0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n185.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:52:38 CST 2018
0.00/0.53	% done 225 iterations in 0.330s
0.00/0.53	% SZS status Theorem for 'stdin'
0.00/0.53	% SZS output start Refutation
0.00/0.53	tff(zf_stmt_3, conjecture,
0.00/0.53	  (![Xr:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.53	     ((![Xx:a,Xy:a]:
0.00/0.53	         (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xr,Xx),Xy) =>
0.00/0.53	          (![Xq:app_encode_fun(a,$o)]:
0.00/0.53	             (((![Xw:a]:
0.00/0.53	                  (app_encode_app(a,$o,
0.00/0.53	                                  app_encode_app(a,app_encode_fun(a,$o),Xr,Xx),
0.00/0.53	                                  Xw) =>
0.00/0.53	                   app_encode_app(a,$o,Xq,Xw))) & 
0.00/0.53	               (![Xv:a,Xw:a]:
0.00/0.53	                  ((app_encode_app(a,$o,Xq,Xv) & 
0.00/0.53	                    app_encode_app(a,$o,
0.00/0.53	                                   app_encode_app(a,app_encode_fun(a,$o),Xr,
0.00/0.53	                                                  Xv),
0.00/0.53	                                   Xw)) =>
0.00/0.53	                   app_encode_app(a,$o,Xq,Xw)))) =>
0.00/0.53	              app_encode_app(a,$o,Xq,Xy))))) & 
0.00/0.53	      (![Xx:a,Xy:a,Xz:a]:
0.00/0.53	         (((![Xq:app_encode_fun(a,$o)]:
0.00/0.53	              (((![Xw:a]:
0.00/0.53	                   (app_encode_app(a,$o,
0.00/0.53	                                   app_encode_app(a,app_encode_fun(a,$o),Xr,
0.00/0.53	                                                  Xx),
0.00/0.53	                                   Xw) =>
0.00/0.53	                    app_encode_app(a,$o,Xq,Xw))) & 
0.00/0.53	                (![Xv:a,Xw:a]:
0.00/0.53	                   ((app_encode_app(a,$o,Xq,Xv) & 
0.00/0.53	                     app_encode_app(a,$o,
0.00/0.53	                                    app_encode_app(a,app_encode_fun(a,$o),Xr,
0.00/0.53	                                                   Xv),
0.00/0.53	                                    Xw)) =>
0.00/0.53	                    app_encode_app(a,$o,Xq,Xw)))) =>
0.00/0.53	               app_encode_app(a,$o,Xq,Xy))) & 
0.00/0.53	           (![Xq:app_encode_fun(a,$o)]:
0.00/0.53	              (((![Xw:a]:
0.00/0.53	                   (app_encode_app(a,$o,
0.00/0.53	                                   app_encode_app(a,app_encode_fun(a,$o),Xr,
0.00/0.53	                                                  Xy),
0.00/0.53	                                   Xw) =>
0.00/0.53	                    app_encode_app(a,$o,Xq,Xw))) & 
0.00/0.53	                (![Xv:a,Xw:a]:
0.00/0.53	                   ((app_encode_app(a,$o,Xq,Xv) & 
0.00/0.53	                     app_encode_app(a,$o,
0.00/0.53	                                    app_encode_app(a,app_encode_fun(a,$o),Xr,
0.00/0.53	                                                   Xv),
0.00/0.53	                                    Xw)) =>
0.00/0.53	                    app_encode_app(a,$o,Xq,Xw)))) =>
0.00/0.53	               app_encode_app(a,$o,Xq,Xz)))) =>
0.00/0.53	          (![Xq:app_encode_fun(a,$o)]:
0.00/0.53	             (((![Xw:a]:
0.00/0.53	                  (app_encode_app(a,$o,
0.00/0.53	                                  app_encode_app(a,app_encode_fun(a,$o),Xr,Xx),
0.00/0.53	                                  Xw) =>
0.00/0.53	                   app_encode_app(a,$o,Xq,Xw))) & 
0.00/0.53	               (![Xv:a,Xw:a]:
0.00/0.53	                  ((app_encode_app(a,$o,Xq,Xv) & 
0.00/0.53	                    app_encode_app(a,$o,
0.00/0.53	                                   app_encode_app(a,app_encode_fun(a,$o),Xr,
0.00/0.53	                                                  Xv),
0.00/0.53	                                   Xw)) =>
0.00/0.53	                   app_encode_app(a,$o,Xq,Xw)))) =>
0.00/0.53	              app_encode_app(a,$o,Xq,Xz)))))))).
0.00/0.53	tff(zf_stmt_0, negated_conjecture,
0.00/0.53	  (~
0.00/0.53	    (![Xr:app_encode_fun(a,app_encode_fun(a,$o))]:
0.00/0.53	       ((![Xx:a,Xy:a]:
0.00/0.53	           (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xr,Xx),
0.00/0.53	                           Xy) =>
0.00/0.53	            (![Xq:app_encode_fun(a,$o)]:
0.00/0.53	               (((![Xw:a]:
0.00/0.53	                    (app_encode_app(a,$o,
0.00/0.53	                                    app_encode_app(a,app_encode_fun(a,$o),Xr,
0.00/0.53	                                                   Xx),
0.00/0.53	                                    Xw) =>
0.00/0.53	                     app_encode_app(a,$o,Xq,Xw))) & 
0.00/0.53	                 (![Xv:a,Xw:a]:
0.00/0.53	                    ((app_encode_app(a,$o,Xq,Xv) & 
0.00/0.53	                      app_encode_app(a,$o,
0.00/0.53	                                     app_encode_app(a,app_encode_fun(a,$o),
0.00/0.53	                                                    Xr,Xv),
0.00/0.53	                                     Xw)) =>
0.00/0.53	                     app_encode_app(a,$o,Xq,Xw)))) =>
0.00/0.53	                app_encode_app(a,$o,Xq,Xy))))) & 
0.00/0.53	        (![Xx:a,Xy:a,Xz:a]:
0.00/0.53	           (((![Xq:app_encode_fun(a,$o)]:
0.00/0.53	                (((![Xw:a]:
0.00/0.53	                     (app_encode_app(a,$o,
0.00/0.53	                                     app_encode_app(a,app_encode_fun(a,$o),
0.00/0.53	                                                    Xr,Xx),
0.00/0.53	                                     Xw) =>
0.00/0.53	                      app_encode_app(a,$o,Xq,Xw))) & 
0.00/0.53	                  (![Xv:a,Xw:a]:
0.00/0.53	                     ((app_encode_app(a,$o,Xq,Xv) & 
0.00/0.53	                       app_encode_app(a,$o,
0.00/0.53	                                      app_encode_app(a,app_encode_fun(a,$o),
0.00/0.53	                                                     Xr,Xv),
0.00/0.53	                                      Xw)) =>
0.00/0.53	                      app_encode_app(a,$o,Xq,Xw)))) =>
0.00/0.53	                 app_encode_app(a,$o,Xq,Xy))) & 
0.00/0.53	             (![Xq:app_encode_fun(a,$o)]:
0.00/0.53	                (((![Xw:a]:
0.00/0.53	                     (app_encode_app(a,$o,
0.00/0.53	                                     app_encode_app(a,app_encode_fun(a,$o),
0.00/0.53	                                                    Xr,Xy),
0.00/0.53	                                     Xw) =>
0.00/0.53	                      app_encode_app(a,$o,Xq,Xw))) & 
0.00/0.54	                  (![Xv:a,Xw:a]:
0.00/0.54	                     ((app_encode_app(a,$o,Xq,Xv) & 
0.00/0.54	                       app_encode_app(a,$o,
0.00/0.54	                                      app_encode_app(a,app_encode_fun(a,$o),
0.00/0.54	                                                     Xr,Xv),
0.00/0.54	                                      Xw)) =>
0.00/0.54	                      app_encode_app(a,$o,Xq,Xw)))) =>
0.00/0.54	                 app_encode_app(a,$o,Xq,Xz)))) =>
0.00/0.54	            (![Xq:app_encode_fun(a,$o)]:
0.00/0.54	               (((![Xw:a]:
0.00/0.54	                    (app_encode_app(a,$o,
0.00/0.54	                                    app_encode_app(a,app_encode_fun(a,$o),Xr,
0.00/0.54	                                                   Xx),
0.00/0.54	                                    Xw) =>
0.00/0.54	                     app_encode_app(a,$o,Xq,Xw))) & 
0.00/0.54	                 (![Xv:a,Xw:a]:
0.00/0.54	                    ((app_encode_app(a,$o,Xq,Xv) & 
0.00/0.54	                      app_encode_app(a,$o,
0.00/0.54	                                     app_encode_app(a,app_encode_fun(a,$o),
0.00/0.54	                                                    Xr,Xv),
0.00/0.54	                                     Xw)) =>
0.00/0.54	                     app_encode_app(a,$o,Xq,Xw)))) =>
0.00/0.54	                app_encode_app(a,$o,Xq,Xz))))))))).
0.00/0.54	tff('0', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X2)), 
0.00/0.54	           sk_Xw2(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('1', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('2', plain,
0.00/0.54	    ![X3 : a, X4 : a]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, X3)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X3), X4)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X4)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('3', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	             X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['1', '2'])).
0.00/0.54	tff('4', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['3'])).
0.00/0.54	tff('5', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('6', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	             X0)),
0.00/0.54	    inference('clc', [status(thm)], ['4', '5'])).
0.00/0.54	tff('7', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X1)), 
0.00/0.54	           sk_Xw(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('8', plain,
0.00/0.54	    ![X5 : a]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X5)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X5)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('9', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['7', '8'])).
0.00/0.54	tff('10', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['9'])).
0.00/0.54	tff('11', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xv(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('12', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['11', '8'])).
0.00/0.54	tff('13', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['12'])).
0.00/0.54	tff('14', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	             X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['13', '2'])).
0.00/0.54	tff('15', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['14'])).
0.00/0.54	tff('16', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X1)), 
0.00/0.54	           sk_Xw(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('17', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xv(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('18', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	             X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['17', '2'])).
0.00/0.54	tff('19', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['18'])).
0.00/0.54	tff('20', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['16', '19'])).
0.00/0.54	tff('21', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['20'])).
0.00/0.54	tff('22', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('23', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('clc', [status(thm)], ['21', '22'])).
0.00/0.54	tff('24', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	             X0)),
0.00/0.54	    inference('clc', [status(thm)], ['15', '23'])).
0.00/0.54	tff('25', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('sup-', [status(thm)], ['10', '24'])).
0.00/0.54	tff('26', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['25'])).
0.00/0.54	tff('27', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))),
0.00/0.54	    inference('clc', [status(thm)], ['26', '23'])).
0.00/0.54	tff('28', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('29', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	         sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['27', '28'])).
0.00/0.54	tff('30', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	       sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('simplify', [status(thm)], ['29'])).
0.00/0.54	tff('31', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['30', '8'])).
0.00/0.54	tff('32', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('simplify', [status(thm)], ['31'])).
0.00/0.54	tff('33', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['32', '23'])).
0.00/0.54	tff('34', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['33', '2'])).
0.00/0.54	tff('35', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('simplify', [status(thm)], ['34'])).
0.00/0.54	tff('36', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X2)), 
0.00/0.54	           sk_Xw2(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('37', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('38', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	             X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['37', '2'])).
0.00/0.54	tff('39', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['38'])).
0.00/0.54	tff('40', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	             X0)),
0.00/0.54	    inference('clc', [status(thm)], ['39', '5'])).
0.00/0.54	tff('41', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['36', '40'])).
0.00/0.54	tff('42', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['41'])).
0.00/0.54	tff('43', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw2(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('44', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('clc', [status(thm)], ['42', '43'])).
0.00/0.54	tff('45', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('clc', [status(thm)], ['44', '5'])).
0.00/0.54	tff('46', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['35', '45'])).
0.00/0.54	tff('47', plain,
0.00/0.54	    (~ app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('simplify', [status(thm)], ['46'])).
0.00/0.54	tff('48', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('clc', [status(thm)], ['6', '47'])).
0.00/0.54	tff('49', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['0', '48'])).
0.00/0.54	tff('50', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['49'])).
0.00/0.54	tff('51', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw2(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('52', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	       sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)),
0.00/0.54	    inference('clc', [status(thm)], ['50', '51'])).
0.00/0.54	tff('53', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
0.00/0.54	    inference('clc', [status(thm)], ['52', '47'])).
0.00/0.54	tff('54', plain,
0.00/0.54	    app_encode_app(a, $o, 
0.00/0.54	      app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), sk_Xy),
0.00/0.54	    inference('clc', [status(thm)], ['53', '5'])).
0.00/0.54	tff('55', plain,
0.00/0.54	    ![X0 : a, X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X2)), 
0.00/0.54	           sk_Xw2(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('56', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
0.00/0.54	           sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '55'])).
0.00/0.54	tff('57', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
0.00/0.54	           sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['56'])).
0.00/0.54	tff('58', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X2)), 
0.00/0.54	           sk_Xw2(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('59', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('60', plain,
0.00/0.54	    ![X3 : a, X4 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, X3)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X3), X4)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X4)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('61', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	             X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['59', '60'])).
0.00/0.54	tff('62', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['61'])).
0.00/0.54	tff('63', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('64', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	             X0)),
0.00/0.54	    inference('clc', [status(thm)], ['62', '63'])).
0.00/0.54	tff('65', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X1)), 
0.00/0.54	           sk_Xw(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('66', plain,
0.00/0.54	    ![X5 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X5)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X5)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('67', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['65', '66'])).
0.00/0.54	tff('68', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['67'])).
0.00/0.54	tff('69', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xv(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('70', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['69', '66'])).
0.00/0.54	tff('71', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['70'])).
0.00/0.54	tff('72', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	             X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['71', '60'])).
0.00/0.54	tff('73', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['72'])).
0.00/0.54	tff('74', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X1)), 
0.00/0.54	           sk_Xw(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('75', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xv(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('76', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	             X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['75', '60'])).
0.00/0.54	tff('77', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['76'])).
0.00/0.54	tff('78', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['74', '77'])).
0.00/0.54	tff('79', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['78'])).
0.00/0.54	tff('80', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('81', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('clc', [status(thm)], ['79', '80'])).
0.00/0.54	tff('82', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(sk_Xq1)), 
0.00/0.54	             X0)),
0.00/0.54	    inference('clc', [status(thm)], ['73', '81'])).
0.00/0.54	tff('83', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('sup-', [status(thm)], ['68', '82'])).
0.00/0.54	tff('84', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['83'])).
0.00/0.54	tff('85', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw(sk_Xq1))),
0.00/0.54	    inference('clc', [status(thm)], ['84', '81'])).
0.00/0.54	tff('86', plain,
0.00/0.54	    ![X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('87', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	         sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['85', '86'])).
0.00/0.54	tff('88', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	       sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('simplify', [status(thm)], ['87'])).
0.00/0.54	tff('89', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['88', '66'])).
0.00/0.54	tff('90', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('simplify', [status(thm)], ['89'])).
0.00/0.54	tff('91', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['90', '81'])).
0.00/0.54	tff('92', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['91', '60'])).
0.00/0.54	tff('93', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('simplify', [status(thm)], ['92'])).
0.00/0.54	tff('94', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X2)), 
0.00/0.54	           sk_Xw2(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('95', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('96', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	             X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['95', '60'])).
0.00/0.54	tff('97', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['96'])).
0.00/0.54	tff('98', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	             X0)),
0.00/0.54	    inference('clc', [status(thm)], ['97', '63'])).
0.00/0.54	tff('99', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['94', '98'])).
0.00/0.54	tff('100', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['99'])).
0.00/0.54	tff('101', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw2(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('102', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('clc', [status(thm)], ['100', '101'])).
0.00/0.54	tff('103', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('clc', [status(thm)], ['102', '63'])).
0.00/0.54	tff('104', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['93', '103'])).
0.00/0.54	tff('105', plain,
0.00/0.54	    (~ app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('simplify', [status(thm)], ['104'])).
0.00/0.54	tff('106', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(sk_Xq1)), 
0.00/0.54	           X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('clc', [status(thm)], ['64', '105'])).
0.00/0.54	tff('107', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['58', '106'])).
0.00/0.54	tff('108', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw2(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('simplify', [status(thm)], ['107'])).
0.00/0.54	tff('109', plain,
0.00/0.54	    ![X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw2(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('110', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	       sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('clc', [status(thm)], ['108', '109'])).
0.00/0.54	tff('111', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
0.00/0.54	    inference('clc', [status(thm)], ['110', '105'])).
0.00/0.54	tff('112', plain, ~ app_encode_app(a, $o, sk_Xq, sk_Xy),
0.00/0.54	    inference('clc', [status(thm)], ['111', '63'])).
0.00/0.54	tff('113', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
0.00/0.54	           sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)),
0.00/0.54	    inference('clc', [status(thm)], ['57', '112'])).
0.00/0.54	tff('114', plain,
0.00/0.54	    ![X0 : a, X3 : a, X4 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, X3)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X3), X4)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X4)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('115', plain,
0.00/0.54	    ![X0 : a, X1 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '114'])).
0.00/0.54	tff('116', plain,
0.00/0.54	    ![X0 : a, X1 : a]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, X1)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)),
0.00/0.54	    inference('simplify', [status(thm)], ['115'])).
0.00/0.54	tff('117', plain,
0.00/0.54	    ![X0 : a, X1 : a]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, X1), X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, X1)),
0.00/0.54	    inference('clc', [status(thm)], ['116', '112'])).
0.00/0.54	tff('118', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))),
0.00/0.54	    inference('sup-', [status(thm)], ['113', '117'])).
0.00/0.54	tff('119', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)),
0.00/0.54	    inference('simplify', [status(thm)], ['118'])).
0.00/0.54	tff('120', plain,
0.00/0.54	    ![X0 : a, X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw2(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('121', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '120'])).
0.00/0.54	tff('122', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['121'])).
0.00/0.54	tff('123', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), sk_Xw3(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)),
0.00/0.54	    inference('clc', [status(thm)], ['122', '112'])).
0.00/0.54	tff('124', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['119', '123'])).
0.00/0.54	tff('125', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
0.00/0.54	    inference('simplify', [status(thm)], ['124'])).
0.00/0.54	tff('126', plain,
0.00/0.54	    ![X0 : a, X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('127', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '126'])).
0.00/0.54	tff('128', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	           sk_Xw3(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['127'])).
0.00/0.54	tff('129', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)),
0.00/0.54	    inference('clc', [status(thm)], ['128', '112'])).
0.00/0.54	tff('130', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	         sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('clc', [status(thm)], ['125', '129'])).
0.00/0.54	tff('131', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('132', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '131'])).
0.00/0.54	tff('133', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xz)),
0.00/0.54	    inference('simplify', [status(thm)], ['132'])).
0.00/0.54	tff('134', plain, ~ app_encode_app(a, $o, sk_Xq1, sk_Xz),
0.00/0.54	    inference('clc', [status(thm)], ['133', '112'])).
0.00/0.54	tff('135', plain,
0.00/0.54	    app_encode_app(a, $o, 
0.00/0.54	      app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xy1), 
0.00/0.54	      sk_Xw3(sk_Xq1)),
0.00/0.54	    inference('clc', [status(thm)], ['130', '134'])).
0.00/0.54	tff('136', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['135', '117'])).
0.00/0.54	tff('137', plain,
0.00/0.54	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xv(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('138', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '137'])).
0.00/0.54	tff('139', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['138'])).
0.00/0.54	tff('140', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['139', '112'])).
0.00/0.54	tff('141', plain,
0.00/0.54	    ![X0 : a, X5 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X5)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X5)),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('142', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '141'])).
0.00/0.54	tff('143', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)
0.00/0.54	       | ~ app_encode_app(a, $o, 
0.00/0.54	             app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)),
0.00/0.54	    inference('simplify', [status(thm)], ['142'])).
0.00/0.54	tff('144', plain,
0.00/0.54	    ![X0 : a]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, X0)),
0.00/0.54	    inference('clc', [status(thm)], ['143', '112'])).
0.00/0.54	tff('145', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))),
0.00/0.54	    inference('sup-', [status(thm)], ['140', '144'])).
0.00/0.54	tff('146', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['145'])).
0.00/0.54	tff('147', plain,
0.00/0.54	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X1)), 
0.00/0.54	           sk_Xw(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('148', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '147'])).
0.00/0.54	tff('149', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['148'])).
0.00/0.54	tff('150', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['149', '112'])).
0.00/0.54	tff('151', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))),
0.00/0.54	    inference('sup-', [status(thm)], ['150', '144'])).
0.00/0.54	tff('152', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['151'])).
0.00/0.54	tff('153', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))),
0.00/0.54	    inference('sup-', [status(thm)], ['152', '117'])).
0.00/0.54	tff('154', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['153'])).
0.00/0.54	tff('155', plain,
0.00/0.54	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw(X1))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('156', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '155'])).
0.00/0.54	tff('157', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	           sk_Xw1(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['156'])).
0.00/0.54	tff('158', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['157', '112'])).
0.00/0.54	tff('159', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, 
0.00/0.54	         app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	         sk_Xw1(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['154', '158'])).
0.00/0.54	tff('160', plain,
0.00/0.54	    (app_encode_app(a, $o, 
0.00/0.54	       app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx1), 
0.00/0.54	       sk_Xw1(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['159'])).
0.00/0.54	tff('161', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))),
0.00/0.54	    inference('clc', [status(thm)], ['160', '144'])).
0.00/0.54	tff('162', plain,
0.00/0.54	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X1)), 
0.00/0.54	           sk_Xw(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('163', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '162'])).
0.00/0.54	tff('164', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['163'])).
0.00/0.54	tff('165', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, X0, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv(X0)), 
0.00/0.54	           sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['164', '112'])).
0.00/0.54	tff('166', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))),
0.00/0.54	    inference('sup-', [status(thm)], ['165', '117'])).
0.00/0.54	tff('167', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['166'])).
0.00/0.54	tff('168', plain,
0.00/0.54	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('169', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '168'])).
0.00/0.54	tff('170', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['169'])).
0.00/0.54	tff('171', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, X0, sk_Xw1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['170', '112'])).
0.00/0.54	tff('172', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['167', '171'])).
0.00/0.54	tff('173', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['172'])).
0.00/0.54	tff('174', plain,
0.00/0.54	    ![X0 : a, X1 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X1, sk_Xv(X1))
0.00/0.54	       | ~ app_encode_app(a, $o, X1, sk_Xw1(X1))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('175', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '174'])).
0.00/0.54	tff('176', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw1(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['175'])).
0.00/0.54	tff('177', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, X0, sk_Xw1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['176', '112'])).
0.00/0.54	tff('178', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))),
0.00/0.54	    inference('clc', [status(thm)], ['173', '177'])).
0.00/0.54	tff('179', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('clc', [status(thm)], ['161', '178'])).
0.00/0.54	tff('180', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('sup-', [status(thm)], ['146', '179'])).
0.00/0.54	tff('181', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xw1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xy1)),
0.00/0.54	    inference('simplify', [status(thm)], ['180'])).
0.00/0.54	tff('182', plain, app_encode_app(a, $o, sk_Xq1, sk_Xy1),
0.00/0.54	    inference('clc', [status(thm)], ['181', '178'])).
0.00/0.54	tff('183', plain,
0.00/0.54	    (~ $true | ~ $true | app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('demod', [status(thm)], ['136', '182'])).
0.00/0.54	tff('184', plain, app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1)),
0.00/0.54	    inference('simplify', [status(thm)], ['183'])).
0.00/0.54	tff('185', plain,
0.00/0.54	    ![X0 : a, X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X2)), 
0.00/0.54	           sk_Xw2(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('186', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
0.00/0.54	           sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '185'])).
0.00/0.54	tff('187', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
0.00/0.54	           sk_Xw2(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['186'])).
0.00/0.54	tff('188', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, X0, sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xv1(X0)), 
0.00/0.54	           sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)),
0.00/0.54	    inference('clc', [status(thm)], ['187', '112'])).
0.00/0.54	tff('189', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
0.00/0.54	       | app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))),
0.00/0.54	    inference('sup-', [status(thm)], ['188', '117'])).
0.00/0.54	tff('190', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq1, sk_Xw2(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)),
0.00/0.54	    inference('simplify', [status(thm)], ['189'])).
0.00/0.54	tff('191', plain,
0.00/0.54	    ![X0 : a, X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw2(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('192', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '191'])).
0.00/0.54	tff('193', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['192'])).
0.00/0.54	tff('194', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, X0, sk_Xw3(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw2(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)),
0.00/0.54	    inference('clc', [status(thm)], ['193', '112'])).
0.00/0.54	tff('195', plain,
0.00/0.54	    (~ $true
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('sup-', [status(thm)], ['190', '194'])).
0.00/0.54	tff('196', plain,
0.00/0.54	    (~ app_encode_app(a, $o, sk_Xq1, sk_Xv1(sk_Xq1))
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))
0.00/0.54	     | app_encode_app(a, $o, sk_Xq1, sk_Xz)),
0.00/0.54	    inference('simplify', [status(thm)], ['195'])).
0.00/0.54	tff('197', plain,
0.00/0.54	    ![X0 : a, X2 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, 
0.00/0.54	           app_encode_app(a, app_encode_fun(a, $o), sk_Xr, sk_Xx), X0)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, X0)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, X2, sk_Xv1(X2))
0.00/0.54	       | ~ app_encode_app(a, $o, X2, sk_Xw3(X2))),
0.00/0.54	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.54	tff('198', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ $true
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, sk_Xq, sk_Xy)),
0.00/0.54	    inference('sup-', [status(thm)], ['54', '197'])).
0.00/0.54	tff('199', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (app_encode_app(a, $o, sk_Xq, sk_Xy)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
0.00/0.54	       | ~ app_encode_app(a, $o, X0, sk_Xw3(X0))),
0.00/0.54	    inference('simplify', [status(thm)], ['198'])).
0.00/0.54	tff('200', plain,
0.00/0.54	    ![X0 : app_encode_fun(a, $o)]:
0.00/0.54	      (~ app_encode_app(a, $o, X0, sk_Xw3(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xv1(X0))
0.00/0.54	       | app_encode_app(a, $o, X0, sk_Xz)),
0.00/0.54	    inference('clc', [status(thm)], ['199', '112'])).
0.00/0.54	tff('201', plain,
0.00/0.54	    (app_encode_app(a, $o, sk_Xq1, sk_Xz)
0.00/0.54	     | ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1))),
0.00/0.54	    inference('clc', [status(thm)], ['196', '200'])).
0.00/0.54	tff('202', plain, ~ app_encode_app(a, $o, sk_Xq1, sk_Xw3(sk_Xq1)),
0.00/0.54	    inference('clc', [status(thm)], ['201', '134'])).
0.00/0.54	tff('203', plain, ~ $true, inference('sup-', [status(thm)], ['184', '202'])).
0.00/0.54	tff('204', plain, $false, inference('simplify', [status(thm)], ['203'])).
0.00/0.54	
0.00/0.54	% SZS output end Refutation
0.00/0.54	EOF
