tff('103', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['99', '102'])).
50.61/50.86	tff('104', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
50.61/50.86	    inference('simplify', [status(thm)], ['103'])).
50.61/50.86	tff('105', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X5)), 
50.61/50.86	           sk_Xw(X5))
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('106', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['105', '9'])).
50.61/50.86	tff('107', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['106'])).
50.61/50.86	tff('108', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))),
50.61/50.86	    inference('sup-', [status(thm)], ['104', '107'])).
50.61/50.86	tff('109', plain,
50.61/50.86	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['108'])).
50.61/50.86	tff('110', plain,
50.61/50.86	    ![X4 : a, X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X5)), 
50.61/50.86	           sk_Xw(X5))
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('111', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
50.61/50.86	           sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['109', '110'])).
50.61/50.86	tff('112', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
50.61/50.86	           sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['111'])).
50.61/50.86	tff('113', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X5)), 
50.61/50.86	           sk_Xw(X5))
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('114', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['113', '43'])).
50.61/50.86	tff('115', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['114'])).
50.61/50.86	tff('116', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))),
50.61/50.86	    inference('sup-', [status(thm)], ['95', '115'])).
50.61/50.86	tff('117', plain,
50.61/50.86	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['116'])).
50.61/50.86	tff('118', plain,
50.61/50.86	    ![X4 : a, X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw(X5))
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('119', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['109', '118'])).
50.61/50.86	tff('120', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['119'])).
50.61/50.86	tff('121', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw(X5))
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('122', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['120', '121'])).
50.61/50.86	tff('123', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['117', '122'])).
50.61/50.86	tff('124', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['123'])).
50.61/50.86	tff('125', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
50.61/50.86	    inference('clc', [status(thm)], ['124', '121'])).
50.61/50.86	tff('126', plain,
50.61/50.86	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['125', '29'])).
50.61/50.86	tff('127', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('clc', [status(thm)], ['126', '104'])).
50.61/50.86	tff('128', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
50.61/50.86	           sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['112', '127'])).
50.61/50.86	tff('129', plain,
50.61/50.86	    ![X0 : a, X1 : a]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['109', '17'])).
50.61/50.86	tff('130', plain,
50.61/50.86	    ![X0 : a, X1 : a]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['129'])).
50.61/50.86	tff('131', plain,
50.61/50.86	    ![X0 : a, X1 : a]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)),
50.61/50.86	    inference('clc', [status(thm)], ['130', '127'])).
50.61/50.86	tff('132', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['128', '131'])).
50.61/50.86	tff('133', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['132'])).
50.61/50.86	tff('134', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))),
50.61/50.86	    inference('sup-', [status(thm)], ['104', '133'])).
50.61/50.86	tff('135', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['134'])).
50.61/50.86	tff('136', plain,
50.61/50.86	    ![X5 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X5, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw(X5))
50.61/50.86	       | ~ app_encode_app(a, $o, X5, sk_Xw1(X5))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('137', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['135', '136'])).
50.61/50.86	tff('138', plain,
50.61/50.86	    (app_encode_app(a, $o, 
50.61/50.86	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['137'])).
50.61/50.86	tff('139', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('clc', [status(thm)], ['138', '104'])).
50.61/50.86	tff('140', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['139', '118'])).
50.61/50.86	tff('141', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))),
50.61/50.86	    inference('simplify', [status(thm)], ['140'])).
50.61/50.86	tff('142', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)),
50.61/50.86	    inference('clc', [status(thm)], ['141', '127'])).
50.61/50.86	tff('143', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['29', '142'])).
50.61/50.86	tff('144', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, X0, sk_Xw1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['143'])).
50.61/50.86	tff('145', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xy1)
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))),
50.61/50.86	    inference('clc', [status(thm)], ['144', '104'])).
50.61/50.86	tff('146', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['135', '145'])).
50.61/50.86	tff('147', plain,
50.61/50.86	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['146'])).
50.61/50.86	tff('148', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))),
50.61/50.86	    inference('clc', [status(thm)], ['147', '104'])).
50.61/50.86	tff('149', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('sup-', [status(thm)], ['29', '148'])).
50.61/50.86	tff('150', plain,
50.61/50.86	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.86	    inference('simplify', [status(thm)], ['149'])).
50.61/50.86	tff('151', plain, app_encode_app(a, $o, sk_Xq1, sk_Xy1),
50.61/50.86	    inference('clc', [status(thm)], ['150', '104'])).
50.61/50.86	tff('152', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | ~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)),
50.61/50.86	    inference('demod', [status(thm)], ['21', '151'])).
50.61/50.86	tff('153', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['152'])).
50.61/50.86	tff('154', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['153'])).
50.61/50.86	tff('155', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))),
50.61/50.86	    inference('simplify', [status(thm)], ['154'])).
50.61/50.86	tff('156', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['155', '9'])).
50.61/50.86	tff('157', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ $true
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('demod', [status(thm)], ['156', '151'])).
50.61/50.86	tff('158', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['157'])).
50.61/50.86	tff('159', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['158'])).
50.61/50.86	tff('160', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['159'])).
50.61/50.86	tff('161', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
50.61/50.86	           sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['160', '14'])).
50.61/50.86	tff('162', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
50.61/50.86	           sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))),
50.61/50.86	    inference('simplify', [status(thm)], ['161'])).
50.61/50.86	tff('163', plain,
50.61/50.86	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X6)), 
50.61/50.86	           sk_Xw2(X6))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X6))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('164', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
50.61/50.86	           sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('clc', [status(thm)], ['162', '163'])).
50.61/50.86	tff('165', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['160', '17'])).
50.61/50.86	tff('166', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))),
50.61/50.86	    inference('simplify', [status(thm)], ['165'])).
50.61/50.86	tff('167', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)),
50.61/50.86	    inference('clc', [status(thm)], ['166', '43'])).
50.61/50.86	tff('168', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))),
50.61/50.86	    inference('sup-', [status(thm)], ['164', '167'])).
50.61/50.86	tff('169', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['168'])).
50.61/50.86	tff('170', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.86	    inference('eq_fact', [status(thm)], ['169'])).
50.61/50.86	tff('171', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['170'])).
50.61/50.86	tff('172', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))),
50.61/50.86	    inference('sup-', [status(thm)], ['171', '167'])).
50.61/50.86	tff('173', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))),
50.61/50.86	    inference('demod', [status(thm)], ['172', '151'])).
50.61/50.86	tff('174', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['173'])).
50.61/50.86	tff('175', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.86	    inference('eq_fact', [status(thm)], ['174'])).
50.61/50.86	tff('176', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['175'])).
50.61/50.86	tff('177', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.86	    inference('eq_fact', [status(thm)], ['176'])).
50.61/50.86	tff('178', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['177'])).
50.61/50.86	tff('179', plain,
50.61/50.86	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.86	       | ~ app_encode_app(a, $o, X6, sk_Xw2(X6))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X6))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('180', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	         sk_Xw3(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['178', '179'])).
50.61/50.86	tff('181', plain,
50.61/50.86	    (app_encode_app(a, $o, 
50.61/50.86	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	     | app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	         sk_Xw3(sk_Xq1))
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['180'])).
50.61/50.86	tff('182', plain,
50.61/50.86	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X6, sk_Xv1(X6))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X6))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('183', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['182', '9'])).
50.61/50.86	tff('184', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['183'])).
50.61/50.86	tff('185', plain,
50.61/50.86	    ![X4 : a, X6 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.86	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X6, sk_Xv1(X6))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X6))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('186', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['184', '185'])).
50.61/50.86	tff('187', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv1(X1))),
50.61/50.86	    inference('simplify', [status(thm)], ['186'])).
50.61/50.86	tff('188', plain,
50.61/50.86	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X6, sk_Xv1(X6))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X6))),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('189', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('clc', [status(thm)], ['187', '188'])).
50.61/50.86	tff('190', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['189'])).
50.61/50.86	tff('191', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['190'])).
50.61/50.86	tff('192', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['184', '17'])).
50.61/50.86	tff('193', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xv1(X2))),
50.61/50.86	    inference('simplify', [status(thm)], ['192'])).
50.61/50.86	tff('194', plain,
50.61/50.86	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X2, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.86	       | ~ app_encode_app(a, $o, 
50.61/50.86	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, X1)),
50.61/50.86	    inference('clc', [status(thm)], ['193', '43'])).
50.61/50.86	tff('195', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv1(X1))),
50.61/50.86	    inference('sup-', [status(thm)], ['191', '194'])).
50.61/50.86	tff('196', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['195'])).
50.61/50.86	tff('197', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['196'])).
50.61/50.86	tff('198', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['197'])).
50.61/50.86	tff('199', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['13', '185'])).
50.61/50.86	tff('200', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['199'])).
50.61/50.86	tff('201', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['200', '19'])).
50.61/50.86	tff('202', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['201'])).
50.61/50.86	tff('203', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | ~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | app_encode_app(a, $o, X2, sk_Xz)),
50.61/50.86	    inference('demod', [status(thm)], ['202', '151'])).
50.61/50.86	tff('204', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o), 
50.61/50.86	      X2 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X2, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X2))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X2))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['203'])).
50.61/50.86	tff('205', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.86	    inference('eq_fact', [status(thm)], ['204'])).
50.61/50.86	tff('206', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))),
50.61/50.86	    inference('simplify', [status(thm)], ['205'])).
50.61/50.86	tff('207', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['206', '179'])).
50.61/50.86	tff('208', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['207'])).
50.61/50.86	tff('209', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['208', '9'])).
50.61/50.86	tff('210', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | ~ $true
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('demod', [status(thm)], ['209', '151'])).
50.61/50.86	tff('211', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, 
50.61/50.86	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.86	    inference('simplify', [status(thm)], ['210'])).
50.61/50.86	tff('212', plain,
50.61/50.86	    (app_encode_app(a, $o, 
50.61/50.86	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('213', plain,
50.61/50.86	    ![X4 : a]:
50.61/50.86	      (~ app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('214', plain,
50.61/50.86	    (~ $true
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.86	     | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['212', '213'])).
50.61/50.86	tff('215', plain,
50.61/50.86	    (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.86	    inference('simplify', [status(thm)], ['214'])).
50.61/50.86	tff('216', plain,
50.61/50.86	    (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.86	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.86	tff('217', plain, ~ app_encode_app(a, $o, sk_Xq1, sk_Xz),
50.61/50.86	    inference('clc', [status(thm)], ['215', '216'])).
50.61/50.86	tff('218', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.86	    inference('clc', [status(thm)], ['211', '217'])).
50.61/50.86	tff('219', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.86	    inference('sup-', [status(thm)], ['218', '185'])).
50.61/50.86	tff('220', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.86	      (app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.86	           sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, X1, sk_Xv1(X1))),
50.61/50.86	    inference('simplify', [status(thm)], ['219'])).
50.61/50.86	tff('221', plain,
50.61/50.86	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.86	      (~ $true
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.86	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.86	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.86	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.86	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.86	       | app_encode_app(a, $o, 
50.61/50.86	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('eq_fact', [status(thm)], ['220'])).
50.61/50.87	tff('222', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['221'])).
50.61/50.87	tff('223', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))),
50.61/50.87	    inference('clc', [status(thm)], ['222', '188'])).
50.61/50.87	tff('224', plain,
50.61/50.87	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['218', '17'])).
50.61/50.87	tff('225', plain,
50.61/50.87	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xv1(X2))),
50.61/50.87	    inference('simplify', [status(thm)], ['224'])).
50.61/50.87	tff('226', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.87	    inference('sup-', [status(thm)], ['223', '225'])).
50.61/50.87	tff('227', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ $true),
50.61/50.87	    inference('demod', [status(thm)], ['226', '151'])).
50.61/50.87	tff('228', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['227'])).
50.61/50.87	tff('229', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))),
50.61/50.87	    inference('sup-', [status(thm)], ['198', '228'])).
50.61/50.87	tff('230', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))),
50.61/50.87	    inference('demod', [status(thm)], ['229', '151'])).
50.61/50.87	tff('231', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['230'])).
50.61/50.87	tff('232', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('eq_fact', [status(thm)], ['231'])).
50.61/50.87	tff('233', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['232'])).
50.61/50.87	tff('234', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['223', '43'])).
50.61/50.87	tff('235', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('demod', [status(thm)], ['234', '151'])).
50.61/50.87	tff('236', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['235'])).
50.61/50.87	tff('237', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['198', '236'])).
50.61/50.87	tff('238', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('demod', [status(thm)], ['237', '151'])).
50.61/50.87	tff('239', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['238'])).
50.61/50.87	tff('240', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('clc', [status(thm)], ['239', '217'])).
50.61/50.87	tff('241', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.87	    inference('clc', [status(thm)], ['233', '240'])).
50.61/50.87	tff('242', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['241', '217'])).
50.61/50.87	tff('243', plain,
50.61/50.87	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X6)), 
50.61/50.87	           sk_Xw2(X6))
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.87	tff('244', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['243', '9'])).
50.61/50.87	tff('245', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['244'])).
50.61/50.87	tff('246', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['242', '245'])).
50.61/50.87	tff('247', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['246'])).
50.61/50.87	tff('248', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['247', '217'])).
50.61/50.87	tff('249', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['248', '185'])).
50.61/50.87	tff('250', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['249'])).
50.61/50.87	tff('251', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('eq_fact', [status(thm)], ['250'])).
50.61/50.87	tff('252', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['251'])).
50.61/50.87	tff('253', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))),
50.61/50.87	    inference('clc', [status(thm)], ['252', '188'])).
50.61/50.87	tff('254', plain,
50.61/50.87	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['248', '17'])).
50.61/50.87	tff('255', plain,
50.61/50.87	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['254'])).
50.61/50.87	tff('256', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['253', '255'])).
50.61/50.87	tff('257', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('demod', [status(thm)], ['256', '151'])).
50.61/50.87	tff('258', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['257'])).
50.61/50.87	tff('259', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('eq_fact', [status(thm)], ['258'])).
50.61/50.87	tff('260', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['259'])).
50.61/50.87	tff('261', plain,
50.61/50.87	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X6)), 
50.61/50.87	           sk_Xw2(X6))
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.87	tff('262', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['261', '43'])).
50.61/50.87	tff('263', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['262'])).
50.61/50.87	tff('264', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['240', '263'])).
50.61/50.87	tff('265', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('simplify', [status(thm)], ['264'])).
50.61/50.87	tff('266', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['265', '217'])).
50.61/50.87	tff('267', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['260', '266'])).
50.61/50.87	tff('268', plain,
50.61/50.87	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw2(X6))
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.87	tff('269', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['267', '268'])).
50.61/50.87	tff('270', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['269'])).
50.61/50.87	tff('271', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('clc', [status(thm)], ['270', '217'])).
50.61/50.87	tff('272', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['271', '242'])).
50.61/50.87	tff('273', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['272', '185'])).
50.61/50.87	tff('274', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['273'])).
50.61/50.87	tff('275', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['188', '43'])).
50.61/50.87	tff('276', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['275'])).
50.61/50.87	tff('277', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['163', '43'])).
50.61/50.87	tff('278', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))),
50.61/50.87	    inference('simplify', [status(thm)], ['277'])).
50.61/50.87	tff('279', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['278', '43'])).
50.61/50.87	tff('280', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['279'])).
50.61/50.87	tff('281', plain,
50.61/50.87	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw2(X6))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X6))),
50.61/50.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.87	tff('282', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	         sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['280', '281'])).
50.61/50.87	tff('283', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	       sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['282'])).
50.61/50.87	tff('284', plain,
50.61/50.87	    (app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.87	    inference('clc', [status(thm)], ['283', '43'])).
50.61/50.87	tff('285', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('clc', [status(thm)], ['284', '217'])).
50.61/50.87	tff('286', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.87	    inference('sup-', [status(thm)], ['276', '285'])).
50.61/50.87	tff('287', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['286'])).
50.61/50.87	tff('288', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.87	    inference('clc', [status(thm)], ['287', '217'])).
50.61/50.87	tff('289', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['288', '263'])).
50.61/50.87	tff('290', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
50.61/50.87	    inference('simplify', [status(thm)], ['289'])).
50.61/50.87	tff('291', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['290', '217'])).
50.61/50.87	tff('292', plain,
50.61/50.87	    ![X4 : a, X6 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.87	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw2(X6))
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.87	tff('293', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['272', '292'])).
50.61/50.87	tff('294', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['293'])).
50.61/50.87	tff('295', plain,
50.61/50.87	    ![X6 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw2(X6))
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.87	tff('296', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('clc', [status(thm)], ['294', '295'])).
50.61/50.87	tff('297', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))),
50.61/50.87	    inference('sup-', [status(thm)], ['7', '296'])).
50.61/50.87	tff('298', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['297'])).
50.61/50.87	tff('299', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))),
50.61/50.87	    inference('clc', [status(thm)], ['298', '242'])).
50.61/50.87	tff('300', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('clc', [status(thm)], ['299', '217'])).
50.61/50.87	tff('301', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.87	    inference('sup-', [status(thm)], ['291', '300'])).
50.61/50.87	tff('302', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.87	    inference('demod', [status(thm)], ['301', '151'])).
50.61/50.87	tff('303', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['302'])).
50.61/50.87	tff('304', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.87	    inference('clc', [status(thm)], ['303', '242'])).
50.61/50.87	tff('305', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['304', '217'])).
50.61/50.87	tff('306', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.87	    inference('sup-', [status(thm)], ['7', '305'])).
50.61/50.87	tff('307', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['306'])).
50.61/50.87	tff('308', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))),
50.61/50.87	    inference('clc', [status(thm)], ['307', '242'])).
50.61/50.87	tff('309', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('clc', [status(thm)], ['308', '217'])).
50.61/50.87	tff('310', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('clc', [status(thm)], ['274', '309'])).
50.61/50.87	tff('311', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('eq_fact', [status(thm)], ['310'])).
50.61/50.87	tff('312', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['311'])).
50.61/50.87	tff('313', plain,
50.61/50.87	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['272', '17'])).
50.61/50.87	tff('314', plain,
50.61/50.87	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['313'])).
50.61/50.87	tff('315', plain,
50.61/50.87	    ![X0 : a, X1 : a, X2 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
50.61/50.87	       | app_encode_app(a, $o, X2, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X2))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)),
50.61/50.87	    inference('clc', [status(thm)], ['314', '43'])).
50.61/50.87	tff('316', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['312', '315'])).
50.61/50.87	tff('317', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('demod', [status(thm)], ['316', '151'])).
50.61/50.87	tff('318', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['317'])).
50.61/50.87	tff('319', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))),
50.61/50.87	    inference('sup-', [status(thm)], ['7', '318'])).
50.61/50.87	tff('320', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['319'])).
50.61/50.87	tff('321', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xv1(X1))),
50.61/50.87	    inference('clc', [status(thm)], ['320', '242'])).
50.61/50.87	tff('322', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('clc', [status(thm)], ['321', '217'])).
50.61/50.87	tff('323', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('eq_fact', [status(thm)], ['322'])).
50.61/50.87	tff('324', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['323'])).
50.61/50.87	tff('325', plain,
50.61/50.87	    (app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	         sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('clc', [status(thm)], ['181', '324'])).
50.61/50.87	tff('326', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	         sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['325', '217'])).
50.61/50.87	tff('327', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['326', '9'])).
50.61/50.87	tff('328', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ $true
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('demod', [status(thm)], ['327', '151'])).
50.61/50.87	tff('329', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['328'])).
50.61/50.87	tff('330', plain,
50.61/50.87	    ![X4 : a, X6 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.87	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw2(X6))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X6))),
50.61/50.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.87	tff('331', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['329', '330'])).
50.61/50.87	tff('332', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['331'])).
50.61/50.87	tff('333', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['160', '292'])).
50.61/50.87	tff('334', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))),
50.61/50.87	    inference('simplify', [status(thm)], ['333'])).
50.61/50.87	tff('335', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o), X1 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X1))
50.61/50.87	       | app_encode_app(a, $o, X1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('clc', [status(thm)], ['334', '295'])).
50.61/50.87	tff('336', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.87	    inference('sup-', [status(thm)], ['291', '335'])).
50.61/50.87	tff('337', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.87	    inference('demod', [status(thm)], ['336', '151'])).
50.61/50.87	tff('338', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['337'])).
50.61/50.87	tff('339', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.87	    inference('clc', [status(thm)], ['338', '217'])).
50.61/50.87	tff('340', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['7', '339'])).
50.61/50.87	tff('341', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['340'])).
50.61/50.87	tff('342', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('clc', [status(thm)], ['341', '217'])).
50.61/50.87	tff('343', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.87	    inference('sup-', [status(thm)], ['288', '342'])).
50.61/50.87	tff('344', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))),
50.61/50.87	    inference('demod', [status(thm)], ['343', '151'])).
50.61/50.87	tff('345', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('simplify', [status(thm)], ['344'])).
50.61/50.87	tff('346', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	         sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['345', '281'])).
50.61/50.87	tff('347', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	       sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('simplify', [status(thm)], ['346'])).
50.61/50.87	tff('348', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	         sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['347', '324'])).
50.61/50.87	tff('349', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	       sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('clc', [status(thm)], ['348', '217'])).
50.61/50.87	tff('350', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['349', '43'])).
50.61/50.87	tff('351', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('demod', [status(thm)], ['350', '151'])).
50.61/50.87	tff('352', plain,
50.61/50.87	    (app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('simplify', [status(thm)], ['351'])).
50.61/50.87	tff('353', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	           sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('clc', [status(thm)], ['332', '352'])).
50.61/50.87	tff('354', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	         sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['178', '353'])).
50.61/50.87	tff('355', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	       sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['354'])).
50.61/50.87	tff('356', plain,
50.61/50.87	    (app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	         sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['355', '324'])).
50.61/50.87	tff('357', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
50.61/50.87	       sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['356', '217'])).
50.61/50.87	tff('358', plain,
50.61/50.87	    ![X0 : a, X1 : a]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['329', '17'])).
50.61/50.87	tff('359', plain,
50.61/50.87	    ![X0 : a, X1 : a]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['358'])).
50.61/50.87	tff('360', plain,
50.61/50.87	    ![X0 : a, X1 : a]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)),
50.61/50.87	    inference('clc', [status(thm)], ['359', '352'])).
50.61/50.87	tff('361', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['357', '360'])).
50.61/50.87	tff('362', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | ~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('demod', [status(thm)], ['361', '151'])).
50.61/50.87	tff('363', plain, app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1)),
50.61/50.87	    inference('simplify', [status(thm)], ['362'])).
50.61/50.87	tff('364', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['363', '245'])).
50.61/50.87	tff('365', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['364'])).
50.61/50.87	tff('366', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['365', '217'])).
50.61/50.87	tff('367', plain,
50.61/50.87	    ![X4 : a, X6 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X4)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, X4)
50.61/50.87	       | app_encode_app(a, $o, X6, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X6)), 
50.61/50.87	           sk_Xw2(X6))
50.61/50.87	       | ~ app_encode_app(a, $o, X6, sk_Xw3(X6))),
50.61/50.87	    inference('cnf', [status(esa)], [zf_stmt_0])).
50.61/50.87	tff('368', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
50.61/50.87	           sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['366', '367'])).
50.61/50.87	tff('369', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
50.61/50.87	           sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['368'])).
50.61/50.87	tff('370', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['352', '263'])).
50.61/50.87	tff('371', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('simplify', [status(thm)], ['370'])).
50.61/50.87	tff('372', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['371', '217'])).
50.61/50.87	tff('373', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, 
50.61/50.87	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
50.61/50.87	           sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('clc', [status(thm)], ['369', '372'])).
50.61/50.87	tff('374', plain,
50.61/50.87	    ![X0 : a, X1 : a]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['366', '17'])).
50.61/50.87	tff('375', plain,
50.61/50.87	    ![X0 : a, X1 : a]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['374'])).
50.61/50.87	tff('376', plain,
50.61/50.87	    ![X0 : a, X1 : a]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, X0)
50.61/50.87	       | ~ app_encode_app(a, $o, 
50.61/50.87	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, X1)),
50.61/50.87	    inference('clc', [status(thm)], ['375', '372'])).
50.61/50.87	tff('377', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['373', '376'])).
50.61/50.87	tff('378', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['377'])).
50.61/50.87	tff('379', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['363', '378'])).
50.61/50.87	tff('380', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['379'])).
50.61/50.87	tff('381', plain,
50.61/50.87	    (app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('clc', [status(thm)], ['380', '217'])).
50.61/50.87	tff('382', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['381', '268'])).
50.61/50.87	tff('383', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | ~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('demod', [status(thm)], ['382', '363'])).
50.61/50.87	tff('384', plain,
50.61/50.87	    (app_encode_app(a, $o, 
50.61/50.87	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['383'])).
50.61/50.87	tff('385', plain,
50.61/50.87	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, 
50.61/50.87	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
50.61/50.87	    inference('clc', [status(thm)], ['384', '217'])).
50.61/50.87	tff('386', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
50.61/50.87	    inference('sup-', [status(thm)], ['385', '292'])).
50.61/50.87	tff('387', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['386'])).
50.61/50.87	tff('388', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)),
50.61/50.87	    inference('clc', [status(thm)], ['387', '295'])).
50.61/50.87	tff('389', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
50.61/50.87	    inference('sup-', [status(thm)], ['7', '388'])).
50.61/50.87	tff('390', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ $true
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	       | ~ $true
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
50.61/50.87	    inference('demod', [status(thm)], ['389', '363'])).
50.61/50.87	tff('391', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (~ app_encode_app(a, $o, X0, sk_Xw3(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('simplify', [status(thm)], ['390'])).
50.61/50.87	tff('392', plain,
50.61/50.87	    ![X0 : app_encode_fun(a, $o)]:
50.61/50.87	      (app_encode_app(a, $o, X0, sk_Xz)
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
50.61/50.87	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
50.61/50.87	    inference('clc', [status(thm)], ['391', '217'])).
50.61/50.87	tff('393', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('sup-', [status(thm)], ['381', '392'])).
50.61/50.87	tff('394', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
50.61/50.87	     | ~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
50.61/50.87	    inference('demod', [status(thm)], ['393', '363'])).
50.61/50.87	tff('395', plain,
50.61/50.87	    (app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))),
50.61/50.87	    inference('simplify', [status(thm)], ['394'])).
50.61/50.87	tff('396', plain, ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1)),
50.61/50.87	    inference('clc', [status(thm)], ['395', '217'])).
50.61/50.87	tff('397', plain,
50.61/50.87	    (~ $true
50.61/50.87	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
50.61/50.87	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
50.61/50.87	    inference('sup-', [status(thm)], ['7', '396'])).
50.61/50.87	tff('398', plain, (~ $true | app_encode_app(a, $o, sk_Xq1, sk_Xz) | ~ $true),
50.61/50.87	    inference('demod', [status(thm)], ['397', '363'])).
50.61/50.87	tff('399', plain, app_encode_app(a, $o, sk_Xq1, sk_Xz),
50.61/50.87	    inference('simplify', [status(thm)], ['398'])).
50.61/50.87	tff('400', plain, ~ $true, inference('sup-', [status(thm)], ['399', '217'])).
50.61/50.87	tff('401', plain, $false, inference('simplify', [status(thm)], ['400'])).
50.61/50.87	
50.61/50.87	% SZS output end Refutation
50.61/50.87	EOF
