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
0.00/0.20	% Computer   : n126.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:41:24 CST 2018
2.54/2.71	% done 1882 iterations in 2.503s
2.54/2.71	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
2.54/2.71	% SZS output start Refutation
2.54/2.71	tff('thm/sets/REAL_SUP_LE_SUBSET_', conjecture,
2.54/2.71	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
2.54/2.71	     (((?[A1:'type/realax/real']:
2.54/2.71	          (![A2:'type/realax/real']:
2.54/2.71	             ('const/sets/IN'('type/realax/real',A2,A0) =>
2.54/2.71	              'const/realax/real_le'(A2,A1)))) & 
2.54/2.71	       'const/sets/SUBSET'('type/realax/real',A,A0) & 
2.54/2.71	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
2.54/2.71	      'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0))))).
2.54/2.71	tff(zf_stmt_0, negated_conjecture,
2.54/2.71	  (~
2.54/2.71	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
2.54/2.71	       (((?[A1:'type/realax/real']:
2.54/2.71	            (![A2:'type/realax/real']:
2.54/2.71	               ('const/sets/IN'('type/realax/real',A2,A0) =>
2.54/2.71	                'const/realax/real_le'(A2,A1)))) & 
2.54/2.71	         'const/sets/SUBSET'('type/realax/real',A,A0) & 
2.54/2.71	         (A != 'const/sets/EMPTY'('type/realax/real'))) =>
2.54/2.71	        'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0)))))).
2.54/2.71	tff('0', plain, 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A0),
2.54/2.71	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.54/2.71	tff('thm/sets/EXTENSION_', axiom,
2.54/2.71	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
2.54/2.71	     ((A0 = A1) <=>
2.54/2.71	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
2.54/2.71	tff('1', plain,
2.54/2.71	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
2.54/2.71	      (X13 = X15
2.54/2.71	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
2.54/2.71	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
2.54/2.71	tff('thm/sets/SUBSET_', axiom,
2.54/2.71	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
2.54/2.71	     ('const/sets/SUBSET'(A,A0,A1) <=>
2.54/2.71	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
2.54/2.71	tff('2', plain,
2.54/2.71	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
2.54/2.71	      (~ 'const/sets/IN'(X16, X17, X18)
2.54/2.71	       | 'const/sets/IN'(X16, X17, X19)
2.54/2.71	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
2.54/2.71	tff('3', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)
2.54/2.71	       | X2 = X1
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X3)),
2.54/2.71	    inference('sup-', [status(thm)], ['1', '2'])).
2.54/2.71	tff('4', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
2.54/2.71	      ('const/sets/IN'(X0, sk_A2(X0, X1, X2), X3)
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
2.54/2.71	       | X2 = X1
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)),
2.54/2.71	    inference('simplify', [status(thm)], ['3'])).
2.54/2.71	tff('thm/sets/NOT_IN_EMPTY_', axiom,
2.54/2.71	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
2.54/2.71	tff('5', plain,
2.54/2.71	    ![X8 : $tType, X9 : X8]:
2.54/2.71	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
2.54/2.71	tff('6', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X2, X1), X1)
2.54/2.71	       | X1 = X2
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))),
2.54/2.71	    inference('sup-', [status(thm)], ['4', '5'])).
2.54/2.71	tff('7', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
2.54/2.71	      (~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
2.54/2.71	       | X1 = X2
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X2, X1), X1)),
2.54/2.71	    inference('simplify', [status(thm)], ['6'])).
2.54/2.71	tff('8', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X2, X1), X2)
2.54/2.71	       | X1 = X2
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X2, X1), X3)),
2.54/2.71	    inference('sup-', [status(thm)], ['1', '2'])).
2.54/2.71	tff('9', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
2.54/2.71	      ('const/sets/IN'(X0, sk_A2(X0, X2, X1), X3)
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
2.54/2.71	       | X1 = X2
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X2, X1), X2)),
2.54/2.71	    inference('simplify', [status(thm)], ['8'])).
2.54/2.71	tff('10', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X1)
2.54/2.71	       | X2 = X1
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X2, X1)),
2.54/2.71	    inference('eq_fact', [status(thm)], ['9'])).
2.54/2.71	tff('11', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
2.54/2.71	      (~ 'const/sets/SUBSET'(X0, X2, X1)
2.54/2.71	       | X2 = X1
2.54/2.71	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X1)),
2.54/2.71	    inference('simplify', [status(thm)], ['10'])).
2.54/2.71	tff('12', plain,
2.54/2.71	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
2.54/2.71	      (X13 = X15
2.54/2.71	       | ~ 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
2.54/2.71	       | ~ 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
2.54/2.71	tff('13', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | X2 = X1
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
2.54/2.71	       | ~ 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)
2.54/2.71	       | X2 = X1),
2.54/2.71	    inference('sup-', [status(thm)], ['11', '12'])).
2.54/2.71	tff('14', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
2.54/2.71	      (~ 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
2.54/2.71	       | X2 = X1),
2.54/2.71	    inference('simplify', [status(thm)], ['13'])).
2.54/2.71	tff('15', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | X1 = X2
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
2.54/2.71	       | X1 = X2
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X1, X2)),
2.54/2.71	    inference('sup-', [status(thm)], ['7', '14'])).
2.54/2.71	tff('16', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
2.54/2.71	      (~ 'const/sets/SUBSET'(X0, X1, X2)
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
2.54/2.71	       | X1 = X2),
2.54/2.71	    inference('simplify', [status(thm)], ['15'])).
2.54/2.71	tff('17', plain,
2.54/2.71	    (~ $true
2.54/2.71	     | sk_A = sk_A0
2.54/2.71	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
2.54/2.71	           'const/sets/EMPTY'('type/realax/real'))),
2.54/2.71	    inference('sup-', [status(thm)], ['0', '16'])).
2.54/2.71	tff('18', plain,
2.54/2.71	    (~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
2.54/2.71	         'const/sets/EMPTY'('type/realax/real'))
2.54/2.71	     | sk_A = sk_A0),
2.54/2.71	    inference('simplify', [status(thm)], ['17'])).
2.54/2.71	tff('thm/sets/SUP_', axiom,
2.54/2.71	  (![A:('type/realax/real' > $o)]:
2.54/2.71	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
2.54/2.71	       (?[A0:'type/realax/real']:
2.54/2.71	          (![A1:'type/realax/real']:
2.54/2.71	             ('const/sets/IN'('type/realax/real',A1,A) =>
2.54/2.71	              'const/realax/real_le'(A1,A0))))) =>
2.54/2.71	      ((![A0:'type/realax/real']:
2.54/2.71	          ('const/sets/IN'('type/realax/real',A0,A) =>
2.54/2.71	           'const/realax/real_le'(A0,'const/sets/sup'(A)))) & 
2.54/2.71	       (![A0:'type/realax/real']:
2.54/2.71	          ((![A1:'type/realax/real']:
2.54/2.71	              ('const/sets/IN'('type/realax/real',A1,A) =>
2.54/2.71	               'const/realax/real_le'(A1,A0))) =>
2.54/2.71	           'const/realax/real_le'('const/sets/sup'(A),A0))))))).
2.54/2.71	tff(zf_stmt_1, axiom,
2.54/2.71	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
2.54/2.71	   zip_tseitin0(A1,A0,A))).
2.54/2.71	tff('19', plain,
2.54/2.71	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
2.54/2.71	      X23 : 'type/realax/real' > $o]:
2.54/2.71	      (zip_tseitin0(X21, X22, X23)
2.54/2.71	       | 'const/sets/IN'('type/realax/real', X21, X23)),
2.54/2.71	    inference('cnf', [status(esa)], [zf_stmt_1])).
2.54/2.71	tff('20', plain,
2.54/2.71	    ![X30 : 'type/realax/real']:
2.54/2.71	      ('const/realax/real_le'(X30, sk_A13)
2.54/2.71	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A0)),
2.54/2.71	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.54/2.71	tff('21', plain,
2.54/2.71	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
2.54/2.71	      (~ $true
2.54/2.71	       | zip_tseitin0(X0, X1, sk_A0)
2.54/2.71	       | 'const/realax/real_le'(X0, sk_A13)),
2.54/2.71	    inference('sup-', [status(thm)], ['19', '20'])).
2.54/2.71	tff('22', plain,
2.54/2.71	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
2.54/2.71	      ('const/realax/real_le'(X0, sk_A13) | zip_tseitin0(X0, X1, sk_A0)),
2.54/2.71	    inference('simplify', [status(thm)], ['21'])).
2.54/2.71	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
2.54/2.71	tff(zf_stmt_3, axiom,
2.54/2.71	  (zip_tseitin2(A) =>
2.54/2.71	   ((![A0:'type/realax/real']:
2.54/2.71	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
2.54/2.71	        'const/realax/real_le'('const/sets/sup'(A),A0))) & 
2.54/2.71	    (![A0:'type/realax/real']:
2.54/2.71	       ('const/sets/IN'('type/realax/real',A0,A) =>
2.54/2.71	        'const/realax/real_le'(A0,'const/sets/sup'(A))))))).
2.54/2.71	tff(zf_stmt_4, type, zip_tseitin1 :
2.54/2.71	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
2.54/2.71	tff(zf_stmt_5, axiom,
2.54/2.71	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
2.54/2.71	   zip_tseitin1(A1,A0,A))).
2.54/2.71	tff(zf_stmt_6, type, zip_tseitin0 :
2.54/2.71	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
2.54/2.71	tff(zf_stmt_7, axiom,
2.54/2.71	  (![A:('type/realax/real' > $o)]:
2.54/2.71	     (((?[A0:'type/realax/real']:
2.54/2.71	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
2.54/2.71	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
2.54/2.71	      zip_tseitin2(A)))).
2.54/2.71	tff('23', plain,
2.54/2.71	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
2.54/2.71	      (zip_tseitin2(X28)
2.54/2.71	       | X28 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
2.54/2.71	    inference('cnf', [status(esa)], [zf_stmt_7])).
2.54/2.71	tff('24', plain,
2.54/2.71	    ![X0 : 'type/realax/real']:
2.54/2.71	      (~ $true
2.54/2.71	       | 'const/realax/real_le'(sk_A12(X0, sk_A0), sk_A13)
2.54/2.71	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | zip_tseitin2(sk_A0)),
2.54/2.71	    inference('sup-', [status(thm)], ['22', '23'])).
2.54/2.71	tff('25', plain,
2.54/2.71	    ![X0 : 'type/realax/real']:
2.54/2.71	      (zip_tseitin2(sk_A0)
2.54/2.71	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | 'const/realax/real_le'(sk_A12(X0, sk_A0), sk_A13)),
2.54/2.71	    inference('simplify', [status(thm)], ['24'])).
2.54/2.71	tff('26', plain,
2.54/2.71	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
2.54/2.71	      X23 : 'type/realax/real' > $o]:
2.54/2.71	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X21, X22)),
2.54/2.71	    inference('cnf', [status(esa)], [zf_stmt_1])).
2.54/2.71	tff('27', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
2.54/2.71	      (~ $true
2.54/2.71	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)
2.54/2.71	       | X0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | zip_tseitin2(X0)),
2.54/2.71	    inference('sup-', [status(thm)], ['26', '23'])).
2.54/2.71	tff('28', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
2.54/2.71	      (zip_tseitin2(X0)
2.54/2.71	       | X0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)),
2.54/2.71	    inference('simplify', [status(thm)], ['27'])).
2.54/2.71	tff('29', plain,
2.54/2.71	    (~ $true
2.54/2.71	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	     | zip_tseitin2(sk_A0)
2.54/2.71	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	     | zip_tseitin2(sk_A0)),
2.54/2.71	    inference('sup-', [status(thm)], ['25', '28'])).
2.54/2.71	tff('30', plain,
2.54/2.71	    (zip_tseitin2(sk_A0) | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
2.54/2.71	    inference('simplify', [status(thm)], ['29'])).
2.54/2.71	tff('thm/sets/REAL_SUP_LE_', axiom,
2.54/2.71	  (![A:('type/realax/real' > $o),A0:'type/realax/real']:
2.54/2.71	     (((![A1:'type/realax/real']:
2.54/2.71	          ('const/sets/IN'('type/realax/real',A1,A) =>
2.54/2.71	           'const/realax/real_le'(A1,A0))) & 
2.54/2.71	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
2.54/2.71	      'const/realax/real_le'('const/sets/sup'(A),A0)))).
2.54/2.71	tff('31', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
2.54/2.71	      (X0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X0)
2.54/2.71	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
2.54/2.71	tff('thm/sets/IN_', axiom,
2.54/2.71	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
2.54/2.71	tff('32', plain,
2.54/2.71	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
2.54/2.71	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/IN_])).
2.54/2.71	tff('33', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
2.54/2.71	      (~ $true
2.54/2.71	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)
2.54/2.71	       | X0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | X0(sk_A1(X1, X0))),
2.54/2.71	    inference('sup-', [status(thm)], ['31', '32'])).
2.54/2.71	tff('34', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
2.54/2.71	      (X0(sk_A1(X1, X0))
2.54/2.71	       | X0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
2.54/2.71	    inference('simplify', [status(thm)], ['33'])).
2.54/2.71	tff('35', plain,
2.54/2.71	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
2.54/2.71	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/IN_])).
2.54/2.71	tff('36', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | ~ X1(X2)
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
2.54/2.71	       | 'const/sets/IN'(X0, X2, X3)),
2.54/2.71	    inference('sup-', [status(thm)], ['35', '2'])).
2.54/2.71	tff('37', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
2.54/2.71	      ('const/sets/IN'(X0, X2, X3)
2.54/2.71	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
2.54/2.71	       | ~ X1(X2)),
2.54/2.71	    inference('simplify', [status(thm)], ['36'])).
2.54/2.71	tff('38', plain,
2.54/2.71	    ![X0 : 'type/realax/real']:
2.54/2.71	      (~ $true | ~ sk_A(X0) | 'const/sets/IN'('type/realax/real', X0, sk_A0)),
2.54/2.71	    inference('sup-', [status(thm)], ['0', '37'])).
2.54/2.71	tff('39', plain,
2.54/2.71	    ![X0 : 'type/realax/real']:
2.54/2.71	      ('const/sets/IN'('type/realax/real', X0, sk_A0) | ~ sk_A(X0)),
2.54/2.71	    inference('simplify', [status(thm)], ['38'])).
2.54/2.71	tff('40', plain,
2.54/2.71	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
2.54/2.71	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
2.54/2.71	       | 'const/realax/real_le'(X27, 'const/sets/sup'(X23))
2.54/2.71	       | ~ zip_tseitin2(X23)),
2.54/2.71	    inference('cnf', [status(esa)], [zf_stmt_3])).
2.54/2.71	tff('41', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
2.54/2.71	      (X0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | ~ 'const/realax/real_le'(sk_A1(X1, X0), X1)
2.54/2.71	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
2.54/2.71	tff('42', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | ~ zip_tseitin2(X0)
2.54/2.71	       | ~ 'const/sets/IN'('type/realax/real', 
2.54/2.71	             sk_A1('const/sets/sup'(X0), X1), X0)
2.54/2.71	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
2.54/2.71	       | X1 = 'const/sets/EMPTY'('type/realax/real')),
2.54/2.71	    inference('sup-', [status(thm)], ['40', '41'])).
2.54/2.71	tff('43', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
2.54/2.71	      (X1 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
2.54/2.71	       | ~ 'const/sets/IN'('type/realax/real', 
2.54/2.71	             sk_A1('const/sets/sup'(X0), X1), X0)
2.54/2.71	       | ~ zip_tseitin2(X0)),
2.54/2.71	    inference('simplify', [status(thm)], ['42'])).
2.54/2.71	tff('44', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | ~ sk_A(sk_A1('const/sets/sup'(sk_A0), X0))
2.54/2.71	       | ~ zip_tseitin2(sk_A0)
2.54/2.71	       | 'const/realax/real_le'('const/sets/sup'(X0), 
2.54/2.71	           'const/sets/sup'(sk_A0))
2.54/2.71	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
2.54/2.71	    inference('sup-', [status(thm)], ['39', '43'])).
2.54/2.71	tff('45', plain,
2.54/2.71	    ![X0 : 'type/realax/real' > $o]:
2.54/2.71	      (X0 = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	       | 'const/realax/real_le'('const/sets/sup'(X0), 
2.54/2.71	           'const/sets/sup'(sk_A0))
2.54/2.71	       | ~ zip_tseitin2(sk_A0)
2.54/2.71	       | ~ sk_A(sk_A1('const/sets/sup'(sk_A0), X0))),
2.54/2.71	    inference('simplify', [status(thm)], ['44'])).
2.54/2.71	tff('46', plain,
2.54/2.71	    (~ $true
2.54/2.71	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
2.54/2.71	         'const/sets/sup'(sk_A0))
2.54/2.71	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	     | ~ zip_tseitin2(sk_A0)
2.54/2.71	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
2.54/2.71	         'const/sets/sup'(sk_A0))
2.54/2.71	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
2.54/2.71	    inference('sup-', [status(thm)], ['34', '45'])).
2.54/2.71	tff('47', plain,
2.54/2.71	    (~ zip_tseitin2(sk_A0)
2.54/2.71	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
2.54/2.71	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
2.54/2.71	         'const/sets/sup'(sk_A0))),
2.54/2.71	    inference('simplify', [status(thm)], ['46'])).
2.54/2.71	tff('48', plain, sk_A != 'const/sets/EMPTY'('type/realax/real'),
2.54/2.71	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.54/2.71	tff('49', plain,
2.54/2.71	    (~ zip_tseitin2(sk_A0)
2.54/2.71	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
2.54/2.71	         'const/sets/sup'(sk_A0))),
2.54/2.71	    inference('simplify_reflect-', [status(thm)], ['47', '48'])).
2.54/2.71	tff('50', plain,
2.54/2.71	    ~ 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0)),
2.54/2.71	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.54/2.71	tff('51', plain, ~ zip_tseitin2(sk_A0),
2.54/2.71	    inference('clc', [status(thm)], ['49', '50'])).
2.54/2.71	tff('52', plain, (~ $true | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
2.54/2.71	    inference('sup-', [status(thm)], ['30', '51'])).
2.54/2.71	tff('53', plain, sk_A0 = 'const/sets/EMPTY'('type/realax/real'),
2.54/2.71	    inference('simplify', [status(thm)], ['52'])).
2.54/2.71	tff('54', plain,
2.54/2.71	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
2.54/2.71	      ('const/sets/SUBSET'(X16, X18, X20)
2.54/2.71	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
2.54/2.71	tff('55', plain,
2.54/2.71	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
2.54/2.71	      ('const/sets/SUBSET'(X16, X18, X20)
2.54/2.71	       | ~ 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X20)),
2.54/2.71	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
2.54/2.71	tff('56', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o]:
2.54/2.71	      (~ $true
2.54/2.71	       | 'const/sets/SUBSET'(X0, X1, X1)
2.54/2.71	       | 'const/sets/SUBSET'(X0, X1, X1)),
2.54/2.71	    inference('sup-', [status(thm)], ['54', '55'])).
2.54/2.71	tff('57', plain,
2.54/2.71	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
2.54/2.71	    inference('simplify', [status(thm)], ['56'])).
2.54/2.71	tff('58', plain, (~ $true | sk_A = sk_A0),
2.54/2.71	    inference('demod', [status(thm)], ['18', '53', '57'])).
2.54/2.71	tff('59', plain, sk_A = sk_A0, inference('simplify', [status(thm)], ['58'])).
2.54/2.71	tff('60', plain, sk_A != sk_A0,
2.54/2.71	    inference('demod', [status(thm)], ['48', '53'])).
2.54/2.71	tff('61', plain, $false,
2.54/2.71	    inference('simplify_reflect-', [status(thm)], ['59', '60'])).
2.54/2.71	
2.54/2.71	% SZS output end Refutation
2.54/2.71	EOF
