0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : appext
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : 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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n184.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:38:54 CST 2018
4.81/5.00	% done 2581 iterations in 4.796s
4.81/5.00	% SZS status Theorem for 'stdin'
4.81/5.00	% SZS output start Refutation
4.81/5.00	tff(zf_stmt_5, conjecture,
4.81/5.00	  (![Xp:app_encode_fun(a,app_encode_fun(a,$o)),
4.81/5.00	     Xp2:app_encode_fun(a,app_encode_fun(b,app_encode_fun(b,$o)))]:
4.81/5.00	     (((![Xx:a,Xy:a]:
4.81/5.00	          (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.81/5.00	                          Xy) =>
4.81/5.00	           app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xy),
4.81/5.00	                          Xx))) & 
4.81/5.00	       (![Xx:a,Xy:a,Xz:a]:
4.81/5.00	          ((app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.81/5.00	                           Xy) & 
4.81/5.00	            app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xy),
4.81/5.00	                           Xz)) =>
4.81/5.00	           app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.81/5.00	                          Xz))) & 
4.81/5.00	       (![Xx:a]:
4.81/5.00	          (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.81/5.00	                          Xx) =>
4.81/5.00	           ((![Xx0:b,Xy:b]:
4.81/5.00	               (app_encode_app(b,$o,
4.81/5.00	                               app_encode_app(b,app_encode_fun(b,$o),
4.81/5.00	                                              app_encode_app(a,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,$o)),Xp2,Xx),
4.81/5.01	                                              Xx0),
4.81/5.01	                               Xy) =>
4.81/5.01	                app_encode_app(b,$o,
4.81/5.01	                               app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                              app_encode_app(a,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,$o)),Xp2,Xx),
4.81/5.01	                                              Xy),
4.81/5.01	                               Xx0))) & 
4.81/5.01	            (![Xx0:b,Xy:b,Xz:b]:
4.81/5.01	               ((app_encode_app(b,$o,
4.81/5.01	                                app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                               app_encode_app(a,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,$o)),Xp2,Xx),
4.81/5.01	                                               Xx0),
4.81/5.01	                                Xy) & 
4.81/5.01	                 app_encode_app(b,$o,
4.81/5.01	                                app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                               app_encode_app(a,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,$o)),Xp2,Xx),
4.81/5.01	                                               Xy),
4.81/5.01	                                Xz)) =>
4.81/5.01	                app_encode_app(b,$o,
4.81/5.01	                               app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                              app_encode_app(a,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,$o)),Xp2,Xx),
4.81/5.01	                                              Xx0),
4.81/5.01	                               Xz)))))) & 
4.81/5.01	       (![Xx:a,Xy:a]:
4.81/5.01	          (app_encode_app(a,$o,app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),
4.81/5.01	                          Xy) =>
4.81/5.01	           (app_encode_app(a,app_encode_fun(b,app_encode_fun(b,$o)),Xp2,Xx) =
4.81/5.01	            app_encode_app(a,app_encode_fun(b,app_encode_fun(b,$o)),Xp2,Xy))))) =>
4.81/5.01	      ((![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
4.81/5.01	          ((![Xx0:a,Xy0:a]:
4.81/5.01	              (app_encode_app(a,$o,
4.81/5.01	                              app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                              Xy0) =>
4.81/5.01	               app_encode_app(b,$o,
4.81/5.01	                              app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                             app_encode_app(a,
4.81/5.01	                                                            app_encode_fun(
4.81/5.01	                                                            b,
4.81/5.01	                                                            app_encode_fun(
4.81/5.01	                                                            b,$o)),Xp2,Xx0),
4.81/5.01	                                             app_encode_app(a,b,Xx,Xx0)),
4.81/5.01	                              app_encode_app(a,b,Xy,Xy0)))) =>
4.81/5.01	           (![Xx0:a,Xy0:a]:
4.81/5.01	              (app_encode_app(a,$o,
4.81/5.01	                              app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                              Xy0) =>
4.81/5.01	               app_encode_app(b,$o,
4.81/5.01	                              app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                             app_encode_app(a,
4.81/5.01	                                                            app_encode_fun(
4.81/5.01	                                                            b,
4.81/5.01	                                                            app_encode_fun(
4.81/5.01	                                                            b,$o)),Xp2,Xx0),
4.81/5.01	                                             app_encode_app(a,b,Xy,Xx0)),
4.81/5.01	                              app_encode_app(a,b,Xx,Xy0)))))) & 
4.81/5.01	       (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
4.81/5.01	          Xz:app_encode_fun(a,b)]:
4.81/5.01	          (((![Xx0:a,Xy0:a]:
4.81/5.01	               (app_encode_app(a,$o,
4.81/5.01	                               app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                               Xy0) =>
4.81/5.01	                app_encode_app(b,$o,
4.81/5.01	                               app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                              app_encode_app(a,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,$o)),Xp2,Xx0),
4.81/5.01	                                              app_encode_app(a,b,Xx,Xx0)),
4.81/5.01	                               app_encode_app(a,b,Xy,Xy0)))) & 
4.81/5.01	            (![Xx0:a,Xy0:a]:
4.81/5.01	               (app_encode_app(a,$o,
4.81/5.01	                               app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                               Xy0) =>
4.81/5.01	                app_encode_app(b,$o,
4.81/5.01	                               app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                              app_encode_app(a,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,
4.81/5.01	                                                             app_encode_fun(
4.81/5.01	                                                             b,$o)),Xp2,Xx0),
4.81/5.01	                                              app_encode_app(a,b,Xy,Xx0)),
4.81/5.01	                               app_encode_app(a,b,Xz,Xy0))))) =>
4.81/5.01	           (![Xx0:a,Xy0:a]:
4.81/5.01	              (app_encode_app(a,$o,
4.81/5.01	                              app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                              Xy0) =>
4.81/5.01	               app_encode_app(b,$o,
4.81/5.01	                              app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                             app_encode_app(a,
4.81/5.01	                                                            app_encode_fun(
4.81/5.01	                                                            b,
4.81/5.01	                                                            app_encode_fun(
4.81/5.01	                                                            b,$o)),Xp2,Xx0),
4.81/5.01	                                             app_encode_app(a,b,Xx,Xx0)),
4.81/5.01	                              app_encode_app(a,b,Xz,Xy0)))))))))).
4.81/5.01	tff(zf_stmt_0, negated_conjecture,
4.81/5.01	  (~
4.81/5.01	    (![Xp:app_encode_fun(a,app_encode_fun(a,$o)),
4.81/5.01	       Xp2:app_encode_fun(a,app_encode_fun(b,app_encode_fun(b,$o)))]:
4.81/5.01	       (((![Xx:a,Xy:a]:
4.81/5.01	            (app_encode_app(a,$o,
4.81/5.01	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xy) =>
4.81/5.01	             app_encode_app(a,$o,
4.81/5.01	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xy),Xx))) & 
4.81/5.01	         (![Xx:a,Xy:a,Xz:a]:
4.81/5.01	            ((app_encode_app(a,$o,
4.81/5.01	                             app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xy) & 
4.81/5.01	              app_encode_app(a,$o,
4.81/5.01	                             app_encode_app(a,app_encode_fun(a,$o),Xp,Xy),Xz)) =>
4.81/5.01	             app_encode_app(a,$o,
4.81/5.01	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xz))) & 
4.81/5.01	         (![Xx:a]:
4.81/5.01	            (app_encode_app(a,$o,
4.81/5.01	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xx) =>
4.81/5.01	             ((![Xx0:b,Xy:b]:
4.81/5.01	                 (app_encode_app(b,$o,
4.81/5.01	                                 app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                                app_encode_app(a,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,$o)),Xp2,Xx),
4.81/5.01	                                                Xx0),
4.81/5.01	                                 Xy) =>
4.81/5.01	                  app_encode_app(b,$o,
4.81/5.01	                                 app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                                app_encode_app(a,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,$o)),Xp2,Xx),
4.81/5.01	                                                Xy),
4.81/5.01	                                 Xx0))) & 
4.81/5.01	              (![Xx0:b,Xy:b,Xz:b]:
4.81/5.01	                 ((app_encode_app(b,$o,
4.81/5.01	                                  app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                                 app_encode_app(a,
4.81/5.01	                                                                app_encode_fun(
4.81/5.01	                                                                b,
4.81/5.01	                                                                app_encode_fun(
4.81/5.01	                                                                b,$o)),Xp2,Xx),
4.81/5.01	                                                 Xx0),
4.81/5.01	                                  Xy) & 
4.81/5.01	                   app_encode_app(b,$o,
4.81/5.01	                                  app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                                 app_encode_app(a,
4.81/5.01	                                                                app_encode_fun(
4.81/5.01	                                                                b,
4.81/5.01	                                                                app_encode_fun(
4.81/5.01	                                                                b,$o)),Xp2,Xx),
4.81/5.01	                                                 Xy),
4.81/5.01	                                  Xz)) =>
4.81/5.01	                  app_encode_app(b,$o,
4.81/5.01	                                 app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                                app_encode_app(a,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,$o)),Xp2,Xx),
4.81/5.01	                                                Xx0),
4.81/5.01	                                 Xz)))))) & 
4.81/5.01	         (![Xx:a,Xy:a]:
4.81/5.01	            (app_encode_app(a,$o,
4.81/5.01	                            app_encode_app(a,app_encode_fun(a,$o),Xp,Xx),Xy) =>
4.81/5.01	             (app_encode_app(a,app_encode_fun(b,app_encode_fun(b,$o)),Xp2,Xx) =
4.81/5.01	              app_encode_app(a,app_encode_fun(b,app_encode_fun(b,$o)),Xp2,Xy))))) =>
4.81/5.01	        ((![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b)]:
4.81/5.01	            ((![Xx0:a,Xy0:a]:
4.81/5.01	                (app_encode_app(a,$o,
4.81/5.01	                                app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                                Xy0) =>
4.81/5.01	                 app_encode_app(b,$o,
4.81/5.01	                                app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                               app_encode_app(a,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,$o)),Xp2,Xx0),
4.81/5.01	                                               app_encode_app(a,b,Xx,Xx0)),
4.81/5.01	                                app_encode_app(a,b,Xy,Xy0)))) =>
4.81/5.01	             (![Xx0:a,Xy0:a]:
4.81/5.01	                (app_encode_app(a,$o,
4.81/5.01	                                app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                                Xy0) =>
4.81/5.01	                 app_encode_app(b,$o,
4.81/5.01	                                app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                               app_encode_app(a,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,$o)),Xp2,Xx0),
4.81/5.01	                                               app_encode_app(a,b,Xy,Xx0)),
4.81/5.01	                                app_encode_app(a,b,Xx,Xy0)))))) & 
4.81/5.01	         (![Xx:app_encode_fun(a,b),Xy:app_encode_fun(a,b),
4.81/5.01	            Xz:app_encode_fun(a,b)]:
4.81/5.01	            (((![Xx0:a,Xy0:a]:
4.81/5.01	                 (app_encode_app(a,$o,
4.81/5.01	                                 app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                                 Xy0) =>
4.81/5.01	                  app_encode_app(b,$o,
4.81/5.01	                                 app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                                app_encode_app(a,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,$o)),Xp2,Xx0),
4.81/5.01	                                                app_encode_app(a,b,Xx,Xx0)),
4.81/5.01	                                 app_encode_app(a,b,Xy,Xy0)))) & 
4.81/5.01	              (![Xx0:a,Xy0:a]:
4.81/5.01	                 (app_encode_app(a,$o,
4.81/5.01	                                 app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                                 Xy0) =>
4.81/5.01	                  app_encode_app(b,$o,
4.81/5.01	                                 app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                                app_encode_app(a,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,
4.81/5.01	                                                               app_encode_fun(
4.81/5.01	                                                               b,$o)),Xp2,Xx0),
4.81/5.01	                                                app_encode_app(a,b,Xy,Xx0)),
4.81/5.01	                                 app_encode_app(a,b,Xz,Xy0))))) =>
4.81/5.01	             (![Xx0:a,Xy0:a]:
4.81/5.01	                (app_encode_app(a,$o,
4.81/5.01	                                app_encode_app(a,app_encode_fun(a,$o),Xp,Xx0),
4.81/5.01	                                Xy0) =>
4.81/5.01	                 app_encode_app(b,$o,
4.81/5.01	                                app_encode_app(b,app_encode_fun(b,$o),
4.81/5.01	                                               app_encode_app(a,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,
4.81/5.01	                                                              app_encode_fun(
4.81/5.01	                                                              b,$o)),Xp2,Xx0),
4.81/5.01	                                               app_encode_app(a,b,Xx,Xx0)),
4.81/5.01	                                app_encode_app(a,b,Xz,Xy0))))))))))).
4.81/5.01	tff('0', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('1', plain,
4.81/5.01	    ![X6 : a, X7 : a]:
4.81/5.01	      (app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X6), app_encode_app(a, b, sk_Xy1, X6)), 
4.81/5.01	           app_encode_app(a, b, sk_Xz, X7))
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X6), X7)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('2', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xz, sk_Xy01))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('sup-', [status(thm)], ['0', '1'])).
4.81/5.01	tff('3', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.01	       app_encode_app(a, b, sk_Xz, sk_Xy01))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['2'])).
4.81/5.01	tff('4', plain,
4.81/5.01	    ![X12 : a, X13 : b, X14 : b]:
4.81/5.01	      (~ app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X12), X13), X14)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X12), X14), X13)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X12), X12)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('5', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | ~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.81/5.01	    inference('sup-', [status(thm)], ['3', '4'])).
4.81/5.01	tff('6', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.01	       app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.01	     | ~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['5'])).
4.81/5.01	tff('7', plain,
4.81/5.01	    ![X18 : a, X19 : a]:
4.81/5.01	      (app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X18), X19)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X19), X18)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('8', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)),
4.81/5.01	    inference('sup-', [status(thm)], ['0', '7'])).
4.81/5.01	tff('9', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['8'])).
4.81/5.01	tff('10', plain,
4.81/5.01	    ![X20 : a, X21 : a, X22 : a]:
4.81/5.01	      (~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X20), X21)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X21), X22)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X20), X22)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('11', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ $true
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)),
4.81/5.01	    inference('sup-', [status(thm)], ['0', '10'])).
4.81/5.01	tff('12', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['11'])).
4.81/5.01	tff('13', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('sup-', [status(thm)], ['9', '12'])).
4.81/5.01	tff('14', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['13'])).
4.81/5.01	tff('15', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.81/5.01	    inference('clc', [status(thm)], ['6', '14'])).
4.81/5.01	tff('16', plain,
4.81/5.01	    ![X10 : a, X11 : a]:
4.81/5.01	      (app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	         X11)
4.81/5.01	        = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	            sk_Xp2, X10)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X11), X10)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('17', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	         sk_Xx0)
4.81/5.01	        = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	            sk_Xp2, sk_Xy0)),
4.81/5.01	    inference('sup-', [status(thm)], ['14', '16'])).
4.81/5.01	tff('18', plain,
4.81/5.01	    (app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	       sk_Xx0)
4.81/5.01	      = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	          sk_Xy0)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['17'])).
4.81/5.01	tff('19', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0)),
4.81/5.01	    inference('sup-', [status(thm)], ['14', '7'])).
4.81/5.01	tff('20', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['19'])).
4.81/5.01	tff('21', plain,
4.81/5.01	    ![X8 : a, X9 : a]:
4.81/5.01	      (~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X8), X9)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X8), app_encode_app(a, b, sk_Xx, X8)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy, X9))
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('22', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.01	    inference('sup-', [status(thm)], ['20', '21'])).
4.81/5.01	tff('23', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	       app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['22'])).
4.81/5.01	tff('24', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)),
4.81/5.01	    inference('sup-', [status(thm)], ['23', '7'])).
4.81/5.01	tff('25', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['24'])).
4.81/5.01	tff('26', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ $true
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)),
4.81/5.01	    inference('sup-', [status(thm)], ['23', '10'])).
4.81/5.01	tff('27', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['26'])).
4.81/5.01	tff('28', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('sup-', [status(thm)], ['25', '27'])).
4.81/5.01	tff('29', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	       app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['28'])).
4.81/5.01	tff('30', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	       app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('sup+', [status(thm)], ['18', '29'])).
4.81/5.01	tff('31', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.01	    inference('simplify', [status(thm)], ['30'])).
4.81/5.01	tff('32', plain,
4.81/5.01	    ![X0 : b, X1 : b]:
4.81/5.01	      (~ app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx0), X1), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xy0)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xy0), X0), X1)),
4.81/5.01	    inference('sup-', [status(thm)], ['18', '4'])).
4.81/5.01	tff('33', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ $true
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), X0)),
4.81/5.01	    inference('sup-', [status(thm)], ['20', '10'])).
4.81/5.01	tff('34', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['33'])).
4.81/5.01	tff('35', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ $true
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), sk_Xy0)),
4.81/5.01	    inference('sup-', [status(thm)], ['34', '7'])).
4.81/5.01	tff('36', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X0), sk_Xy0)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['35'])).
4.81/5.01	tff('37', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xy0)),
4.81/5.01	    inference('sup-', [status(thm)], ['14', '36'])).
4.81/5.01	tff('38', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xy0)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['37'])).
4.81/5.01	tff('39', plain,
4.81/5.01	    ![X0 : b, X1 : b]:
4.81/5.01	      (app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), X0), X1)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	       | ~ app_encode_app(b, $o, 
4.81/5.01	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	                 sk_Xp2, sk_Xx0), X1), X0)),
4.81/5.01	    inference('clc', [status(thm)], ['32', '38'])).
4.81/5.01	tff('40', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.81/5.01	    inference('sup-', [status(thm)], ['31', '39'])).
4.81/5.01	tff('41', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xy0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	       app_encode_app(a, b, sk_Xx, sk_Xy0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('simplify', [status(thm)], ['40'])).
4.81/5.01	tff('42', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	       app_encode_app(a, b, sk_Xx, sk_Xy0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('sup+', [status(thm)], ['18', '41'])).
4.81/5.01	tff('43', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.81/5.01	    inference('simplify', [status(thm)], ['42'])).
4.81/5.01	tff('44', plain,
4.81/5.01	    (~ app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('45', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | ~ app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)),
4.81/5.01	    inference('sup-', [status(thm)], ['44', '7'])).
4.81/5.01	tff('46', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), sk_Xx01)
4.81/5.01	     | ~ app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.81/5.01	    inference('simplify', [status(thm)], ['45'])).
4.81/5.01	tff('47', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ $true
4.81/5.01	       | ~ app_encode_app(b, $o, 
4.81/5.01	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	                 sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	             app_encode_app(a, b, sk_Xx, sk_Xy0))
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)),
4.81/5.01	    inference('sup-', [status(thm)], ['44', '10'])).
4.81/5.01	tff('48', plain,
4.81/5.01	    ![X0 : a]:
4.81/5.01	      (~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy01), X0)
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), X0)
4.81/5.01	       | ~ app_encode_app(b, $o, 
4.81/5.01	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	                 sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	             app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.81/5.01	    inference('simplify', [status(thm)], ['47'])).
4.81/5.01	tff('49', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | ~ app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.81/5.01	     | ~ app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)),
4.81/5.01	    inference('sup-', [status(thm)], ['46', '48'])).
4.81/5.01	tff('50', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | ~ app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.81/5.01	    inference('simplify', [status(thm)], ['49'])).
4.81/5.01	tff('51', plain,
4.81/5.01	    app_encode_app(a, $o, 
4.81/5.01	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01),
4.81/5.01	    inference('clc', [status(thm)], ['43', '50'])).
4.81/5.01	tff('52', plain,
4.81/5.01	    ![X4 : a, X5 : a]:
4.81/5.01	      (app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X4), app_encode_app(a, b, sk_Xx1, X4)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy1, X5))
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X4), X5)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('53', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('sup-', [status(thm)], ['51', '52'])).
4.81/5.01	tff('54', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.81/5.01	    inference('simplify', [status(thm)], ['53'])).
4.81/5.01	tff('55', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | ~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.01	    inference('sup-', [status(thm)], ['54', '4'])).
4.81/5.01	tff('56', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | ~ $true
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.01	    inference('demod', [status(thm)], ['55', '51'])).
4.81/5.01	tff('57', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.01	       app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['56'])).
4.81/5.01	tff('58', plain,
4.81/5.01	    ![X12 : a, X15 : b, X16 : b, X17 : b]:
4.81/5.01	      (app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, X12), X15), X16)
4.81/5.01	       | ~ app_encode_app(b, $o, 
4.81/5.01	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	                 sk_Xp2, X12), X17), X16)
4.81/5.01	       | ~ app_encode_app(b, $o, 
4.81/5.01	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	                 sk_Xp2, X12), X15), X17)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X12), X12)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('59', plain,
4.81/5.01	    ![X0 : b]:
4.81/5.01	      (~ $true
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), 
4.81/5.01	             sk_Xx01)
4.81/5.01	       | ~ app_encode_app(b, $o, 
4.81/5.01	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	                 sk_Xp2, sk_Xx01), X0), 
4.81/5.01	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.01	    inference('sup-', [status(thm)], ['57', '58'])).
4.81/5.01	tff('60', plain,
4.81/5.01	    ![X0 : b]:
4.81/5.01	      (~ $true
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	       | ~ $true
4.81/5.01	       | ~ app_encode_app(b, $o, 
4.81/5.01	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	                 sk_Xp2, sk_Xx01), X0), 
4.81/5.01	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.01	    inference('demod', [status(thm)], ['59', '51'])).
4.81/5.01	tff('61', plain,
4.81/5.01	    ![X0 : b]:
4.81/5.01	      (app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.81/5.01	       | ~ app_encode_app(b, $o, 
4.81/5.01	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	                 sk_Xp2, sk_Xx01), X0), 
4.81/5.01	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.01	       | app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['60'])).
4.81/5.01	tff('62', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.01	    inference('sup-', [status(thm)], ['15', '61'])).
4.81/5.01	tff('63', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.01	       app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['62'])).
4.81/5.01	tff('64', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | ~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.81/5.01	    inference('sup-', [status(thm)], ['63', '4'])).
4.81/5.01	tff('65', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | ~ $true
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.81/5.01	    inference('demod', [status(thm)], ['64', '51'])).
4.81/5.01	tff('66', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.01	       app_encode_app(a, b, sk_Xz, sk_Xy01))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)),
4.81/5.01	    inference('simplify', [status(thm)], ['65'])).
4.81/5.01	tff('67', plain,
4.81/5.01	    (app_encode_app(a, $o, 
4.81/5.01	       app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0)
4.81/5.01	     | ~ app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.01	           app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('68', plain,
4.81/5.01	    app_encode_app(a, $o, 
4.81/5.01	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xy0),
4.81/5.01	    inference('clc', [status(thm)], ['66', '67'])).
4.81/5.01	tff('69', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0)),
4.81/5.01	    inference('sup-', [status(thm)], ['68', '7'])).
4.81/5.01	tff('70', plain,
4.81/5.01	    app_encode_app(a, $o, 
4.81/5.01	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), sk_Xx0),
4.81/5.01	    inference('simplify', [status(thm)], ['69'])).
4.81/5.01	tff('71', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.01	    inference('sup-', [status(thm)], ['70', '21'])).
4.81/5.01	tff('72', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	       app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.81/5.01	    inference('simplify', [status(thm)], ['71'])).
4.81/5.01	tff('73', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	         sk_Xx0)
4.81/5.01	        = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	            sk_Xp2, sk_Xy0)),
4.81/5.01	    inference('sup-', [status(thm)], ['68', '16'])).
4.81/5.01	tff('74', plain,
4.81/5.01	    app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	      sk_Xx0)
4.81/5.01	     = app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	         sk_Xy0),
4.81/5.01	    inference('simplify', [status(thm)], ['73'])).
4.81/5.01	tff('75', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	       app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(a, $o, 
4.81/5.01	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xy01)),
4.81/5.01	    inference('demod', [status(thm)], ['72', '74'])).
4.81/5.01	tff('76', plain,
4.81/5.01	    ![X6 : a, X7 : a, X8 : a, X9 : a]:
4.81/5.01	      (~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X8), X9)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X8), app_encode_app(a, b, sk_Xx, X8)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy, X9))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X6), app_encode_app(a, b, sk_Xy1, X6)), 
4.81/5.01	           app_encode_app(a, b, sk_Xz, X7))
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X6), X7)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('77', plain,
4.81/5.01	    ![X0 : a, X1 : a]:
4.81/5.01	      (~ $true
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X1), app_encode_app(a, b, sk_Xy1, X1)), 
4.81/5.01	           app_encode_app(a, b, sk_Xz, X0))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.01	    inference('sup-', [status(thm)], ['70', '76'])).
4.81/5.01	tff('78', plain,
4.81/5.01	    ![X0 : a, X1 : a]:
4.81/5.01	      (app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X1), app_encode_app(a, b, sk_Xy1, X1)), 
4.81/5.01	           app_encode_app(a, b, sk_Xz, X0))
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)),
4.81/5.01	    inference('simplify', [status(thm)], ['77'])).
4.81/5.01	tff('79', plain,
4.81/5.01	    ![X0 : a, X1 : a]:
4.81/5.01	      (app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X1), app_encode_app(a, b, sk_Xy1, X1)), 
4.81/5.01	           app_encode_app(a, b, sk_Xz, X0))
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)),
4.81/5.01	    inference('demod', [status(thm)], ['78', '74'])).
4.81/5.01	tff('80', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xz, sk_Xy01))
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.01	    inference('sup-', [status(thm)], ['75', '79'])).
4.81/5.01	tff('81', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.01	       app_encode_app(a, b, sk_Xz, sk_Xy01))
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.01	    inference('simplify', [status(thm)], ['80'])).
4.81/5.01	tff('82', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | ~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.81/5.01	    inference('sup-', [status(thm)], ['81', '4'])).
4.81/5.01	tff('83', plain,
4.81/5.01	    (~ $true
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	     | ~ $true
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.81/5.01	    inference('demod', [status(thm)], ['82', '51'])).
4.81/5.01	tff('84', plain,
4.81/5.01	    (app_encode_app(b, $o, 
4.81/5.01	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.01	           sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.01	       app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.01	     | app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.01	    inference('simplify', [status(thm)], ['83'])).
4.81/5.01	tff('85', plain,
4.81/5.01	    ![X4 : a, X5 : a, X8 : a, X9 : a]:
4.81/5.01	      (~ app_encode_app(a, $o, 
4.81/5.01	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X8), X9)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X8), app_encode_app(a, b, sk_Xx, X8)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy, X9))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X4), app_encode_app(a, b, sk_Xx1, X4)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy1, X5))
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X4), X5)),
4.81/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.81/5.01	tff('86', plain,
4.81/5.01	    ![X0 : a, X1 : a]:
4.81/5.01	      (~ $true
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X1), app_encode_app(a, b, sk_Xx1, X1)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy1, X0))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.01	    inference('sup-', [status(thm)], ['70', '85'])).
4.81/5.01	tff('87', plain,
4.81/5.01	    ![X0 : a, X1 : a]:
4.81/5.01	      (app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.01	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.01	       | app_encode_app(b, $o, 
4.81/5.01	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.01	               sk_Xp2, X1), app_encode_app(a, b, sk_Xx1, X1)), 
4.81/5.01	           app_encode_app(a, b, sk_Xy1, X0))
4.81/5.01	       | ~ app_encode_app(a, $o, 
4.81/5.01	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)),
4.81/5.01	    inference('simplify', [status(thm)], ['86'])).
4.81/5.01	tff('88', plain,
4.81/5.01	    ![X0 : a, X1 : a]:
4.81/5.01	      (app_encode_app(b, $o, 
4.81/5.01	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.01	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	       | app_encode_app(b, $o, 
4.81/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	               sk_Xp2, X1), app_encode_app(a, b, sk_Xx1, X1)), 
4.81/5.02	           app_encode_app(a, b, sk_Xy1, X0))
4.81/5.02	       | ~ app_encode_app(a, $o, 
4.81/5.02	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X1), X0)),
4.81/5.02	    inference('demod', [status(thm)], ['87', '74'])).
4.81/5.02	tff('89', plain,
4.81/5.02	    (~ $true
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.02	    inference('sup-', [status(thm)], ['51', '88'])).
4.81/5.02	tff('90', plain,
4.81/5.02	    (app_encode_app(b, $o, 
4.81/5.02	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.02	           sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	       app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.81/5.02	    inference('simplify', [status(thm)], ['89'])).
4.81/5.02	tff('91', plain,
4.81/5.02	    (~ $true
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	     | ~ app_encode_app(a, $o, 
4.81/5.02	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.02	         app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.02	    inference('sup-', [status(thm)], ['90', '4'])).
4.81/5.02	tff('92', plain,
4.81/5.02	    (~ $true
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	     | ~ $true
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.02	         app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.02	    inference('demod', [status(thm)], ['91', '51'])).
4.81/5.02	tff('93', plain,
4.81/5.02	    (app_encode_app(b, $o, 
4.81/5.02	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.02	           sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.81/5.02	       app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.02	    inference('simplify', [status(thm)], ['92'])).
4.81/5.02	tff('94', plain,
4.81/5.02	    ![X0 : b]:
4.81/5.02	      (~ $true
4.81/5.02	       | app_encode_app(b, $o, 
4.81/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	           app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	       | ~ app_encode_app(a, $o, 
4.81/5.02	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), 
4.81/5.02	             sk_Xx01)
4.81/5.02	       | ~ app_encode_app(b, $o, 
4.81/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	                 sk_Xp2, sk_Xx01), X0), 
4.81/5.02	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.02	       | app_encode_app(b, $o, 
4.81/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	               sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.02	    inference('sup-', [status(thm)], ['93', '58'])).
4.81/5.02	tff('95', plain,
4.81/5.02	    ![X0 : b]:
4.81/5.02	      (~ $true
4.81/5.02	       | app_encode_app(b, $o, 
4.81/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	           app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	       | ~ $true
4.81/5.02	       | ~ app_encode_app(b, $o, 
4.81/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	                 sk_Xp2, sk_Xx01), X0), 
4.81/5.02	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.02	       | app_encode_app(b, $o, 
4.81/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	               sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.02	    inference('demod', [status(thm)], ['94', '51'])).
4.81/5.02	tff('96', plain,
4.81/5.02	    ![X0 : b]:
4.81/5.02	      (app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.81/5.02	       | ~ app_encode_app(b, $o, 
4.81/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	                 sk_Xp2, sk_Xx01), X0), 
4.81/5.02	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.81/5.02	       | app_encode_app(b, $o, 
4.81/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	           app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.02	    inference('simplify', [status(thm)], ['95'])).
4.81/5.02	tff('97', plain,
4.81/5.02	    (~ $true
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.02	         app_encode_app(a, b, sk_Xx1, sk_Xx01))),
4.81/5.02	    inference('sup-', [status(thm)], ['84', '96'])).
4.81/5.02	tff('98', plain,
4.81/5.02	    (app_encode_app(b, $o, 
4.81/5.02	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.02	           sk_Xx01), app_encode_app(a, b, sk_Xz, sk_Xy01)), 
4.81/5.02	       app_encode_app(a, b, sk_Xx1, sk_Xx01))
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.02	    inference('simplify', [status(thm)], ['97'])).
4.81/5.02	tff('99', plain,
4.81/5.02	    (~ $true
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	     | ~ app_encode_app(a, $o, 
4.81/5.02	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), sk_Xx01)
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.02	         app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.81/5.02	    inference('sup-', [status(thm)], ['98', '4'])).
4.81/5.02	tff('100', plain,
4.81/5.02	    (~ $true
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))
4.81/5.02	     | ~ $true
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.02	         app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.81/5.02	    inference('demod', [status(thm)], ['99', '51'])).
4.81/5.02	tff('101', plain,
4.81/5.02	    (app_encode_app(b, $o, 
4.81/5.02	       app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.81/5.02	           sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.81/5.02	       app_encode_app(a, b, sk_Xz, sk_Xy01))
4.81/5.02	     | app_encode_app(b, $o, 
4.81/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.81/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.81/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.81/5.02	    inference('simplify', [status(thm)], ['100'])).
4.81/5.02	tff('102', plain,
4.81/5.02	    ![X8 : a, X9 : a]:
4.81/5.02	      (~ app_encode_app(a, $o, 
4.81/5.02	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X8), X9)
4.81/5.02	       | app_encode_app(b, $o, 
4.81/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.81/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, X8), app_encode_app(a, b, sk_Xx, X8)), 
4.85/5.02	           app_encode_app(a, b, sk_Xy, X9))
4.85/5.02	       | ~ app_encode_app(b, $o, 
4.85/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	                 sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	             app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.85/5.02	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.85/5.02	tff('103', plain,
4.85/5.02	    (~ $true
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	           app_encode_app(a, b, sk_Xz, sk_Xy01))
4.85/5.02	     | app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.85/5.02	         app_encode_app(a, b, sk_Xy, sk_Xx0))),
4.85/5.02	    inference('sup-', [status(thm)], ['70', '102'])).
4.85/5.02	tff('104', plain,
4.85/5.02	    (app_encode_app(b, $o, 
4.85/5.02	       app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.85/5.02	           sk_Xy0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.85/5.02	       app_encode_app(a, b, sk_Xy, sk_Xx0))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	           app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.85/5.02	    inference('simplify', [status(thm)], ['103'])).
4.85/5.02	tff('105', plain,
4.85/5.02	    (app_encode_app(b, $o, 
4.85/5.02	       app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.85/5.02	           sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.85/5.02	       app_encode_app(a, b, sk_Xy, sk_Xx0))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	           app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.85/5.02	    inference('demod', [status(thm)], ['104', '74'])).
4.85/5.02	tff('106', plain,
4.85/5.02	    app_encode_app(b, $o, 
4.85/5.02	      app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	        app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.85/5.02	          sk_Xx0), app_encode_app(a, b, sk_Xx, sk_Xy0)), 
4.85/5.02	      app_encode_app(a, b, sk_Xy, sk_Xx0)),
4.85/5.02	    inference('clc', [status(thm)], ['101', '105'])).
4.85/5.02	tff('107', plain,
4.85/5.02	    (~ $true
4.85/5.02	     | ~ app_encode_app(a, $o, 
4.85/5.02	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0)
4.85/5.02	     | app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	         app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.85/5.02	    inference('sup-', [status(thm)], ['106', '4'])).
4.85/5.02	tff('108', plain,
4.85/5.02	    ![X0 : a]:
4.85/5.02	      (~ $true
4.85/5.02	       | app_encode_app(a, $o, 
4.85/5.02	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), X0)
4.85/5.02	       | ~ app_encode_app(a, $o, 
4.85/5.02	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)),
4.85/5.02	    inference('sup-', [status(thm)], ['68', '10'])).
4.85/5.02	tff('109', plain,
4.85/5.02	    ![X0 : a]:
4.85/5.02	      (~ app_encode_app(a, $o, 
4.85/5.02	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xy0), X0)
4.85/5.02	       | app_encode_app(a, $o, 
4.85/5.02	           app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), X0)),
4.85/5.02	    inference('simplify', [status(thm)], ['108'])).
4.85/5.02	tff('110', plain,
4.85/5.02	    (~ $true
4.85/5.02	     | app_encode_app(a, $o, 
4.85/5.02	         app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0)),
4.85/5.02	    inference('sup-', [status(thm)], ['70', '109'])).
4.85/5.02	tff('111', plain,
4.85/5.02	    app_encode_app(a, $o, 
4.85/5.02	      app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx0), sk_Xx0),
4.85/5.02	    inference('simplify', [status(thm)], ['110'])).
4.85/5.02	tff('112', plain,
4.85/5.02	    (~ $true
4.85/5.02	     | ~ $true
4.85/5.02	     | app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	         app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.85/5.02	    inference('demod', [status(thm)], ['107', '111'])).
4.85/5.02	tff('113', plain,
4.85/5.02	    app_encode_app(b, $o, 
4.85/5.02	      app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	        app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.85/5.02	          sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	      app_encode_app(a, b, sk_Xx, sk_Xy0)),
4.85/5.02	    inference('simplify', [status(thm)], ['112'])).
4.85/5.02	tff('114', plain,
4.85/5.02	    ![X6 : a, X7 : a]:
4.85/5.02	      (~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	       | app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, X6), app_encode_app(a, b, sk_Xy1, X6)), 
4.85/5.02	           app_encode_app(a, b, sk_Xz, X7))
4.85/5.02	       | ~ app_encode_app(a, $o, 
4.85/5.02	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X6), X7)),
4.85/5.02	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.85/5.02	tff('115', plain,
4.85/5.02	    (~ $true
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	     | app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.85/5.02	         app_encode_app(a, b, sk_Xz, sk_Xy01))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.85/5.02	    inference('sup-', [status(thm)], ['44', '114'])).
4.85/5.02	tff('116', plain,
4.85/5.02	    (app_encode_app(b, $o, 
4.85/5.02	       app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	         app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), sk_Xp2, 
4.85/5.02	           sk_Xx01), app_encode_app(a, b, sk_Xy1, sk_Xx01)), 
4.85/5.02	       app_encode_app(a, b, sk_Xz, sk_Xy01))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.85/5.02	    inference('simplify', [status(thm)], ['115'])).
4.85/5.02	tff('117', plain,
4.85/5.02	    ![X0 : b]:
4.85/5.02	      (~ $true
4.85/5.02	       | ~ app_encode_app(b, $o, 
4.85/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	                 sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	             app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	       | ~ app_encode_app(a, $o, 
4.85/5.02	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), 
4.85/5.02	             sk_Xx01)
4.85/5.02	       | ~ app_encode_app(b, $o, 
4.85/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	                 sk_Xp2, sk_Xx01), X0), 
4.85/5.02	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.85/5.02	       | app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.85/5.02	    inference('sup-', [status(thm)], ['116', '58'])).
4.85/5.02	tff('118', plain,
4.85/5.02	    ![X0 : b]:
4.85/5.02	      (app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xz, sk_Xy01))
4.85/5.02	       | ~ app_encode_app(b, $o, 
4.85/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	                 sk_Xp2, sk_Xx01), X0), 
4.85/5.02	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.85/5.02	       | ~ app_encode_app(a, $o, 
4.85/5.02	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, sk_Xx01), 
4.85/5.02	             sk_Xx01)
4.85/5.02	       | ~ app_encode_app(b, $o, 
4.85/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	                 sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	             app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.85/5.02	    inference('simplify', [status(thm)], ['117'])).
4.85/5.02	tff('119', plain,
4.85/5.02	    ![X0 : b]:
4.85/5.02	      (app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xz, sk_Xy01))
4.85/5.02	       | ~ app_encode_app(b, $o, 
4.85/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	                 sk_Xp2, sk_Xx01), X0), 
4.85/5.02	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.85/5.02	       | ~ $true
4.85/5.02	       | ~ app_encode_app(b, $o, 
4.85/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	                 sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	             app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.85/5.02	    inference('demod', [status(thm)], ['118', '51'])).
4.85/5.02	tff('120', plain,
4.85/5.02	    ![X0 : b]:
4.85/5.02	      (~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	       | ~ app_encode_app(b, $o, 
4.85/5.02	             app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	               app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	                 sk_Xp2, sk_Xx01), X0), 
4.85/5.02	             app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.85/5.02	       | app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx01), X0), app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.85/5.02	    inference('simplify', [status(thm)], ['119'])).
4.85/5.02	tff('121', plain,
4.85/5.02	    (~ app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	           app_encode_app(a, b, sk_Xz, sk_Xy01))),
4.85/5.02	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.85/5.02	tff('122', plain,
4.85/5.02	    (~ $true
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	           app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.85/5.02	    inference('sup-', [status(thm)], ['120', '121'])).
4.85/5.02	tff('123', plain,
4.85/5.02	    (~ app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	           app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.85/5.02	    inference('simplify', [status(thm)], ['122'])).
4.85/5.02	tff('124', plain,
4.85/5.02	    ![X4 : a, X5 : a]:
4.85/5.02	      (~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	       | app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, X4), app_encode_app(a, b, sk_Xx1, X4)), 
4.85/5.02	           app_encode_app(a, b, sk_Xy1, X5))
4.85/5.02	       | ~ app_encode_app(a, $o, 
4.85/5.02	             app_encode_app(a, app_encode_fun(a, $o), sk_Xp, X4), X5)),
4.85/5.02	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.85/5.02	tff('125', plain,
4.85/5.02	    (~ $true
4.85/5.02	     | app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	         app_encode_app(a, b, sk_Xy1, sk_Xx01))
4.85/5.02	     | ~ app_encode_app(b, $o, 
4.85/5.02	           app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	             app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	               sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	           app_encode_app(a, b, sk_Xx, sk_Xy0))),
4.85/5.02	    inference('sup-', [status(thm)], ['51', '124'])).
4.85/5.02	tff('126', plain,
4.85/5.02	    (~ app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	         app_encode_app(a, b, sk_Xx, sk_Xy0))
4.85/5.02	     | app_encode_app(b, $o, 
4.85/5.02	         app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	           app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	             sk_Xp2, sk_Xx01), app_encode_app(a, b, sk_Xx1, sk_Xx01)), 
4.85/5.02	         app_encode_app(a, b, sk_Xy1, sk_Xx01))),
4.85/5.02	    inference('simplify', [status(thm)], ['125'])).
4.85/5.02	tff('127', plain,
4.85/5.02	    ~ app_encode_app(b, $o, 
4.85/5.02	        app_encode_app(b, app_encode_fun(b, $o), 
4.85/5.02	          app_encode_app(a, app_encode_fun(b, app_encode_fun(b, $o)), 
4.85/5.02	            sk_Xp2, sk_Xx0), app_encode_app(a, b, sk_Xy, sk_Xx0)), 
4.85/5.02	        app_encode_app(a, b, sk_Xx, sk_Xy0)),
4.85/5.02	    inference('clc', [status(thm)], ['123', '126'])).
4.85/5.02	tff('128', plain, ~ $true, inference('sup-', [status(thm)], ['113', '127'])).
4.85/5.02	tff('129', plain, $false, inference('simplify', [status(thm)], ['128'])).
4.85/5.02	
4.85/5.02	% SZS output end Refutation
4.85/5.02	EOF
