0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : fo
0.00/0.00	% Ordering    : rpo6
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   : n145.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 18:43:09 CST 2018
17.14/17.36	% done 4377 iterations in 17.166s
17.14/17.36	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
17.14/17.36	% SZS output start Refutation
17.14/17.36	tff('thm/sets/REAL_LE_INF_SUBSET_', conjecture,
17.14/17.36	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
17.14/17.36	     (((?[A1:'type/realax/real']:
17.14/17.36	          (![A2:'type/realax/real']:
17.14/17.36	             ('const/sets/IN'('type/realax/real',A2,A) =>
17.14/17.36	              'const/realax/real_le'(A1,A2)))) & 
17.14/17.36	       'const/sets/SUBSET'('type/realax/real',A0,A) & 
17.14/17.36	       (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
17.14/17.36	      'const/realax/real_le'('const/sets/inf'(A),'const/sets/inf'(A0))))).
17.14/17.36	tff(zf_stmt_0, negated_conjecture,
17.14/17.36	  (~
17.14/17.36	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
17.14/17.36	       (((?[A1:'type/realax/real']:
17.14/17.36	            (![A2:'type/realax/real']:
17.14/17.36	               ('const/sets/IN'('type/realax/real',A2,A) =>
17.14/17.36	                'const/realax/real_le'(A1,A2)))) & 
17.14/17.36	         'const/sets/SUBSET'('type/realax/real',A0,A) & 
17.14/17.36	         (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
17.14/17.36	        'const/realax/real_le'('const/sets/inf'(A),'const/sets/inf'(A0)))))).
17.14/17.36	tff('0', plain, 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A),
17.14/17.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
17.14/17.36	tff('thm/sets/EXTENSION_', axiom,
17.14/17.36	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
17.14/17.36	     ((A0 = A1) <=>
17.14/17.36	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
17.14/17.36	tff('1', plain,
17.14/17.36	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
17.14/17.36	      (X13 = X15
17.14/17.36	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
17.14/17.36	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
17.14/17.36	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
17.14/17.36	tff('thm/sets/SUBSET_', axiom,
17.14/17.36	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
17.14/17.36	     ('const/sets/SUBSET'(A,A0,A1) <=>
17.14/17.36	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
17.14/17.36	tff('2', plain,
17.14/17.36	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
17.14/17.36	      (~ 'const/sets/IN'(X16, X17, X18)
17.14/17.36	       | 'const/sets/IN'(X16, X17, X19)
17.14/17.36	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
17.14/17.36	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
17.14/17.36	tff('3', plain,
17.14/17.36	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
17.14/17.36	      (~ $true
17.14/17.36	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)
17.14/17.36	       | X2 = X1
17.14/17.36	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
17.14/17.36	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X3)),
17.14/17.36	    inference('sup-', [status(thm)], ['1', '2'])).
17.14/17.36	tff('4', plain,
17.14/17.36	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
17.14/17.36	      ('const/sets/IN'(X0, sk_A2(X0, X1, X2), X3)
17.14/17.36	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
17.14/17.36	       | X2 = X1
17.14/17.36	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)),
17.14/17.36	    inference('simplify', [status(thm)], ['3'])).
17.14/17.36	tff('5', plain,
17.14/17.36	    ![X0 : 'type/realax/real' > $o]:
17.14/17.36	      (~ $true
17.14/17.36	       | 'const/sets/IN'('type/realax/real', 
17.14/17.36	           sk_A2('type/realax/real', sk_A0, X0), X0)
17.14/17.36	       | X0 = sk_A0
17.14/17.36	       | 'const/sets/IN'('type/realax/real', 
17.14/17.36	           sk_A2('type/realax/real', sk_A0, X0), sk_A)),
17.14/17.36	    inference('sup-', [status(thm)], ['0', '4'])).
17.14/17.36	tff('6', plain,
17.14/17.36	    ![X0 : 'type/realax/real' > $o]:
17.14/17.36	      ('const/sets/IN'('type/realax/real', 
17.14/17.36	         sk_A2('type/realax/real', sk_A0, X0), sk_A)
17.14/17.36	       | X0 = sk_A0
17.14/17.36	       | 'const/sets/IN'('type/realax/real', 
17.14/17.36	           sk_A2('type/realax/real', sk_A0, X0), X0)),
17.14/17.36	    inference('simplify', [status(thm)], ['5'])).
17.14/17.36	tff('7', plain,
17.14/17.36	    (~ $true
17.14/17.36	     | 'const/sets/IN'('type/realax/real', 
17.14/17.36	         sk_A2('type/realax/real', sk_A0, sk_A), sk_A)
17.14/17.36	     | sk_A = sk_A0),
17.14/17.36	    inference('eq_fact', [status(thm)], ['6'])).
17.14/17.36	tff('8', plain,
17.14/17.36	    (sk_A = sk_A0
17.14/17.36	     | 'const/sets/IN'('type/realax/real', 
17.14/17.36	         sk_A2('type/realax/real', sk_A0, sk_A), sk_A)),
17.14/17.36	    inference('simplify', [status(thm)], ['7'])).
17.14/17.36	tff('9', plain,
17.14/17.36	    ![X0 : 'type/realax/real' > $o]:
17.14/17.36	      (~ $true
17.14/17.36	       | sk_A = sk_A0
17.14/17.36	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, X0)
17.14/17.36	       | 'const/sets/IN'('type/realax/real', 
17.14/17.36	           sk_A2('type/realax/real', sk_A0, sk_A), X0)),
17.14/17.36	    inference('sup-', [status(thm)], ['8', '2'])).
17.14/17.36	tff('10', plain,
17.14/17.36	    ![X0 : 'type/realax/real' > $o]:
17.14/17.36	      ('const/sets/IN'('type/realax/real', 
17.14/17.36	         sk_A2('type/realax/real', sk_A0, sk_A), X0)
17.14/17.36	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, X0)
17.14/17.36	       | sk_A = sk_A0),
17.14/17.36	    inference('simplify', [status(thm)], ['9'])).
17.14/17.36	tff('thm/sets/REAL_LE_INF_', axiom,
17.14/17.36	  (![A:('type/realax/real' > $o),A0:'type/realax/real']:
17.14/17.36	     (((![A1:'type/realax/real']:
17.14/17.36	          ('const/sets/IN'('type/realax/real',A1,A) =>
17.14/17.36	           'const/realax/real_le'(A0,A1))) & 
17.14/17.36	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
17.14/17.36	      'const/realax/real_le'(A0,'const/sets/inf'(A))))).
17.14/17.36	tff('11', plain,
17.14/17.36	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
17.14/17.36	      (X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.36	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X0)
17.14/17.36	       | 'const/realax/real_le'(X1, 'const/sets/inf'(X0))),
17.14/17.36	    inference('cnf', [status(esa)], [thm/sets/REAL_LE_INF_])).
17.14/17.36	tff('12', plain,
17.14/17.36	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
17.14/17.36	      X2 : 'type/realax/real' > $o]:
17.14/17.36	      (~ $true
17.14/17.36	       | 'const/realax/real_le'(X1, 'const/sets/inf'(X0))
17.14/17.36	       | X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.36	       | ~ 'const/sets/SUBSET'('type/realax/real', X0, X2)
17.14/17.36	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X2)),
17.14/17.36	    inference('sup-', [status(thm)], ['11', '2'])).
17.14/17.36	tff('13', plain,
17.14/17.36	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
17.14/17.36	      X2 : 'type/realax/real' > $o]:
17.14/17.36	      ('const/sets/IN'('type/realax/real', sk_A1(X1, X0), X2)
17.14/17.36	       | ~ 'const/sets/SUBSET'('type/realax/real', X0, X2)
17.14/17.36	       | X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.36	       | 'const/realax/real_le'(X1, 'const/sets/inf'(X0))),
17.14/17.36	    inference('simplify', [status(thm)], ['12'])).
17.14/17.36	tff('14', plain,
17.14/17.36	    ![X0 : 'type/realax/real']:
17.14/17.36	      (~ $true
17.14/17.36	       | 'const/realax/real_le'(X0, 'const/sets/inf'(sk_A0))
17.14/17.36	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.36	       | 'const/sets/IN'('type/realax/real', sk_A1(X0, sk_A0), sk_A)),
17.14/17.36	    inference('sup-', [status(thm)], ['0', '13'])).
17.14/17.36	tff('15', plain,
17.14/17.36	    ![X0 : 'type/realax/real']:
17.14/17.36	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A0), sk_A)
17.14/17.36	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.36	       | 'const/realax/real_le'(X0, 'const/sets/inf'(sk_A0))),
17.14/17.36	    inference('simplify', [status(thm)], ['14'])).
17.14/17.36	tff('16', plain, sk_A0 != 'const/sets/EMPTY'('type/realax/real'),
17.14/17.36	    inference('cnf', [status(esa)], [zf_stmt_0])).
17.14/17.36	tff('17', plain,
17.14/17.36	    ![X0 : 'type/realax/real']:
17.14/17.36	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A0), sk_A)
17.14/17.36	       | 'const/realax/real_le'(X0, 'const/sets/inf'(sk_A0))),
17.14/17.36	    inference('simplify_reflect-', [status(thm)], ['15', '16'])).
17.14/17.36	tff('thm/sets/INF_', axiom,
17.14/17.36	  (![A:('type/realax/real' > $o)]:
17.14/17.36	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
17.14/17.36	       (?[A0:'type/realax/real']:
17.14/17.36	          (![A1:'type/realax/real']:
17.14/17.36	             ('const/sets/IN'('type/realax/real',A1,A) =>
17.14/17.36	              'const/realax/real_le'(A0,A1))))) =>
17.14/17.36	      ((![A0:'type/realax/real']:
17.14/17.36	          ('const/sets/IN'('type/realax/real',A0,A) =>
17.14/17.36	           'const/realax/real_le'('const/sets/inf'(A),A0))) & 
17.14/17.36	       (![A0:'type/realax/real']:
17.14/17.36	          ((![A1:'type/realax/real']:
17.14/17.36	              ('const/sets/IN'('type/realax/real',A1,A) =>
17.14/17.36	               'const/realax/real_le'(A0,A1))) =>
17.14/17.36	           'const/realax/real_le'(A0,'const/sets/inf'(A)))))))).
17.14/17.36	tff(zf_stmt_1, axiom,
17.14/17.36	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A0,A1)) =>
17.14/17.36	   zip_tseitin0(A1,A0,A))).
17.14/17.36	tff('18', plain,
17.14/17.36	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
17.14/17.36	      X23 : 'type/realax/real' > $o]:
17.14/17.36	      (zip_tseitin0(X21, X22, X23)
17.14/17.36	       | 'const/sets/IN'('type/realax/real', X21, X23)),
17.14/17.36	    inference('cnf', [status(esa)], [zf_stmt_1])).
17.14/17.36	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
17.14/17.36	tff(zf_stmt_3, axiom,
17.14/17.36	  (zip_tseitin2(A) =>
17.14/17.36	   ((![A0:'type/realax/real']:
17.14/17.36	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
17.14/17.36	        'const/realax/real_le'(A0,'const/sets/inf'(A)))) & 
17.14/17.36	    (![A0:'type/realax/real']:
17.14/17.36	       ('const/sets/IN'('type/realax/real',A0,A) =>
17.14/17.36	        'const/realax/real_le'('const/sets/inf'(A),A0)))))).
17.14/17.36	tff(zf_stmt_4, type, zip_tseitin1 :
17.14/17.36	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
17.14/17.36	tff(zf_stmt_5, axiom,
17.14/17.36	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A0,A1)) =>
17.14/17.36	   zip_tseitin1(A1,A0,A))).
17.14/17.36	tff(zf_stmt_6, type, zip_tseitin0 :
17.14/17.36	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
17.14/17.36	tff(zf_stmt_7, axiom,
17.14/17.36	  (![A:('type/realax/real' > $o)]:
17.14/17.36	     (((?[A0:'type/realax/real']:
17.14/17.36	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
17.14/17.36	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
17.14/17.36	      zip_tseitin2(A)))).
17.14/17.36	tff('19', plain,
17.14/17.36	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
17.14/17.36	      (zip_tseitin2(X28)
17.14/17.36	       | X28 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.36	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
17.14/17.36	    inference('cnf', [status(esa)], [zf_stmt_7])).
17.14/17.36	tff('20', plain,
17.14/17.36	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
17.14/17.36	      (~ $true
17.14/17.36	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)
17.14/17.36	       | X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.36	       | zip_tseitin2(X0)),
17.14/17.37	    inference('sup-', [status(thm)], ['18', '19'])).
17.14/17.37	tff('21', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
17.14/17.37	      (zip_tseitin2(X0)
17.14/17.37	       | X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)),
17.14/17.37	    inference('simplify', [status(thm)], ['20'])).
17.14/17.37	tff('22', plain,
17.14/17.37	    ![X30 : 'type/realax/real']:
17.14/17.37	      ('const/realax/real_le'(sk_A13, X30)
17.14/17.37	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A)),
17.14/17.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
17.14/17.37	tff('23', plain,
17.14/17.37	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
17.14/17.37	      X23 : 'type/realax/real' > $o]:
17.14/17.37	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X22, X21)),
17.14/17.37	    inference('cnf', [status(esa)], [zf_stmt_1])).
17.14/17.37	tff('24', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
17.14/17.37	      (~ $true
17.14/17.37	       | ~ 'const/realax/real_le'(X1, sk_A12(X1, X0))
17.14/17.37	       | X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | zip_tseitin2(X0)),
17.14/17.37	    inference('sup-', [status(thm)], ['23', '19'])).
17.14/17.37	tff('25', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
17.14/17.37	      (zip_tseitin2(X0)
17.14/17.37	       | X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | ~ 'const/realax/real_le'(X1, sk_A12(X1, X0))),
17.14/17.37	    inference('simplify', [status(thm)], ['24'])).
17.14/17.37	tff('26', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o]:
17.14/17.37	      (~ $true
17.14/17.37	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A)
17.14/17.37	       | X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | zip_tseitin2(X0)),
17.14/17.37	    inference('sup-', [status(thm)], ['22', '25'])).
17.14/17.37	tff('27', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o]:
17.14/17.37	      (zip_tseitin2(X0)
17.14/17.37	       | X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A)),
17.14/17.37	    inference('simplify', [status(thm)], ['26'])).
17.14/17.37	tff('28', plain,
17.14/17.37	    (~ $true
17.14/17.37	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	     | zip_tseitin2(sk_A)
17.14/17.37	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	     | zip_tseitin2(sk_A)),
17.14/17.37	    inference('sup-', [status(thm)], ['21', '27'])).
17.14/17.37	tff('29', plain,
17.14/17.37	    (zip_tseitin2(sk_A) | sk_A = 'const/sets/EMPTY'('type/realax/real')),
17.14/17.37	    inference('simplify', [status(thm)], ['28'])).
17.14/17.37	tff('30', plain,
17.14/17.37	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
17.14/17.37	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
17.14/17.37	       | 'const/realax/real_le'('const/sets/inf'(X23), X27)
17.14/17.37	       | ~ zip_tseitin2(X23)),
17.14/17.37	    inference('cnf', [status(esa)], [zf_stmt_3])).
17.14/17.37	tff('31', plain,
17.14/17.37	    ![X0 : 'type/realax/real']:
17.14/17.37	      (~ $true
17.14/17.37	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | 'const/realax/real_le'('const/sets/inf'(sk_A), X0)
17.14/17.37	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
17.14/17.37	    inference('sup-', [status(thm)], ['29', '30'])).
17.14/17.37	tff('32', plain,
17.14/17.37	    ![X0 : 'type/realax/real']:
17.14/17.37	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
17.14/17.37	       | 'const/realax/real_le'('const/sets/inf'(sk_A), X0)
17.14/17.37	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
17.14/17.37	    inference('simplify', [status(thm)], ['31'])).
17.14/17.37	tff('33', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
17.14/17.37	      (X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | ~ 'const/realax/real_le'(X1, sk_A1(X1, X0))
17.14/17.37	       | 'const/realax/real_le'(X1, 'const/sets/inf'(X0))),
17.14/17.37	    inference('cnf', [status(esa)], [thm/sets/REAL_LE_INF_])).
17.14/17.37	tff('34', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o]:
17.14/17.37	      (~ $true
17.14/17.37	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | ~ 'const/sets/IN'('type/realax/real', 
17.14/17.37	             sk_A1('const/sets/inf'(sk_A), X0), sk_A)
17.14/17.37	       | 'const/realax/real_le'('const/sets/inf'(sk_A), 'const/sets/inf'(X0))
17.14/17.37	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
17.14/17.37	    inference('sup-', [status(thm)], ['32', '33'])).
17.14/17.37	tff('35', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o]:
17.14/17.37	      (X0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	       | 'const/realax/real_le'('const/sets/inf'(sk_A), 'const/sets/inf'(X0))
17.14/17.37	       | ~ 'const/sets/IN'('type/realax/real', 
17.14/17.37	             sk_A1('const/sets/inf'(sk_A), X0), sk_A)
17.14/17.37	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
17.14/17.37	    inference('simplify', [status(thm)], ['34'])).
17.14/17.37	tff('36', plain,
17.14/17.37	    (~ $true
17.14/17.37	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
17.14/17.37	         'const/sets/inf'(sk_A0))
17.14/17.37	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
17.14/17.37	         'const/sets/inf'(sk_A0))
17.14/17.37	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
17.14/17.37	    inference('sup-', [status(thm)], ['17', '35'])).
17.14/17.37	tff('37', plain,
17.14/17.37	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
17.14/17.37	         'const/sets/inf'(sk_A0))),
17.14/17.37	    inference('simplify', [status(thm)], ['36'])).
17.14/17.37	tff('38', plain,
17.14/17.37	    (sk_A = 'const/sets/EMPTY'('type/realax/real')
17.14/17.37	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
17.14/17.37	         'const/sets/inf'(sk_A0))),
17.14/17.37	    inference('simplify_reflect-', [status(thm)], ['37', '16'])).
17.14/17.37	tff('39', plain,
17.14/17.37	    ~ 'const/realax/real_le'('const/sets/inf'(sk_A), 'const/sets/inf'(sk_A0)),
17.14/17.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
17.14/17.37	tff('40', plain, sk_A = 'const/sets/EMPTY'('type/realax/real'),
17.14/17.37	    inference('clc', [status(thm)], ['38', '39'])).
17.14/17.37	tff('41', plain,
17.14/17.37	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
17.14/17.37	      ('const/sets/SUBSET'(X16, X18, X20)
17.14/17.37	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
17.14/17.37	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
17.14/17.37	tff('thm/sets/NOT_IN_EMPTY_', axiom,
17.14/17.37	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
17.14/17.37	tff('42', plain,
17.14/17.37	    ![X8 : $tType, X9 : X8]:
17.14/17.37	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
17.14/17.37	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
17.14/17.37	tff('43', plain,
17.14/17.37	    ![X0 : $tType, X1 : X0 > $o]:
17.14/17.37	      (~ $true | 'const/sets/SUBSET'(X0, 'const/sets/EMPTY'(X0), X1)),
17.14/17.37	    inference('sup-', [status(thm)], ['41', '42'])).
17.14/17.37	tff('44', plain,
17.14/17.37	    ![X0 : $tType, X1 : X0 > $o]:
17.14/17.37	      'const/sets/SUBSET'(X0, 'const/sets/EMPTY'(X0), X1),
17.14/17.37	    inference('simplify', [status(thm)], ['43'])).
17.14/17.37	tff('45', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o]:
17.14/17.37	      ('const/sets/IN'('type/realax/real', 
17.14/17.37	         sk_A2('type/realax/real', sk_A0, 
17.14/17.37	           'const/sets/EMPTY'('type/realax/real')), X0)
17.14/17.37	       | ~ $true
17.14/17.37	       | 'const/sets/EMPTY'('type/realax/real') = sk_A0),
17.14/17.37	    inference('demod', [status(thm)], ['10', '40', '40', '44', '40'])).
17.14/17.37	tff('46', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o]:
17.14/17.37	      ('const/sets/EMPTY'('type/realax/real') = sk_A0
17.14/17.37	       | 'const/sets/IN'('type/realax/real', 
17.14/17.37	           sk_A2('type/realax/real', sk_A0, 
17.14/17.37	             'const/sets/EMPTY'('type/realax/real')), X0)),
17.14/17.37	    inference('simplify', [status(thm)], ['45'])).
17.14/17.37	tff('47', plain,
17.14/17.37	    ![X0 : 'type/realax/real' > $o]:
17.14/17.37	      'const/sets/IN'('type/realax/real', 
17.14/17.37	        sk_A2('type/realax/real', sk_A0, 
17.14/17.37	          'const/sets/EMPTY'('type/realax/real')), X0),
17.14/17.37	    inference('simplify_reflect-', [status(thm)], ['46', '16'])).
17.14/17.37	tff('48', plain,
17.14/17.37	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
17.14/17.37	      (X13 = X15
17.14/17.37	       | ~ 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
17.14/17.37	       | ~ 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
17.14/17.37	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
17.14/17.37	tff('49', plain,
17.14/17.37	    (~ $true
17.14/17.37	     | ~ 'const/sets/IN'('type/realax/real', 
17.14/17.37	           sk_A2('type/realax/real', sk_A0, 
17.14/17.37	             'const/sets/EMPTY'('type/realax/real')), 
17.14/17.37	           'const/sets/EMPTY'('type/realax/real'))
17.14/17.37	     | 'const/sets/EMPTY'('type/realax/real') = sk_A0),
17.14/17.37	    inference('sup-', [status(thm)], ['47', '48'])).
17.14/17.37	tff('50', plain,
17.14/17.37	    (~ $true | ~ $true | 'const/sets/EMPTY'('type/realax/real') = sk_A0),
17.14/17.37	    inference('demod', [status(thm)], ['49', '47'])).
17.14/17.37	tff('51', plain, 'const/sets/EMPTY'('type/realax/real') = sk_A0,
17.14/17.37	    inference('simplify', [status(thm)], ['50'])).
17.14/17.37	tff('52', plain, $false,
17.14/17.37	    inference('simplify_reflect-', [status(thm)], ['51', '16'])).
17.14/17.37	
17.14/17.37	% SZS output end Refutation
17.14/17.37	EOF
