0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : app
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n176.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:38:09 CST 2018
0.00/0.27	% done 50 iterations in 0.057s
0.00/0.27	% SZS status Theorem for 'stdin'
0.00/0.27	% SZS output start Refutation
0.00/0.27	tff(zf_stmt_9, conjecture,
0.00/0.27	  (![A:$tType,B:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(B,$o),
0.00/0.27	     A2:app_encode_fun(A,B),A3:app_encode_fun(B,A)]:
0.00/0.27	     (((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A0) | 
0.00/0.27	        app_encode_app(app_encode_fun(B,$o),$o,'const/sets/FINITE'(B),A1)) & 
0.00/0.27	       (![A4:A]:
0.00/0.27	          (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                          app_encode_app(A,
0.00/0.27	                                         app_encode_fun(app_encode_fun(A,$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'(A),A4),
0.00/0.27	                          A0) =>
0.00/0.27	           (app_encode_app(app_encode_fun(B,$o),$o,
0.00/0.27	                           app_encode_app(B,
0.00/0.27	                                          app_encode_fun(app_encode_fun(B,$o),
0.00/0.27	                                                         $o),
0.00/0.27	                                          'const/sets/IN'(B),
0.00/0.27	                                          app_encode_app(A,B,A2,A4)),
0.00/0.27	                           A1) & 
0.00/0.27	            (app_encode_app(B,A,A3,app_encode_app(A,B,A2,A4)) = A4)))) & 
0.00/0.27	       (![A4:B]:
0.00/0.27	          (app_encode_app(app_encode_fun(B,$o),$o,
0.00/0.27	                          app_encode_app(B,
0.00/0.27	                                         app_encode_fun(app_encode_fun(B,$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'(B),A4),
0.00/0.27	                          A1) =>
0.00/0.27	           (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                           app_encode_app(A,
0.00/0.27	                                          app_encode_fun(app_encode_fun(A,$o),
0.00/0.27	                                                         $o),
0.00/0.27	                                          'const/sets/IN'(A),
0.00/0.27	                                          app_encode_app(B,A,A3,A4)),
0.00/0.27	                           A0) & 
0.00/0.27	            (app_encode_app(A,B,A2,app_encode_app(B,A,A3,A4)) = A4))))) =>
0.00/0.27	      (app_encode_app(app_encode_fun(A,$o),'type/nums/num',
0.00/0.27	                      'const/sets/CARD'(A),A0) =
0.00/0.27	       app_encode_app(app_encode_fun(B,$o),'type/nums/num',
0.00/0.27	                      'const/sets/CARD'(B),A1))))).
0.00/0.27	tff(zf_stmt_0, negated_conjecture,
0.00/0.27	  (~
0.00/0.27	    (![A:$tType,B:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(B,$o),
0.00/0.27	       A2:app_encode_fun(A,B),A3:app_encode_fun(B,A)]:
0.00/0.27	       (((app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A0) | 
0.00/0.27	          app_encode_app(app_encode_fun(B,$o),$o,'const/sets/FINITE'(B),A1)) & 
0.00/0.27	         (![A4:A]:
0.00/0.27	            (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                            app_encode_app(A,
0.00/0.27	                                           app_encode_fun(app_encode_fun(
0.00/0.27	                                                          A,$o),$o),
0.00/0.27	                                           'const/sets/IN'(A),A4),
0.00/0.27	                            A0) =>
0.00/0.27	             (app_encode_app(app_encode_fun(B,$o),$o,
0.00/0.27	                             app_encode_app(B,
0.00/0.27	                                            app_encode_fun(app_encode_fun(
0.00/0.27	                                                           B,$o),$o),
0.00/0.27	                                            'const/sets/IN'(B),
0.00/0.27	                                            app_encode_app(A,B,A2,A4)),
0.00/0.27	                             A1) & 
0.00/0.27	              (app_encode_app(B,A,A3,app_encode_app(A,B,A2,A4)) = A4)))) & 
0.00/0.27	         (![A4:B]:
0.00/0.27	            (app_encode_app(app_encode_fun(B,$o),$o,
0.00/0.27	                            app_encode_app(B,
0.00/0.27	                                           app_encode_fun(app_encode_fun(
0.00/0.27	                                                          B,$o),$o),
0.00/0.27	                                           'const/sets/IN'(B),A4),
0.00/0.27	                            A1) =>
0.00/0.27	             (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                             app_encode_app(A,
0.00/0.27	                                            app_encode_fun(app_encode_fun(
0.00/0.27	                                                           A,$o),$o),
0.00/0.27	                                            'const/sets/IN'(A),
0.00/0.27	                                            app_encode_app(B,A,A3,A4)),
0.00/0.27	                             A0) & 
0.00/0.27	              (app_encode_app(A,B,A2,app_encode_app(B,A,A3,A4)) = A4))))) =>
0.00/0.27	        (app_encode_app(app_encode_fun(A,$o),'type/nums/num',
0.00/0.27	                        'const/sets/CARD'(A),A0) =
0.00/0.27	         app_encode_app(app_encode_fun(B,$o),'type/nums/num',
0.00/0.27	                        'const/sets/CARD'(B),A1)))))).
0.00/0.27	tff('0', plain,
0.00/0.27	    (app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.00/0.27	       sk_A0)
0.00/0.27	     | app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	         'const/sets/FINITE'(sk_B), sk_A1)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff(zf_stmt_8, axiom,
0.00/0.27	  (![A:$tType,B:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(B,$o),
0.00/0.27	     A2:app_encode_fun(A,B),A3:app_encode_fun(B,A)]:
0.00/0.27	     (((![A4:B]:
0.00/0.27	          (app_encode_app(app_encode_fun(B,$o),$o,
0.00/0.27	                          app_encode_app(B,
0.00/0.27	                                         app_encode_fun(app_encode_fun(B,$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'(B),A4),
0.00/0.27	                          A1) =>
0.00/0.27	           ((app_encode_app(A,B,A2,app_encode_app(B,A,A3,A4)) = A4) & 
0.00/0.27	            app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                           app_encode_app(A,
0.00/0.27	                                          app_encode_fun(app_encode_fun(A,$o),
0.00/0.27	                                                         $o),
0.00/0.27	                                          'const/sets/IN'(A),
0.00/0.27	                                          app_encode_app(B,A,A3,A4)),
0.00/0.27	                           A0)))) & 
0.00/0.27	       (![A4:A]:
0.00/0.27	          (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                          app_encode_app(A,
0.00/0.27	                                         app_encode_fun(app_encode_fun(A,$o),
0.00/0.27	                                                        $o),
0.00/0.27	                                         'const/sets/IN'(A),A4),
0.00/0.27	                          A0) =>
0.00/0.27	           ((app_encode_app(B,A,A3,app_encode_app(A,B,A2,A4)) = A4) & 
0.00/0.27	            app_encode_app(app_encode_fun(B,$o),$o,
0.00/0.27	                           app_encode_app(B,
0.00/0.27	                                          app_encode_fun(app_encode_fun(B,$o),
0.00/0.27	                                                         $o),
0.00/0.27	                                          'const/sets/IN'(B),
0.00/0.27	                                          app_encode_app(A,B,A2,A4)),
0.00/0.27	                           A1))))) =>
0.00/0.27	      (![A4:'type/nums/num']:
0.00/0.27	         (app_encode_app('type/nums/num',$o,
0.00/0.27	                         app_encode_app(app_encode_fun(A,$o),
0.00/0.27	                                        app_encode_fun('type/nums/num',$o),
0.00/0.27	                                        'const/sets/HAS_SIZE'(A),A0),
0.00/0.27	                         A4) <=>
0.00/0.27	          app_encode_app('type/nums/num',$o,
0.00/0.27	                         app_encode_app(app_encode_fun(B,$o),
0.00/0.27	                                        app_encode_fun('type/nums/num',$o),
0.00/0.27	                                        'const/sets/HAS_SIZE'(B),A1),
0.00/0.27	                         A4)))))).
0.00/0.27	tff(zf_stmt_1, axiom,
0.00/0.27	  ((app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                   app_encode_app(A,app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.27	                                  'const/sets/IN'(A),A4),
0.00/0.27	                   A0) =>
0.00/0.27	    (app_encode_app(app_encode_fun(B,$o),$o,
0.00/0.27	                    app_encode_app(B,app_encode_fun(app_encode_fun(B,$o),$o),
0.00/0.27	                                   'const/sets/IN'(B),
0.00/0.27	                                   app_encode_app(A,B,A2,A4)),
0.00/0.27	                    A1) & 
0.00/0.27	     (app_encode_app(B,A,A3,app_encode_app(A,B,A2,A4)) = A4))) =>
0.00/0.27	   zip_tseitin1(B,A,A4,A3,A2,A1,A0))).
0.00/0.27	tff('1', plain,
0.00/0.27	    ![X4 : $tType, X5 : $tType, X7 : app_encode_fun(X4, X5), 
0.00/0.27	      X8 : app_encode_fun(X5, X4), X9 : app_encode_fun(X4, $o), 
0.00/0.27	      X10 : app_encode_fun(X5, $o), X11 : X5]:
0.00/0.27	      (zip_tseitin1(X4, X5, X11, X7, X8, X9, X10)
0.00/0.27	       | app_encode_app(app_encode_fun(X5, $o), $o, 
0.00/0.27	           app_encode_app(X5, app_encode_fun(app_encode_fun(X5, $o), $o), 
0.00/0.27	             'const/sets/IN'(X5), X11), X10)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.27	tff('2', plain,
0.00/0.27	    ![X20 : sk_B]:
0.00/0.27	      (app_encode_app(sk_A, sk_B, sk_A2, 
0.00/0.27	         app_encode_app(sk_B, sk_A, sk_A3, X20))
0.00/0.27	        = X20
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	             app_encode_app(sk_B, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_B, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_B), X20), sk_A1)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('3', plain,
0.00/0.27	    ![X0 : sk_B, X1 : $tType, X2 : app_encode_fun(X1, $o), 
0.00/0.27	      X3 : app_encode_fun(sk_B, X1), X4 : app_encode_fun(X1, sk_B)]:
0.00/0.27	      (~ $true
0.00/0.27	       | zip_tseitin1(X1, sk_B, X0, X4, X3, X2, sk_A1)
0.00/0.27	       | app_encode_app(sk_A, sk_B, sk_A2, 
0.00/0.27	           app_encode_app(sk_B, sk_A, sk_A3, X0))
0.00/0.27	          = X0),
0.00/0.27	    inference('sup-', [status(thm)], ['1', '2'])).
0.00/0.27	tff('4', plain,
0.00/0.27	    ![X0 : sk_B, X1 : $tType, X2 : app_encode_fun(X1, $o), 
0.00/0.27	      X3 : app_encode_fun(sk_B, X1), X4 : app_encode_fun(X1, sk_B)]:
0.00/0.27	      (app_encode_app(sk_A, sk_B, sk_A2, 
0.00/0.27	         app_encode_app(sk_B, sk_A, sk_A3, X0))
0.00/0.27	        = X0
0.00/0.27	       | zip_tseitin1(X1, sk_B, X0, X4, X3, X2, sk_A1)),
0.00/0.27	    inference('simplify', [status(thm)], ['3'])).
0.00/0.27	tff('5', plain,
0.00/0.27	    ![X20 : sk_B]:
0.00/0.27	      (app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	         app_encode_app(sk_A, app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	           'const/sets/IN'(sk_A), app_encode_app(sk_B, sk_A, sk_A3, X20)), 
0.00/0.27	         sk_A0)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	             app_encode_app(sk_B, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_B, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_B), X20), sk_A1)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('6', plain,
0.00/0.27	    ![X4 : $tType, X5 : $tType, X7 : app_encode_fun(X4, X5), 
0.00/0.27	      X8 : app_encode_fun(X5, X4), X9 : app_encode_fun(X4, $o), 
0.00/0.27	      X10 : app_encode_fun(X5, $o), X11 : X5]:
0.00/0.27	      (zip_tseitin1(X4, X5, X11, X7, X8, X9, X10)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X4, $o), $o, 
0.00/0.27	             app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.00/0.27	               'const/sets/IN'(X4), app_encode_app(X5, X4, X8, X11)), X9)
0.00/0.27	       | app_encode_app(X4, X5, X7, app_encode_app(X5, X4, X8, X11)) != X11),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_1])).
0.00/0.27	tff('7', plain,
0.00/0.27	    ![X0 : sk_B, X1 : app_encode_fun(sk_A, sk_B), 
0.00/0.27	      X2 : app_encode_fun(sk_B, $o)]:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	             app_encode_app(sk_B, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_B, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_B), X0), sk_A1)
0.00/0.27	       | app_encode_app(sk_A, sk_B, X1, 
0.00/0.27	           app_encode_app(sk_B, sk_A, sk_A3, X0))
0.00/0.27	          != X0
0.00/0.27	       | zip_tseitin1(sk_A, sk_B, X0, X1, sk_A3, sk_A0, X2)),
0.00/0.27	    inference('sup-', [status(thm)], ['5', '6'])).
0.00/0.27	tff('8', plain,
0.00/0.27	    ![X0 : sk_B, X1 : app_encode_fun(sk_A, sk_B), 
0.00/0.27	      X2 : app_encode_fun(sk_B, $o)]:
0.00/0.27	      (zip_tseitin1(sk_A, sk_B, X0, X1, sk_A3, sk_A0, X2)
0.00/0.27	       | app_encode_app(sk_A, sk_B, X1, 
0.00/0.27	           app_encode_app(sk_B, sk_A, sk_A3, X0))
0.00/0.27	          != X0
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	             app_encode_app(sk_B, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_B, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_B), X0), sk_A1)),
0.00/0.27	    inference('simplify', [status(thm)], ['7'])).
0.00/0.27	tff('9', plain,
0.00/0.27	    ![X0 : sk_B, X1 : app_encode_fun(sk_B, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o), X4 : app_encode_fun(sk_B, X2), 
0.00/0.27	      X5 : app_encode_fun(X2, sk_B)]:
0.00/0.27	      (X0 != X0
0.00/0.27	       | zip_tseitin1(X2, sk_B, X0, X5, X4, X3, sk_A1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	             app_encode_app(sk_B, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_B, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_B), X0), sk_A1)
0.00/0.27	       | zip_tseitin1(sk_A, sk_B, X0, sk_A2, sk_A3, sk_A0, X1)),
0.00/0.27	    inference('sup-', [status(thm)], ['4', '8'])).
0.00/0.27	tff('10', plain,
0.00/0.27	    ![X0 : sk_B, X1 : app_encode_fun(sk_B, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o), X4 : app_encode_fun(sk_B, X2), 
0.00/0.27	      X5 : app_encode_fun(X2, sk_B)]:
0.00/0.27	      (zip_tseitin1(sk_A, sk_B, X0, sk_A2, sk_A3, sk_A0, X1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	             app_encode_app(sk_B, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_B, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_B), X0), sk_A1)
0.00/0.27	       | zip_tseitin1(X2, sk_B, X0, X5, X4, X3, sk_A1)),
0.00/0.27	    inference('simplify', [status(thm)], ['9'])).
0.00/0.27	tff('11', plain,
0.00/0.27	    ![X0 : sk_B, X1 : app_encode_fun(sk_B, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o), X4 : app_encode_fun(sk_B, X2), 
0.00/0.27	      X5 : app_encode_fun(X2, sk_B)]:
0.00/0.27	      (zip_tseitin1(X2, sk_B, X0, X5, X4, X3, sk_A1)
0.00/0.27	       | zip_tseitin1(sk_A, sk_B, X0, sk_A2, sk_A3, sk_A0, X1)),
0.00/0.27	    inference('clc', [status(thm)], ['10', '1'])).
0.00/0.27	tff('12', plain,
0.00/0.27	    ![X0 : sk_B]:
0.00/0.27	      (~ $true | zip_tseitin1(sk_A, sk_B, X0, sk_A2, sk_A3, sk_A0, sk_A1)),
0.00/0.27	    inference('eq_fact', [status(thm)], ['11'])).
0.00/0.27	tff('13', plain,
0.00/0.27	    ![X0 : sk_B]: zip_tseitin1(sk_A, sk_B, X0, sk_A2, sk_A3, sk_A0, sk_A1),
0.00/0.27	    inference('simplify', [status(thm)], ['12'])).
0.00/0.27	tff(zf_stmt_2, type, zip_tseitin2 :
0.00/0.27	    !>[B:$tType,A:$tType]:
0.00/0.27	      (('type/nums/num' * app_encode_fun(B,$o) * app_encode_fun(A,$o)) > $o)).
0.00/0.27	tff(zf_stmt_3, axiom,
0.00/0.27	  (zip_tseitin2(B,A,A4,A1,A0) =>
0.00/0.27	   (app_encode_app('type/nums/num',$o,
0.00/0.27	                   app_encode_app(app_encode_fun(A,$o),
0.00/0.27	                                  app_encode_fun('type/nums/num',$o),
0.00/0.27	                                  'const/sets/HAS_SIZE'(A),A0),
0.00/0.27	                   A4) <=>
0.00/0.27	    app_encode_app('type/nums/num',$o,
0.00/0.27	                   app_encode_app(app_encode_fun(B,$o),
0.00/0.27	                                  app_encode_fun('type/nums/num',$o),
0.00/0.27	                                  'const/sets/HAS_SIZE'(B),A1),
0.00/0.27	                   A4)))).
0.00/0.27	tff(zf_stmt_4, type, zip_tseitin1 :
0.00/0.27	    !>[B:$tType,A:$tType]:
0.00/0.27	      ((A * 
0.00/0.27	        app_encode_fun(B,A) * 
0.00/0.27	        app_encode_fun(A,B) * 
0.00/0.27	        app_encode_fun(B,$o) * 
0.00/0.27	        app_encode_fun(A,$o)) > $o)).
0.00/0.27	tff(zf_stmt_5, type, zip_tseitin0 :
0.00/0.27	    !>[B:$tType,A:$tType]:
0.00/0.27	      ((B * 
0.00/0.27	        app_encode_fun(B,A) * 
0.00/0.27	        app_encode_fun(A,B) * 
0.00/0.27	        app_encode_fun(B,$o) * 
0.00/0.27	        app_encode_fun(A,$o)) > $o)).
0.00/0.27	tff(zf_stmt_6, axiom,
0.00/0.27	  ((app_encode_app(app_encode_fun(B,$o),$o,
0.00/0.27	                   app_encode_app(B,app_encode_fun(app_encode_fun(B,$o),$o),
0.00/0.27	                                  'const/sets/IN'(B),A4),
0.00/0.27	                   A1) =>
0.00/0.27	    (app_encode_app(app_encode_fun(A,$o),$o,
0.00/0.27	                    app_encode_app(A,app_encode_fun(app_encode_fun(A,$o),$o),
0.00/0.27	                                   'const/sets/IN'(A),
0.00/0.27	                                   app_encode_app(B,A,A3,A4)),
0.00/0.27	                    A0) & 
0.00/0.27	     (app_encode_app(A,B,A2,app_encode_app(B,A,A3,A4)) = A4))) =>
0.00/0.27	   zip_tseitin0(B,A,A4,A3,A2,A1,A0))).
0.00/0.27	tff(zf_stmt_7, axiom,
0.00/0.27	  (![A:$tType,B:$tType,A0:app_encode_fun(A,$o),A1:app_encode_fun(B,$o),
0.00/0.27	     A2:app_encode_fun(A,B),A3:app_encode_fun(B,A)]:
0.00/0.27	     (((![A4:A]: zip_tseitin1(B,A,A4,A3,A2,A1,A0)) & 
0.00/0.27	       (![A4:B]: zip_tseitin0(B,A,A4,A3,A2,A1,A0))) =>
0.00/0.27	      (![A4:'type/nums/num']: zip_tseitin2(B,A,A4,A1,A0))))).
0.00/0.27	tff('14', plain,
0.00/0.27	    ![X13 : $tType, X14 : $tType, X15 : 'type/nums/num', 
0.00/0.27	      X16 : app_encode_fun(X13, $o), X17 : app_encode_fun(X14, $o), 
0.00/0.27	      X18 : app_encode_fun(X13, X14), X19 : app_encode_fun(X14, X13)]:
0.00/0.27	      (zip_tseitin2(X13, X14, X15, X16, X17)
0.00/0.27	       | ~ zip_tseitin1(X13, X14, sk_A41(X13, X14, X18, X19, X16, X17), X18, 
0.00/0.27	             X19, X16, X17)
0.00/0.27	       | ~ zip_tseitin0(X13, X14, sk_A4(X13, X14, X18, X19, X16, X17), X18, 
0.00/0.27	             X19, X16, X17)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.27	tff('15', plain,
0.00/0.27	    ![X0 : 'type/nums/num']:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ zip_tseitin0(sk_A, sk_B, 
0.00/0.27	             sk_A4(sk_A, sk_B, sk_A2, sk_A3, sk_A0, sk_A1), sk_A2, sk_A3, 
0.00/0.27	             sk_A0, sk_A1)
0.00/0.27	       | zip_tseitin2(sk_A, sk_B, X0, sk_A0, sk_A1)),
0.00/0.27	    inference('sup-', [status(thm)], ['13', '14'])).
0.00/0.27	tff('16', plain,
0.00/0.27	    ![X4 : $tType, X5 : $tType, X6 : X4, X7 : app_encode_fun(X4, X5), 
0.00/0.27	      X8 : app_encode_fun(X5, X4), X9 : app_encode_fun(X4, $o), 
0.00/0.27	      X10 : app_encode_fun(X5, $o)]:
0.00/0.27	      (zip_tseitin0(X4, X5, X6, X7, X8, X9, X10)
0.00/0.27	       | app_encode_app(app_encode_fun(X4, $o), $o, 
0.00/0.27	           app_encode_app(X4, app_encode_fun(app_encode_fun(X4, $o), $o), 
0.00/0.27	             'const/sets/IN'(X4), X6), X9)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_6])).
0.00/0.27	tff('17', plain,
0.00/0.27	    ![X21 : sk_A]:
0.00/0.27	      (app_encode_app(sk_B, sk_A, sk_A3, 
0.00/0.27	         app_encode_app(sk_A, sk_B, sk_A2, X21))
0.00/0.27	        = X21
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X21), sk_A0)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('18', plain,
0.00/0.27	    ![X0 : sk_A, X1 : $tType, X2 : app_encode_fun(X1, $o), 
0.00/0.27	      X3 : app_encode_fun(X1, sk_A), X4 : app_encode_fun(sk_A, X1)]:
0.00/0.27	      (~ $true
0.00/0.27	       | zip_tseitin0(sk_A, X1, X0, X4, X3, sk_A0, X2)
0.00/0.27	       | app_encode_app(sk_B, sk_A, sk_A3, 
0.00/0.27	           app_encode_app(sk_A, sk_B, sk_A2, X0))
0.00/0.27	          = X0),
0.00/0.27	    inference('sup-', [status(thm)], ['16', '17'])).
0.00/0.27	tff('19', plain,
0.00/0.27	    ![X0 : sk_A, X1 : $tType, X2 : app_encode_fun(X1, $o), 
0.00/0.27	      X3 : app_encode_fun(X1, sk_A), X4 : app_encode_fun(sk_A, X1)]:
0.00/0.27	      (app_encode_app(sk_B, sk_A, sk_A3, 
0.00/0.27	         app_encode_app(sk_A, sk_B, sk_A2, X0))
0.00/0.27	        = X0
0.00/0.27	       | zip_tseitin0(sk_A, X1, X0, X4, X3, sk_A0, X2)),
0.00/0.27	    inference('simplify', [status(thm)], ['18'])).
0.00/0.27	tff('20', plain,
0.00/0.27	    ![X21 : sk_A]:
0.00/0.27	      (app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	         app_encode_app(sk_B, app_encode_fun(app_encode_fun(sk_B, $o), $o), 
0.00/0.27	           'const/sets/IN'(sk_B), app_encode_app(sk_A, sk_B, sk_A2, X21)), 
0.00/0.27	         sk_A1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X21), sk_A0)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('21', plain,
0.00/0.27	    ![X4 : $tType, X5 : $tType, X6 : X4, X7 : app_encode_fun(X4, X5), 
0.00/0.27	      X8 : app_encode_fun(X5, X4), X9 : app_encode_fun(X4, $o), 
0.00/0.27	      X10 : app_encode_fun(X5, $o)]:
0.00/0.27	      (zip_tseitin0(X4, X5, X6, X7, X8, X9, X10)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X5, $o), $o, 
0.00/0.27	             app_encode_app(X5, app_encode_fun(app_encode_fun(X5, $o), $o), 
0.00/0.27	               'const/sets/IN'(X5), app_encode_app(X4, X5, X7, X6)), X10)
0.00/0.27	       | app_encode_app(X5, X4, X8, app_encode_app(X4, X5, X7, X6)) != X6),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_6])).
0.00/0.27	tff('22', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_B, sk_A), 
0.00/0.27	      X2 : app_encode_fun(sk_A, $o)]:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), sk_A0)
0.00/0.27	       | app_encode_app(sk_B, sk_A, X1, 
0.00/0.27	           app_encode_app(sk_A, sk_B, sk_A2, X0))
0.00/0.27	          != X0
0.00/0.27	       | zip_tseitin0(sk_A, sk_B, X0, sk_A2, X1, X2, sk_A1)),
0.00/0.27	    inference('sup-', [status(thm)], ['20', '21'])).
0.00/0.27	tff('23', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_B, sk_A), 
0.00/0.27	      X2 : app_encode_fun(sk_A, $o)]:
0.00/0.27	      (zip_tseitin0(sk_A, sk_B, X0, sk_A2, X1, X2, sk_A1)
0.00/0.27	       | app_encode_app(sk_B, sk_A, X1, 
0.00/0.27	           app_encode_app(sk_A, sk_B, sk_A2, X0))
0.00/0.27	          != X0
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), sk_A0)),
0.00/0.27	    inference('simplify', [status(thm)], ['22'])).
0.00/0.27	tff('24', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_A, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o), X4 : app_encode_fun(X2, sk_A), 
0.00/0.27	      X5 : app_encode_fun(sk_A, X2)]:
0.00/0.27	      (X0 != X0
0.00/0.27	       | zip_tseitin0(sk_A, X2, X0, X5, X4, sk_A0, X3)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), sk_A0)
0.00/0.27	       | zip_tseitin0(sk_A, sk_B, X0, sk_A2, sk_A3, X1, sk_A1)),
0.00/0.27	    inference('sup-', [status(thm)], ['19', '23'])).
0.00/0.27	tff('25', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_A, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o), X4 : app_encode_fun(X2, sk_A), 
0.00/0.27	      X5 : app_encode_fun(sk_A, X2)]:
0.00/0.27	      (zip_tseitin0(sk_A, sk_B, X0, sk_A2, sk_A3, X1, sk_A1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	             app_encode_app(sk_A, 
0.00/0.27	               app_encode_fun(app_encode_fun(sk_A, $o), $o), 
0.00/0.27	               'const/sets/IN'(sk_A), X0), sk_A0)
0.00/0.27	       | zip_tseitin0(sk_A, X2, X0, X5, X4, sk_A0, X3)),
0.00/0.27	    inference('simplify', [status(thm)], ['24'])).
0.00/0.27	tff('26', plain,
0.00/0.27	    ![X0 : sk_A, X1 : app_encode_fun(sk_A, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o), X4 : app_encode_fun(X2, sk_A), 
0.00/0.27	      X5 : app_encode_fun(sk_A, X2)]:
0.00/0.27	      (zip_tseitin0(sk_A, X2, X0, X5, X4, sk_A0, X3)
0.00/0.27	       | zip_tseitin0(sk_A, sk_B, X0, sk_A2, sk_A3, X1, sk_A1)),
0.00/0.27	    inference('clc', [status(thm)], ['25', '16'])).
0.00/0.27	tff('27', plain,
0.00/0.27	    ![X0 : sk_A]:
0.00/0.27	      (~ $true | zip_tseitin0(sk_A, sk_B, X0, sk_A2, sk_A3, sk_A0, sk_A1)),
0.00/0.27	    inference('eq_fact', [status(thm)], ['26'])).
0.00/0.27	tff('28', plain,
0.00/0.27	    ![X0 : sk_A]: zip_tseitin0(sk_A, sk_B, X0, sk_A2, sk_A3, sk_A0, sk_A1),
0.00/0.27	    inference('simplify', [status(thm)], ['27'])).
0.00/0.27	tff('29', plain,
0.00/0.27	    ![X0 : 'type/nums/num']:
0.00/0.27	      (~ $true | ~ $true | zip_tseitin2(sk_A, sk_B, X0, sk_A0, sk_A1)),
0.00/0.27	    inference('demod', [status(thm)], ['15', '28'])).
0.00/0.27	tff('30', plain,
0.00/0.27	    ![X0 : 'type/nums/num']: zip_tseitin2(sk_A, sk_B, X0, sk_A0, sk_A1),
0.00/0.27	    inference('simplify', [status(thm)], ['29'])).
0.00/0.27	tff(zf_stmt_7, axiom,
0.00/0.27	  (![A:$tType,A0:app_encode_fun(A,$o),A1:'type/nums/num']:
0.00/0.27	     (app_encode_app('type/nums/num',$o,
0.00/0.27	                     app_encode_app(app_encode_fun(A,$o),
0.00/0.27	                                    app_encode_fun('type/nums/num',$o),
0.00/0.27	                                    'const/sets/HAS_SIZE'(A),A0),
0.00/0.27	                     A1) <=>
0.00/0.27	      (app_encode_app(app_encode_fun(A,$o),$o,'const/sets/FINITE'(A),A0) & 
0.00/0.27	       (app_encode_app(app_encode_fun(A,$o),'type/nums/num',
0.00/0.27	                       'const/sets/CARD'(A),A0) =
0.00/0.27	        A1))))).
0.00/0.27	tff('31', plain,
0.00/0.27	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X3 : 'type/nums/num']:
0.00/0.27	      (app_encode_app('type/nums/num', $o, 
0.00/0.27	         app_encode_app(app_encode_fun(X0, $o), 
0.00/0.27	           app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X0), 
0.00/0.27	           X1), X3)
0.00/0.27	       | app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	           'const/sets/CARD'(X0), X1)
0.00/0.27	          != X3
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(X0), X1)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.27	tff('32', plain,
0.00/0.27	    ![X0 : $tType, X1 : app_encode_fun(X0, $o)]:
0.00/0.27	      (~ app_encode_app(app_encode_fun(X0, $o), $o, 'const/sets/FINITE'(X0), 
0.00/0.27	           X1)
0.00/0.27	       | app_encode_app('type/nums/num', $o, 
0.00/0.27	           app_encode_app(app_encode_fun(X0, $o), 
0.00/0.27	             app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X0), 
0.00/0.27	             X1), 
0.00/0.27	           app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	             'const/sets/CARD'(X0), X1))),
0.00/0.27	    inference('simplify', [status(thm)], ['31'])).
0.00/0.27	tff('33', plain,
0.00/0.27	    ![X4 : $tType, X5 : $tType, X9 : app_encode_fun(X4, $o), 
0.00/0.27	      X10 : app_encode_fun(X5, $o), X12 : 'type/nums/num']:
0.00/0.27	      (~ app_encode_app('type/nums/num', $o, 
0.00/0.27	           app_encode_app(app_encode_fun(X5, $o), 
0.00/0.27	             app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X5), 
0.00/0.27	             X10), X12)
0.00/0.27	       | app_encode_app('type/nums/num', $o, 
0.00/0.27	           app_encode_app(app_encode_fun(X4, $o), 
0.00/0.27	             app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X4), 
0.00/0.27	             X9), X12)
0.00/0.27	       | ~ zip_tseitin2(X4, X5, X12, X9, X10)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.00/0.27	tff('34', plain,
0.00/0.27	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o)]:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(X0), X1)
0.00/0.27	       | ~ zip_tseitin2(X2, X0, 
0.00/0.27	             app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	               'const/sets/CARD'(X0), X1), X3, X1)
0.00/0.27	       | app_encode_app('type/nums/num', $o, 
0.00/0.27	           app_encode_app(app_encode_fun(X2, $o), 
0.00/0.27	             app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X2), 
0.00/0.27	             X3), 
0.00/0.27	           app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	             'const/sets/CARD'(X0), X1))),
0.00/0.27	    inference('sup-', [status(thm)], ['32', '33'])).
0.00/0.27	tff('35', plain,
0.00/0.27	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o)]:
0.00/0.27	      (app_encode_app('type/nums/num', $o, 
0.00/0.27	         app_encode_app(app_encode_fun(X2, $o), 
0.00/0.27	           app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X2), 
0.00/0.27	           X3), 
0.00/0.27	         app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	           'const/sets/CARD'(X0), X1))
0.00/0.27	       | ~ zip_tseitin2(X2, X0, 
0.00/0.27	             app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	               'const/sets/CARD'(X0), X1), X3, X1)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(X0), X1)),
0.00/0.27	    inference('simplify', [status(thm)], ['34'])).
0.00/0.27	tff('36', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_B), sk_A1)
0.00/0.27	     | app_encode_app('type/nums/num', $o, 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	           app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(sk_A), 
0.00/0.27	           sk_A0), 
0.00/0.27	         app_encode_app(app_encode_fun(sk_B, $o), 'type/nums/num', 
0.00/0.27	           'const/sets/CARD'(sk_B), sk_A1))),
0.00/0.27	    inference('sup-', [status(thm)], ['30', '35'])).
0.00/0.27	tff('37', plain,
0.00/0.27	    (app_encode_app('type/nums/num', $o, 
0.00/0.27	       app_encode_app(app_encode_fun(sk_A, $o), 
0.00/0.27	         app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(sk_A), 
0.00/0.27	         sk_A0), 
0.00/0.27	       app_encode_app(app_encode_fun(sk_B, $o), 'type/nums/num', 
0.00/0.27	         'const/sets/CARD'(sk_B), sk_A1))
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_B), sk_A1)),
0.00/0.27	    inference('simplify', [status(thm)], ['36'])).
0.00/0.27	tff('38', plain,
0.00/0.27	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : 'type/nums/num']:
0.00/0.27	      (app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	         'const/sets/CARD'(X0), X1)
0.00/0.27	        = X2
0.00/0.27	       | ~ app_encode_app('type/nums/num', $o, 
0.00/0.27	             app_encode_app(app_encode_fun(X0, $o), 
0.00/0.27	               app_encode_fun('type/nums/num', $o), 
0.00/0.27	               'const/sets/HAS_SIZE'(X0), X1), X2)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_7])).
0.00/0.27	tff('39', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_B), sk_A1)
0.00/0.27	     | app_encode_app(app_encode_fun(sk_A, $o), 'type/nums/num', 
0.00/0.27	         'const/sets/CARD'(sk_A), sk_A0)
0.00/0.27	        = app_encode_app(app_encode_fun(sk_B, $o), 'type/nums/num', 
0.00/0.27	            'const/sets/CARD'(sk_B), sk_A1)),
0.00/0.27	    inference('sup-', [status(thm)], ['37', '38'])).
0.00/0.27	tff('40', plain,
0.00/0.27	    (app_encode_app(app_encode_fun(sk_A, $o), 'type/nums/num', 
0.00/0.27	       'const/sets/CARD'(sk_A), sk_A0)
0.00/0.27	      = app_encode_app(app_encode_fun(sk_B, $o), 'type/nums/num', 
0.00/0.27	          'const/sets/CARD'(sk_B), sk_A1)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_B), sk_A1)),
0.00/0.27	    inference('simplify', [status(thm)], ['39'])).
0.00/0.27	tff('41', plain,
0.00/0.27	    app_encode_app(app_encode_fun(sk_A, $o), 'type/nums/num', 
0.00/0.27	      'const/sets/CARD'(sk_A), sk_A0)
0.00/0.27	     != app_encode_app(app_encode_fun(sk_B, $o), 'type/nums/num', 
0.00/0.27	          'const/sets/CARD'(sk_B), sk_A1),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.27	tff('42', plain,
0.00/0.27	    ~ app_encode_app(app_encode_fun(sk_B, $o), $o, 
0.00/0.27	        'const/sets/FINITE'(sk_B), sk_A1),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['40', '41'])).
0.00/0.27	tff('43', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	         'const/sets/FINITE'(sk_A), sk_A0)),
0.00/0.27	    inference('sup-', [status(thm)], ['0', '42'])).
0.00/0.27	tff('44', plain,
0.00/0.27	    app_encode_app(app_encode_fun(sk_A, $o), $o, 'const/sets/FINITE'(sk_A), 
0.00/0.27	      sk_A0),
0.00/0.27	    inference('simplify', [status(thm)], ['43'])).
0.00/0.27	tff('45', plain,
0.00/0.27	    ![X4 : $tType, X5 : $tType, X9 : app_encode_fun(X4, $o), 
0.00/0.27	      X10 : app_encode_fun(X5, $o), X12 : 'type/nums/num']:
0.00/0.27	      (~ app_encode_app('type/nums/num', $o, 
0.00/0.27	           app_encode_app(app_encode_fun(X4, $o), 
0.00/0.27	             app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X4), 
0.00/0.27	             X9), X12)
0.00/0.27	       | app_encode_app('type/nums/num', $o, 
0.00/0.27	           app_encode_app(app_encode_fun(X5, $o), 
0.00/0.27	             app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X5), 
0.00/0.27	             X10), X12)
0.00/0.27	       | ~ zip_tseitin2(X4, X5, X12, X9, X10)),
0.00/0.27	    inference('cnf', [status(esa)], [zf_stmt_3])).
0.00/0.27	tff('46', plain,
0.00/0.27	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o)]:
0.00/0.27	      (~ $true
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(X0), X1)
0.00/0.27	       | ~ zip_tseitin2(X0, X2, 
0.00/0.27	             app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	               'const/sets/CARD'(X0), X1), X1, X3)
0.00/0.27	       | app_encode_app('type/nums/num', $o, 
0.00/0.27	           app_encode_app(app_encode_fun(X2, $o), 
0.00/0.27	             app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X2), 
0.00/0.27	             X3), 
0.00/0.27	           app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	             'const/sets/CARD'(X0), X1))),
0.00/0.27	    inference('sup-', [status(thm)], ['32', '45'])).
0.00/0.27	tff('47', plain,
0.00/0.27	    ![X0 : $tType, X1 : app_encode_fun(X0, $o), X2 : $tType, 
0.00/0.27	      X3 : app_encode_fun(X2, $o)]:
0.00/0.27	      (app_encode_app('type/nums/num', $o, 
0.00/0.27	         app_encode_app(app_encode_fun(X2, $o), 
0.00/0.27	           app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(X2), 
0.00/0.27	           X3), 
0.00/0.27	         app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	           'const/sets/CARD'(X0), X1))
0.00/0.27	       | ~ zip_tseitin2(X0, X2, 
0.00/0.27	             app_encode_app(app_encode_fun(X0, $o), 'type/nums/num', 
0.00/0.27	               'const/sets/CARD'(X0), X1), X1, X3)
0.00/0.27	       | ~ app_encode_app(app_encode_fun(X0, $o), $o, 
0.00/0.27	             'const/sets/FINITE'(X0), X1)),
0.00/0.27	    inference('simplify', [status(thm)], ['46'])).
0.00/0.27	tff('48', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_A), sk_A0)
0.00/0.27	     | app_encode_app('type/nums/num', $o, 
0.00/0.27	         app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.27	           app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(sk_B), 
0.00/0.27	           sk_A1), 
0.00/0.27	         app_encode_app(app_encode_fun(sk_A, $o), 'type/nums/num', 
0.00/0.27	           'const/sets/CARD'(sk_A), sk_A0))),
0.00/0.27	    inference('sup-', [status(thm)], ['30', '47'])).
0.00/0.27	tff('49', plain,
0.00/0.27	    (app_encode_app('type/nums/num', $o, 
0.00/0.27	       app_encode_app(app_encode_fun(sk_B, $o), 
0.00/0.27	         app_encode_fun('type/nums/num', $o), 'const/sets/HAS_SIZE'(sk_B), 
0.00/0.27	         sk_A1), 
0.00/0.27	       app_encode_app(app_encode_fun(sk_A, $o), 'type/nums/num', 
0.00/0.27	         'const/sets/CARD'(sk_A), sk_A0))
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_A), sk_A0)),
0.00/0.27	    inference('simplify', [status(thm)], ['48'])).
0.00/0.27	tff('50', plain,
0.00/0.27	    (~ $true
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_A), sk_A0)
0.00/0.27	     | app_encode_app(app_encode_fun(sk_B, $o), 'type/nums/num', 
0.00/0.27	         'const/sets/CARD'(sk_B), sk_A1)
0.00/0.27	        = app_encode_app(app_encode_fun(sk_A, $o), 'type/nums/num', 
0.00/0.27	            'const/sets/CARD'(sk_A), sk_A0)),
0.00/0.27	    inference('sup-', [status(thm)], ['49', '38'])).
0.00/0.27	tff('51', plain,
0.00/0.27	    (app_encode_app(app_encode_fun(sk_B, $o), 'type/nums/num', 
0.00/0.27	       'const/sets/CARD'(sk_B), sk_A1)
0.00/0.27	      = app_encode_app(app_encode_fun(sk_A, $o), 'type/nums/num', 
0.00/0.27	          'const/sets/CARD'(sk_A), sk_A0)
0.00/0.27	     | ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	           'const/sets/FINITE'(sk_A), sk_A0)),
0.00/0.27	    inference('simplify', [status(thm)], ['50'])).
0.00/0.27	tff('52', plain,
0.00/0.27	    ~ app_encode_app(app_encode_fun(sk_A, $o), $o, 
0.00/0.27	        'const/sets/FINITE'(sk_A), sk_A0),
0.00/0.27	    inference('simplify_reflect-', [status(thm)], ['51', '41'])).
0.00/0.27	tff('53', plain, ~ $true, inference('sup-', [status(thm)], ['44', '52'])).
0.00/0.27	tff('54', plain, $false, inference('simplify', [status(thm)], ['53'])).
0.00/0.27	
0.00/0.27	% SZS output end Refutation
0.00/0.27	EOF
