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    : 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 $2 \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n073.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:34:08 CST 2018
58.43/58.63	% done 11251 iterations in 58.426s
58.43/58.63	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
58.43/58.63	% SZS output start Refutation
58.43/58.63	tff('thm/sets/IN_INTERS_', axiom,
58.43/58.63	  (![A:$tType,A0:(A > $o > $o),A1:A]:
58.43/58.63	     ('const/sets/IN'(A,A1,'const/sets/INTERS'(A,A0)) <=>
58.43/58.63	      (![A2:(A > $o)]:
58.43/58.63	         ('const/sets/IN'(A > $o,A2,A0) => 'const/sets/IN'(A,A1,A2)))))).
58.43/58.63	tff('0', plain,
58.43/58.63	    ![X6 : $tType, X8 : X6 > $o > $o, X10 : X6]:
58.43/58.63	      ('const/sets/IN'(X6, X10, 'const/sets/INTERS'(X6, X8))
58.43/58.63	       | 'const/sets/IN'((> $o, X6), sk_A2(X6, X10, X8), X8)),
58.43/58.63	    inference('cnf', [status(esa)], [thm/sets/IN_INTERS_])).
58.43/58.63	tff('thm/sets/SUBSET_', axiom,
58.43/58.63	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
58.43/58.63	     ('const/sets/SUBSET'(A,A0,A1) <=>
58.43/58.63	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
58.43/58.63	tff('1', plain,
58.43/58.63	    ![X11 : $tType, X13 : X11 > $o, X15 : X11 > $o]:
58.43/58.63	      ('const/sets/SUBSET'(X11, X13, X15)
58.43/58.63	       | 'const/sets/IN'(X11, sk_A21(X11, X15, X13), X13)),
58.43/58.63	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
58.43/58.63	tff('thm/sets/IN_', axiom,
58.43/58.63	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
58.43/58.63	tff('2', plain,
58.43/58.63	    ![X2 : $tType, X3 : X2 > $o, X5 : X2]:
58.43/58.63	      ('const/sets/IN'(X2, X5, X3) | ~ X3(X5)),
58.43/58.63	    inference('cnf', [status(esa)], [thm/sets/IN_])).
58.43/58.63	tff('3', plain,
58.43/58.63	    ![X6 : $tType, X7 : X6 > $o, X8 : X6 > $o > $o, X9 : X6]:
58.43/58.63	      (~ 'const/sets/IN'((> $o, X6), X7, X8)
58.43/58.63	       | 'const/sets/IN'(X6, X9, X7)
58.43/58.63	       | ~ 'const/sets/IN'(X6, X9, 'const/sets/INTERS'(X6, X8))),
58.43/58.63	    inference('cnf', [status(esa)], [thm/sets/IN_INTERS_])).
58.43/58.63	tff('4', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ X1(X2)
58.43/58.63	       | ~ 'const/sets/IN'(X0, X3, 'const/sets/INTERS'(X0, X1))
58.43/58.63	       | 'const/sets/IN'(X0, X3, X2)),
58.43/58.63	    inference('sup-', [status(thm)], ['2', '3'])).
58.43/58.63	tff('5', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0]:
58.43/58.63	      ('const/sets/IN'(X0, X3, X2)
58.43/58.63	       | ~ 'const/sets/IN'(X0, X3, 'const/sets/INTERS'(X0, X1))
58.43/58.63	       | ~ X1(X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['4'])).
58.43/58.63	tff('6', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1), X2)
58.43/58.63	       | ~ X1(X3)
58.43/58.63	       | 'const/sets/IN'(X0, sk_A21(X0, X2, 'const/sets/INTERS'(X0, X1)), X3)),
58.43/58.63	    inference('sup-', [status(thm)], ['1', '5'])).
58.43/58.63	tff('7', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'(X0, sk_A21(X0, X2, 'const/sets/INTERS'(X0, X1)), X3)
58.43/58.63	       | ~ X1(X3)
58.43/58.63	       | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1), X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['6'])).
58.43/58.63	tff('8', plain,
58.43/58.63	    ![X2 : $tType, X3 : X2 > $o, X4 : X2]:
58.43/58.63	      (X3(X4) | ~ 'const/sets/IN'(X2, X4, X3)),
58.43/58.63	    inference('cnf', [status(esa)], [thm/sets/IN_])).
58.43/58.63	tff('9', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X2), X3)
58.43/58.63	       | ~ X2(X1)
58.43/58.63	       | X1(sk_A21(X0, X3, 'const/sets/INTERS'(X0, X2)))),
58.43/58.63	    inference('sup-', [status(thm)], ['7', '8'])).
58.43/58.63	tff('10', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o, X3 : X0 > $o]:
58.43/58.63	      (X1(sk_A21(X0, X3, 'const/sets/INTERS'(X0, X2)))
58.43/58.63	       | ~ X2(X1)
58.43/58.63	       | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X2), X3)),
58.43/58.63	    inference('simplify', [status(thm)], ['9'])).
58.43/58.63	tff('11', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
58.43/58.63	      (~ $true | 'const/sets/SUBSET'(X0, X1, X2) | X1(sk_A21(X0, X2, X1))),
58.43/58.63	    inference('sup-', [status(thm)], ['1', '8'])).
58.43/58.63	tff('12', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
58.43/58.63	      (X1(sk_A21(X0, X2, X1)) | 'const/sets/SUBSET'(X0, X1, X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['11'])).
58.43/58.63	tff('13', plain,
58.43/58.63	    ![X11 : $tType, X13 : X11 > $o, X15 : X11 > $o]:
58.43/58.63	      ('const/sets/SUBSET'(X11, X13, X15)
58.43/58.63	       | ~ 'const/sets/IN'(X11, sk_A21(X11, X15, X13), X15)),
58.43/58.63	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
58.43/58.63	tff('14', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(X0, X1, X1)
58.43/58.63	       | 'const/sets/SUBSET'(X0, X1, X1)),
58.43/58.63	    inference('sup-', [status(thm)], ['1', '13'])).
58.43/58.63	tff('15', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
58.43/58.63	    inference('simplify', [status(thm)], ['14'])).
58.43/58.63	tff('16', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X2), X1)
58.43/58.63	       | ~ X2(X1)
58.43/58.63	       | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X2), X1)),
58.43/58.63	    inference('sup-', [status(thm)], ['7', '13'])).
58.43/58.63	tff('17', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
58.43/58.63	      (~ X2(X1) | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X2), X1)),
58.43/58.63	    inference('simplify', [status(thm)], ['16'])).
58.43/58.63	tff('18', plain,
58.43/58.63	    ![X11 : $tType, X12 : X11, X13 : X11 > $o, X14 : X11 > $o]:
58.43/58.63	      (~ 'const/sets/IN'(X11, X12, X13)
58.43/58.63	       | 'const/sets/IN'(X11, X12, X14)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X11, X13, X14)),
58.43/58.63	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
58.43/58.63	tff('19', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(X0, X1, X2)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
58.43/58.63	       | 'const/sets/IN'(X0, sk_A21(X0, X2, X1), X3)),
58.43/58.63	    inference('sup-', [status(thm)], ['1', '18'])).
58.43/58.63	tff('20', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'(X0, sk_A21(X0, X2, X1), X3)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
58.43/58.63	       | 'const/sets/SUBSET'(X0, X1, X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['19'])).
58.43/58.63	tff('21', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(X0, X2, X3)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
58.43/58.63	       | X1(sk_A21(X0, X3, X2))),
58.43/58.63	    inference('sup-', [status(thm)], ['20', '8'])).
58.43/58.63	tff('22', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
58.43/58.63	      (X1(sk_A21(X0, X3, X2))
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
58.43/58.63	       | 'const/sets/SUBSET'(X0, X2, X3)),
58.43/58.63	    inference('simplify', [status(thm)], ['21'])).
58.43/58.63	tff('23', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/IN'(X0, X2, 'const/sets/INTERS'(X0, X1))
58.43/58.63	       | X1(sk_A2(X0, X2, X1))),
58.43/58.63	    inference('sup-', [status(thm)], ['0', '8'])).
58.43/58.63	tff('24', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
58.43/58.63	      (X1(sk_A2(X0, X2, X1))
58.43/58.63	       | 'const/sets/IN'(X0, X2, 'const/sets/INTERS'(X0, X1))),
58.43/58.63	    inference('simplify', [status(thm)], ['23'])).
58.43/58.63	tff('25', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ X1(X2)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
58.43/58.63	       | 'const/sets/IN'(X0, X2, X3)),
58.43/58.63	    inference('sup-', [status(thm)], ['2', '18'])).
58.43/58.63	tff('26', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'(X0, X2, X3)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
58.43/58.63	       | ~ X1(X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['25'])).
58.43/58.63	tff('27', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/IN'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))
58.43/58.63	       | ~ X1(X3)
58.43/58.63	       | 'const/sets/IN'(X0, X3, sk_A2(X0, X2, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['24', '26'])).
58.43/58.63	tff('28', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0]:
58.43/58.63	      ('const/sets/IN'(X0, X3, sk_A2(X0, X2, 'const/sets/SUBSET'(X0, X1)))
58.43/58.63	       | ~ X1(X3)
58.43/58.63	       | 'const/sets/IN'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('simplify', [status(thm)], ['27'])).
58.43/58.63	tff('29', plain,
58.43/58.63	    ![X6 : $tType, X8 : X6 > $o > $o, X10 : X6]:
58.43/58.63	      ('const/sets/IN'(X6, X10, 'const/sets/INTERS'(X6, X8))
58.43/58.63	       | ~ 'const/sets/IN'(X6, X10, sk_A2(X6, X10, X8))),
58.43/58.63	    inference('cnf', [status(esa)], [thm/sets/IN_INTERS_])).
58.43/58.63	tff('30', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/IN'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))
58.43/58.63	       | ~ X1(X2)
58.43/58.63	       | 'const/sets/IN'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['28', '29'])).
58.43/58.63	tff('31', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
58.43/58.63	      (~ X1(X2)
58.43/58.63	       | 'const/sets/IN'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('simplify', [status(thm)], ['30'])).
58.43/58.63	tff('32', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ X1(
58.43/58.63	             sk_A21(X0, 
58.43/58.63	               'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)), X2))
58.43/58.63	       | 'const/sets/SUBSET'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['31', '13'])).
58.43/58.63	tff('33', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
58.43/58.63	      ('const/sets/SUBSET'(X0, X2, 
58.43/58.63	         'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))
58.43/58.63	       | ~ X1(
58.43/58.63	             sk_A21(X0, 
58.43/58.63	               'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)), X2))),
58.43/58.63	    inference('simplify', [status(thm)], ['32'])).
58.43/58.63	tff('34', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
58.43/58.63	       | 'const/sets/SUBSET'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['22', '33'])).
58.43/58.63	tff('35', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
58.43/58.63	      (~ 'const/sets/SUBSET'(X0, X2, X1)
58.43/58.63	       | 'const/sets/SUBSET'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('simplify', [status(thm)], ['34'])).
58.43/58.63	tff('36', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/IN'(X0, X1, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/IN'(X0, X1)))
58.43/58.63	       | 'const/sets/IN'(X0, X1, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/IN'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['24', '29'])).
58.43/58.63	tff('37', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0]:
58.43/58.63	      'const/sets/IN'(X0, X1, 
58.43/58.63	        'const/sets/INTERS'(X0, 'const/sets/IN'(X0, X1))),
58.43/58.63	    inference('simplify', [status(thm)], ['36'])).
58.43/58.63	tff('38', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, 
58.43/58.63	             'const/sets/INTERS'(X0, 'const/sets/IN'(X0, X1)), X2)
58.43/58.63	       | 'const/sets/IN'(X0, X1, X2)),
58.43/58.63	    inference('sup-', [status(thm)], ['37', '18'])).
58.43/58.63	tff('39', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'(X0, X1, X2)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, 
58.43/58.63	             'const/sets/INTERS'(X0, 'const/sets/IN'(X0, X1)), X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['38'])).
58.43/58.63	tff('40', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, 
58.43/58.63	             'const/sets/INTERS'(X0, 'const/sets/IN'(X0, X2)), X1)
58.43/58.63	       | 'const/sets/IN'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['35', '39'])).
58.43/58.63	tff('41', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
58.43/58.63	      ('const/sets/IN'(X0, X2, 
58.43/58.63	         'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, 
58.43/58.63	             'const/sets/INTERS'(X0, 'const/sets/IN'(X0, X2)), X1)),
58.43/58.63	    inference('simplify', [status(thm)], ['40'])).
58.43/58.63	tff('42', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'(X0, X2, X1)
58.43/58.63	       | 'const/sets/IN'(X0, X2, 
58.43/58.63	           'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['17', '41'])).
58.43/58.63	tff('43', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
58.43/58.63	      ('const/sets/IN'(X0, X2, 
58.43/58.63	         'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)))
58.43/58.63	       | ~ 'const/sets/IN'(X0, X2, X1)),
58.43/58.63	    inference('simplify', [status(thm)], ['42'])).
58.43/58.63	tff('44', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'(X0, X2, X1)
58.43/58.63	       | 'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1), X2)),
58.43/58.63	    inference('sup-', [status(thm)], ['43', '8'])).
58.43/58.63	tff('45', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
58.43/58.63	      ('const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1), X2)
58.43/58.63	       | ~ 'const/sets/IN'(X0, X2, X1)),
58.43/58.63	    inference('simplify', [status(thm)], ['44'])).
58.43/58.63	tff('46', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
58.43/58.63	      (~ $true | ~ X1(sk_A21(X0, X1, X2)) | 'const/sets/SUBSET'(X0, X2, X1)),
58.43/58.63	    inference('sup-', [status(thm)], ['2', '13'])).
58.43/58.63	tff('47', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
58.43/58.63	      ('const/sets/SUBSET'(X0, X2, X1) | ~ X1(sk_A21(X0, X1, X2))),
58.43/58.63	    inference('simplify', [status(thm)], ['46'])).
58.43/58.63	tff('48', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ X1(
58.43/58.63	             sk_A21((> $o, X0), 
58.43/58.63	               'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1)), X2))
58.43/58.63	       | 'const/sets/SUBSET'((> $o, X0), X2, 
58.43/58.63	           'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['17', '47'])).
58.43/58.63	tff('49', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o > $o]:
58.43/58.63	      ('const/sets/SUBSET'((> $o, X0), X2, 
58.43/58.63	         'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1)))
58.43/58.63	       | ~ X1(
58.43/58.63	             sk_A21((> $o, X0), 
58.43/58.63	               'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1)), X2))),
58.43/58.63	    inference('simplify', [status(thm)], ['48'])).
58.43/58.63	tff('50', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'((> $o, X0), X1, 
58.43/58.63	           'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1)))
58.43/58.63	       | 'const/sets/SUBSET'((> $o, X0), X1, 
58.43/58.63	           'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['12', '49'])).
58.43/58.63	tff('51', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o]:
58.43/58.63	      'const/sets/SUBSET'((> $o, X0), X1, 
58.43/58.63	        'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1))),
58.43/58.63	    inference('simplify', [status(thm)], ['50'])).
58.43/58.63	tff('52', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/INTERS'(X0, X1, X2)
58.43/58.63	       | ~ X1(X3)
58.43/58.63	       | 'const/sets/IN'(X0, X2, X3)),
58.43/58.63	    inference('sup-', [status(thm)], ['2', '5'])).
58.43/58.63	tff('53', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'(X0, X2, X3)
58.43/58.63	       | ~ X1(X3)
58.43/58.63	       | ~ 'const/sets/INTERS'(X0, X1, X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['52'])).
58.43/58.63	tff('54', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/INTERS'((> $o, X0), 
58.43/58.63	             'const/sets/SUBSET'((> $o, X0), X1), X2)
58.43/58.63	       | 'const/sets/IN'((> $o, X0), X2, 
58.43/58.63	           'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1)))),
58.43/58.63	    inference('sup-', [status(thm)], ['51', '53'])).
58.43/58.63	tff('55', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'((> $o, X0), X2, 
58.43/58.63	         'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1)))
58.43/58.63	       | ~ 'const/sets/INTERS'((> $o, X0), 
58.43/58.63	             'const/sets/SUBSET'((> $o, X0), X1), X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['54'])).
58.43/58.63	tff('56', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/INTERS'((> $o, X0), 
58.43/58.63	             'const/sets/SUBSET'((> $o, X0), X1), X2)
58.43/58.63	       | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1), X2)),
58.43/58.63	    inference('sup-', [status(thm)], ['55', '8'])).
58.43/58.63	tff('57', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o]:
58.43/58.63	      ('const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X1), X2)
58.43/58.63	       | ~ 'const/sets/INTERS'((> $o, X0), 
58.43/58.63	             'const/sets/SUBSET'((> $o, X0), X1), X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['56'])).
58.43/58.63	tff('58', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'((> $o, X0), X1, X2)
58.43/58.63	       | 'const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X2), X1)),
58.43/58.63	    inference('sup-', [status(thm)], ['45', '57'])).
58.43/58.63	tff('59', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
58.43/58.63	      ('const/sets/SUBSET'(X0, 'const/sets/INTERS'(X0, X2), X1)
58.43/58.63	       | ~ 'const/sets/IN'((> $o, X0), X1, X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['58'])).
58.43/58.63	tff('60', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ X1(X2)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, 
58.43/58.63	             'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)), X3)
58.43/58.63	       | 'const/sets/IN'(X0, X2, X3)),
58.43/58.63	    inference('sup-', [status(thm)], ['31', '18'])).
58.43/58.63	tff('61', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'(X0, X2, X3)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, 
58.43/58.63	             'const/sets/INTERS'(X0, 'const/sets/SUBSET'(X0, X1)), X3)
58.43/58.63	       | ~ X1(X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['60'])).
58.43/58.63	tff('62', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'((> $o, X0), X1, 'const/sets/SUBSET'(X0, X2))
58.43/58.63	       | ~ X2(X3)
58.43/58.63	       | 'const/sets/IN'(X0, X3, X1)),
58.43/58.63	    inference('sup-', [status(thm)], ['59', '61'])).
58.43/58.63	tff('63', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0]:
58.43/58.63	      ('const/sets/IN'(X0, X3, X1)
58.43/58.63	       | ~ X2(X3)
58.43/58.63	       | ~ 'const/sets/IN'((> $o, X0), X1, 'const/sets/SUBSET'(X0, X2))),
58.43/58.63	    inference('simplify', [status(thm)], ['62'])).
58.43/58.63	tff('64', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'((> $o, (> $o, X0)), X2, 
58.43/58.63	             'const/sets/SUBSET'((> $o, X0), 'const/sets/SUBSET'(X0, X1)))
58.43/58.63	       | 'const/sets/IN'((> $o, X0), X1, X2)),
58.43/58.63	    inference('sup-', [status(thm)], ['15', '63'])).
58.43/58.63	tff('65', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
58.43/58.63	      ('const/sets/IN'((> $o, X0), X1, X2)
58.43/58.63	       | ~ 'const/sets/IN'((> $o, (> $o, X0)), X2, 
58.43/58.63	             'const/sets/SUBSET'((> $o, X0), 'const/sets/SUBSET'(X0, X1)))),
58.43/58.63	    inference('simplify', [status(thm)], ['64'])).
58.43/58.63	tff('66', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/SUBSET'((> $o, X0), 'const/sets/SUBSET'(X0, X1), X2)
58.43/58.63	       | 'const/sets/IN'((> $o, X0), X1, X2)),
58.43/58.63	    inference('sup-', [status(thm)], ['2', '65'])).
58.43/58.63	tff('67', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
58.43/58.63	      ('const/sets/IN'((> $o, X0), X1, X2)
58.43/58.63	       | ~ 'const/sets/SUBSET'((> $o, X0), 'const/sets/SUBSET'(X0, X1), X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['66'])).
58.43/58.63	tff('68', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o]:
58.43/58.63	      (~ $true | 'const/sets/IN'((> $o, X0), X1, 'const/sets/SUBSET'(X0, X1))),
58.43/58.63	    inference('sup-', [status(thm)], ['15', '67'])).
58.43/58.63	tff('69', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o]:
58.43/58.63	      'const/sets/IN'((> $o, X0), X1, 'const/sets/SUBSET'(X0, X1)),
58.43/58.63	    inference('simplify', [status(thm)], ['68'])).
58.43/58.63	tff('thm/sets/SUBSET_INTERS_', conjecture,
58.43/58.63	  (![A:$tType,A0:(A > $o),A1:(A > $o > $o)]:
58.43/58.63	     ('const/sets/SUBSET'(A,A0,'const/sets/INTERS'(A,A1)) <=>
58.43/58.63	      (![A2:(A > $o)]:
58.43/58.63	         ('const/sets/IN'(A > $o,A2,A1) => 'const/sets/SUBSET'(A,A0,A2)))))).
58.43/58.63	tff(zf_stmt_0, negated_conjecture,
58.43/58.63	  (~
58.43/58.63	    (![A:$tType,A0:(A > $o),A1:(A > $o > $o)]:
58.43/58.63	       ('const/sets/SUBSET'(A,A0,'const/sets/INTERS'(A,A1)) <=>
58.43/58.63	        (![A2:(A > $o)]:
58.43/58.63	           ('const/sets/IN'(A > $o,A2,A1) => 'const/sets/SUBSET'(A,A0,A2))))))).
58.43/58.63	tff('70', plain,
58.43/58.63	    ![X16 : sk_A > $o]:
58.43/58.63	      (~ 'const/sets/IN'((> $o, sk_A), X16, sk_A1)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X16)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
58.43/58.63	tff('71', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ sk_A1(X0)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
58.43/58.63	    inference('sup-', [status(thm)], ['2', '70'])).
58.43/58.63	tff('72', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      ('const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	       | ~ sk_A1(X0)),
58.43/58.63	    inference('simplify', [status(thm)], ['71'])).
58.43/58.63	tff('73', plain,
58.43/58.63	    ('const/sets/IN'((> $o, sk_A), sk_A22, sk_A1)
58.43/58.63	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
58.43/58.63	tff('74', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ sk_A1(X0)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | 'const/sets/IN'((> $o, sk_A), sk_A22, sk_A1)),
58.43/58.63	    inference('sup-', [status(thm)], ['72', '73'])).
58.43/58.63	tff('75', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      ('const/sets/IN'((> $o, sk_A), sk_A22, sk_A1)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | ~ sk_A1(X0)),
58.43/58.63	    inference('simplify', [status(thm)], ['74'])).
58.43/58.63	tff('76', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ sk_A1(X0)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | sk_A1(sk_A22)),
58.43/58.63	    inference('sup-', [status(thm)], ['75', '8'])).
58.43/58.63	tff('77', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (sk_A1(sk_A22) | 'const/sets/SUBSET'(sk_A, sk_A0, X0) | ~ sk_A1(X0)),
58.43/58.63	    inference('simplify', [status(thm)], ['76'])).
58.43/58.63	tff('78', plain,
58.43/58.63	    ![X0 : sk_A > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ sk_A1(sk_A21((> $o, sk_A), 'const/sets/SUBSET'(sk_A, sk_A0), X0))
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | 'const/sets/SUBSET'((> $o, sk_A), X0, 
58.43/58.63	           'const/sets/SUBSET'(sk_A, sk_A0))),
58.43/58.63	    inference('sup-', [status(thm)], ['77', '47'])).
58.43/58.63	tff('79', plain,
58.43/58.63	    ![X0 : sk_A > $o > $o]:
58.43/58.63	      ('const/sets/SUBSET'((> $o, sk_A), X0, 
58.43/58.63	         'const/sets/SUBSET'(sk_A, sk_A0))
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | ~ sk_A1(sk_A21((> $o, sk_A), 'const/sets/SUBSET'(sk_A, sk_A0), X0))),
58.43/58.63	    inference('simplify', [status(thm)], ['78'])).
58.43/58.63	tff('80', plain,
58.43/58.63	    ![X0 : sk_A > $o > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'((> $o, sk_A), 
58.43/58.63	           'const/sets/INTERS'((> $o, sk_A), X0), 
58.43/58.63	           'const/sets/SUBSET'(sk_A, sk_A0))
58.43/58.63	       | ~ X0(sk_A1)
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | 'const/sets/SUBSET'((> $o, sk_A), 
58.43/58.63	           'const/sets/INTERS'((> $o, sk_A), X0), 
58.43/58.63	           'const/sets/SUBSET'(sk_A, sk_A0))),
58.43/58.63	    inference('sup-', [status(thm)], ['10', '79'])).
58.43/58.63	tff('81', plain,
58.43/58.63	    ![X0 : sk_A > $o > $o > $o]:
58.43/58.63	      (sk_A1(sk_A22)
58.43/58.63	       | ~ X0(sk_A1)
58.43/58.63	       | 'const/sets/SUBSET'((> $o, sk_A), 
58.43/58.63	           'const/sets/INTERS'((> $o, sk_A), X0), 
58.43/58.63	           'const/sets/SUBSET'(sk_A, sk_A0))),
58.43/58.63	    inference('simplify', [status(thm)], ['80'])).
58.43/58.63	tff('82', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A1)
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | 'const/sets/IN'((> $o, sk_A), X0, 'const/sets/SUBSET'(sk_A, sk_A0))),
58.43/58.63	    inference('sup-', [status(thm)], ['81', '39'])).
58.43/58.63	tff('83', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      ('const/sets/IN'((> $o, sk_A), X0, 'const/sets/SUBSET'(sk_A, sk_A0))
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A1)),
58.43/58.63	    inference('simplify', [status(thm)], ['82'])).
58.43/58.63	tff('84', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A1)
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
58.43/58.63	    inference('sup-', [status(thm)], ['83', '8'])).
58.43/58.63	tff('85', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      ('const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A1)),
58.43/58.63	    inference('simplify', [status(thm)], ['84'])).
58.43/58.63	tff('86', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A2(sk_A, X0, sk_A1))),
58.43/58.63	    inference('sup-', [status(thm)], ['0', '85'])).
58.43/58.63	tff('87', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      ('const/sets/SUBSET'(sk_A, sk_A0, sk_A2(sk_A, X0, sk_A1))
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('simplify', [status(thm)], ['86'])).
58.43/58.63	tff('88', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(X0, X2, X3)
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X2, sk_A2(X0, sk_A21(X0, X3, X2), X1))
58.43/58.63	       | 'const/sets/IN'(X0, sk_A21(X0, X3, X2), 'const/sets/INTERS'(X0, X1))),
58.43/58.63	    inference('sup-', [status(thm)], ['20', '29'])).
58.43/58.63	tff('89', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'(X0, sk_A21(X0, X3, X2), 'const/sets/INTERS'(X0, X1))
58.43/58.63	       | ~ 'const/sets/SUBSET'(X0, X2, sk_A2(X0, sk_A21(X0, X3, X2), X1))
58.43/58.63	       | 'const/sets/SUBSET'(X0, X2, X3)),
58.43/58.63	    inference('simplify', [status(thm)], ['88'])).
58.43/58.63	tff('90', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/IN'(sk_A, sk_A21(sk_A, X0, sk_A0), 
58.43/58.63	           'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | 'const/sets/IN'(sk_A, sk_A21(sk_A, X0, sk_A0), 
58.43/58.63	           'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('sup-', [status(thm)], ['87', '89'])).
58.43/58.63	tff('91', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      ('const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | sk_A1(sk_A22)
58.43/58.63	       | 'const/sets/IN'(sk_A, sk_A21(sk_A, X0, sk_A0), 
58.43/58.63	           'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('simplify', [status(thm)], ['90'])).
58.43/58.63	tff('92', plain,
58.43/58.63	    (~ $true
58.43/58.63	     | sk_A1(sk_A22)
58.43/58.63	     | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	     | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('sup-', [status(thm)], ['91', '13'])).
58.43/58.63	tff('93', plain,
58.43/58.63	    ('const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	     | sk_A1(sk_A22)),
58.43/58.63	    inference('simplify', [status(thm)], ['92'])).
58.43/58.63	tff('94', plain,
58.43/58.63	    (~ $true | sk_A1(sk_A22) | 'const/sets/IN'((> $o, sk_A), sk_A22, sk_A1)),
58.43/58.63	    inference('sup-', [status(thm)], ['93', '73'])).
58.43/58.63	tff('95', plain,
58.43/58.63	    ('const/sets/IN'((> $o, sk_A), sk_A22, sk_A1) | sk_A1(sk_A22)),
58.43/58.63	    inference('simplify', [status(thm)], ['94'])).
58.43/58.63	tff('96', plain, sk_A1(sk_A22), inference('clc', [status(thm)], ['95', '8'])).
58.43/58.63	tff('97', plain,
58.43/58.63	    ![X0 : sk_A > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'((> $o, (> $o, sk_A)), X0, 
58.43/58.63	             'const/sets/SUBSET'((> $o, sk_A), sk_A1))
58.43/58.63	       | 'const/sets/IN'((> $o, sk_A), sk_A22, X0)),
58.43/58.63	    inference('sup-', [status(thm)], ['96', '63'])).
58.43/58.63	tff('98', plain,
58.43/58.63	    ![X0 : sk_A > $o > $o]:
58.43/58.63	      ('const/sets/IN'((> $o, sk_A), sk_A22, X0)
58.43/58.63	       | ~ 'const/sets/IN'((> $o, (> $o, sk_A)), X0, 
58.43/58.63	             'const/sets/SUBSET'((> $o, sk_A), sk_A1))),
58.43/58.63	    inference('simplify', [status(thm)], ['97'])).
58.43/58.63	tff('99', plain, (~ $true | 'const/sets/IN'((> $o, sk_A), sk_A22, sk_A1)),
58.43/58.63	    inference('sup-', [status(thm)], ['69', '98'])).
58.43/58.63	tff('100', plain, 'const/sets/IN'((> $o, sk_A), sk_A22, sk_A1),
58.43/58.63	    inference('simplify', [status(thm)], ['99'])).
58.43/58.63	tff('101', plain,
58.43/58.63	    (~ $true
58.43/58.63	     | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	     | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)),
58.43/58.63	    inference('sup-', [status(thm)], ['100', '70'])).
58.43/58.63	tff('102', plain,
58.43/58.63	    ('const/sets/SUBSET'(sk_A, sk_A0, sk_A22)
58.43/58.63	     | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('simplify', [status(thm)], ['101'])).
58.43/58.63	tff('103', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)
58.43/58.63	       | ~ sk_A0(X0)
58.43/58.63	       | 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('sup-', [status(thm)], ['102', '26'])).
58.43/58.63	tff('104', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      ('const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	       | ~ sk_A0(X0)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)),
58.43/58.63	    inference('simplify', [status(thm)], ['103'])).
58.43/58.63	tff('105', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o > $o, X3 : X0]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'((> $o, X0), X1, X2)
58.43/58.63	       | ~ 'const/sets/IN'(X0, X3, 'const/sets/INTERS'(X0, X1))
58.43/58.63	       | 'const/sets/IN'(X0, X3, sk_A21((> $o, X0), X2, X1))),
58.43/58.63	    inference('sup-', [status(thm)], ['1', '3'])).
58.43/58.63	tff('106', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o > $o, X3 : X0]:
58.43/58.63	      ('const/sets/IN'(X0, X3, sk_A21((> $o, X0), X2, X1))
58.43/58.63	       | ~ 'const/sets/IN'(X0, X3, 'const/sets/INTERS'(X0, X1))
58.43/58.63	       | 'const/sets/SUBSET'((> $o, X0), X1, X2)),
58.43/58.63	    inference('simplify', [status(thm)], ['105'])).
58.43/58.63	tff('107', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0, X2 : X0 > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'((> $o, X0), X2, 'const/sets/IN'(X0, X1))
58.43/58.63	       | ~ 'const/sets/IN'(X0, X1, 'const/sets/INTERS'(X0, X2))
58.43/58.63	       | 'const/sets/SUBSET'((> $o, X0), X2, 'const/sets/IN'(X0, X1))),
58.43/58.63	    inference('sup-', [status(thm)], ['106', '47'])).
58.43/58.63	tff('108', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0, X2 : X0 > $o > $o]:
58.43/58.63	      (~ 'const/sets/IN'(X0, X1, 'const/sets/INTERS'(X0, X2))
58.43/58.63	       | 'const/sets/SUBSET'((> $o, X0), X2, 'const/sets/IN'(X0, X1))),
58.43/58.63	    inference('simplify', [status(thm)], ['107'])).
58.43/58.63	tff('109', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0, X2 : X0 > $o > $o, X3 : X0 > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'(X0, X1, 'const/sets/INTERS'(X0, X2))
58.43/58.63	       | ~ X2(X3)
58.43/58.63	       | 'const/sets/IN'((> $o, X0), X3, 'const/sets/IN'(X0, X1))),
58.43/58.63	    inference('sup-', [status(thm)], ['108', '26'])).
58.43/58.63	tff('110', plain,
58.43/58.63	    ![X0 : $tType, X1 : X0, X2 : X0 > $o > $o, X3 : X0 > $o]:
58.43/58.63	      ('const/sets/IN'((> $o, X0), X3, 'const/sets/IN'(X0, X1))
58.43/58.63	       | ~ X2(X3)
58.43/58.63	       | ~ 'const/sets/IN'(X0, X1, 'const/sets/INTERS'(X0, X2))),
58.43/58.63	    inference('simplify', [status(thm)], ['109'])).
58.43/58.63	tff('111', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	       | 'const/sets/IN'((> $o, sk_A), sk_A22, 'const/sets/IN'(sk_A, X0))),
58.43/58.63	    inference('sup-', [status(thm)], ['96', '110'])).
58.43/58.63	tff('112', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      ('const/sets/IN'((> $o, sk_A), sk_A22, 'const/sets/IN'(sk_A, X0))
58.43/58.63	       | ~ 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('simplify', [status(thm)], ['111'])).
58.43/58.63	tff('113', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.63	       | 'const/sets/IN'(sk_A, X0, sk_A22)),
58.43/58.63	    inference('sup-', [status(thm)], ['112', '8'])).
58.43/58.63	tff('114', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      ('const/sets/IN'(sk_A, X0, sk_A22)
58.43/58.63	       | ~ 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('simplify', [status(thm)], ['113'])).
58.43/58.63	tff('115', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      (~ $true
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)
58.43/58.63	       | ~ sk_A0(X0)
58.43/58.63	       | 'const/sets/IN'(sk_A, X0, sk_A22)),
58.43/58.63	    inference('sup-', [status(thm)], ['104', '114'])).
58.43/58.63	tff('116', plain,
58.43/58.63	    ![X0 : sk_A]:
58.43/58.63	      ('const/sets/IN'(sk_A, X0, sk_A22)
58.43/58.63	       | ~ sk_A0(X0)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)),
58.43/58.63	    inference('simplify', [status(thm)], ['115'])).
58.43/58.63	tff('117', plain,
58.43/58.63	    ![X0 : sk_A]: (~ sk_A0(X0) | 'const/sets/IN'(sk_A, X0, sk_A22)),
58.43/58.63	    inference('clc', [status(thm)], ['116', '26'])).
58.43/58.63	tff('118', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ sk_A0(sk_A21(sk_A, sk_A22, X0))
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, X0, sk_A22)),
58.43/58.63	    inference('sup-', [status(thm)], ['117', '13'])).
58.43/58.63	tff('119', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      ('const/sets/SUBSET'(sk_A, X0, sk_A22)
58.43/58.63	       | ~ sk_A0(sk_A21(sk_A, sk_A22, X0))),
58.43/58.63	    inference('simplify', [status(thm)], ['118'])).
58.43/58.63	tff('120', plain,
58.43/58.63	    (~ $true
58.43/58.63	     | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)
58.43/58.63	     | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)),
58.43/58.63	    inference('sup-', [status(thm)], ['12', '119'])).
58.43/58.63	tff('121', plain, 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22),
58.43/58.63	    inference('simplify', [status(thm)], ['120'])).
58.43/58.63	tff('122', plain,
58.43/58.63	    (~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)
58.43/58.63	     | ~ 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.63	    inference('cnf', [status(esa)], [zf_stmt_0])).
58.43/58.63	tff('123', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ sk_A1(X0)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)),
58.43/58.63	    inference('sup-', [status(thm)], ['72', '122'])).
58.43/58.63	tff('124', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)
58.43/58.63	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.63	       | ~ sk_A1(X0)),
58.43/58.63	    inference('simplify', [status(thm)], ['123'])).
58.43/58.63	tff('125', plain,
58.43/58.63	    ![X0 : sk_A > $o]:
58.43/58.63	      (~ $true | ~ sk_A1(X0) | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
58.43/58.63	    inference('sup-', [status(thm)], ['121', '124'])).
58.43/58.63	tff('126', plain,
58.43/58.63	    ![X0 : sk_A > $o]: ('const/sets/SUBSET'(sk_A, sk_A0, X0) | ~ sk_A1(X0)),
58.43/58.63	    inference('simplify', [status(thm)], ['125'])).
58.43/58.63	tff('127', plain,
58.43/58.63	    ![X0 : sk_A > $o > $o]:
58.43/58.63	      (~ $true
58.43/58.63	       | ~ sk_A1(sk_A21((> $o, sk_A), 'const/sets/SUBSET'(sk_A, sk_A0), X0))
58.43/58.63	       | 'const/sets/SUBSET'((> $o, sk_A), X0, 
58.43/58.63	           'const/sets/SUBSET'(sk_A, sk_A0))),
58.43/58.64	    inference('sup-', [status(thm)], ['126', '47'])).
58.43/58.64	tff('128', plain,
58.43/58.64	    ![X0 : sk_A > $o > $o]:
58.43/58.64	      ('const/sets/SUBSET'((> $o, sk_A), X0, 
58.43/58.64	         'const/sets/SUBSET'(sk_A, sk_A0))
58.43/58.64	       | ~ sk_A1(sk_A21((> $o, sk_A), 'const/sets/SUBSET'(sk_A, sk_A0), X0))),
58.43/58.64	    inference('simplify', [status(thm)], ['127'])).
58.43/58.64	tff('129', plain,
58.43/58.64	    ![X0 : sk_A > $o > $o > $o]:
58.43/58.64	      (~ $true
58.43/58.64	       | 'const/sets/SUBSET'((> $o, sk_A), 
58.43/58.64	           'const/sets/INTERS'((> $o, sk_A), X0), 
58.43/58.64	           'const/sets/SUBSET'(sk_A, sk_A0))
58.43/58.64	       | ~ X0(sk_A1)
58.43/58.64	       | 'const/sets/SUBSET'((> $o, sk_A), 
58.43/58.64	           'const/sets/INTERS'((> $o, sk_A), X0), 
58.43/58.64	           'const/sets/SUBSET'(sk_A, sk_A0))),
58.43/58.64	    inference('sup-', [status(thm)], ['10', '128'])).
58.43/58.64	tff('130', plain,
58.43/58.64	    ![X0 : sk_A > $o > $o > $o]:
58.43/58.64	      (~ X0(sk_A1)
58.43/58.64	       | 'const/sets/SUBSET'((> $o, sk_A), 
58.43/58.64	           'const/sets/INTERS'((> $o, sk_A), X0), 
58.43/58.64	           'const/sets/SUBSET'(sk_A, sk_A0))),
58.43/58.64	    inference('simplify', [status(thm)], ['129'])).
58.43/58.64	tff('131', plain,
58.43/58.64	    ![X0 : sk_A > $o]:
58.43/58.64	      (~ $true
58.43/58.64	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A1)
58.43/58.64	       | 'const/sets/IN'((> $o, sk_A), X0, 'const/sets/SUBSET'(sk_A, sk_A0))),
58.43/58.64	    inference('sup-', [status(thm)], ['130', '39'])).
58.43/58.64	tff('132', plain,
58.43/58.64	    ![X0 : sk_A > $o]:
58.43/58.64	      ('const/sets/IN'((> $o, sk_A), X0, 'const/sets/SUBSET'(sk_A, sk_A0))
58.43/58.64	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A1)),
58.43/58.64	    inference('simplify', [status(thm)], ['131'])).
58.43/58.64	tff('133', plain,
58.43/58.64	    ![X0 : sk_A > $o]:
58.43/58.64	      (~ $true
58.43/58.64	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A1)
58.43/58.64	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)),
58.43/58.64	    inference('sup-', [status(thm)], ['132', '8'])).
58.43/58.64	tff('134', plain,
58.43/58.64	    ![X0 : sk_A > $o]:
58.43/58.64	      ('const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.64	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A1)),
58.43/58.64	    inference('simplify', [status(thm)], ['133'])).
58.43/58.64	tff('135', plain,
58.43/58.64	    ![X0 : sk_A]:
58.43/58.64	      (~ $true
58.43/58.64	       | 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.64	       | 'const/sets/SUBSET'(sk_A, sk_A0, sk_A2(sk_A, X0, sk_A1))),
58.43/58.64	    inference('sup-', [status(thm)], ['0', '134'])).
58.43/58.64	tff('136', plain,
58.43/58.64	    ![X0 : sk_A]:
58.43/58.64	      ('const/sets/SUBSET'(sk_A, sk_A0, sk_A2(sk_A, X0, sk_A1))
58.43/58.64	       | 'const/sets/IN'(sk_A, X0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.64	    inference('simplify', [status(thm)], ['135'])).
58.43/58.64	tff('137', plain,
58.43/58.64	    ![X0 : sk_A > $o]:
58.43/58.64	      (~ $true
58.43/58.64	       | 'const/sets/IN'(sk_A, sk_A21(sk_A, X0, sk_A0), 
58.43/58.64	           'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.64	       | 'const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.64	       | 'const/sets/IN'(sk_A, sk_A21(sk_A, X0, sk_A0), 
58.43/58.64	           'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.64	    inference('sup-', [status(thm)], ['136', '89'])).
58.43/58.64	tff('138', plain,
58.43/58.64	    ![X0 : sk_A > $o]:
58.43/58.64	      ('const/sets/SUBSET'(sk_A, sk_A0, X0)
58.43/58.64	       | 'const/sets/IN'(sk_A, sk_A21(sk_A, X0, sk_A0), 
58.43/58.64	           'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.64	    inference('simplify', [status(thm)], ['137'])).
58.43/58.64	tff('139', plain,
58.43/58.64	    (~ $true
58.43/58.64	     | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))
58.43/58.64	     | 'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1))),
58.43/58.64	    inference('sup-', [status(thm)], ['138', '13'])).
58.43/58.64	tff('140', plain,
58.43/58.64	    'const/sets/SUBSET'(sk_A, sk_A0, 'const/sets/INTERS'(sk_A, sk_A1)),
58.43/58.64	    inference('simplify', [status(thm)], ['139'])).
58.43/58.64	tff('141', plain, (~ $true | ~ 'const/sets/SUBSET'(sk_A, sk_A0, sk_A22)),
58.43/58.64	    inference('sup-', [status(thm)], ['140', '122'])).
58.43/58.64	tff('142', plain, (~ $true | ~ $true),
58.43/58.64	    inference('demod', [status(thm)], ['141', '121'])).
58.43/58.64	tff('143', plain, $false, inference('simplify', [status(thm)], ['142'])).
58.43/58.64	
58.43/58.64	% SZS output end Refutation
58.43/58.64	EOF
