0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n113.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:31:09 CST 2018
250.08/250.38	% done 8834 iterations in 250.177s
250.08/250.38	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
250.08/250.38	% SZS output start Refutation
250.08/250.39	tff('thm/sets/SUBSET_IMAGE_INJ_', axiom,
250.08/250.39	  (![B:$tType,A:$tType,A0:(A > B),A1:(B > $o),A2:(A > $o)]:
250.08/250.39	     ('const/sets/SUBSET'(B,A1,'const/sets/IMAGE'(A,B,A0,A2)) <=>
250.08/250.39	      (?[A3:(A > $o)]:
250.08/250.39	         ((A1 = 'const/sets/IMAGE'(A,B,A0,A3)) & 
250.08/250.39	          (![A4:A,A5:A]:
250.08/250.39	             (('const/sets/IN'(A,A5,A3) & 'const/sets/IN'(A,A4,A3)) =>
250.08/250.39	              ((A0(A4) = A0(A5)) <=> (A4 = A5)))) & 
250.08/250.39	          'const/sets/SUBSET'(A,A3,A2)))))).
250.08/250.39	tff('0', plain,
250.08/250.39	    ![X2 : $tType, X3 : $tType, X4 : X2 > X3, X5 : X2 > $o, X6 : X3 > $o]:
250.08/250.39	      (X6 = 'const/sets/IMAGE'(X2, X3, X4, sk_A3(X2, X3, X5, X6, X4))
250.08/250.39	       | ~ 'const/sets/SUBSET'(X3, X6, 'const/sets/IMAGE'(X2, X3, X4, X5))),
250.08/250.39	    inference('cnf', [status(esa)], [thm/sets/SUBSET_IMAGE_INJ_])).
250.08/250.39	tff('thm/sets/EXISTS_SUBSET_IMAGE_INJ_', conjecture,
250.08/250.39	  (![A:$tType,A0:$tType,P:(A > $o > $o),A1:(A0 > A),A2:(A0 > $o)]:
250.08/250.39	     ((?[A3:(A > $o)]:
250.08/250.39	         ('const/sets/SUBSET'(A,A3,'const/sets/IMAGE'(A0,A,A1,A2)) & P(A3))) <=>
250.08/250.39	      (?[A3:(A0 > $o)]:
250.08/250.39	         ('const/sets/SUBSET'(A0,A3,A2) & 
250.08/250.39	          (![A4:A0,A5:A0]:
250.08/250.39	             (('const/sets/IN'(A0,A4,A3) & 'const/sets/IN'(A0,A5,A3)) =>
250.08/250.39	              ((A1(A4) = A1(A5)) <=> (A4 = A5)))) & 
250.08/250.39	          P('const/sets/IMAGE'(A0,A,A1,A3))))))).
250.08/250.39	tff(zf_stmt_0, type, zip_tseitin1 :
250.08/250.39	    !>[A0:$tType,A:$tType]: ((A0 * A0 * A0 > $o * A0 > A) > $o)).
250.08/250.39	tff(zf_stmt_1, axiom,
250.08/250.39	  (zip_tseitin1(A0,A,A5,A4,A3,A1) <=>
250.08/250.39	   (('const/sets/IN'(A0,A5,A3) & 'const/sets/IN'(A0,A4,A3)) =>
250.08/250.39	    ((A1(A4) = A1(A5)) <=> (A4 = A5))))).
250.08/250.39	tff(zf_stmt_2, type, zip_tseitin0 :
250.08/250.39	    !>[A0:$tType,A:$tType]: ((A > $o * A0 > $o * A0 > A * A > $o > $o) > $o)).
250.08/250.39	tff(zf_stmt_3, axiom,
250.08/250.39	  (zip_tseitin0(A0,A,A3,A2,A1,P) <=>
250.08/250.39	   (P(A3) & 'const/sets/SUBSET'(A,A3,'const/sets/IMAGE'(A0,A,A1,A2))))).
250.08/250.39	tff(zf_stmt_4, conjecture,
250.08/250.39	  (![A:$tType,A0:$tType,P:(A > $o > $o),A1:(A0 > A),A2:(A0 > $o)]:
250.08/250.39	     ((?[A3:(A > $o)]: zip_tseitin0(A0,A,A3,A2,A1,P)) <=>
250.08/250.39	      (?[A3:(A0 > $o)]:
250.08/250.39	         (P('const/sets/IMAGE'(A0,A,A1,A3)) & 
250.08/250.39	          (![A4:A0,A5:A0]: zip_tseitin1(A0,A,A5,A4,A3,A1)) & 
250.08/250.39	          'const/sets/SUBSET'(A0,A3,A2)))))).
250.08/250.39	tff(zf_stmt_5, negated_conjecture,
250.08/250.39	  (~
250.08/250.39	    (![A:$tType,A0:$tType,P:(A > $o > $o),A1:(A0 > A),A2:(A0 > $o)]:
250.08/250.39	       ((?[A3:(A > $o)]: zip_tseitin0(A0,A,A3,A2,A1,P)) <=>
250.08/250.39	        (?[A3:(A0 > $o)]:
250.08/250.39	           (P('const/sets/IMAGE'(A0,A,A1,A3)) & 
250.08/250.39	            (![A4:A0,A5:A0]: zip_tseitin1(A0,A,A5,A4,A3,A1)) & 
250.08/250.39	            'const/sets/SUBSET'(A0,A3,A2))))))).
250.08/250.39	tff('1', plain,
250.08/250.39	    (sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_5])).
250.08/250.39	tff('2', plain,
250.08/250.39	    ![X11 : $tType, X14 : $tType, X16 : X14 > X11, X17 : X14, 
250.08/250.39	      X18 : X14 > $o, X19 : X14]:
250.08/250.39	      (zip_tseitin1(X14, X11, X17, X19, X18, X16)
250.08/250.39	       | 'const/sets/IN'(X14, X19, X18)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
250.08/250.39	tff('3', plain,
250.08/250.39	    ![X22 : sk_A0 > $o, X23 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, X22, sk_A2)
250.08/250.39	       | ~ zip_tseitin1(sk_A0, sk_A, sk_A51(X22), sk_A41(X22), X22, sk_A1)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X22))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X23, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_5])).
250.08/250.39	tff('4', plain,
250.08/250.39	    ![X0 : sk_A0 > $o, X1 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(X0), X0)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X1, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X0))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, X0, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['2', '3'])).
250.08/250.39	tff('5', plain,
250.08/250.39	    ![X0 : sk_A0 > $o, X1 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, X0, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X0))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X1, sk_A2, sk_A1, sk_P)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(X0), X0)),
250.08/250.39	    inference('simplify', [status(thm)], ['4'])).
250.08/250.39	tff('6', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o, X2 : sk_A > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X2, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['0', '5'])).
250.08/250.39	tff('7', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['1', '6'])).
250.08/250.39	tff('8', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['7'])).
250.08/250.39	tff('9', plain,
250.08/250.39	    ![X11 : $tType, X14 : $tType, X16 : X14 > X11, X17 : X14, 
250.08/250.39	      X18 : X14 > $o, X19 : X14]:
250.08/250.39	      (zip_tseitin1(X14, X11, X17, X19, X18, X16)
250.08/250.39	       | 'const/sets/IN'(X14, X17, X18)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
250.08/250.39	tff('10', plain,
250.08/250.39	    ![X0 : sk_A0 > $o, X1 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(X0), X0)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X1, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X0))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, X0, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['9', '3'])).
250.08/250.39	tff('11', plain,
250.08/250.39	    ![X0 : sk_A0 > $o, X1 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, X0, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X0))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X1, sk_A2, sk_A1, sk_P)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(X0), X0)),
250.08/250.39	    inference('simplify', [status(thm)], ['10'])).
250.08/250.39	tff('12', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o, X2 : sk_A > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X2, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['0', '11'])).
250.08/250.39	tff('13', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['1', '12'])).
250.08/250.39	tff('14', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['13'])).
250.08/250.39	tff('15', plain,
250.08/250.39	    ![X11 : $tType, X12 : X11 > $o > $o, X13 : X11 > $o, X14 : $tType, 
250.08/250.39	      X15 : X14 > $o, X16 : X14 > X11]:
250.08/250.39	      ('const/sets/SUBSET'(X11, X13, 'const/sets/IMAGE'(X14, X11, X16, X15))
250.08/250.39	       | ~ zip_tseitin0(X14, X11, X13, X15, X16, X12)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_3])).
250.08/250.39	tff('16', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['1', '15'])).
250.08/250.39	tff('17', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	       'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['16'])).
250.08/250.39	tff('18', plain,
250.08/250.39	    ![X2 : $tType, X3 : $tType, X4 : X2 > X3, X5 : X2 > $o, X6 : X3 > $o]:
250.08/250.39	      ('const/sets/SUBSET'(X2, sk_A3(X2, X3, X5, X6, X4), X5)
250.08/250.39	       | ~ 'const/sets/SUBSET'(X3, X6, 'const/sets/IMAGE'(X2, X3, X4, X5))),
250.08/250.39	    inference('cnf', [status(esa)], [thm/sets/SUBSET_IMAGE_INJ_])).
250.08/250.39	tff('19', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), 
250.08/250.39	         sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['17', '18'])).
250.08/250.39	tff('20', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), 
250.08/250.39	       sk_A2)
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['19'])).
250.08/250.39	tff('21', plain,
250.08/250.39	    ![X11 : $tType, X14 : $tType, X16 : X14 > X11, X17 : X14, 
250.08/250.39	      X18 : X14 > $o, X19 : X14]:
250.08/250.39	      (zip_tseitin1(X14, X11, X17, X19, X18, X16)
250.08/250.39	       | X19 = X17
250.08/250.39	       | X16(X19) = X16(X17)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
250.08/250.39	tff('22', plain,
250.08/250.39	    ![X0 : $tType, X1 : $tType, X2 : X0 > X1, X3 : X0 > $o, X4 : X0, X5 : X0]:
250.08/250.39	      (zip_tseitin1(X0, X1, X5, X4, X3, X2) | X2(X4) = X2(X5)),
250.08/250.39	    inference('condensation', [status(thm)], ['21'])).
250.08/250.39	tff('23', plain,
250.08/250.39	    ![X0 : sk_A0 > $o, X1 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_A1(sk_A41(X0)) = sk_A1(sk_A51(X0))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X1, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X0))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, X0, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['22', '3'])).
250.08/250.39	tff('24', plain,
250.08/250.39	    ![X0 : sk_A0 > $o, X1 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, X0, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X0))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X1, sk_A2, sk_A1, sk_P)
250.08/250.39	       | sk_A1(sk_A41(X0)) = sk_A1(sk_A51(X0))),
250.08/250.39	    inference('simplify', [status(thm)], ['23'])).
250.08/250.39	tff('25', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o, X2 : sk_A > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X2, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['0', '24'])).
250.08/250.39	tff('26', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['1', '25'])).
250.08/250.39	tff('27', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['26'])).
250.08/250.39	tff('28', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['20', '27'])).
250.08/250.39	tff('29', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_5])).
250.08/250.39	tff('30', plain,
250.08/250.39	    ![X11 : $tType, X12 : X11 > $o > $o, X13 : X11 > $o, X14 : $tType, 
250.08/250.39	      X15 : X14 > $o, X16 : X14 > X11]:
250.08/250.39	      (X12(X13) | ~ zip_tseitin0(X14, X11, X13, X15, X16, X12)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_3])).
250.08/250.39	tff('31', plain,
250.08/250.39	    (~ $true | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2) | sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['29', '30'])).
250.08/250.39	tff('32', plain, (sk_P(sk_A32) | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['31'])).
250.08/250.39	tff('33', plain,
250.08/250.39	    ![X2 : $tType, X3 : $tType, X4 : X2 > X3, X6 : X3 > $o, X9 : X2 > $o, 
250.08/250.39	      X10 : X2 > $o]:
250.08/250.39	      ('const/sets/SUBSET'(X3, X6, 'const/sets/IMAGE'(X2, X3, X4, X9))
250.08/250.39	       | ~ 'const/sets/SUBSET'(X2, X10, X9)
250.08/250.39	       | X4(sk_A4(X2, X3, X10, X4)) != X4(sk_A5(X2, X3, X10, X4))
250.08/250.39	       | sk_A4(X2, X3, X10, X4) != sk_A5(X2, X3, X10, X4)
250.08/250.39	       | X6 != 'const/sets/IMAGE'(X2, X3, X4, X10)),
250.08/250.39	    inference('cnf', [status(esa)], [thm/sets/SUBSET_IMAGE_INJ_])).
250.08/250.39	tff('34', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X2) != sk_A5(sk_A0, X0, sk_A31, X2)
250.08/250.39	       | X2(sk_A4(sk_A0, X0, sk_A31, X2)) != X2(sk_A5(sk_A0, X0, sk_A31, X2))
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['32', '33'])).
250.08/250.39	tff('35', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X1, 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))
250.08/250.39	       | X2(sk_A4(sk_A0, X0, sk_A31, X2)) != X2(sk_A5(sk_A0, X0, sk_A31, X2))
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X2) != sk_A5(sk_A0, X0, sk_A31, X2)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['34'])).
250.08/250.39	tff('36', plain,
250.08/250.39	    ![X2 : $tType, X3 : $tType, X4 : X2 > X3, X6 : X3 > $o, X9 : X2 > $o, 
250.08/250.39	      X10 : X2 > $o]:
250.08/250.39	      ('const/sets/SUBSET'(X3, X6, 'const/sets/IMAGE'(X2, X3, X4, X9))
250.08/250.39	       | ~ 'const/sets/SUBSET'(X2, X10, X9)
250.08/250.39	       | X4(sk_A4(X2, X3, X10, X4)) = X4(sk_A5(X2, X3, X10, X4))
250.08/250.39	       | sk_A4(X2, X3, X10, X4) = sk_A5(X2, X3, X10, X4)
250.08/250.39	       | X6 != 'const/sets/IMAGE'(X2, X3, X4, X10)),
250.08/250.39	    inference('cnf', [status(esa)], [thm/sets/SUBSET_IMAGE_INJ_])).
250.08/250.39	tff('37', plain,
250.08/250.39	    ![X0 : $tType, X1 : $tType, X2 : X1 > $o, X3 : X1 > X0, X4 : X0 > $o, 
250.08/250.39	      X5 : X1 > $o]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X4, 'const/sets/IMAGE'(X1, X0, X3, X2))
250.08/250.39	       | ~ 'const/sets/SUBSET'(X1, X5, X2)
250.08/250.39	       | X3(sk_A4(X1, X0, X5, X3)) = X3(sk_A5(X1, X0, X5, X3))
250.08/250.39	       | X4 != 'const/sets/IMAGE'(X1, X0, X3, X5)),
250.08/250.39	    inference('condensation', [status(thm)], ['36'])).
250.08/250.39	tff('38', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | X2(sk_A4(sk_A0, X0, sk_A31, X2)) = X2(sk_A5(sk_A0, X0, sk_A31, X2))
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['32', '37'])).
250.08/250.39	tff('39', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X1, 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))
250.08/250.39	       | X2(sk_A4(sk_A0, X0, sk_A31, X2)) = X2(sk_A5(sk_A0, X0, sk_A31, X2))
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['38'])).
250.08/250.39	tff('40', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (sk_P(sk_A32)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X2) != sk_A5(sk_A0, X0, sk_A31, X2)
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('clc', [status(thm)], ['35', '39'])).
250.08/250.39	tff('41', plain,
250.08/250.39	    ![X11 : $tType, X12 : X11 > $o > $o, X13 : X11 > $o, X14 : $tType, 
250.08/250.39	      X15 : X14 > $o, X16 : X14 > X11]:
250.08/250.39	      (zip_tseitin0(X14, X11, X13, X15, X16, X12)
250.08/250.39	       | ~ 'const/sets/SUBSET'(X11, X13, 
250.08/250.39	             'const/sets/IMAGE'(X14, X11, X16, X15))
250.08/250.39	       | ~ X12(X13)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_3])).
250.08/250.39	tff('42', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X1) != sk_A5(sk_A0, X0, sk_A31, X1)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)),
250.08/250.39	    inference('sup-', [status(thm)], ['40', '41'])).
250.08/250.39	tff('43', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X1) != sk_A5(sk_A0, X0, sk_A31, X1)),
250.08/250.39	    inference('simplify', [status(thm)], ['42'])).
250.08/250.39	tff('44', plain,
250.08/250.39	    ![X20 : sk_A0, X21 : sk_A0]:
250.08/250.39	      (zip_tseitin1(sk_A0, sk_A, X20, X21, sk_A31, sk_A1)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_5])).
250.08/250.39	tff('45', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['44', '30'])).
250.08/250.39	tff('46', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (sk_P(sk_A32) | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['45'])).
250.08/250.39	tff('47', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['46', '3'])).
250.08/250.39	tff('48', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['47'])).
250.08/250.39	tff('49', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (sk_P(sk_A32)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('clc', [status(thm)], ['48', '32'])).
250.08/250.39	tff('50', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['1', '30'])).
250.08/250.39	tff('51', plain,
250.08/250.39	    (sk_P(sk_A32) | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['50'])).
250.08/250.39	tff('52', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P) | sk_P(sk_A32)),
250.08/250.39	    inference('clc', [status(thm)], ['49', '51'])).
250.08/250.39	tff('53', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	          != sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['43', '52'])).
250.08/250.39	tff('54', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	          != sk_A5(sk_A0, sk_A, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['53'])).
250.08/250.39	tff('55', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | X1(sk_A4(sk_A0, X0, sk_A31, X1)) = X1(sk_A5(sk_A0, X0, sk_A31, X1))
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)),
250.08/250.39	    inference('sup-', [status(thm)], ['39', '41'])).
250.08/250.39	tff('56', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | X1(sk_A4(sk_A0, X0, sk_A31, X1)) = X1(sk_A5(sk_A0, X0, sk_A31, X1))
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['55'])).
250.08/250.39	tff('57', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	          = sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['56', '52'])).
250.08/250.39	tff('58', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	          = sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['57'])).
250.08/250.39	tff('59', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	        != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	     | sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	        = sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['51', '58'])).
250.08/250.39	tff('60', plain,
250.08/250.39	    (sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	      = sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	     | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['59'])).
250.08/250.39	tff('61', plain,
250.08/250.39	    ![X2 : $tType, X3 : $tType, X4 : X2 > X3, X6 : X3 > $o, X9 : X2 > $o, 
250.08/250.39	      X10 : X2 > $o]:
250.08/250.39	      ('const/sets/SUBSET'(X3, X6, 'const/sets/IMAGE'(X2, X3, X4, X9))
250.08/250.39	       | ~ 'const/sets/SUBSET'(X2, X10, X9)
250.08/250.39	       | 'const/sets/IN'(X2, sk_A5(X2, X3, X10, X4), X10)
250.08/250.39	       | X6 != 'const/sets/IMAGE'(X2, X3, X4, X10)),
250.08/250.39	    inference('cnf', [status(esa)], [thm/sets/SUBSET_IMAGE_INJ_])).
250.08/250.39	tff('62', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, X0, sk_A31, X2), sk_A31)
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['32', '61'])).
250.08/250.39	tff('63', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X1, 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, X0, sk_A31, X2), sk_A31)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['62'])).
250.08/250.39	tff('64', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, X0, sk_A31, X1), sk_A31)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)),
250.08/250.39	    inference('sup-', [status(thm)], ['63', '41'])).
250.08/250.39	tff('65', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, X0, sk_A31, X1), sk_A31)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['64'])).
250.08/250.39	tff('66', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['65', '52'])).
250.08/250.39	tff('67', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['66'])).
250.08/250.39	tff('68', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	        != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	     | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)),
250.08/250.39	    inference('sup-', [status(thm)], ['51', '67'])).
250.08/250.39	tff('69', plain,
250.08/250.39	    ('const/sets/IN'(sk_A0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	     | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['68'])).
250.08/250.39	tff('70', plain,
250.08/250.39	    ![X2 : $tType, X3 : $tType, X4 : X2 > X3, X6 : X3 > $o, X9 : X2 > $o, 
250.08/250.39	      X10 : X2 > $o]:
250.08/250.39	      ('const/sets/SUBSET'(X3, X6, 'const/sets/IMAGE'(X2, X3, X4, X9))
250.08/250.39	       | ~ 'const/sets/SUBSET'(X2, X10, X9)
250.08/250.39	       | 'const/sets/IN'(X2, sk_A4(X2, X3, X10, X4), X10)
250.08/250.39	       | X6 != 'const/sets/IMAGE'(X2, X3, X4, X10)),
250.08/250.39	    inference('cnf', [status(esa)], [thm/sets/SUBSET_IMAGE_INJ_])).
250.08/250.39	tff('71', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, X0, sk_A31, X2), sk_A31)
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['32', '70'])).
250.08/250.39	tff('72', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X1, 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, X0, sk_A31, X2), sk_A31)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['71'])).
250.08/250.39	tff('73', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, X0, sk_A31, X1), sk_A31)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)),
250.08/250.39	    inference('sup-', [status(thm)], ['72', '41'])).
250.08/250.39	tff('74', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, X0, sk_A31, X1), sk_A31)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['73'])).
250.08/250.39	tff('75', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['74', '52'])).
250.08/250.39	tff('76', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['75'])).
250.08/250.39	tff('77', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	        != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	     | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)),
250.08/250.39	    inference('sup-', [status(thm)], ['51', '76'])).
250.08/250.39	tff('78', plain,
250.08/250.39	    ('const/sets/IN'(sk_A0, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	     | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['77'])).
250.08/250.39	tff('79', plain,
250.08/250.39	    ![X11 : $tType, X14 : $tType, X16 : X14 > X11, X17 : X14, 
250.08/250.39	      X18 : X14 > $o, X19 : X14]:
250.08/250.39	      (~ 'const/sets/IN'(X14, X17, X18)
250.08/250.39	       | ~ 'const/sets/IN'(X14, X19, X18)
250.08/250.39	       | X16(X19) != X16(X17)
250.08/250.39	       | X19 = X17
250.08/250.39	       | ~ zip_tseitin1(X14, X11, X17, X19, X18, X16)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
250.08/250.39	tff('80', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X0 = X1
250.08/250.39	       | sk_A1(X0) != sk_A1(X1)
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A31)
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X1, sk_A31)),
250.08/250.39	    inference('sup-', [status(thm)], ['46', '79'])).
250.08/250.39	tff('81', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (~ 'const/sets/IN'(sk_A0, X1, sk_A31)
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A31)
250.08/250.39	       | sk_A1(X0) != sk_A1(X1)
250.08/250.39	       | X0 = X1
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['80'])).
250.08/250.39	tff('82', plain,
250.08/250.39	    ![X0 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | X0 = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	       | sk_A1(X0) != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A31)),
250.08/250.39	    inference('sup-', [status(thm)], ['78', '81'])).
250.08/250.39	tff('83', plain,
250.08/250.39	    ![X0 : sk_A0]:
250.08/250.39	      (~ 'const/sets/IN'(sk_A0, X0, sk_A31)
250.08/250.39	       | sk_A1(X0) != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	       | X0 = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	       | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['82'])).
250.08/250.39	tff('84', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | sk_A5(sk_A0, sk_A, sk_A31, sk_A1) = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	     | sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	        != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['69', '83'])).
250.08/250.39	tff('85', plain,
250.08/250.39	    (sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	      != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	     | sk_A5(sk_A0, sk_A, sk_A31, sk_A1) = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	     | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['84'])).
250.08/250.39	tff('86', plain,
250.08/250.39	    (sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	      != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | sk_P(sk_A32)
250.08/250.39	     | sk_A5(sk_A0, sk_A, sk_A31, sk_A1) = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)),
250.08/250.39	    inference('sup-', [status(thm)], ['60', '85'])).
250.08/250.39	tff('87', plain,
250.08/250.39	    (sk_A5(sk_A0, sk_A, sk_A31, sk_A1) = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	     | sk_P(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['86'])).
250.08/250.39	tff('88', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_P(sk_A32)
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('clc', [status(thm)], ['54', '87'])).
250.08/250.39	tff('89', plain,
250.08/250.39	    (~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)) | sk_P(sk_A32)),
250.08/250.39	    inference('eq_res', [status(thm)], ['88'])).
250.08/250.39	tff('90', plain, sk_P(sk_A32), inference('clc', [status(thm)], ['89', '51'])).
250.08/250.39	tff('91', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ $true),
250.08/250.39	    inference('demod', [status(thm)], ['28', '90'])).
250.08/250.39	tff('92', plain,
250.08/250.39	    (~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['91'])).
250.08/250.39	tff('93', plain,
250.08/250.39	    (sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
250.08/250.39	    inference('clc', [status(thm)], ['92', '17'])).
250.08/250.39	tff('94', plain,
250.08/250.39	    ![X2 : $tType, X3 : $tType, X4 : X2 > X3, X5 : X2 > $o, X6 : X3 > $o, 
250.08/250.39	      X7 : X2, X8 : X2]:
250.08/250.39	      (X4(X8) != X4(X7)
250.08/250.39	       | X8 = X7
250.08/250.39	       | ~ 'const/sets/IN'(X2, X7, sk_A3(X2, X3, X5, X6, X4))
250.08/250.39	       | ~ 'const/sets/IN'(X2, X8, sk_A3(X2, X3, X5, X6, X4))
250.08/250.39	       | ~ 'const/sets/SUBSET'(X3, X6, 'const/sets/IMAGE'(X2, X3, X4, X5))),
250.08/250.39	    inference('cnf', [status(esa)], [thm/sets/SUBSET_IMAGE_INJ_])).
250.08/250.39	tff('95', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0 > $o, X2 : sk_A > $o]:
250.08/250.39	      (sk_A1(X0) != sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X2, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A3(sk_A0, sk_A, X1, X2, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X2, sk_A1))
250.08/250.39	       | X0 = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['93', '94'])).
250.08/250.39	tff('96', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('eq_res', [status(thm)], ['95'])).
250.08/250.39	tff('97', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ sk_P(sk_A32)
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['14', '96'])).
250.08/250.39	tff('98', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('demod', [status(thm)], ['97', '90'])).
250.08/250.39	tff('99', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['98'])).
250.08/250.39	tff('100', plain,
250.08/250.39	    (sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('clc', [status(thm)], ['99', '17'])).
250.08/250.39	tff('101', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('clc', [status(thm)], ['100', '20'])).
250.08/250.39	tff('102', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ sk_P(sk_A32)
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['8', '101'])).
250.08/250.39	tff('103', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('demod', [status(thm)], ['102', '90'])).
250.08/250.39	tff('104', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['103'])).
250.08/250.39	tff('105', plain,
250.08/250.39	    (sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('clc', [status(thm)], ['104', '17'])).
250.08/250.39	tff('106', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('clc', [status(thm)], ['105', '20'])).
250.08/250.39	tff('107', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ zip_tseitin1(sk_A0, sk_A, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A1)
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['106', '3'])).
250.08/250.39	tff('108', plain,
250.08/250.39	    ![X11 : $tType, X14 : $tType, X16 : X14 > X11, X17 : X14, 
250.08/250.39	      X18 : X14 > $o, X19 : X14]:
250.08/250.39	      (zip_tseitin1(X14, X11, X17, X19, X18, X16)
250.08/250.39	       | X19 != X17
250.08/250.39	       | X16(X19) != X16(X17)),
250.08/250.39	    inference('cnf', [status(esa)], [zf_stmt_1])).
250.08/250.39	tff('109', plain,
250.08/250.39	    ![X11 : $tType, X14 : $tType, X16 : X14 > X11, X17 : X14, X18 : X14 > $o]:
250.08/250.39	      (X16(X17) != X16(X17) | zip_tseitin1(X14, X11, X17, X17, X18, X16)),
250.08/250.39	    inference('simplify', [status(thm)], ['108'])).
250.08/250.39	tff('110', plain,
250.08/250.39	    ![X11 : $tType, X14 : $tType, X16 : X14 > X11, X17 : X14, X18 : X14 > $o]:
250.08/250.39	      zip_tseitin1(X14, X11, X17, X17, X18, X16),
250.08/250.39	    inference('simplify', [status(thm)], ['109'])).
250.08/250.39	tff('111', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)),
250.08/250.39	    inference('demod', [status(thm)], ['107', '110'])).
250.08/250.39	tff('112', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['111'])).
250.08/250.39	tff('113', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['44', '15'])).
250.08/250.39	tff('114', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      ('const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['113'])).
250.08/250.39	tff('115', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['114', '18'])).
250.08/250.39	tff('116', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      ('const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), 
250.08/250.39	         sk_A2)
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['115'])).
250.08/250.39	tff('117', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['116', '3'])).
250.08/250.39	tff('118', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['117'])).
250.08/250.39	tff('119', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['29', '15'])).
250.08/250.39	tff('120', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	       'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['119'])).
250.08/250.39	tff('121', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), 
250.08/250.39	         sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['120', '18'])).
250.08/250.39	tff('122', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), 
250.08/250.39	       sk_A2)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['121'])).
250.08/250.39	tff('123', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      ('const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), 
250.08/250.39	         sk_A2)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('clc', [status(thm)], ['118', '122'])).
250.08/250.39	tff('124', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)),
250.08/250.39	    inference('clc', [status(thm)], ['123', '20'])).
250.08/250.39	tff('125', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
250.08/250.39	    inference('clc', [status(thm)], ['112', '124'])).
250.08/250.39	tff('126', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ sk_P(
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('sup-', [status(thm)], ['1', '125'])).
250.08/250.39	tff('127', plain,
250.08/250.39	    (~ sk_P(
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['126'])).
250.08/250.39	tff('128', plain,
250.08/250.39	    (~ sk_P(sk_A32)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('sup-', [status(thm)], ['0', '127'])).
250.08/250.39	tff('129', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('demod', [status(thm)], ['128', '90'])).
250.08/250.39	tff('130', plain,
250.08/250.39	    (sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))),
250.08/250.39	    inference('simplify', [status(thm)], ['129'])).
250.08/250.39	tff('131', plain, sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)),
250.08/250.39	    inference('clc', [status(thm)], ['130', '17'])).
250.08/250.39	tff('132', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['29', '6'])).
250.08/250.39	tff('133', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['132'])).
250.08/250.39	tff('134', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['29', '12'])).
250.08/250.39	tff('135', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['134'])).
250.08/250.39	tff('136', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['29', '25'])).
250.08/250.39	tff('137', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['136'])).
250.08/250.39	tff('138', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['122', '137'])).
250.08/250.39	tff('139', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ $true),
250.08/250.39	    inference('demod', [status(thm)], ['138', '90'])).
250.08/250.39	tff('140', plain,
250.08/250.39	    (~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['139'])).
250.08/250.39	tff('141', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
250.08/250.39	    inference('clc', [status(thm)], ['140', '120'])).
250.08/250.39	tff('142', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0 > $o, X2 : sk_A > $o]:
250.08/250.39	      (sk_A1(X0) != sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X2, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A3(sk_A0, sk_A, X1, X2, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X2, sk_A1))
250.08/250.39	       | X0 = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['141', '94'])).
250.08/250.39	tff('143', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('eq_res', [status(thm)], ['142'])).
250.08/250.39	tff('144', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ sk_P(sk_A32)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['135', '143'])).
250.08/250.39	tff('145', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('demod', [status(thm)], ['144', '90'])).
250.08/250.39	tff('146', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['145'])).
250.08/250.39	tff('147', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('clc', [status(thm)], ['146', '120'])).
250.08/250.39	tff('148', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('clc', [status(thm)], ['147', '122'])).
250.08/250.39	tff('149', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ sk_P(sk_A32)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['133', '148'])).
250.08/250.39	tff('150', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('demod', [status(thm)], ['149', '90'])).
250.08/250.39	tff('151', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['150'])).
250.08/250.39	tff('152', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('clc', [status(thm)], ['151', '120'])).
250.08/250.39	tff('153', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('clc', [status(thm)], ['152', '122'])).
250.08/250.39	tff('154', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ zip_tseitin1(sk_A0, sk_A, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A1)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['153', '3'])).
250.08/250.39	tff('155', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)),
250.08/250.39	    inference('demod', [status(thm)], ['154', '110'])).
250.08/250.39	tff('156', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['155'])).
250.08/250.39	tff('157', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      ('const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
250.08/250.39	    inference('clc', [status(thm)], ['156', '124'])).
250.08/250.39	tff('158', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ sk_P(
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['29', '157'])).
250.08/250.39	tff('159', plain,
250.08/250.39	    (~ sk_P(
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['158'])).
250.08/250.39	tff('160', plain,
250.08/250.39	    (~ sk_P(sk_A32)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['0', '159'])).
250.08/250.39	tff('161', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('demod', [status(thm)], ['160', '90'])).
250.08/250.39	tff('162', plain,
250.08/250.39	    ('const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))),
250.08/250.39	    inference('simplify', [status(thm)], ['161'])).
250.08/250.39	tff('163', plain, 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2),
250.08/250.39	    inference('clc', [status(thm)], ['162', '120'])).
250.08/250.39	tff('164', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (~ $true
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, X0, sk_A31, X2), sk_A31)
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['163', '61'])).
250.08/250.39	tff('165', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X1, 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, X0, sk_A31, X2), sk_A31)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['164'])).
250.08/250.39	tff('166', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, X0, sk_A31, X1), sk_A31)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)),
250.08/250.39	    inference('sup-', [status(thm)], ['165', '41'])).
250.08/250.39	tff('167', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, X0, sk_A31, X1), sk_A31)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['166'])).
250.08/250.39	tff('168', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['44', '3'])).
250.08/250.39	tff('169', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('simplify', [status(thm)], ['168'])).
250.08/250.39	tff('170', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('clc', [status(thm)], ['169', '29'])).
250.08/250.39	tff('171', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('clc', [status(thm)], ['170', '1'])).
250.08/250.39	tff('172', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['167', '171'])).
250.08/250.39	tff('173', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['172'])).
250.08/250.39	tff('174', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	        != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	     | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['131', '173'])).
250.08/250.39	tff('175', plain,
250.08/250.39	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	     | 'const/sets/IN'(sk_A0, sk_A5(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['174'])).
250.08/250.39	tff('176', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (~ $true
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, X0, sk_A31, X2), sk_A31)
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['163', '70'])).
250.08/250.39	tff('177', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X1, 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, X0, sk_A31, X2), sk_A31)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['176'])).
250.08/250.39	tff('178', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, X0, sk_A31, X1), sk_A31)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)),
250.08/250.39	    inference('sup-', [status(thm)], ['177', '41'])).
250.08/250.39	tff('179', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, X0, sk_A31, X1), sk_A31)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['178'])).
250.08/250.39	tff('180', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['179', '171'])).
250.08/250.39	tff('181', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['180'])).
250.08/250.39	tff('182', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	        != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	     | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['131', '181'])).
250.08/250.39	tff('183', plain,
250.08/250.39	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	     | 'const/sets/IN'(sk_A0, sk_A4(sk_A0, sk_A, sk_A31, sk_A1), sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['182'])).
250.08/250.39	tff('184', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | X0 = X1
250.08/250.39	       | sk_A1(X0) != sk_A1(X1)
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A31)
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X1, sk_A31)),
250.08/250.39	    inference('sup-', [status(thm)], ['44', '79'])).
250.08/250.39	tff('185', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (~ 'const/sets/IN'(sk_A0, X1, sk_A31)
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A31)
250.08/250.39	       | sk_A1(X0) != sk_A1(X1)
250.08/250.39	       | X0 = X1
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('simplify', [status(thm)], ['184'])).
250.08/250.39	tff('186', plain,
250.08/250.39	    ![X0 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | X0 = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	       | sk_A1(X0) != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A31)),
250.08/250.39	    inference('sup-', [status(thm)], ['183', '185'])).
250.08/250.39	tff('187', plain,
250.08/250.39	    ![X0 : sk_A0]:
250.08/250.39	      (~ 'const/sets/IN'(sk_A0, X0, sk_A31)
250.08/250.39	       | sk_A1(X0) != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	       | X0 = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('simplify', [status(thm)], ['186'])).
250.08/250.39	tff('188', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	     | sk_A5(sk_A0, sk_A, sk_A31, sk_A1) = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	     | sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	        != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['175', '187'])).
250.08/250.39	tff('189', plain,
250.08/250.39	    (sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	      != sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	     | sk_A5(sk_A0, sk_A, sk_A31, sk_A1) = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('simplify', [status(thm)], ['188'])).
250.08/250.39	tff('190', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (~ $true
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | X2(sk_A4(sk_A0, X0, sk_A31, X2)) = X2(sk_A5(sk_A0, X0, sk_A31, X2))
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['163', '37'])).
250.08/250.39	tff('191', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X1, 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))
250.08/250.39	       | X2(sk_A4(sk_A0, X0, sk_A31, X2)) = X2(sk_A5(sk_A0, X0, sk_A31, X2))
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['190'])).
250.08/250.39	tff('192', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | X1(sk_A4(sk_A0, X0, sk_A31, X1)) = X1(sk_A5(sk_A0, X0, sk_A31, X1))
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)),
250.08/250.39	    inference('sup-', [status(thm)], ['191', '41'])).
250.08/250.39	tff('193', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | X1(sk_A4(sk_A0, X0, sk_A31, X1)) = X1(sk_A5(sk_A0, X0, sk_A31, X1))
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['192'])).
250.08/250.39	tff('194', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	          = sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['193', '171'])).
250.08/250.39	tff('195', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	          = sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['194'])).
250.08/250.39	tff('196', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	        != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	     | sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	        = sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['131', '195'])).
250.08/250.39	tff('197', plain,
250.08/250.39	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	     | sk_A1(sk_A4(sk_A0, sk_A, sk_A31, sk_A1))
250.08/250.39	        = sk_A1(sk_A5(sk_A0, sk_A, sk_A31, sk_A1))),
250.08/250.39	    inference('simplify', [status(thm)], ['196'])).
250.08/250.39	tff('198', plain,
250.08/250.39	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	     | sk_A5(sk_A0, sk_A, sk_A31, sk_A1) = sk_A4(sk_A0, sk_A, sk_A31, sk_A1)),
250.08/250.39	    inference('clc', [status(thm)], ['189', '197'])).
250.08/250.39	tff('199', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (~ $true
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X2) != sk_A5(sk_A0, X0, sk_A31, X2)
250.08/250.39	       | X2(sk_A4(sk_A0, X0, sk_A31, X2)) != X2(sk_A5(sk_A0, X0, sk_A31, X2))
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['163', '33'])).
250.08/250.39	tff('200', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      ('const/sets/SUBSET'(X0, X1, 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))
250.08/250.39	       | X2(sk_A4(sk_A0, X0, sk_A31, X2)) != X2(sk_A5(sk_A0, X0, sk_A31, X2))
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X2) != sk_A5(sk_A0, X0, sk_A31, X2)
250.08/250.39	       | X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)),
250.08/250.39	    inference('simplify', [status(thm)], ['199'])).
250.08/250.39	tff('201', plain,
250.08/250.39	    ![X0 : $tType, X1 : X0 > $o, X2 : sk_A0 > X0]:
250.08/250.39	      (X1 != 'const/sets/IMAGE'(sk_A0, X0, X2, sk_A31)
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X2) != sk_A5(sk_A0, X0, sk_A31, X2)
250.08/250.39	       | 'const/sets/SUBSET'(X0, X1, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, X0, X2, sk_A2))),
250.08/250.39	    inference('clc', [status(thm)], ['200', '191'])).
250.08/250.39	tff('202', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X1) != sk_A5(sk_A0, X0, sk_A31, X1)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)),
250.08/250.39	    inference('sup-', [status(thm)], ['201', '41'])).
250.08/250.39	tff('203', plain,
250.08/250.39	    ![X0 : $tType, X1 : sk_A0 > X0, X2 : X0 > $o, X3 : X0 > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, X0, X2, sk_A2, X1, X3)
250.08/250.39	       | ~ X3(X2)
250.08/250.39	       | X2 != 'const/sets/IMAGE'(sk_A0, X0, X1, sk_A31)
250.08/250.39	       | sk_A4(sk_A0, X0, sk_A31, X1) != sk_A5(sk_A0, X0, sk_A31, X1)),
250.08/250.39	    inference('simplify', [status(thm)], ['202'])).
250.08/250.39	tff('204', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	          != sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['203', '171'])).
250.08/250.39	tff('205', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(X0)
250.08/250.39	       | X0 != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	       | sk_A4(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	          != sk_A5(sk_A0, sk_A, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['204'])).
250.08/250.39	tff('206', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_A4(sk_A0, sk_A, sk_A31, sk_A1) != sk_A5(sk_A0, sk_A, sk_A31, sk_A1)
250.08/250.39	     | 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	        != 'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31)
250.08/250.39	     | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['131', '205'])).
250.08/250.39	tff('207', plain,
250.08/250.39	    (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P)
250.08/250.39	     | sk_A4(sk_A0, sk_A, sk_A31, sk_A1) != sk_A5(sk_A0, sk_A, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['206'])).
250.08/250.39	tff('208', plain, zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, sk_P),
250.08/250.39	    inference('clc', [status(thm)], ['198', '207'])).
250.08/250.39	tff('209', plain,
250.08/250.39	    ![X0 : sk_A > $o > $o, X1 : sk_A0, X2 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X2, X1, sk_A31, sk_A1)
250.08/250.39	       | ~ X0(sk_A32)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['114', '41'])).
250.08/250.39	tff('210', plain,
250.08/250.39	    ![X0 : sk_A > $o > $o, X1 : sk_A0, X2 : sk_A0]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X0)
250.08/250.39	       | ~ X0(sk_A32)
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X2, X1, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['209'])).
250.08/250.39	tff('211', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | ~ X1(sk_A32)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X1)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['210', '3'])).
250.08/250.39	tff('212', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A > $o > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X1)
250.08/250.39	       | ~ X1(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['211'])).
250.08/250.39	tff('213', plain,
250.08/250.39	    ![X0 : sk_A > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ X0(sk_A32)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['120', '41'])).
250.08/250.39	tff('214', plain,
250.08/250.39	    ![X0 : sk_A > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X0)
250.08/250.39	       | ~ X0(sk_A32)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['213'])).
250.08/250.39	tff('215', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A > $o > $o]:
250.08/250.39	      (~ X1(sk_A32)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X1)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('clc', [status(thm)], ['212', '214'])).
250.08/250.39	tff('216', plain,
250.08/250.39	    ![X0 : sk_A > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ X0(sk_A32)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['17', '41'])).
250.08/250.39	tff('217', plain,
250.08/250.39	    ![X0 : sk_A > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X0)
250.08/250.39	       | ~ X0(sk_A32)
250.08/250.39	       | sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('simplify', [status(thm)], ['216'])).
250.08/250.39	tff('218', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A > $o > $o]:
250.08/250.39	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X1)
250.08/250.39	       | ~ X1(sk_A32)),
250.08/250.39	    inference('clc', [status(thm)], ['215', '217'])).
250.08/250.39	tff('219', plain,
250.08/250.39	    ![X0 : sk_A > $o > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | ~ X0(sk_A32)
250.08/250.39	       | zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['208', '218'])).
250.08/250.39	tff('220', plain,
250.08/250.39	    ![X0 : sk_A > $o > $o]:
250.08/250.39	      (zip_tseitin0(sk_A0, sk_A, sk_A32, sk_A2, sk_A1, X0) | ~ X0(sk_A32)),
250.08/250.39	    inference('simplify', [status(thm)], ['219'])).
250.08/250.39	tff('221', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | ~ sk_P(sk_A32)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['220', '6'])).
250.08/250.39	tff('222', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | ~ $true
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('demod', [status(thm)], ['221', '90'])).
250.08/250.39	tff('223', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['222'])).
250.08/250.39	tff('224', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | ~ sk_P(sk_A32)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['220', '12'])).
250.08/250.39	tff('225', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | ~ $true
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('demod', [status(thm)], ['224', '90'])).
250.08/250.39	tff('226', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | 'const/sets/IN'(sk_A0, sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['225'])).
250.08/250.39	tff('227', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o, X2 : sk_A0, X3 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X3, X2, sk_A31, sk_A1)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ sk_P(X0)),
250.08/250.39	    inference('sup-', [status(thm)], ['44', '25'])).
250.08/250.39	tff('228', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o, X2 : sk_A0, X3 : sk_A0]:
250.08/250.39	      (~ sk_P(X0)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, X1, X0, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, X1, X0, sk_A1), 
250.08/250.39	             sk_A2)
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X3, X2, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['227'])).
250.08/250.39	tff('229', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0, X2 : sk_A0, X3 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X3, X2, sk_A31, sk_A1)
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	       | ~ sk_P(sk_A32)),
250.08/250.39	    inference('sup-', [status(thm)], ['116', '228'])).
250.08/250.39	tff('230', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0, X2 : sk_A0, X3 : sk_A0]:
250.08/250.39	      (~ $true
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X3, X2, sk_A31, sk_A1)
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	       | ~ $true),
250.08/250.39	    inference('demod', [status(thm)], ['229', '90'])).
250.08/250.39	tff('231', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0, X2 : sk_A0, X3 : sk_A0]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X3, X2, sk_A31, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['230'])).
250.08/250.39	tff('232', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)),
250.08/250.39	    inference('condensation', [status(thm)], ['231'])).
250.08/250.39	tff('233', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0]:
250.08/250.39	      (zip_tseitin1(sk_A0, sk_A, X1, X0, sk_A31, sk_A1)
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
250.08/250.39	    inference('clc', [status(thm)], ['232', '114'])).
250.08/250.39	tff('234', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['233', '3'])).
250.08/250.39	tff('235', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
250.08/250.39	    inference('simplify', [status(thm)], ['234'])).
250.08/250.39	tff('236', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('clc', [status(thm)], ['235', '141'])).
250.08/250.39	tff('237', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	          = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
250.08/250.39	    inference('clc', [status(thm)], ['236', '93'])).
250.08/250.39	tff('238', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	        = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))),
250.08/250.39	    inference('sup-', [status(thm)], ['208', '237'])).
250.08/250.39	tff('239', plain,
250.08/250.39	    sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	     = sk_A1(sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('simplify', [status(thm)], ['238'])).
250.08/250.39	tff('240', plain,
250.08/250.39	    ![X0 : sk_A0, X1 : sk_A0 > $o, X2 : sk_A > $o]:
250.08/250.39	      (sk_A1(X0) != sk_A1(sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X2, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, X0, sk_A3(sk_A0, sk_A, X1, X2, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X2, sk_A1))
250.08/250.39	       | X0 = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['239', '94'])).
250.08/250.39	tff('241', plain,
250.08/250.39	    ![X0 : sk_A > $o, X1 : sk_A0 > $o]:
250.08/250.39	      (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	             sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	             sk_A3(sk_A0, sk_A, X1, X0, sk_A1))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, X0, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, X1))),
250.08/250.39	    inference('eq_res', [status(thm)], ['240'])).
250.08/250.39	tff('242', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ sk_P(sk_A32)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['226', '241'])).
250.08/250.39	tff('243', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), 
250.08/250.39	         sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['208', '124'])).
250.08/250.39	tff('244', plain,
250.08/250.39	    'const/sets/SUBSET'(sk_A0, sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), 
250.08/250.39	      sk_A2),
250.08/250.39	    inference('simplify', [status(thm)], ['243'])).
250.08/250.39	tff('245', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['114', '3'])).
250.08/250.39	tff('246', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ 'const/sets/SUBSET'(sk_A0, sk_A31, sk_A2)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))),
250.08/250.39	    inference('simplify', [status(thm)], ['245'])).
250.08/250.39	tff('247', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      ('const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P('const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A31))),
250.08/250.39	    inference('clc', [status(thm)], ['246', '120'])).
250.08/250.39	tff('248', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))),
250.08/250.39	    inference('clc', [status(thm)], ['247', '17'])).
250.08/250.39	tff('249', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	         'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))),
250.08/250.39	    inference('sup-', [status(thm)], ['208', '248'])).
250.08/250.39	tff('250', plain,
250.08/250.39	    'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	      'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2)),
250.08/250.39	    inference('simplify', [status(thm)], ['249'])).
250.08/250.39	tff('251', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | ~ $true
250.08/250.39	     | ~ $true
250.08/250.39	     | ~ $true
250.08/250.39	     | ~ $true
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('demod', [status(thm)], ['242', '244', '250', '90', '250'])).
250.08/250.39	tff('252', plain,
250.08/250.39	    (sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	      = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     | ~ 'const/sets/IN'(sk_A0, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('simplify', [status(thm)], ['251'])).
250.08/250.39	tff('253', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)
250.08/250.39	     | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	     | ~ sk_P(sk_A32)
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('sup-', [status(thm)], ['223', '252'])).
250.08/250.39	tff('254', plain,
250.08/250.39	    (~ $true
250.08/250.39	     | ~ $true
250.08/250.39	     | ~ $true
250.08/250.39	     | ~ $true
250.08/250.39	     | sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	        = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))),
250.08/250.39	    inference('demod', [status(thm)], ['253', '244', '250', '90'])).
250.08/250.39	tff('255', plain,
250.08/250.39	    sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1))
250.08/250.39	     = sk_A51(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)),
250.08/250.39	    inference('simplify', [status(thm)], ['254'])).
250.08/250.39	tff('256', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ zip_tseitin1(sk_A0, sk_A, 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A41(sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)), 
250.08/250.39	           sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A1)
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A0, 
250.08/250.39	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1), sk_A2)),
250.08/250.39	    inference('sup-', [status(thm)], ['255', '3'])).
250.08/250.39	tff('257', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)
250.08/250.39	       | ~ sk_P(
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	               sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ $true),
250.08/250.39	    inference('demod', [status(thm)], ['256', '110', '244'])).
250.08/250.39	tff('258', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ sk_P(
250.08/250.39	           'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, 
250.08/250.39	             sk_A3(sk_A0, sk_A, sk_A2, sk_A32, sk_A1)))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('simplify', [status(thm)], ['257'])).
250.08/250.39	tff('259', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ sk_P(sk_A32)
250.08/250.39	       | ~ 'const/sets/SUBSET'(sk_A, sk_A32, 
250.08/250.39	             'const/sets/IMAGE'(sk_A0, sk_A, sk_A1, sk_A2))
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('sup-', [status(thm)], ['0', '258'])).
250.08/250.39	tff('260', plain,
250.08/250.39	    ![X0 : sk_A > $o]:
250.08/250.39	      (~ $true
250.08/250.39	       | ~ $true
250.08/250.39	       | ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P)),
250.08/250.39	    inference('demod', [status(thm)], ['259', '90', '250'])).
250.08/250.39	tff('261', plain,
250.08/250.39	    ![X0 : sk_A > $o]: ~ zip_tseitin0(sk_A0, sk_A, X0, sk_A2, sk_A1, sk_P),
250.08/250.39	    inference('simplify', [status(thm)], ['260'])).
250.08/250.39	tff('262', plain, ~ $true, inference('sup-', [status(thm)], ['208', '261'])).
250.08/250.39	tff('263', plain, $false, inference('simplify', [status(thm)], ['262'])).
250.08/250.39	
250.08/250.39	% SZS output end Refutation
250.08/250.39	EOF
