0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
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-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n039.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:27:09 CST 2018
6.37/6.58	% done 1200 iterations in 6.382s
6.37/6.58	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
6.37/6.58	% SZS output start Refutation
6.37/6.58	tff('thm/sets/SUBSET_', axiom,
6.37/6.58	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
6.37/6.58	     ('const/sets/SUBSET'(A,A0,A1) <=>
6.37/6.58	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
6.37/6.58	tff('0', plain,
6.37/6.58	    ![X10 : $tType, X12 : X10 > $o, X14 : X10 > $o]:
6.37/6.58	      ('const/sets/SUBSET'(X10, X12, X14)
6.37/6.58	       | 'const/sets/IN'(X10, sk_A21(X10, X14, X12), X12)),
6.37/6.58	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
6.37/6.58	tff('1', plain,
6.37/6.58	    ![X10 : $tType, X12 : X10 > $o, X14 : X10 > $o]:
6.37/6.58	      ('const/sets/SUBSET'(X10, X12, X14)
6.37/6.58	       | ~ 'const/sets/IN'(X10, sk_A21(X10, X14, X12), X14)),
6.37/6.58	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
6.37/6.58	tff('2', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(X0, X1, X1)
6.37/6.58	       | 'const/sets/SUBSET'(X0, X1, X1)),
6.37/6.58	    inference('sup-', [status(thm)], ['0', '1'])).
6.37/6.58	tff('3', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
6.37/6.58	    inference('simplify', [status(thm)], ['2'])).
6.37/6.58	tff('thm/sets/IN_', axiom,
6.37/6.58	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
6.37/6.58	tff('4', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X3 : X0]:
6.37/6.58	      ('const/sets/IN'(X0, X3, X1) | ~ X1(X3)),
6.37/6.58	    inference('cnf', [status(esa)], [thm/sets/IN_])).
6.37/6.58	tff('5', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X3 : X0, X4 : X0 > $o]:
6.37/6.58	      (X4 != X1 | 'const/sets/IN'(X0, X3, X1) | ~ X4(X3)),
6.37/6.58	    inference('ho.purify_applied_variable', [status(thm)], ['4'])).
6.37/6.58	tff('6', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/IN'((> $o, X0), X1, X2)
6.37/6.58	       | 'const/sets/SUBSET'(X0, X1) != X2),
6.37/6.58	    inference('sup-', [status(thm)], ['3', '5'])).
6.37/6.58	tff('7', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
6.37/6.58	      ('const/sets/SUBSET'(X0, X1) != X2
6.37/6.58	       | 'const/sets/IN'((> $o, X0), X1, X2)),
6.37/6.58	    inference('simplify', [status(thm)], ['6'])).
6.37/6.58	tff('8', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
6.37/6.58	      (X1(X2) | ~ 'const/sets/IN'(X0, X2, X1)),
6.37/6.58	    inference('cnf', [status(esa)], [thm/sets/IN_])).
6.37/6.58	tff('9', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
6.37/6.58	      (X3 != X1 | X1(X2) | ~ 'const/sets/IN'(X0, X2, X3)),
6.37/6.58	    inference('ho.purify_applied_variable', [status(thm)], ['8'])).
6.37/6.58	tff('10', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0 > $o > $o]:
6.37/6.58	      (~ $true | 'const/sets/SUBSET'(X0, X2) != X1 | X3(X2) | X1 != X3),
6.37/6.58	    inference('sup-', [status(thm)], ['7', '9'])).
6.37/6.58	tff('11', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0 > $o > $o]:
6.37/6.58	      (X1 != X3 | X3(X2) | 'const/sets/SUBSET'(X0, X2) != X1),
6.37/6.58	    inference('simplify', [status(thm)], ['10'])).
6.37/6.58	tff('thm/sets/SUBSET_ANTISYM_EQ_', conjecture,
6.37/6.58	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
6.37/6.58	     (('const/sets/SUBSET'(A,A1,A0) & 'const/sets/SUBSET'(A,A0,A1)) <=>
6.37/6.58	      (A0 = A1)))).
6.37/6.58	tff(zf_stmt_0, negated_conjecture,
6.37/6.58	  (~
6.37/6.58	    (![A:$tType,A0:(A > $o),A1:(A > $o)]:
6.37/6.58	       (('const/sets/SUBSET'(A,A1,A0) & 'const/sets/SUBSET'(A,A0,A1)) <=>
6.37/6.58	        (A0 = A1))))).
6.37/6.58	tff('12', plain,
6.37/6.58	    (sk_A0 != sk_A1
6.37/6.58	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.58	     | ~ 'const/sets/SUBSET'(sk_A, sk_A1, sk_A0)),
6.37/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.37/6.58	tff('13', plain,
6.37/6.58	    (sk_A0('#k1') != sk_A1('#k1')
6.37/6.58	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.58	     | ~ 'const/sets/SUBSET'(sk_A, sk_A1, sk_A0)),
6.37/6.58	    inference('rw_lit', [status(thm)], ['12'])).
6.37/6.58	tff('14', plain,
6.37/6.58	    ![X0 : sk_A > $o > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A0) != X0
6.37/6.58	       | X0 != 'const/sets/SUBSET'(sk_A, sk_A1)
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.58	       | sk_A0('#k1') != sk_A1('#k1')),
6.37/6.58	    inference('sup-', [status(thm)], ['11', '13'])).
6.37/6.58	tff('15', plain,
6.37/6.58	    ![X0 : sk_A > $o > $o]:
6.37/6.58	      (sk_A0('#k1') != sk_A1('#k1')
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.58	       | X0 != 'const/sets/SUBSET'(sk_A, sk_A1)
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A0) != X0),
6.37/6.58	    inference('simplify', [status(thm)], ['14'])).
6.37/6.58	tff('16', plain,
6.37/6.58	    ![X0 : sk_A > $o > $o]:
6.37/6.58	      ('const/sets/SUBSET'(sk_A, sk_A0) != X0
6.37/6.58	       | X0 != 'const/sets/SUBSET'(sk_A, sk_A1)
6.37/6.58	       | sk_A0('#k1') != sk_A1('#k1')),
6.37/6.58	    inference('clc', [status(thm)], ['15', '11'])).
6.37/6.58	tff('17', plain,
6.37/6.58	    (sk_A0('#k1') != sk_A1('#k1')
6.37/6.58	     | 'const/sets/SUBSET'(sk_A, sk_A0) != 'const/sets/SUBSET'(sk_A, sk_A1)),
6.37/6.58	    inference('eq_res', [status(thm)], ['16'])).
6.37/6.58	tff('18', plain,
6.37/6.58	    (sk_A0('#k1') != sk_A1('#k1')
6.37/6.58	     | 'const/sets/SUBSET'(sk_A, sk_A0, '#k39')
6.37/6.58	        != 'const/sets/SUBSET'(sk_A, sk_A1, '#k39')),
6.37/6.58	    inference('rw_lit', [status(thm)], ['17'])).
6.37/6.58	tff('19', plain, (sk_A0 = sk_A1 | 'const/sets/SUBSET'(sk_A, sk_A1, sk_A0)),
6.37/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.37/6.58	tff('20', plain,
6.37/6.58	    (~ $true
6.37/6.58	     | sk_A0 = sk_A1
6.37/6.58	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.58	     | sk_A0('#k1') != sk_A1('#k1')),
6.37/6.58	    inference('sup-', [status(thm)], ['19', '13'])).
6.37/6.58	tff('21', plain,
6.37/6.58	    (sk_A0('#k1') != sk_A1('#k1')
6.37/6.58	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.58	     | sk_A0 = sk_A1),
6.37/6.58	    inference('simplify', [status(thm)], ['20'])).
6.37/6.58	tff('22', plain, (sk_A0 = sk_A1 | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)),
6.37/6.58	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.37/6.58	tff('23', plain, (sk_A0 = sk_A1 | sk_A0('#k1') != sk_A1('#k1')),
6.37/6.58	    inference('clc', [status(thm)], ['21', '22'])).
6.37/6.58	tff('24', plain, sk_A0('#k1') != sk_A1('#k1'),
6.37/6.58	    inference('clc', [status(thm)], ['18', '23'])).
6.37/6.58	tff('thm/sets/EXTENSION_', axiom,
6.37/6.58	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
6.37/6.58	     ((A0 = A1) <=>
6.37/6.58	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
6.37/6.58	tff('25', plain,
6.37/6.58	    ![X4 : $tType, X7 : X4 > $o, X9 : X4 > $o]:
6.37/6.58	      (X7 = X9
6.37/6.58	       | 'const/sets/IN'(X4, sk_A2(X4, X9, X7), X9)
6.37/6.58	       | 'const/sets/IN'(X4, sk_A2(X4, X9, X7), X7)),
6.37/6.58	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
6.37/6.58	tff('26', plain,
6.37/6.58	    ![X10 : $tType, X11 : X10, X12 : X10 > $o, X13 : X10 > $o]:
6.37/6.58	      (~ 'const/sets/IN'(X10, X11, X12)
6.37/6.58	       | 'const/sets/IN'(X10, X11, X13)
6.37/6.58	       | ~ 'const/sets/SUBSET'(X10, X12, X13)),
6.37/6.58	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
6.37/6.58	tff('27', plain,
6.37/6.58	    ![X0 : sk_A]:
6.37/6.58	      (~ $true
6.37/6.58	       | sk_A0 = sk_A1
6.37/6.58	       | 'const/sets/IN'(sk_A, X0, sk_A0)
6.37/6.58	       | ~ 'const/sets/IN'(sk_A, X0, sk_A1)),
6.37/6.58	    inference('sup-', [status(thm)], ['19', '26'])).
6.37/6.58	tff('28', plain,
6.37/6.58	    ![X0 : sk_A]:
6.37/6.58	      (~ 'const/sets/IN'(sk_A, X0, sk_A1)
6.37/6.58	       | 'const/sets/IN'(sk_A, X0, sk_A0)
6.37/6.58	       | sk_A0 = sk_A1),
6.37/6.58	    inference('simplify', [status(thm)], ['27'])).
6.37/6.58	tff('29', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, X0), X0)
6.37/6.58	       | X0 = sk_A1
6.37/6.58	       | sk_A0 = sk_A1
6.37/6.58	       | 'const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, X0), sk_A0)),
6.37/6.58	    inference('sup-', [status(thm)], ['25', '28'])).
6.37/6.58	tff('30', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      ('const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, X0), sk_A0)
6.37/6.58	       | sk_A0 = sk_A1
6.37/6.58	       | X0 = sk_A1
6.37/6.58	       | 'const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, X0), X0)),
6.37/6.58	    inference('simplify', [status(thm)], ['29'])).
6.37/6.58	tff('31', plain,
6.37/6.58	    (~ $true
6.37/6.58	     | 'const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, sk_A0), sk_A0)
6.37/6.58	     | sk_A0 = sk_A1
6.37/6.58	     | sk_A0 = sk_A1),
6.37/6.58	    inference('eq_fact', [status(thm)], ['30'])).
6.37/6.58	tff('32', plain,
6.37/6.58	    (sk_A0 = sk_A1 | 'const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, sk_A0), sk_A0)),
6.37/6.58	    inference('simplify', [status(thm)], ['31'])).
6.37/6.58	tff('33', plain,
6.37/6.58	    ![X4 : $tType, X7 : X4 > $o, X9 : X4 > $o]:
6.37/6.58	      (X7 = X9
6.37/6.58	       | ~ 'const/sets/IN'(X4, sk_A2(X4, X9, X7), X9)
6.37/6.58	       | ~ 'const/sets/IN'(X4, sk_A2(X4, X9, X7), X7)),
6.37/6.58	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
6.37/6.58	tff('34', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X3, X1)
6.37/6.58	       | ~ 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X3)
6.37/6.58	       | ~ 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)
6.37/6.58	       | X2 = X1),
6.37/6.58	    inference('sup-', [status(thm)], ['26', '33'])).
6.37/6.58	tff('35', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (X2 = X1
6.37/6.58	       | ~ 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)
6.37/6.58	       | ~ 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X3)
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X3, X1)),
6.37/6.58	    inference('simplify', [status(thm)], ['34'])).
6.37/6.58	tff('36', plain,
6.37/6.58	    (~ $true
6.37/6.58	     | sk_A0 = sk_A1
6.37/6.58	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.58	     | ~ 'const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, sk_A0), sk_A0)
6.37/6.58	     | sk_A0 = sk_A1),
6.37/6.58	    inference('sup-', [status(thm)], ['32', '35'])).
6.37/6.58	tff('37', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(X0, X1, X2)
6.37/6.58	       | X3(sk_A21(X0, X2, X1))
6.37/6.58	       | X1 != X3),
6.37/6.58	    inference('sup-', [status(thm)], ['0', '9'])).
6.37/6.58	tff('38', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (X1 != X3 | X3(sk_A21(X0, X2, X1)) | 'const/sets/SUBSET'(X0, X1, X2)),
6.37/6.58	    inference('simplify', [status(thm)], ['37'])).
6.37/6.58	tff('39', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o, X4 : X0 > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(X0, X2, X3)
6.37/6.58	       | X2 != X1
6.37/6.58	       | 'const/sets/IN'(X0, sk_A21(X0, X3, X2), X4)
6.37/6.58	       | X1 != X4),
6.37/6.58	    inference('sup-', [status(thm)], ['38', '5'])).
6.37/6.58	tff('40', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o, X4 : X0 > $o]:
6.37/6.58	      (X1 != X4
6.37/6.58	       | 'const/sets/IN'(X0, sk_A21(X0, X3, X2), X4)
6.37/6.58	       | X2 != X1
6.37/6.58	       | 'const/sets/SUBSET'(X0, X2, X3)),
6.37/6.58	    inference('simplify', [status(thm)], ['39'])).
6.37/6.58	tff('41', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(X0, X2, X1)
6.37/6.58	       | X2 != X3
6.37/6.58	       | X3 != X1
6.37/6.58	       | 'const/sets/SUBSET'(X0, X2, X1)),
6.37/6.58	    inference('sup-', [status(thm)], ['40', '1'])).
6.37/6.58	tff('42', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (X3 != X1 | X2 != X3 | 'const/sets/SUBSET'(X0, X2, X1)),
6.37/6.58	    inference('simplify', [status(thm)], ['41'])).
6.37/6.58	tff('43', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
6.37/6.58	      ('const/sets/SUBSET'(X0, X2, X1) | X2 != X1),
6.37/6.58	    inference('eq_res', [status(thm)], ['42'])).
6.37/6.58	tff('44', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A1, X0)
6.37/6.58	       | sk_A0 = sk_A1
6.37/6.58	       | 'const/sets/IN'(sk_A, sk_A21(sk_A, X0, sk_A1), sk_A0)),
6.37/6.58	    inference('sup-', [status(thm)], ['0', '28'])).
6.37/6.58	tff('45', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      ('const/sets/IN'(sk_A, sk_A21(sk_A, X0, sk_A1), sk_A0)
6.37/6.58	       | sk_A0 = sk_A1
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A1, X0)),
6.37/6.58	    inference('simplify', [status(thm)], ['44'])).
6.37/6.58	tff('46', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(X0, X1, X2)
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
6.37/6.58	       | 'const/sets/IN'(X0, sk_A21(X0, X2, X1), X3)),
6.37/6.58	    inference('sup-', [status(thm)], ['0', '26'])).
6.37/6.58	tff('47', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      ('const/sets/IN'(X0, sk_A21(X0, X2, X1), X3)
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
6.37/6.58	       | 'const/sets/SUBSET'(X0, X1, X2)),
6.37/6.58	    inference('simplify', [status(thm)], ['46'])).
6.37/6.58	tff('48', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X3, X1)
6.37/6.58	       | ~ 'const/sets/IN'(X0, sk_A21(X0, X1, X2), X3)
6.37/6.58	       | 'const/sets/SUBSET'(X0, X2, X1)),
6.37/6.58	    inference('sup-', [status(thm)], ['26', '1'])).
6.37/6.58	tff('49', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      ('const/sets/SUBSET'(X0, X2, X1)
6.37/6.58	       | ~ 'const/sets/IN'(X0, sk_A21(X0, X1, X2), X3)
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X3, X1)),
6.37/6.58	    inference('simplify', [status(thm)], ['48'])).
6.37/6.58	tff('50', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(X0, X2, X3)
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
6.37/6.58	       | 'const/sets/SUBSET'(X0, X2, X3)),
6.37/6.58	    inference('sup-', [status(thm)], ['47', '49'])).
6.37/6.58	tff('51', plain,
6.37/6.58	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
6.37/6.58	      (~ 'const/sets/SUBSET'(X0, X1, X3)
6.37/6.58	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
6.37/6.58	       | 'const/sets/SUBSET'(X0, X2, X3)),
6.37/6.58	    inference('simplify', [status(thm)], ['50'])).
6.37/6.58	tff('52', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | sk_A0 = sk_A1
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, X0, sk_A0)
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, X0, sk_A1)),
6.37/6.58	    inference('sup-', [status(thm)], ['19', '51'])).
6.37/6.58	tff('53', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      (~ 'const/sets/SUBSET'(sk_A, X0, sk_A1)
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, X0, sk_A0)
6.37/6.58	       | sk_A0 = sk_A1),
6.37/6.58	    inference('simplify', [status(thm)], ['52'])).
6.37/6.58	tff('54', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | X0 != sk_A1
6.37/6.58	       | sk_A0 = sk_A1
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, X0, sk_A0)),
6.37/6.58	    inference('sup-', [status(thm)], ['43', '53'])).
6.37/6.58	tff('55', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      ('const/sets/SUBSET'(sk_A, X0, sk_A0) | sk_A0 = sk_A1 | X0 != sk_A1),
6.37/6.58	    inference('simplify', [status(thm)], ['54'])).
6.37/6.58	tff('56', plain,
6.37/6.58	    ![X0 : sk_A > $o]: (X0 != sk_A1 | 'const/sets/SUBSET'(sk_A, X0, sk_A0)),
6.37/6.58	    inference('clc', [status(thm)], ['55', '42'])).
6.37/6.58	tff('57', plain,
6.37/6.58	    ![X0 : sk_A > $o, X1 : sk_A]:
6.37/6.58	      (~ $true
6.37/6.58	       | X0 != sk_A1
6.37/6.58	       | 'const/sets/IN'(sk_A, X1, sk_A0)
6.37/6.58	       | ~ 'const/sets/IN'(sk_A, X1, X0)),
6.37/6.58	    inference('sup-', [status(thm)], ['56', '26'])).
6.37/6.58	tff('58', plain,
6.37/6.58	    ![X0 : sk_A > $o, X1 : sk_A]:
6.37/6.58	      (~ 'const/sets/IN'(sk_A, X1, X0)
6.37/6.58	       | 'const/sets/IN'(sk_A, X1, sk_A0)
6.37/6.58	       | X0 != sk_A1),
6.37/6.58	    inference('simplify', [status(thm)], ['57'])).
6.37/6.58	tff('59', plain,
6.37/6.58	    ![X0 : sk_A > $o, X1 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | X1 != sk_A1
6.37/6.58	       | ~ 'const/sets/IN'(sk_A, sk_A21(sk_A, sk_A0, X0), X1)
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, X0, sk_A0)),
6.37/6.58	    inference('sup-', [status(thm)], ['58', '1'])).
6.37/6.58	tff('60', plain,
6.37/6.58	    ![X0 : sk_A > $o, X1 : sk_A > $o]:
6.37/6.58	      ('const/sets/SUBSET'(sk_A, X0, sk_A0)
6.37/6.58	       | ~ 'const/sets/IN'(sk_A, sk_A21(sk_A, sk_A0, X0), X1)
6.37/6.58	       | X1 != sk_A1),
6.37/6.58	    inference('simplify', [status(thm)], ['59'])).
6.37/6.58	tff('61', plain,
6.37/6.58	    (~ $true
6.37/6.58	     | 'const/sets/SUBSET'(sk_A, sk_A1, sk_A0)
6.37/6.58	     | sk_A0 = sk_A1
6.37/6.58	     | sk_A0 != sk_A1
6.37/6.58	     | 'const/sets/SUBSET'(sk_A, sk_A1, sk_A0)),
6.37/6.58	    inference('sup-', [status(thm)], ['45', '60'])).
6.37/6.58	tff('62', plain,
6.37/6.58	    (sk_A0 != sk_A1 | sk_A0 = sk_A1 | 'const/sets/SUBSET'(sk_A, sk_A1, sk_A0)),
6.37/6.58	    inference('simplify', [status(thm)], ['61'])).
6.37/6.58	tff('63', plain,
6.37/6.58	    (sk_A0('#k1') != sk_A1('#k1')
6.37/6.58	     | sk_A0 = sk_A1
6.37/6.58	     | 'const/sets/SUBSET'(sk_A, sk_A1, sk_A0)),
6.37/6.58	    inference('rw_lit', [status(thm)], ['62'])).
6.37/6.58	tff('64', plain, ('const/sets/SUBSET'(sk_A, sk_A1, sk_A0) | sk_A0 = sk_A1),
6.37/6.58	    inference('clc', [status(thm)], ['63', '19'])).
6.37/6.58	tff('65', plain, 'const/sets/SUBSET'(sk_A, sk_A1, sk_A0),
6.37/6.58	    inference('clc', [status(thm)], ['64', '43'])).
6.37/6.58	tff('66', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A1, X0)
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
6.37/6.58	    inference('sup-', [status(thm)], ['65', '51'])).
6.37/6.58	tff('67', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      (~ 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A1, X0)),
6.37/6.58	    inference('simplify', [status(thm)], ['66'])).
6.37/6.58	tff('68', plain,
6.37/6.58	    ![X0 : sk_A > $o, X1 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A1, X1)
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, X0, X1)),
6.37/6.58	    inference('sup-', [status(thm)], ['67', '51'])).
6.37/6.58	tff('69', plain,
6.37/6.58	    ![X0 : sk_A > $o, X1 : sk_A > $o]:
6.37/6.58	      (~ 'const/sets/SUBSET'(sk_A, X0, X1)
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A1, X1)
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
6.37/6.58	    inference('simplify', [status(thm)], ['68'])).
6.37/6.58	tff('70', plain,
6.37/6.58	    ![X0 : sk_A > $o, X1 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | X1 != X0
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, X1)
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A1, X0)),
6.37/6.58	    inference('sup-', [status(thm)], ['43', '69'])).
6.37/6.58	tff('71', plain,
6.37/6.58	    ![X0 : sk_A > $o, X1 : sk_A > $o]:
6.37/6.58	      ('const/sets/SUBSET'(sk_A, sk_A1, X0)
6.37/6.58	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, X1)
6.37/6.58	       | X1 != X0),
6.37/6.58	    inference('simplify', [status(thm)], ['70'])).
6.37/6.58	tff('72', plain,
6.37/6.58	    ![X0 : sk_A > $o]:
6.37/6.58	      (~ $true
6.37/6.58	       | sk_A0 = sk_A1
6.37/6.58	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, sk_A1, X0)),
6.37/6.59	    inference('sup-', [status(thm)], ['22', '51'])).
6.37/6.59	tff('73', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      (~ 'const/sets/SUBSET'(sk_A, sk_A1, X0)
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | sk_A0 = sk_A1),
6.37/6.59	    inference('simplify', [status(thm)], ['72'])).
6.37/6.59	tff('74', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      (~ $true
6.37/6.59	       | sk_A1 != X0
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
6.37/6.59	    inference('sup-', [status(thm)], ['43', '73'])).
6.37/6.59	tff('75', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      ('const/sets/SUBSET'(sk_A, sk_A0, X0) | sk_A0 = sk_A1 | sk_A1 != X0),
6.37/6.59	    inference('simplify', [status(thm)], ['74'])).
6.37/6.59	tff('76', plain,
6.37/6.59	    ![X0 : sk_A > $o]: (sk_A1 != X0 | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
6.37/6.59	    inference('clc', [status(thm)], ['75', '42'])).
6.37/6.59	tff('77', plain,
6.37/6.59	    ![X0 : sk_A > $o, X1 : sk_A > $o]:
6.37/6.59	      (~ $true
6.37/6.59	       | sk_A1 != X0
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, X1)
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, X0, X1)),
6.37/6.59	    inference('sup-', [status(thm)], ['76', '51'])).
6.37/6.59	tff('78', plain,
6.37/6.59	    ![X0 : sk_A > $o, X1 : sk_A > $o]:
6.37/6.59	      (~ 'const/sets/SUBSET'(sk_A, X0, X1)
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, X1)
6.37/6.59	       | sk_A1 != X0),
6.37/6.59	    inference('simplify', [status(thm)], ['77'])).
6.37/6.59	tff('79', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      (~ $true
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A1, X0)
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A1, X0)),
6.37/6.59	    inference('sup-', [status(thm)], ['45', '49'])).
6.37/6.59	tff('80', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      (~ 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A1, X0)),
6.37/6.59	    inference('simplify', [status(thm)], ['79'])).
6.37/6.59	tff('81', plain,
6.37/6.59	    ![X0 : sk_A > $o, X1 : sk_A > $o > $o]:
6.37/6.59	      (~ $true
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, X0) != X1
6.37/6.59	       | X1 != 'const/sets/SUBSET'(sk_A, sk_A1)
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
6.37/6.59	    inference('sup-', [status(thm)], ['11', '73'])).
6.37/6.59	tff('82', plain,
6.37/6.59	    ![X0 : sk_A > $o, X1 : sk_A > $o > $o]:
6.37/6.59	      ('const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | X1 != 'const/sets/SUBSET'(sk_A, sk_A1)
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, X0) != X1),
6.37/6.59	    inference('simplify', [status(thm)], ['81'])).
6.37/6.59	tff('83', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      ('const/sets/SUBSET'(sk_A, X0) != 'const/sets/SUBSET'(sk_A, sk_A1)
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
6.37/6.59	    inference('eq_res', [status(thm)], ['82'])).
6.37/6.59	tff('84', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      ('const/sets/SUBSET'(sk_A, X0, '#k25'(X0))
6.37/6.59	        != 'const/sets/SUBSET'(sk_A, sk_A1, '#k25'(X0))
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
6.37/6.59	    inference('rw_lit', [status(thm)], ['83'])).
6.37/6.59	tff('85', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      ('const/sets/SUBSET'(sk_A, X0, '#k25'(X0)) != $true
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, '#k25'(X0))
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | sk_A0 = sk_A1),
6.37/6.59	    inference('sup-', [status(thm)], ['80', '84'])).
6.37/6.59	tff('86', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      ('const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, '#k25'(X0))
6.37/6.59	       | sk_A0 = sk_A1
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, X0, '#k25'(X0)) != $true),
6.37/6.59	    inference('simplify', [status(thm)], ['85'])).
6.37/6.59	tff('87', plain,
6.37/6.59	    ($true != $true
6.37/6.59	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, '#k25'(sk_A1))
6.37/6.59	     | sk_A0 = sk_A1
6.37/6.59	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, '#k25'(sk_A1))
6.37/6.59	     | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)),
6.37/6.59	    inference('sup-', [status(thm)], ['67', '86'])).
6.37/6.59	tff('88', plain,
6.37/6.59	    ('const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.59	     | sk_A0 = sk_A1
6.37/6.59	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, '#k25'(sk_A1))),
6.37/6.59	    inference('simplify', [status(thm)], ['87'])).
6.37/6.59	tff('89', plain,
6.37/6.59	    (~ 'const/sets/SUBSET'(sk_A, sk_A0, '#k25'(sk_A1))
6.37/6.59	     | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)),
6.37/6.59	    inference('clc', [status(thm)], ['88', '43'])).
6.37/6.59	tff('90', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      (~ $true
6.37/6.59	       | sk_A1 != X0
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, X0, '#k25'(sk_A1))
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)),
6.37/6.59	    inference('sup-', [status(thm)], ['78', '89'])).
6.37/6.59	tff('91', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      ('const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, X0, '#k25'(sk_A1))
6.37/6.59	       | sk_A1 != X0),
6.37/6.59	    inference('simplify', [status(thm)], ['90'])).
6.37/6.59	tff('92', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      (~ $true
6.37/6.59	       | X0 != '#k25'(sk_A1)
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | sk_A1 != sk_A1
6.37/6.59	       | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)),
6.37/6.59	    inference('sup-', [status(thm)], ['71', '91'])).
6.37/6.59	tff('93', plain,
6.37/6.59	    ![X0 : sk_A > $o]:
6.37/6.59	      ('const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.59	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, X0)
6.37/6.59	       | X0 != '#k25'(sk_A1)),
6.37/6.59	    inference('simplify', [status(thm)], ['92'])).
6.37/6.59	tff('94', plain,
6.37/6.59	    (~ $true
6.37/6.59	     | sk_A0 = sk_A1
6.37/6.59	     | sk_A1 != '#k25'(sk_A1)
6.37/6.59	     | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)),
6.37/6.59	    inference('sup-', [status(thm)], ['22', '93'])).
6.37/6.59	tff('95', plain,
6.37/6.59	    ('const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.59	     | sk_A1 != '#k25'(sk_A1)
6.37/6.59	     | sk_A0 = sk_A1),
6.37/6.59	    inference('simplify', [status(thm)], ['94'])).
6.37/6.59	tff('96', plain,
6.37/6.59	    ('const/sets/SUBSET'(sk_A, sk_A0, sk_A1)
6.37/6.59	     | sk_A1('#k135') != '#k25'(sk_A1, '#k135')
6.37/6.59	     | sk_A0 = sk_A1),
6.37/6.59	    inference('rw_lit', [status(thm)], ['95'])).
6.37/6.59	tff('97', plain, (sk_A0 = sk_A1 | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1)),
6.37/6.59	    inference('clc', [status(thm)], ['96', '22'])).
6.37/6.59	tff('98', plain, 'const/sets/SUBSET'(sk_A, sk_A0, sk_A1),
6.37/6.59	    inference('clc', [status(thm)], ['97', '43'])).
6.37/6.59	tff('99', plain,
6.37/6.59	    (~ $true
6.37/6.59	     | sk_A0 = sk_A1
6.37/6.59	     | ~ $true
6.37/6.59	     | ~ 'const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, sk_A0), sk_A0)
6.37/6.59	     | sk_A0 = sk_A1),
6.37/6.59	    inference('demod', [status(thm)], ['36', '98'])).
6.37/6.59	tff('100', plain,
6.37/6.59	    (~ 'const/sets/IN'(sk_A, sk_A2(sk_A, sk_A1, sk_A0), sk_A0)
6.37/6.59	     | sk_A0 = sk_A1),
6.37/6.59	    inference('simplify', [status(thm)], ['99'])).
6.37/6.59	tff('101', plain, sk_A0 = sk_A1,
6.37/6.59	    inference('clc', [status(thm)], ['100', '32'])).
6.37/6.59	tff('102', plain, ![X1 : sk_A]: sk_A0(X1) = sk_A1(X1),
6.37/6.59	    inference('ho_complete_eq', [status(thm)], ['101'])).
6.37/6.59	tff('103', plain, sk_A0('#k1') != sk_A0('#k1'),
6.37/6.59	    inference('demod', [status(thm)], ['24', '102'])).
6.37/6.59	tff('104', plain, $false, inference('simplify', [status(thm)], ['103'])).
6.37/6.59	
6.37/6.59	% SZS output end Refutation
6.37/6.59	EOF
