0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : app
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-ho \
0.00/0.00	  --no-avatar \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n032.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:31:23 CST 2018
37.82/38.06	% done 1749 iterations in 37.861s
37.82/38.06	% SZS status Theorem for 'stdin'
37.82/38.06	% SZS output start Refutation
37.82/38.07	tff(zf_stmt_7, axiom,
37.82/38.07	  (![B:$tType,A:$tType,A0:app_encode_fun(A,B),A1:app_encode_fun(B,$o),
37.82/38.07	     A2:app_encode_fun(A,$o)]:
37.82/38.07	     (app_encode_app(app_encode_fun(B,$o),$o,
37.82/38.07	                     app_encode_app(app_encode_fun(B,$o),
37.82/38.07	                                    app_encode_fun(app_encode_fun(B,$o),$o),
37.82/38.07	                                    'const/sets/SUBSET'(B),A1),
37.82/38.07	                     app_encode_app(app_encode_fun(A,$o),
37.82/38.07	                                    app_encode_fun(B,$o),
37.82/38.07	                                    app_encode_app(app_encode_fun(A,B),
37.82/38.07	                                                   app_encode_fun(app_encode_fun(
37.82/38.07	                                                                  A,$o),
37.82/38.07	                                                                  app_encode_fun(
37.82/38.07	                                                                  B,$o)),
37.82/38.07	                                                   'const/sets/IMAGE'(A,B),A0),
37.82/38.07	                                    A2)) <=>
37.82/38.07	      (?[A3:app_encode_fun(A,$o)]:
37.82/38.07	         (app_encode_app(app_encode_fun(A,$o),$o,
37.82/38.07	                         app_encode_app(app_encode_fun(A,$o),
37.82/38.07	                                        app_encode_fun(app_encode_fun(A,$o),
37.82/38.07	                                                       $o),
37.82/38.07	                                        'const/sets/SUBSET'(A),A3),
37.82/38.07	                         A2) & 
37.82/38.07	          (![A4:A,A5:A]:
37.82/38.07	             ((app_encode_app(app_encode_fun(A,$o),$o,
37.82/38.07	                              app_encode_app(A,
37.82/38.07	                                             app_encode_fun(app_encode_fun(
37.82/38.07	                                                            A,$o),$o),
37.82/38.07	                                             'const/sets/IN'(A),A4),
37.82/38.07	                              A3) & 
37.82/38.07	               app_encode_app(app_encode_fun(A,$o),$o,
37.82/38.07	                              app_encode_app(A,
37.82/38.07	                                             app_encode_fun(app_encode_fun(
37.82/38.07	                                                            A,$o),$o),
37.82/38.07	                                             'const/sets/IN'(A),A5),
37.82/38.07	                              A3)) =>
37.82/38.07	              ((app_encode_app(A,B,A0,A4) = app_encode_app(A,B,A0,A5)) <=>
37.82/38.07	               (A4 = A5)))) & 
37.82/38.07	          (A1 =
37.82/38.07	           app_encode_app(app_encode_fun(A,$o),app_encode_fun(B,$o),
37.82/38.07	                          app_encode_app(app_encode_fun(A,B),
37.82/38.07	                                         app_encode_fun(app_encode_fun(A,$o),
37.82/38.07	                                                        app_encode_fun(B,$o)),
37.82/38.07	                                         'const/sets/IMAGE'(A,B),A0),
37.82/38.07	                          A3))))))).
37.82/38.07	tff('0', plain,
37.82/38.07	    ![X2 : $tType, X3 : $tType, X5 : app_encode_fun(X3, $o), 
37.82/38.07	      X6 : app_encode_fun(X2, X3), X9 : app_encode_fun(X2, $o), 
37.82/38.07	      X10 : app_encode_fun(X2, $o)]:
37.82/38.07	      (app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	         app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	           app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	           'const/sets/SUBSET'(X3), X5), 
37.82/38.07	         app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	             app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.07	             'const/sets/IMAGE'(X2, X3), X6), X9))
37.82/38.07	       | X5
37.82/38.07	          != app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.07	               X10)
37.82/38.07	       | app_encode_app(X2, X3, X6, sk_A4(X2, X3, X10, X6))
37.82/38.07	          != app_encode_app(X2, X3, X6, sk_A5(X2, X3, X10, X6))
37.82/38.07	       | sk_A4(X2, X3, X10, X6) != sk_A5(X2, X3, X10, X6)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(X2, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(X2), X10), X9)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_7])).
37.82/38.07	tff('1', plain,
37.82/38.07	    ![X2 : $tType, X3 : $tType, X6 : app_encode_fun(X2, X3), 
37.82/38.07	      X9 : app_encode_fun(X2, $o), X10 : app_encode_fun(X2, $o)]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X2, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X2), X10), X9)
37.82/38.07	       | sk_A4(X2, X3, X10, X6) != sk_A5(X2, X3, X10, X6)
37.82/38.07	       | app_encode_app(X2, X3, X6, sk_A4(X2, X3, X10, X6))
37.82/38.07	          != app_encode_app(X2, X3, X6, sk_A5(X2, X3, X10, X6))
37.82/38.07	       | app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X3), 
37.82/38.07	             app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.07	               X10)), 
37.82/38.07	           app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	               app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.07	               'const/sets/IMAGE'(X2, X3), X6), X9))),
37.82/38.07	    inference('simplify', [status(thm)], ['0'])).
37.82/38.07	tff(zf_stmt_8, conjecture,
37.82/38.07	  (![A:$tType,A0:$tType,P:app_encode_fun(app_encode_fun(A,$o),$o),
37.82/38.07	     A1:app_encode_fun(A0,A),A2:app_encode_fun(A0,$o)]:
37.82/38.07	     ((?[A3:app_encode_fun(A,$o)]:
37.82/38.07	         (app_encode_app(app_encode_fun(A,$o),$o,P,A3) & 
37.82/38.07	          app_encode_app(app_encode_fun(A,$o),$o,
37.82/38.07	                         app_encode_app(app_encode_fun(A,$o),
37.82/38.07	                                        app_encode_fun(app_encode_fun(A,$o),
37.82/38.07	                                                       $o),
37.82/38.07	                                        'const/sets/SUBSET'(A),A3),
37.82/38.07	                         app_encode_app(app_encode_fun(A0,$o),
37.82/38.07	                                        app_encode_fun(A,$o),
37.82/38.07	                                        app_encode_app(app_encode_fun(A0,A),
37.82/38.07	                                                       app_encode_fun(
37.82/38.07	                                                       app_encode_fun(A0,$o),
37.82/38.07	                                                       app_encode_fun(A,$o)),
37.82/38.07	                                                       'const/sets/IMAGE'(
37.82/38.07	                                                       A0,A),A1),
37.82/38.07	                                        A2)))) <=>
37.82/38.07	      (?[A3:app_encode_fun(A0,$o)]:
37.82/38.07	         (app_encode_app(app_encode_fun(A,$o),$o,P,
37.82/38.07	                         app_encode_app(app_encode_fun(A0,$o),
37.82/38.07	                                        app_encode_fun(A,$o),
37.82/38.07	                                        app_encode_app(app_encode_fun(A0,A),
37.82/38.07	                                                       app_encode_fun(
37.82/38.07	                                                       app_encode_fun(A0,$o),
37.82/38.07	                                                       app_encode_fun(A,$o)),
37.82/38.07	                                                       'const/sets/IMAGE'(
37.82/38.07	                                                       A0,A),A1),
37.82/38.07	                                        A3)) & 
37.82/38.07	          (![A4:A0,A5:A0]:
37.82/38.07	             ((app_encode_app(app_encode_fun(A0,$o),$o,
37.82/38.07	                              app_encode_app(A0,
37.82/38.07	                                             app_encode_fun(app_encode_fun(
37.82/38.07	                                                            A0,$o),$o),
37.82/38.07	                                             'const/sets/IN'(A0),A5),
37.82/38.07	                              A3) & 
37.82/38.07	               app_encode_app(app_encode_fun(A0,$o),$o,
37.82/38.07	                              app_encode_app(A0,
37.82/38.07	                                             app_encode_fun(app_encode_fun(
37.82/38.07	                                                            A0,$o),$o),
37.82/38.07	                                             'const/sets/IN'(A0),A4),
37.82/38.07	                              A3)) =>
37.82/38.07	              ((app_encode_app(A0,A,A1,A4) = app_encode_app(A0,A,A1,A5)) <=>
37.82/38.07	               (A4 = A5)))) & 
37.82/38.07	          app_encode_app(app_encode_fun(A0,$o),$o,
37.82/38.07	                         app_encode_app(app_encode_fun(A0,$o),
37.82/38.07	                                        app_encode_fun(app_encode_fun(A0,$o),
37.82/38.07	                                                       $o),
37.82/38.07	                                        'const/sets/SUBSET'(A0),A3),
37.82/38.07	                         A2)))))).
37.82/38.07	tff(zf_stmt_0, type, zip_tseitin1 :
37.82/38.07	    !>[A0:$tType,A:$tType]:
37.82/38.07	      ((A0 * A0 * app_encode_fun(A0,$o) * app_encode_fun(A0,A)) > $o)).
37.82/38.07	tff(zf_stmt_1, axiom,
37.82/38.07	  (zip_tseitin1(A0,A,A5,A4,A3,A1) <=>
37.82/38.07	   ((app_encode_app(app_encode_fun(A0,$o),$o,
37.82/38.07	                    app_encode_app(A0,
37.82/38.07	                                   app_encode_fun(app_encode_fun(A0,$o),$o),
37.82/38.07	                                   'const/sets/IN'(A0),A4),
37.82/38.07	                    A3) & 
37.82/38.07	     app_encode_app(app_encode_fun(A0,$o),$o,
37.82/38.07	                    app_encode_app(A0,
37.82/38.07	                                   app_encode_fun(app_encode_fun(A0,$o),$o),
37.82/38.07	                                   'const/sets/IN'(A0),A5),
37.82/38.07	                    A3)) =>
37.82/38.07	    ((app_encode_app(A0,A,A1,A4) = app_encode_app(A0,A,A1,A5)) <=> (A4 = A5))))).
37.82/38.07	tff(zf_stmt_2, type, zip_tseitin0 :
37.82/38.07	    !>[A0:$tType,A:$tType]:
37.82/38.07	      ((app_encode_fun(A,$o) * 
37.82/38.07	        app_encode_fun(A0,$o) * 
37.82/38.07	        app_encode_fun(A0,A) * 
37.82/38.07	        app_encode_fun(app_encode_fun(A,$o),$o)) > $o)).
37.82/38.07	tff(zf_stmt_3, axiom,
37.82/38.07	  (zip_tseitin0(A0,A,A3,A2,A1,P) <=>
37.82/38.07	   (app_encode_app(app_encode_fun(A,$o),$o,
37.82/38.07	                   app_encode_app(app_encode_fun(A,$o),
37.82/38.07	                                  app_encode_fun(app_encode_fun(A,$o),$o),
37.82/38.07	                                  'const/sets/SUBSET'(A),A3),
37.82/38.07	                   app_encode_app(app_encode_fun(A0,$o),app_encode_fun(A,$o),
37.82/38.07	                                  app_encode_app(app_encode_fun(A0,A),
37.82/38.07	                                                 app_encode_fun(app_encode_fun(
37.82/38.07	                                                                A0,$o),
37.82/38.07	                                                                app_encode_fun(
37.82/38.07	                                                                A,$o)),
37.82/38.07	                                                 'const/sets/IMAGE'(A0,A),A1),
37.82/38.07	                                  A2)) & 
37.82/38.07	    app_encode_app(app_encode_fun(A,$o),$o,P,A3)))).
37.82/38.07	tff(zf_stmt_4, conjecture,
37.82/38.07	  (![A:$tType,A0:$tType,P:app_encode_fun(app_encode_fun(A,$o),$o),
37.82/38.07	     A1:app_encode_fun(A0,A),A2:app_encode_fun(A0,$o)]:
37.82/38.07	     ((?[A3:app_encode_fun(A,$o)]: zip_tseitin0(A0,A,A3,A2,A1,P)) <=>
37.82/38.07	      (?[A3:app_encode_fun(A0,$o)]:
37.82/38.07	         (app_encode_app(app_encode_fun(A0,$o),$o,
37.82/38.07	                         app_encode_app(app_encode_fun(A0,$o),
37.82/38.07	                                        app_encode_fun(app_encode_fun(A0,$o),
37.82/38.07	                                                       $o),
37.82/38.07	                                        'const/sets/SUBSET'(A0),A3),
37.82/38.07	                         A2) & 
37.82/38.07	          (![A4:A0,A5:A0]: zip_tseitin1(A0,A,A5,A4,A3,A1)) & 
37.82/38.07	          app_encode_app(app_encode_fun(A,$o),$o,P,
37.82/38.07	                         app_encode_app(app_encode_fun(A0,$o),
37.82/38.07	                                        app_encode_fun(A,$o),
37.82/38.07	                                        app_encode_app(app_encode_fun(A0,A),
37.82/38.07	                                                       app_encode_fun(
37.82/38.07	                                                       app_encode_fun(A0,$o),
37.82/38.07	                                                       app_encode_fun(A,$o)),
37.82/38.07	                                                       'const/sets/IMAGE'(
37.82/38.07	                                                       A0,A),A1),
37.82/38.07	                                        A3))))))).
37.82/38.07	tff(zf_stmt_5, negated_conjecture,
37.82/38.07	  (~
37.82/38.07	    (![A:$tType,A0:$tType,P:app_encode_fun(app_encode_fun(A,$o),$o),
37.82/38.07	       A1:app_encode_fun(A0,A),A2:app_encode_fun(A0,$o)]:
37.82/38.07	       ((?[A3:app_encode_fun(A,$o)]: zip_tseitin0(A0,A,A3,A2,A1,P)) <=>
37.82/38.07	        (?[A3:app_encode_fun(A0,$o)]:
37.82/38.07	           (app_encode_app(app_encode_fun(A0,$o),$o,
37.82/38.07	                           app_encode_app(app_encode_fun(A0,$o),
37.82/38.07	                                          app_encode_fun(app_encode_fun(
37.82/38.07	                                                         A0,$o),$o),
37.82/38.07	                                          'const/sets/SUBSET'(A0),A3),
37.82/38.07	                           A2) & 
37.82/38.07	            (![A4:A0,A5:A0]: zip_tseitin1(A0,A,A5,A4,A3,A1)) & 
37.82/38.07	            app_encode_app(app_encode_fun(A,$o),$o,P,
37.82/38.07	                           app_encode_app(app_encode_fun(A0,$o),
37.82/38.07	                                          app_encode_fun(A,$o),
37.82/38.07	                                          app_encode_app(app_encode_fun(A0,A),
37.82/38.07	                                                         app_encode_fun(
37.82/38.07	                                                         app_encode_fun(
37.82/38.07	                                                         A0,$o),
37.82/38.07	                                                         app_encode_fun(A,$o)),
37.82/38.07	                                                         'const/sets/IMAGE'(
37.82/38.07	                                                         A0,A),A1),
37.82/38.07	                                          A3)))))))).
37.82/38.07	tff('2', plain,
37.82/38.07	    (app_encode_app(app_encode_fun(sk_A, $o), $o, sk_P, 
37.82/38.07	       app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.07	         app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	           app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	           sk_A1), sk_A31))
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_5])).
37.82/38.07	tff('3', plain,
37.82/38.07	    ![X11 : $tType, X12 : app_encode_fun(X11, $o), X13 : $tType, 
37.82/38.07	      X14 : app_encode_fun(X13, X11), X15 : app_encode_fun(X13, $o), 
37.82/38.07	      X16 : app_encode_fun(app_encode_fun(X11, $o), $o)]:
37.82/38.07	      (zip_tseitin0(X13, X11, X12, X15, X14, X16)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(X11, $o), $o, X16, X12)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(X11, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(X11, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(X11, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(X11), X12), 
37.82/38.07	             app_encode_app(app_encode_fun(X13, $o), 
37.82/38.07	               app_encode_fun(X11, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X13, X11), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X13, $o), 
37.82/38.07	                   app_encode_fun(X11, $o)), 'const/sets/IMAGE'(X13, X11), 
37.82/38.07	                 X14), X15))),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_3])).
37.82/38.07	tff('4', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, sk_A)]:
37.82/38.07	      (~ $true
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A), 
37.82/38.07	               app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o), 
37.82/38.07	                 app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	                   app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                     app_encode_fun(sk_A, $o)), 
37.82/38.07	                   'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A31)), 
37.82/38.07	             app_encode_app(app_encode_fun(X0, $o), 
37.82/38.07	               app_encode_fun(sk_A, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X0, sk_A), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X0, $o), 
37.82/38.07	                   app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(X0, sk_A), 
37.82/38.07	                 X2), X1))
37.82/38.07	       | zip_tseitin0(X0, sk_A, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(sk_A, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	               sk_A1), sk_A31), X1, X2, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['2', '3'])).
37.82/38.07	tff('5', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, sk_A)]:
37.82/38.07	      (zip_tseitin0(X0, sk_A, 
37.82/38.07	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	             sk_A1), sk_A31), X1, X2, sk_P)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A), 
37.82/38.07	               app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o), 
37.82/38.07	                 app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	                   app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                     app_encode_fun(sk_A, $o)), 
37.82/38.07	                   'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A31)), 
37.82/38.07	             app_encode_app(app_encode_fun(X0, $o), 
37.82/38.07	               app_encode_fun(sk_A, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X0, sk_A), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X0, $o), 
37.82/38.07	                   app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(X0, sk_A), 
37.82/38.07	                 X2), X1))
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('simplify', [status(thm)], ['4'])).
37.82/38.07	tff('6', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (~ $true
37.82/38.07	       | app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	           sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	          != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	               sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	          != sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(sk_A, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	               sk_A1), sk_A31), X0, sk_A1, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['1', '5'])).
37.82/38.07	tff('7', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	             sk_A1), sk_A31), X0, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	          != sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	           sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	          != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	               sk_A5(sk_A0, sk_A, sk_A31, sk_A1))),
37.82/38.07	    inference('simplify', [status(thm)], ['6'])).
37.82/38.07	tff('8', plain,
37.82/38.07	    ![X2 : $tType, X3 : $tType, X5 : app_encode_fun(X3, $o), 
37.82/38.07	      X6 : app_encode_fun(X2, X3), X9 : app_encode_fun(X2, $o), 
37.82/38.07	      X10 : app_encode_fun(X2, $o)]:
37.82/38.07	      (app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	         app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	           app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	           'const/sets/SUBSET'(X3), X5), 
37.82/38.07	         app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	             app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.07	             'const/sets/IMAGE'(X2, X3), X6), X9))
37.82/38.07	       | X5
37.82/38.07	          != app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.07	               X10)
37.82/38.07	       | app_encode_app(X2, X3, X6, sk_A4(X2, X3, X10, X6))
37.82/38.07	          = app_encode_app(X2, X3, X6, sk_A5(X2, X3, X10, X6))
37.82/38.07	       | sk_A4(X2, X3, X10, X6) = sk_A5(X2, X3, X10, X6)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(X2, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(X2), X10), X9)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_7])).
37.82/38.07	tff('9', plain,
37.82/38.07	    ![X2 : $tType, X3 : $tType, X6 : app_encode_fun(X2, X3), 
37.82/38.07	      X9 : app_encode_fun(X2, $o), X10 : app_encode_fun(X2, $o)]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X2, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X2), X10), X9)
37.82/38.07	       | sk_A4(X2, X3, X10, X6) = sk_A5(X2, X3, X10, X6)
37.82/38.07	       | app_encode_app(X2, X3, X6, sk_A4(X2, X3, X10, X6))
37.82/38.07	          = app_encode_app(X2, X3, X6, sk_A5(X2, X3, X10, X6))
37.82/38.07	       | app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X3), 
37.82/38.07	             app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.07	               X10)), 
37.82/38.07	           app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	               app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.07	               'const/sets/IMAGE'(X2, X3), X6), X9))),
37.82/38.07	    inference('simplify', [status(thm)], ['8'])).
37.82/38.07	tff('10', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : app_encode_fun(X0, $o), 
37.82/38.07	      X3 : $tType, X4 : app_encode_fun(X0, X3)]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X0, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X0, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X0), X2), X1)
37.82/38.07	       | app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X3), 
37.82/38.07	             app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X0, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X0, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X0, X3), X4), 
37.82/38.07	               X2)), 
37.82/38.07	           app_encode_app(app_encode_fun(X0, $o), app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(X0, X3), 
37.82/38.07	               app_encode_fun(app_encode_fun(X0, $o), app_encode_fun(X3, $o)), 
37.82/38.07	               'const/sets/IMAGE'(X0, X3), X4), X1))
37.82/38.07	       | app_encode_app(X0, X3, X4, sk_A4(X0, X3, X2, X4))
37.82/38.07	          = app_encode_app(X0, X3, X4, sk_A5(X0, X3, X2, X4))),
37.82/38.07	    inference('condensation', [status(thm)], ['9'])).
37.82/38.07	tff('11', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (~ $true
37.82/38.07	       | app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	           sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	          = app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	              sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(sk_A, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	               sk_A1), sk_A31), X0, sk_A1, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['10', '5'])).
37.82/38.07	tff('12', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	             sk_A1), sk_A31), X0, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	           sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	          = app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	              sk_A5(sk_A0, sk_A, sk_A31, sk_A1))),
37.82/38.07	    inference('simplify', [status(thm)], ['11'])).
37.82/38.07	tff('13', plain,
37.82/38.07	    ![X22 : app_encode_fun(sk_A0, $o), X23 : app_encode_fun(sk_A, $o)]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(sk_A, $o), $o, sk_P, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(sk_A, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	               sk_A1), X22))
37.82/38.07	       | ~ zip_tseitin1(sk_A0, sk_A, sk_A51(X22), sk_A41(X22), X22, sk_A1)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), X22), sk_A2)
37.82/38.07	       | ~ zip_tseitin0(sk_A0, sk_A, X23, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_5])).
37.82/38.07	tff('14', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.07	      (~ $true
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	       | ~ zip_tseitin1(sk_A0, sk_A, sk_A51(sk_A31), sk_A41(sk_A31), sk_A31, 
37.82/38.07	             sk_A1)),
37.82/38.07	    inference('sup-', [status(thm)], ['2', '13'])).
37.82/38.07	tff('15', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.07	      (~ zip_tseitin1(sk_A0, sk_A, sk_A51(sk_A31), sk_A41(sk_A31), sk_A31, 
37.82/38.07	           sk_A1)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('simplify', [status(thm)], ['14'])).
37.82/38.07	tff('16', plain,
37.82/38.07	    ![X20 : sk_A0, X21 : sk_A0]:
37.82/38.07	      (zip_tseitin1(sk_A0, sk_A, X20, X21, sk_A31, sk_A1)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_5])).
37.82/38.07	tff('17', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.07	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)),
37.82/38.07	    inference('clc', [status(thm)], ['15', '16'])).
37.82/38.07	tff('18', plain,
37.82/38.07	    (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	       app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	         app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	         'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_5])).
37.82/38.07	tff('19', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.07	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('clc', [status(thm)], ['17', '18'])).
37.82/38.07	tff('20', plain,
37.82/38.07	    (~ $true
37.82/38.07	     | app_encode_app(sk_A0, sk_A, sk_A1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	        = app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	            sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['12', '19'])).
37.82/38.07	tff('21', plain,
37.82/38.07	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	     | app_encode_app(sk_A0, sk_A, sk_A1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	        = app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	            sk_A5(sk_A0, sk_A, sk_A31, sk_A1))),
37.82/38.07	    inference('simplify', [status(thm)], ['20'])).
37.82/38.07	tff('22', plain,
37.82/38.07	    (app_encode_app(sk_A0, sk_A, sk_A1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	      = app_encode_app(sk_A0, sk_A, sk_A1, sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('clc', [status(thm)], ['21', '18'])).
37.82/38.07	tff('23', plain,
37.82/38.07	    ![X2 : $tType, X3 : $tType, X5 : app_encode_fun(X3, $o), 
37.82/38.07	      X6 : app_encode_fun(X2, X3), X9 : app_encode_fun(X2, $o), 
37.82/38.07	      X10 : app_encode_fun(X2, $o)]:
37.82/38.07	      (app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	         app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	           app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	           'const/sets/SUBSET'(X3), X5), 
37.82/38.07	         app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	             app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.07	             'const/sets/IMAGE'(X2, X3), X6), X9))
37.82/38.07	       | X5
37.82/38.07	          != app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.07	               X10)
37.82/38.07	       | app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	           app_encode_app(X2, app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	             'const/sets/IN'(X2), sk_A5(X2, X3, X10, X6)), X10)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(X2, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(X2), X10), X9)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_7])).
37.82/38.07	tff('24', plain,
37.82/38.07	    ![X2 : $tType, X3 : $tType, X6 : app_encode_fun(X2, X3), 
37.82/38.07	      X9 : app_encode_fun(X2, $o), X10 : app_encode_fun(X2, $o)]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X2, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X2), X10), X9)
37.82/38.07	       | app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	           app_encode_app(X2, app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	             'const/sets/IN'(X2), sk_A5(X2, X3, X10, X6)), X10)
37.82/38.07	       | app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X3), 
37.82/38.07	             app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.07	               X10)), 
37.82/38.07	           app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	               app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.07	               'const/sets/IMAGE'(X2, X3), X6), X9))),
37.82/38.07	    inference('simplify', [status(thm)], ['23'])).
37.82/38.07	tff('25', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (~ $true
37.82/38.07	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(sk_A0, 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/IN'(sk_A0), sk_A5(sk_A0, sk_A, sk_A31, sk_A1)), 
37.82/38.07	           sk_A31)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(sk_A, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	               sk_A1), sk_A31), X0, sk_A1, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['24', '5'])).
37.82/38.07	tff('26', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	             sk_A1), sk_A31), X0, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(sk_A0, 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/IN'(sk_A0), sk_A5(sk_A0, sk_A, sk_A31, sk_A1)), 
37.82/38.07	           sk_A31)),
37.82/38.07	    inference('simplify', [status(thm)], ['25'])).
37.82/38.07	tff('27', plain,
37.82/38.07	    (~ $true
37.82/38.07	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	         app_encode_app(sk_A0, 
37.82/38.07	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	           'const/sets/IN'(sk_A0), sk_A5(sk_A0, sk_A, sk_A31, sk_A1)), 
37.82/38.07	         sk_A31)
37.82/38.07	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['26', '19'])).
37.82/38.07	tff('28', plain,
37.82/38.07	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	         app_encode_app(sk_A0, 
37.82/38.07	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	           'const/sets/IN'(sk_A0), sk_A5(sk_A0, sk_A, sk_A31, sk_A1)), 
37.82/38.07	         sk_A31)),
37.82/38.07	    inference('simplify', [status(thm)], ['27'])).
37.82/38.07	tff('29', plain,
37.82/38.07	    (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	       app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	         'const/sets/IN'(sk_A0), sk_A5(sk_A0, sk_A, sk_A31, sk_A1)), sk_A31)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('clc', [status(thm)], ['28', '18'])).
37.82/38.07	tff('30', plain,
37.82/38.07	    ![X2 : $tType, X3 : $tType, X5 : app_encode_fun(X3, $o), 
37.82/38.07	      X6 : app_encode_fun(X2, X3), X9 : app_encode_fun(X2, $o), 
37.82/38.07	      X10 : app_encode_fun(X2, $o)]:
37.82/38.07	      (app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	         app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	           app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	           'const/sets/SUBSET'(X3), X5), 
37.82/38.07	         app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	             app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.07	             'const/sets/IMAGE'(X2, X3), X6), X9))
37.82/38.07	       | X5
37.82/38.07	          != app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.07	               X10)
37.82/38.07	       | app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	           app_encode_app(X2, app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	             'const/sets/IN'(X2), sk_A4(X2, X3, X10, X6)), X10)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(X2, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(X2), X10), X9)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_7])).
37.82/38.07	tff('31', plain,
37.82/38.07	    ![X2 : $tType, X3 : $tType, X6 : app_encode_fun(X2, X3), 
37.82/38.07	      X9 : app_encode_fun(X2, $o), X10 : app_encode_fun(X2, $o)]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X2, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X2), X10), X9)
37.82/38.07	       | app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.07	           app_encode_app(X2, app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.07	             'const/sets/IN'(X2), sk_A4(X2, X3, X10, X6)), X10)
37.82/38.07	       | app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(X3), 
37.82/38.07	             app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.07	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.07	               X10)), 
37.82/38.07	           app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(X2, X3), 
37.82/38.07	               app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.07	               'const/sets/IMAGE'(X2, X3), X6), X9))),
37.82/38.07	    inference('simplify', [status(thm)], ['30'])).
37.82/38.07	tff('32', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (~ $true
37.82/38.07	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(sk_A0, 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/IN'(sk_A0), sk_A4(sk_A0, sk_A, sk_A31, sk_A1)), 
37.82/38.07	           sk_A31)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(sk_A, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	               sk_A1), sk_A31), X0, sk_A1, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['31', '5'])).
37.82/38.07	tff('33', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	             sk_A1), sk_A31), X0, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(sk_A0, 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/IN'(sk_A0), sk_A4(sk_A0, sk_A, sk_A31, sk_A1)), 
37.82/38.07	           sk_A31)),
37.82/38.07	    inference('simplify', [status(thm)], ['32'])).
37.82/38.07	tff('34', plain,
37.82/38.07	    (~ $true
37.82/38.07	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	         app_encode_app(sk_A0, 
37.82/38.07	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	           'const/sets/IN'(sk_A0), sk_A4(sk_A0, sk_A, sk_A31, sk_A1)), 
37.82/38.07	         sk_A31)
37.82/38.07	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['33', '19'])).
37.82/38.07	tff('35', plain,
37.82/38.07	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.07	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	         app_encode_app(sk_A0, 
37.82/38.07	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	           'const/sets/IN'(sk_A0), sk_A4(sk_A0, sk_A, sk_A31, sk_A1)), 
37.82/38.07	         sk_A31)),
37.82/38.07	    inference('simplify', [status(thm)], ['34'])).
37.82/38.07	tff('36', plain,
37.82/38.07	    (app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	       app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	         'const/sets/IN'(sk_A0), sk_A4(sk_A0, sk_A, sk_A31, sk_A1)), sk_A31)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('clc', [status(thm)], ['35', '18'])).
37.82/38.07	tff('37', plain,
37.82/38.07	    ![X11 : $tType, X13 : $tType, X14 : app_encode_fun(X13, X11), X17 : X13, 
37.82/38.07	      X18 : app_encode_fun(X13, $o), X19 : X13]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(X13, $o), $o, 
37.82/38.07	           app_encode_app(X13, app_encode_fun(app_encode_fun(X13, $o), $o), 
37.82/38.07	             'const/sets/IN'(X13), X17), X18)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(X13, $o), $o, 
37.82/38.07	             app_encode_app(X13, 
37.82/38.07	               app_encode_fun(app_encode_fun(X13, $o), $o), 
37.82/38.07	               'const/sets/IN'(X13), X19), X18)
37.82/38.07	       | app_encode_app(X13, X11, X14, X17)
37.82/38.07	          != app_encode_app(X13, X11, X14, X19)
37.82/38.07	       | X17 = X19
37.82/38.07	       | ~ zip_tseitin1(X13, X11, X19, X17, X18, X14)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_1])).
37.82/38.07	tff('38', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0), X2 : sk_A0]:
37.82/38.07	      (~ $true
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ zip_tseitin1(sk_A0, X0, X2, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), 
37.82/38.07	             sk_A31, X1)
37.82/38.07	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1) = X2
37.82/38.07	       | app_encode_app(sk_A0, X0, X1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	          != app_encode_app(sk_A0, X0, X1, X2)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(sk_A0, 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/IN'(sk_A0), X2), sk_A31)),
37.82/38.07	    inference('sup-', [status(thm)], ['36', '37'])).
37.82/38.07	tff('39', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0), X2 : sk_A0]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	           app_encode_app(sk_A0, 
37.82/38.07	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	             'const/sets/IN'(sk_A0), X2), sk_A31)
37.82/38.07	       | app_encode_app(sk_A0, X0, X1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	          != app_encode_app(sk_A0, X0, X1, X2)
37.82/38.07	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1) = X2
37.82/38.07	       | ~ zip_tseitin1(sk_A0, X0, X2, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), 
37.82/38.07	             sk_A31, X1)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('simplify', [status(thm)], ['38'])).
37.82/38.07	tff('40', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
37.82/38.07	      (~ $true
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | ~ zip_tseitin1(sk_A0, X0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), 
37.82/38.07	             sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31, X1)
37.82/38.07	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	          = sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | app_encode_app(sk_A0, X0, X1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	          != app_encode_app(sk_A0, X0, X1, sk_A5(sk_A0, sk_A, sk_A31, sk_A1))),
37.82/38.07	    inference('sup-', [status(thm)], ['29', '39'])).
37.82/38.07	tff('41', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
37.82/38.07	      (app_encode_app(sk_A0, X0, X1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	        != app_encode_app(sk_A0, X0, X1, sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	          = sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | ~ zip_tseitin1(sk_A0, X0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), 
37.82/38.07	             sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31, X1)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('simplify', [status(thm)], ['40'])).
37.82/38.07	tff('42', plain,
37.82/38.07	    ![X11 : $tType, X13 : $tType, X14 : app_encode_fun(X13, X11), X17 : X13, 
37.82/38.07	      X18 : app_encode_fun(X13, $o), X19 : X13]:
37.82/38.07	      (zip_tseitin1(X13, X11, X19, X17, X18, X14)
37.82/38.07	       | app_encode_app(app_encode_fun(X13, $o), $o, 
37.82/38.07	           app_encode_app(X13, app_encode_fun(app_encode_fun(X13, $o), $o), 
37.82/38.07	             'const/sets/IN'(X13), X19), X18)),
37.82/38.07	    inference('cnf', [status(esa)], [zf_stmt_1])).
37.82/38.07	tff('43', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, X3 : $tType, 
37.82/38.07	      X4 : app_encode_fun(X0, X3), X5 : X0, X6 : $tType, 
37.82/38.07	      X7 : app_encode_fun(X0, X6), X8 : X0]:
37.82/38.07	      (~ $true
37.82/38.07	       | zip_tseitin1(X0, X6, X2, X8, X1, X7)
37.82/38.07	       | ~ zip_tseitin1(X0, X3, X5, X2, X1, X4)
37.82/38.07	       | X2 = X5
37.82/38.07	       | app_encode_app(X0, X3, X4, X2) != app_encode_app(X0, X3, X4, X5)
37.82/38.07	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
37.82/38.07	             app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
37.82/38.07	               'const/sets/IN'(X0), X5), X1)),
37.82/38.07	    inference('sup-', [status(thm)], ['42', '37'])).
37.82/38.07	tff('44', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : X0, X3 : $tType, 
37.82/38.07	      X4 : app_encode_fun(X0, X3), X5 : X0, X6 : $tType, 
37.82/38.07	      X7 : app_encode_fun(X0, X6), X8 : X0]:
37.82/38.07	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 
37.82/38.07	           app_encode_app(X0, app_encode_fun(app_encode_fun(X0, $o), $o), 
37.82/38.07	             'const/sets/IN'(X0), X5), X1)
37.82/38.07	       | app_encode_app(X0, X3, X4, X2) != app_encode_app(X0, X3, X4, X5)
37.82/38.07	       | X2 = X5
37.82/38.07	       | ~ zip_tseitin1(X0, X3, X5, X2, X1, X4)
37.82/38.07	       | zip_tseitin1(X0, X6, X2, X8, X1, X7)),
37.82/38.07	    inference('simplify', [status(thm)], ['43'])).
37.82/38.07	tff('45', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0), X2 : sk_A0, X3 : sk_A0, 
37.82/38.07	      X4 : $tType, X5 : app_encode_fun(sk_A0, X4)]:
37.82/38.07	      (~ $true
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin1(sk_A0, X0, X3, X2, sk_A31, X1)
37.82/38.07	       | ~ zip_tseitin1(sk_A0, X4, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), X3, 
37.82/38.07	             sk_A31, X5)
37.82/38.07	       | X3 = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | app_encode_app(sk_A0, X4, X5, X3)
37.82/38.07	          != app_encode_app(sk_A0, X4, X5, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))),
37.82/38.07	    inference('sup-', [status(thm)], ['36', '44'])).
37.82/38.07	tff('46', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0), X2 : sk_A0, X3 : sk_A0, 
37.82/38.07	      X4 : $tType, X5 : app_encode_fun(sk_A0, X4)]:
37.82/38.07	      (app_encode_app(sk_A0, X4, X5, X3)
37.82/38.07	        != app_encode_app(sk_A0, X4, X5, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	       | X3 = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | ~ zip_tseitin1(sk_A0, X4, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), X3, 
37.82/38.07	             sk_A31, X5)
37.82/38.07	       | zip_tseitin1(sk_A0, X0, X3, X2, sk_A31, X1)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('simplify', [status(thm)], ['45'])).
37.82/38.07	tff('47', plain,
37.82/38.07	    ![X0 : sk_A0, X1 : $tType, X2 : app_encode_fun(sk_A0, X1), X3 : sk_A0]:
37.82/38.07	      (~ $true
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin1(sk_A0, X1, X0, X3, sk_A31, X2)
37.82/38.07	       | X0 = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | app_encode_app(sk_A0, sk_A, sk_A1, X0)
37.82/38.07	          != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	               sk_A4(sk_A0, sk_A, sk_A31, sk_A1))),
37.82/38.07	    inference('sup-', [status(thm)], ['16', '46'])).
37.82/38.07	tff('48', plain,
37.82/38.07	    ![X0 : sk_A0, X1 : $tType, X2 : app_encode_fun(sk_A0, X1), X3 : sk_A0]:
37.82/38.07	      (app_encode_app(sk_A0, sk_A, sk_A1, X0)
37.82/38.07	        != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	             sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	       | X0 = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | zip_tseitin1(sk_A0, X1, X0, X3, sk_A31, X2)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('simplify', [status(thm)], ['47'])).
37.82/38.07	tff('49', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0), X2 : sk_A0]:
37.82/38.07	      (app_encode_app(sk_A0, sk_A, sk_A1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	        != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	             sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin1(sk_A0, X0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), X2, 
37.82/38.07	           sk_A31, X1)
37.82/38.07	       | sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	          = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)),
37.82/38.07	    inference('sup-', [status(thm)], ['22', '48'])).
37.82/38.07	tff('50', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0), X2 : sk_A0]:
37.82/38.07	      (sk_A5(sk_A0, sk_A, sk_A31, sk_A1) = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | zip_tseitin1(sk_A0, X0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), X2, 
37.82/38.07	           sk_A31, X1)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('simplify', [status(thm)], ['49'])).
37.82/38.07	tff('51', plain,
37.82/38.07	    ![X0 : $tType, X1 : app_encode_fun(sk_A0, X0)]:
37.82/38.07	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	          = sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	       | app_encode_app(sk_A0, X0, X1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	          != app_encode_app(sk_A0, X0, X1, sk_A5(sk_A0, sk_A, sk_A31, sk_A1))),
37.82/38.07	    inference('clc', [status(thm)], ['41', '50'])).
37.82/38.07	tff('52', plain,
37.82/38.07	    (app_encode_app(sk_A0, sk_A, sk_A1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	      != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	           sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	     | sk_A4(sk_A0, sk_A, sk_A31, sk_A1) = sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('sup-', [status(thm)], ['22', '51'])).
37.82/38.07	tff('53', plain,
37.82/38.07	    (sk_A4(sk_A0, sk_A, sk_A31, sk_A1) = sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
37.82/38.07	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.07	    inference('simplify', [status(thm)], ['52'])).
37.82/38.07	tff('54', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (app_encode_app(sk_A0, sk_A, sk_A1, sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	        != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.07	             sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
37.82/38.07	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.07	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.07	       | zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.07	             app_encode_fun(sk_A, $o), 
37.82/38.07	             app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.07	               app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.07	                 app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.07	               sk_A1), sk_A31), X0, sk_A1, sk_P)),
37.82/38.07	    inference('clc', [status(thm)], ['7', '53'])).
37.82/38.07	tff('55', plain,
37.82/38.07	    ![X0 : app_encode_fun(sk_A0, $o)]:
37.82/38.07	      (zip_tseitin0(sk_A0, sk_A, 
37.82/38.07	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.07	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.08	             app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.08	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.08	             sk_A1), sk_A31), X0, sk_A1, sk_P)
37.82/38.08	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	               'const/sets/SUBSET'(sk_A0), sk_A31), X0)),
37.82/38.08	    inference('clc', [status(thm)], ['54', '53'])).
37.82/38.08	tff('56', plain,
37.82/38.08	    (~ $true
37.82/38.08	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.08	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	             'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)
37.82/38.08	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.08	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
37.82/38.08	    inference('sup-', [status(thm)], ['55', '19'])).
37.82/38.08	tff('57', plain,
37.82/38.08	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
37.82/38.08	     | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	           app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.08	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	             'const/sets/SUBSET'(sk_A0), sk_A31), sk_A2)),
37.82/38.08	    inference('simplify', [status(thm)], ['56'])).
37.82/38.08	tff('58', plain, zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P),
37.82/38.08	    inference('clc', [status(thm)], ['57', '18'])).
37.82/38.08	tff('59', plain,
37.82/38.08	    ![X11 : $tType, X12 : app_encode_fun(X11, $o), X13 : $tType, 
37.82/38.08	      X14 : app_encode_fun(X13, X11), X15 : app_encode_fun(X13, $o), 
37.82/38.08	      X16 : app_encode_fun(app_encode_fun(X11, $o), $o)]:
37.82/38.08	      (app_encode_app(app_encode_fun(X11, $o), $o, 
37.82/38.08	         app_encode_app(app_encode_fun(X11, $o), 
37.82/38.08	           app_encode_fun(app_encode_fun(X11, $o), $o), 
37.82/38.08	           'const/sets/SUBSET'(X11), X12), 
37.82/38.08	         app_encode_app(app_encode_fun(X13, $o), app_encode_fun(X11, $o), 
37.82/38.08	           app_encode_app(app_encode_fun(X13, X11), 
37.82/38.08	             app_encode_fun(app_encode_fun(X13, $o), app_encode_fun(X11, $o)), 
37.82/38.08	             'const/sets/IMAGE'(X13, X11), X14), X15))
37.82/38.08	       | ~ zip_tseitin0(X13, X11, X12, X15, X14, X16)),
37.82/38.08	    inference('cnf', [status(esa)], [zf_stmt_3])).
37.82/38.08	tff('60', plain,
37.82/38.08	    (~ $true
37.82/38.08	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
37.82/38.08	         app_encode_app(app_encode_fun(sk_A, $o), 
37.82/38.08	           app_encode_fun(app_encode_fun(sk_A, $o), $o), 
37.82/38.08	           'const/sets/SUBSET'(sk_A), sk_A32), 
37.82/38.08	         app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.08	           app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.08	             app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.08	               app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.08	             sk_A1), sk_A2))),
37.82/38.08	    inference('sup-', [status(thm)], ['58', '59'])).
37.82/38.08	tff('61', plain,
37.82/38.08	    app_encode_app(app_encode_fun(sk_A, $o), $o, 
37.82/38.08	      app_encode_app(app_encode_fun(sk_A, $o), 
37.82/38.08	        app_encode_fun(app_encode_fun(sk_A, $o), $o), 
37.82/38.08	        'const/sets/SUBSET'(sk_A), sk_A32), 
37.82/38.08	      app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.08	        app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.08	          app_encode_fun(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o)), 
37.82/38.08	          'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), sk_A2)),
37.82/38.08	    inference('simplify', [status(thm)], ['60'])).
37.82/38.08	tff('62', plain,
37.82/38.08	    ![X2 : $tType, X3 : $tType, X4 : app_encode_fun(X2, $o), 
37.82/38.08	      X5 : app_encode_fun(X3, $o), X6 : app_encode_fun(X2, X3)]:
37.82/38.08	      (X5
37.82/38.08	        = app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.08	            app_encode_app(app_encode_fun(X2, X3), 
37.82/38.08	              app_encode_fun(app_encode_fun(X2, $o), app_encode_fun(X3, $o)), 
37.82/38.08	              'const/sets/IMAGE'(X2, X3), X6), sk_A3(X2, X3, X4, X5, X6))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.08	             app_encode_app(app_encode_fun(X3, $o), 
37.82/38.08	               app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.08	               'const/sets/SUBSET'(X3), X5), 
37.82/38.08	             app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.08	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.08	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.08	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.08	               X4))),
37.82/38.08	    inference('cnf', [status(esa)], [zf_stmt_7])).
37.82/38.08	tff('63', plain,
37.82/38.08	    (~ $true
37.82/38.08	     | sk_A32
37.82/38.08	        = app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.08	            app_encode_fun(sk_A, $o), 
37.82/38.08	            app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.08	              app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.08	                app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.08	              sk_A1), sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
37.82/38.08	    inference('sup-', [status(thm)], ['61', '62'])).
37.82/38.08	tff('64', plain,
37.82/38.08	    sk_A32
37.82/38.08	     = app_encode_app(app_encode_fun(sk_A0, $o), app_encode_fun(sk_A, $o), 
37.82/38.08	         app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.08	           app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.08	             app_encode_fun(sk_A, $o)), 'const/sets/IMAGE'(sk_A0, sk_A), 
37.82/38.08	           sk_A1), sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)),
37.82/38.08	    inference('simplify', [status(thm)], ['63'])).
37.82/38.08	tff('65', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ app_encode_app(app_encode_fun(sk_A, $o), $o, sk_P, sk_A32)
37.82/38.08	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	               'const/sets/SUBSET'(sk_A0), 
37.82/38.08	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), sk_A2)
37.82/38.08	       | ~ zip_tseitin1(sk_A0, sk_A, 
37.82/38.08	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
37.82/38.08	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
37.82/38.08	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A1)),
37.82/38.08	    inference('sup-', [status(thm)], ['64', '13'])).
37.82/38.08	tff('66', plain,
37.82/38.08	    ![X11 : $tType, X12 : app_encode_fun(X11, $o), X13 : $tType, 
37.82/38.08	      X14 : app_encode_fun(X13, X11), X15 : app_encode_fun(X13, $o), 
37.82/38.08	      X16 : app_encode_fun(app_encode_fun(X11, $o), $o)]:
37.82/38.08	      (app_encode_app(app_encode_fun(X11, $o), $o, X16, X12)
37.82/38.08	       | ~ zip_tseitin0(X13, X11, X12, X15, X14, X16)),
37.82/38.08	    inference('cnf', [status(esa)], [zf_stmt_3])).
37.82/38.08	tff('67', plain,
37.82/38.08	    (~ $true | app_encode_app(app_encode_fun(sk_A, $o), $o, sk_P, sk_A32)),
37.82/38.08	    inference('sup-', [status(thm)], ['58', '66'])).
37.82/38.08	tff('68', plain, app_encode_app(app_encode_fun(sk_A, $o), $o, sk_P, sk_A32),
37.82/38.08	    inference('simplify', [status(thm)], ['67'])).
37.82/38.08	tff('69', plain,
37.82/38.08	    ![X2 : $tType, X3 : $tType, X4 : app_encode_fun(X2, $o), 
37.82/38.08	      X5 : app_encode_fun(X3, $o), X6 : app_encode_fun(X2, X3)]:
37.82/38.08	      (app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.08	         app_encode_app(app_encode_fun(X2, $o), 
37.82/38.08	           app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.08	           'const/sets/SUBSET'(X2), sk_A3(X2, X3, X4, X5, X6)), X4)
37.82/38.08	       | ~ app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.08	             app_encode_app(app_encode_fun(X3, $o), 
37.82/38.08	               app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.08	               'const/sets/SUBSET'(X3), X5), 
37.82/38.08	             app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.08	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.08	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.08	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.08	               X4))),
37.82/38.08	    inference('cnf', [status(esa)], [zf_stmt_7])).
37.82/38.08	tff('70', plain,
37.82/38.08	    (~ $true
37.82/38.08	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	         app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.08	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	           'const/sets/SUBSET'(sk_A0), 
37.82/38.08	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), sk_A2)),
37.82/38.08	    inference('sup-', [status(thm)], ['61', '69'])).
37.82/38.08	tff('71', plain,
37.82/38.08	    app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	      app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.08	        app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	        'const/sets/SUBSET'(sk_A0), sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
37.82/38.08	      sk_A2),
37.82/38.08	    inference('simplify', [status(thm)], ['70'])).
37.82/38.08	tff('72', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ $true
37.82/38.08	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.08	       | ~ $true
37.82/38.08	       | ~ zip_tseitin1(sk_A0, sk_A, 
37.82/38.08	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
37.82/38.08	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
37.82/38.08	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A1)),
37.82/38.08	    inference('demod', [status(thm)], ['65', '68', '71'])).
37.82/38.08	tff('73', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ zip_tseitin1(sk_A0, sk_A, 
37.82/38.08	           sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
37.82/38.08	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
37.82/38.08	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A1)
37.82/38.08	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)),
37.82/38.08	    inference('simplify', [status(thm)], ['72'])).
37.82/38.08	tff('74', plain,
37.82/38.08	    ![X11 : $tType, X13 : $tType, X14 : app_encode_fun(X13, X11), X17 : X13, 
37.82/38.08	      X18 : app_encode_fun(X13, $o), X19 : X13]:
37.82/38.08	      (zip_tseitin1(X13, X11, X19, X17, X18, X14)
37.82/38.08	       | app_encode_app(app_encode_fun(X13, $o), $o, 
37.82/38.08	           app_encode_app(X13, app_encode_fun(app_encode_fun(X13, $o), $o), 
37.82/38.08	             'const/sets/IN'(X13), X17), X18)),
37.82/38.08	    inference('cnf', [status(esa)], [zf_stmt_1])).
37.82/38.08	tff('75', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ $true
37.82/38.08	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	           app_encode_app(sk_A0, 
37.82/38.08	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	             'const/sets/IN'(sk_A0), 
37.82/38.08	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)),
37.82/38.08	    inference('sup-', [status(thm)], ['74', '73'])).
37.82/38.08	tff('76', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.08	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	           app_encode_app(sk_A0, 
37.82/38.08	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	             'const/sets/IN'(sk_A0), 
37.82/38.08	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
37.82/38.08	    inference('simplify', [status(thm)], ['75'])).
37.82/38.08	tff('77', plain,
37.82/38.08	    (~ $true
37.82/38.08	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	         app_encode_app(sk_A0, 
37.82/38.08	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	           'const/sets/IN'(sk_A0), 
37.82/38.08	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	         sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
37.82/38.08	    inference('sup-', [status(thm)], ['58', '76'])).
37.82/38.08	tff('78', plain,
37.82/38.08	    app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	      app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	        'const/sets/IN'(sk_A0), 
37.82/38.08	        sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	      sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)),
37.82/38.08	    inference('simplify', [status(thm)], ['77'])).
37.82/38.08	tff('79', plain,
37.82/38.08	    ![X11 : $tType, X13 : $tType, X14 : app_encode_fun(X13, X11), X17 : X13, 
37.82/38.08	      X18 : app_encode_fun(X13, $o), X19 : X13]:
37.82/38.08	      (zip_tseitin1(X13, X11, X19, X17, X18, X14)
37.82/38.08	       | X17 = X19
37.82/38.08	       | app_encode_app(X13, X11, X14, X17)
37.82/38.08	          = app_encode_app(X13, X11, X14, X19)),
37.82/38.08	    inference('cnf', [status(esa)], [zf_stmt_1])).
37.82/38.08	tff('80', plain,
37.82/38.08	    ![X0 : $tType, X1 : $tType, X2 : app_encode_fun(X1, X0), 
37.82/38.08	      X3 : app_encode_fun(X1, $o), X4 : X1, X5 : X1]:
37.82/38.08	      (zip_tseitin1(X1, X0, X5, X4, X3, X2)
37.82/38.08	       | app_encode_app(X1, X0, X2, X4) = app_encode_app(X1, X0, X2, X5)),
37.82/38.08	    inference('condensation', [status(thm)], ['79'])).
37.82/38.08	tff('81', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ $true
37.82/38.08	       | app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
37.82/38.08	          = app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	              sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
37.82/38.08	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)),
37.82/38.08	    inference('sup-', [status(thm)], ['80', '73'])).
37.82/38.08	tff('82', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.08	       | app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
37.82/38.08	          = app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	              sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
37.82/38.08	    inference('simplify', [status(thm)], ['81'])).
37.82/38.08	tff('83', plain,
37.82/38.08	    (~ $true
37.82/38.08	     | app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	         sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
37.82/38.08	        = app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	            sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
37.82/38.08	    inference('sup-', [status(thm)], ['58', '82'])).
37.82/38.08	tff('84', plain,
37.82/38.08	    app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	      sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
37.82/38.08	     = app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	         sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
37.82/38.08	    inference('simplify', [status(thm)], ['83'])).
37.82/38.08	tff('85', plain,
37.82/38.08	    ![X2 : $tType, X3 : $tType, X4 : app_encode_fun(X2, $o), 
37.82/38.08	      X5 : app_encode_fun(X3, $o), X6 : app_encode_fun(X2, X3), X7 : X2, 
37.82/38.08	      X8 : X2]:
37.82/38.08	      (app_encode_app(X2, X3, X6, X8) != app_encode_app(X2, X3, X6, X7)
37.82/38.08	       | X8 = X7
37.82/38.08	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.08	             app_encode_app(X2, app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.08	               'const/sets/IN'(X2), X7), sk_A3(X2, X3, X4, X5, X6))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(X2, $o), $o, 
37.82/38.08	             app_encode_app(X2, app_encode_fun(app_encode_fun(X2, $o), $o), 
37.82/38.08	               'const/sets/IN'(X2), X8), sk_A3(X2, X3, X4, X5, X6))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(X3, $o), $o, 
37.82/38.08	             app_encode_app(app_encode_fun(X3, $o), 
37.82/38.08	               app_encode_fun(app_encode_fun(X3, $o), $o), 
37.82/38.08	               'const/sets/SUBSET'(X3), X5), 
37.82/38.08	             app_encode_app(app_encode_fun(X2, $o), app_encode_fun(X3, $o), 
37.82/38.08	               app_encode_app(app_encode_fun(X2, X3), 
37.82/38.08	                 app_encode_fun(app_encode_fun(X2, $o), 
37.82/38.08	                   app_encode_fun(X3, $o)), 'const/sets/IMAGE'(X2, X3), X6), 
37.82/38.08	               X4))),
37.82/38.08	    inference('cnf', [status(esa)], [zf_stmt_7])).
37.82/38.08	tff('86', plain,
37.82/38.08	    ![X0 : sk_A0, X1 : app_encode_fun(sk_A0, $o), 
37.82/38.08	      X2 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (app_encode_app(sk_A0, sk_A, sk_A1, X0)
37.82/38.08	        != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
37.82/38.08	             app_encode_app(app_encode_fun(sk_A, $o), 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
37.82/38.08	               'const/sets/SUBSET'(sk_A), X2), 
37.82/38.08	             app_encode_app(app_encode_fun(sk_A0, $o), 
37.82/38.08	               app_encode_fun(sk_A, $o), 
37.82/38.08	               app_encode_app(app_encode_fun(sk_A0, sk_A), 
37.82/38.08	                 app_encode_fun(app_encode_fun(sk_A0, $o), 
37.82/38.08	                   app_encode_fun(sk_A, $o)), 
37.82/38.08	                 'const/sets/IMAGE'(sk_A0, sk_A), sk_A1), X1))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	             app_encode_app(sk_A0, 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	               'const/sets/IN'(sk_A0), X0), 
37.82/38.08	             sk_A3(sk_A0, sk_A, X1, X2, sk_A1))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	             app_encode_app(sk_A0, 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	               'const/sets/IN'(sk_A0), 
37.82/38.08	               sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	             sk_A3(sk_A0, sk_A, X1, X2, sk_A1))
37.82/38.08	       | X0 = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
37.82/38.08	    inference('sup-', [status(thm)], ['84', '85'])).
37.82/38.08	tff('87', plain,
37.82/38.08	    ![X0 : sk_A0]:
37.82/38.08	      (~ $true
37.82/38.08	       | X0 = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	             app_encode_app(sk_A0, 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	               'const/sets/IN'(sk_A0), 
37.82/38.08	               sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	             app_encode_app(sk_A0, 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	               'const/sets/IN'(sk_A0), X0), 
37.82/38.08	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	       | app_encode_app(sk_A0, sk_A, sk_A1, X0)
37.82/38.08	          != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	               sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
37.82/38.08	    inference('sup-', [status(thm)], ['61', '86'])).
37.82/38.08	tff('88', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ $true
37.82/38.08	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	           app_encode_app(sk_A0, 
37.82/38.08	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	             'const/sets/IN'(sk_A0), 
37.82/38.08	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)),
37.82/38.08	    inference('sup-', [status(thm)], ['42', '73'])).
37.82/38.08	tff('89', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
37.82/38.08	       | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	           app_encode_app(sk_A0, 
37.82/38.08	             app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	             'const/sets/IN'(sk_A0), 
37.82/38.08	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
37.82/38.08	    inference('simplify', [status(thm)], ['88'])).
37.82/38.08	tff('90', plain,
37.82/38.08	    (~ $true
37.82/38.08	     | app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	         app_encode_app(sk_A0, 
37.82/38.08	           app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	           'const/sets/IN'(sk_A0), 
37.82/38.08	           sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	         sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
37.82/38.08	    inference('sup-', [status(thm)], ['58', '89'])).
37.82/38.08	tff('91', plain,
37.82/38.08	    app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	      app_encode_app(sk_A0, app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	        'const/sets/IN'(sk_A0), 
37.82/38.08	        sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))), 
37.82/38.08	      sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)),
37.82/38.08	    inference('simplify', [status(thm)], ['90'])).
37.82/38.08	tff('92', plain,
37.82/38.08	    ![X0 : sk_A0]:
37.82/38.08	      (~ $true
37.82/38.08	       | X0 = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	       | ~ $true
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	             app_encode_app(sk_A0, 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	               'const/sets/IN'(sk_A0), X0), 
37.82/38.08	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	       | app_encode_app(sk_A0, sk_A, sk_A1, X0)
37.82/38.08	          != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	               sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
37.82/38.08	    inference('demod', [status(thm)], ['87', '91'])).
37.82/38.08	tff('93', plain,
37.82/38.08	    ![X0 : sk_A0]:
37.82/38.08	      (app_encode_app(sk_A0, sk_A, sk_A1, X0)
37.82/38.08	        != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
37.82/38.08	       | ~ app_encode_app(app_encode_fun(sk_A0, $o), $o, 
37.82/38.08	             app_encode_app(sk_A0, 
37.82/38.08	               app_encode_fun(app_encode_fun(sk_A0, $o), $o), 
37.82/38.08	               'const/sets/IN'(sk_A0), X0), 
37.82/38.08	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	       | X0 = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
37.82/38.08	    inference('simplify', [status(thm)], ['92'])).
37.82/38.08	tff('94', plain,
37.82/38.08	    (~ $true
37.82/38.08	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	     | app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	         sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
37.82/38.08	        != app_encode_app(sk_A0, sk_A, sk_A1, 
37.82/38.08	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
37.82/38.08	    inference('sup-', [status(thm)], ['78', '93'])).
37.82/38.08	tff('95', plain,
37.82/38.08	    sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
37.82/38.08	     = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)),
37.82/38.08	    inference('simplify', [status(thm)], ['94'])).
37.82/38.08	tff('96', plain,
37.82/38.08	    ![X11 : $tType, X13 : $tType, X14 : app_encode_fun(X13, X11), X17 : X13, 
37.82/38.08	      X18 : app_encode_fun(X13, $o), X19 : X13]:
37.82/38.08	      (zip_tseitin1(X13, X11, X19, X17, X18, X14)
37.82/38.08	       | X17 != X19
37.82/38.08	       | app_encode_app(X13, X11, X14, X17)
37.82/38.08	          != app_encode_app(X13, X11, X14, X19)),
37.82/38.08	    inference('cnf', [status(esa)], [zf_stmt_1])).
37.82/38.08	tff('97', plain,
37.82/38.08	    ![X11 : $tType, X13 : $tType, X14 : app_encode_fun(X13, X11), 
37.82/38.08	      X18 : app_encode_fun(X13, $o), X19 : X13]:
37.82/38.08	      (app_encode_app(X13, X11, X14, X19)
37.82/38.08	        != app_encode_app(X13, X11, X14, X19)
37.82/38.08	       | zip_tseitin1(X13, X11, X19, X19, X18, X14)),
37.82/38.08	    inference('simplify', [status(thm)], ['96'])).
37.82/38.08	tff('98', plain,
37.82/38.08	    ![X11 : $tType, X13 : $tType, X14 : app_encode_fun(X13, X11), 
37.82/38.08	      X18 : app_encode_fun(X13, $o), X19 : X13]:
37.82/38.08	      zip_tseitin1(X13, X11, X19, X19, X18, X14),
37.82/38.08	    inference('simplify', [status(thm)], ['97'])).
37.82/38.08	tff('99', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      (~ $true | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)),
37.82/38.08	    inference('demod', [status(thm)], ['73', '95', '98'])).
37.82/38.08	tff('100', plain,
37.82/38.08	    ![X0 : app_encode_fun(sk_A, $o)]:
37.82/38.08	      ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P),
37.82/38.08	    inference('simplify', [status(thm)], ['99'])).
37.82/38.08	tff('101', plain, ~ $true, inference('sup-', [status(thm)], ['58', '100'])).
37.82/38.08	tff('102', plain, $false, inference('simplify', [status(thm)], ['101'])).
37.82/38.08	
37.82/38.08	% SZS output end Refutation
37.82/38.08	EOF
