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    : purification_int
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n130.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:41:24 CST 2018
11.16/11.41	% done 3157 iterations in 11.209s
11.16/11.41	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
11.16/11.41	% SZS output start Refutation
11.23/11.41	tff('thm/sets/EXTENSION_', axiom,
11.23/11.41	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
11.23/11.41	     ((A0 = A1) <=>
11.23/11.41	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
11.23/11.41	tff('0', plain,
11.23/11.41	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
11.23/11.41	      (X13 = X15
11.23/11.41	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
11.23/11.41	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
11.23/11.41	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
11.23/11.41	tff('thm/sets/NOT_IN_EMPTY_', axiom,
11.23/11.41	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
11.23/11.41	tff('1', plain,
11.23/11.41	    ![X8 : $tType, X9 : X8]:
11.23/11.41	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
11.23/11.41	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
11.23/11.41	tff('2', plain,
11.23/11.41	    ![X0 : $tType, X1 : X0 > $o]:
11.23/11.41	      (~ $true
11.23/11.41	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)
11.23/11.41	       | X1 = 'const/sets/EMPTY'(X0)),
11.23/11.41	    inference('sup-', [status(thm)], ['0', '1'])).
11.23/11.41	tff('3', plain,
11.23/11.41	    ![X0 : $tType, X1 : X0 > $o]:
11.23/11.41	      (X1 = 'const/sets/EMPTY'(X0)
11.23/11.41	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)),
11.23/11.43	    inference('simplify', [status(thm)], ['2'])).
11.23/11.43	tff('thm/sets/REAL_SUP_LE_SUBSET_', conjecture,
11.23/11.43	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
11.23/11.43	     (((?[A1:'type/realax/real']:
11.23/11.43	          (![A2:'type/realax/real']:
11.23/11.43	             ('const/sets/IN'('type/realax/real',A2,A0) =>
11.23/11.43	              'const/realax/real_le'(A2,A1)))) & 
11.23/11.43	       'const/sets/SUBSET'('type/realax/real',A,A0) & 
11.23/11.43	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
11.23/11.43	      'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0))))).
11.23/11.43	tff(zf_stmt_0, negated_conjecture,
11.23/11.43	  (~
11.23/11.43	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
11.23/11.43	       (((?[A1:'type/realax/real']:
11.23/11.43	            (![A2:'type/realax/real']:
11.23/11.43	               ('const/sets/IN'('type/realax/real',A2,A0) =>
11.23/11.43	                'const/realax/real_le'(A2,A1)))) & 
11.23/11.43	         'const/sets/SUBSET'('type/realax/real',A,A0) & 
11.23/11.43	         (A != 'const/sets/EMPTY'('type/realax/real'))) =>
11.23/11.43	        'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0)))))).
11.23/11.43	tff('4', plain, 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A0),
11.23/11.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.23/11.43	tff('thm/sets/SUBSET_', axiom,
11.23/11.43	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
11.23/11.43	     ('const/sets/SUBSET'(A,A0,A1) <=>
11.23/11.43	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
11.23/11.43	tff('5', plain,
11.23/11.43	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
11.23/11.43	      (~ 'const/sets/IN'(X16, X17, X18)
11.23/11.43	       | 'const/sets/IN'(X16, X17, X19)
11.23/11.43	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
11.23/11.43	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
11.23/11.43	tff('6', plain,
11.23/11.43	    ![X0 : 'type/realax/real']:
11.23/11.43	      (~ $true
11.23/11.43	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)
11.23/11.43	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
11.23/11.43	    inference('sup-', [status(thm)], ['4', '5'])).
11.23/11.43	tff('7', plain,
11.23/11.43	    ![X0 : 'type/realax/real']:
11.23/11.43	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
11.23/11.43	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)),
11.23/11.43	    inference('simplify', [status(thm)], ['6'])).
11.23/11.43	tff('8', plain,
11.23/11.43	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
11.23/11.43	      (~ $true
11.23/11.43	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
11.23/11.43	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
11.23/11.43	       | 'const/sets/IN'('type/realax/real', X0, X1)),
11.23/11.43	    inference('sup-', [status(thm)], ['7', '5'])).
11.23/11.43	tff('9', plain,
11.23/11.43	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
11.23/11.43	      ('const/sets/IN'('type/realax/real', X0, X1)
11.23/11.43	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
11.23/11.43	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
11.23/11.43	    inference('simplify', [status(thm)], ['8'])).
11.23/11.43	tff('10', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      (~ $true
11.23/11.43	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
11.23/11.43	       | 'const/sets/IN'('type/realax/real', 
11.23/11.43	           sk_A2('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
11.23/11.43	             sk_A), X0)),
11.23/11.43	    inference('sup-', [status(thm)], ['3', '9'])).
11.23/11.43	tff('11', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      ('const/sets/IN'('type/realax/real', 
11.23/11.43	         sk_A2('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
11.23/11.43	           sk_A), X0)
11.23/11.43	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
11.23/11.43	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
11.23/11.43	    inference('simplify', [status(thm)], ['10'])).
11.23/11.43	tff('12', plain, sk_A != 'const/sets/EMPTY'('type/realax/real'),
11.23/11.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.23/11.43	tff('13', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      ('const/sets/IN'('type/realax/real', 
11.23/11.43	         sk_A2('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
11.23/11.43	           sk_A), X0)
11.23/11.43	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)),
11.23/11.43	    inference('simplify_reflect-', [status(thm)], ['11', '12'])).
11.23/11.43	tff('14', plain,
11.23/11.43	    (~ $true
11.23/11.43	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
11.23/11.43	           'const/sets/EMPTY'('type/realax/real'))),
11.23/11.43	    inference('sup-', [status(thm)], ['13', '1'])).
11.23/11.43	tff('15', plain,
11.23/11.43	    ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
11.23/11.43	        'const/sets/EMPTY'('type/realax/real')),
11.23/11.43	    inference('simplify', [status(thm)], ['14'])).
11.23/11.43	tff('thm/sets/SUP_', axiom,
11.23/11.43	  (![A:('type/realax/real' > $o)]:
11.23/11.43	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
11.23/11.43	       (?[A0:'type/realax/real']:
11.23/11.43	          (![A1:'type/realax/real']:
11.23/11.43	             ('const/sets/IN'('type/realax/real',A1,A) =>
11.23/11.43	              'const/realax/real_le'(A1,A0))))) =>
11.23/11.43	      ((![A0:'type/realax/real']:
11.23/11.43	          ('const/sets/IN'('type/realax/real',A0,A) =>
11.23/11.43	           'const/realax/real_le'(A0,'const/sets/sup'(A)))) & 
11.23/11.43	       (![A0:'type/realax/real']:
11.23/11.43	          ((![A1:'type/realax/real']:
11.23/11.43	              ('const/sets/IN'('type/realax/real',A1,A) =>
11.23/11.43	               'const/realax/real_le'(A1,A0))) =>
11.23/11.43	           'const/realax/real_le'('const/sets/sup'(A),A0))))))).
11.23/11.43	tff(zf_stmt_1, axiom,
11.23/11.43	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
11.23/11.43	   zip_tseitin0(A1,A0,A))).
11.23/11.43	tff('16', plain,
11.23/11.43	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
11.23/11.43	      X23 : 'type/realax/real' > $o]:
11.23/11.43	      (zip_tseitin0(X21, X22, X23)
11.23/11.43	       | 'const/sets/IN'('type/realax/real', X21, X23)),
11.23/11.43	    inference('cnf', [status(esa)], [zf_stmt_1])).
11.23/11.43	tff('17', plain,
11.23/11.43	    ![X30 : 'type/realax/real']:
11.23/11.43	      ('const/realax/real_le'(X30, sk_A13)
11.23/11.43	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A0)),
11.23/11.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.23/11.43	tff('18', plain,
11.23/11.43	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
11.23/11.43	      (~ $true
11.23/11.43	       | zip_tseitin0(X0, X1, sk_A0)
11.23/11.43	       | 'const/realax/real_le'(X0, sk_A13)),
11.23/11.43	    inference('sup-', [status(thm)], ['16', '17'])).
11.23/11.43	tff('19', plain,
11.23/11.43	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
11.23/11.43	      ('const/realax/real_le'(X0, sk_A13) | zip_tseitin0(X0, X1, sk_A0)),
11.23/11.43	    inference('simplify', [status(thm)], ['18'])).
11.23/11.43	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
11.23/11.43	tff(zf_stmt_3, axiom,
11.23/11.43	  (zip_tseitin2(A) =>
11.23/11.43	   ((![A0:'type/realax/real']:
11.23/11.43	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
11.23/11.43	        'const/realax/real_le'('const/sets/sup'(A),A0))) & 
11.23/11.43	    (![A0:'type/realax/real']:
11.23/11.43	       ('const/sets/IN'('type/realax/real',A0,A) =>
11.23/11.43	        'const/realax/real_le'(A0,'const/sets/sup'(A))))))).
11.23/11.43	tff(zf_stmt_4, type, zip_tseitin1 :
11.23/11.43	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
11.23/11.43	tff(zf_stmt_5, axiom,
11.23/11.43	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
11.23/11.43	   zip_tseitin1(A1,A0,A))).
11.23/11.43	tff(zf_stmt_6, type, zip_tseitin0 :
11.23/11.43	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
11.23/11.43	tff(zf_stmt_7, axiom,
11.23/11.43	  (![A:('type/realax/real' > $o)]:
11.23/11.43	     (((?[A0:'type/realax/real']:
11.23/11.43	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
11.23/11.43	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
11.23/11.43	      zip_tseitin2(A)))).
11.23/11.43	tff('20', plain,
11.23/11.43	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
11.23/11.43	      (zip_tseitin2(X28)
11.23/11.43	       | X28 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
11.23/11.43	    inference('cnf', [status(esa)], [zf_stmt_7])).
11.23/11.43	tff('21', plain,
11.23/11.43	    ![X0 : 'type/realax/real']:
11.23/11.43	      (~ $true
11.23/11.43	       | 'const/realax/real_le'(sk_A12(X0, sk_A0), sk_A13)
11.23/11.43	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | zip_tseitin2(sk_A0)),
11.23/11.43	    inference('sup-', [status(thm)], ['19', '20'])).
11.23/11.43	tff('22', plain,
11.23/11.43	    ![X0 : 'type/realax/real']:
11.23/11.43	      (zip_tseitin2(sk_A0)
11.23/11.43	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | 'const/realax/real_le'(sk_A12(X0, sk_A0), sk_A13)),
11.23/11.43	    inference('simplify', [status(thm)], ['21'])).
11.23/11.43	tff('23', plain,
11.23/11.43	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
11.23/11.43	      X23 : 'type/realax/real' > $o]:
11.23/11.43	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X21, X22)),
11.23/11.43	    inference('cnf', [status(esa)], [zf_stmt_1])).
11.23/11.43	tff('24', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
11.23/11.43	      (~ $true
11.23/11.43	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)
11.23/11.43	       | X0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | zip_tseitin2(X0)),
11.23/11.43	    inference('sup-', [status(thm)], ['23', '20'])).
11.23/11.43	tff('25', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
11.23/11.43	      (zip_tseitin2(X0)
11.23/11.43	       | X0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)),
11.23/11.43	    inference('simplify', [status(thm)], ['24'])).
11.23/11.43	tff('26', plain,
11.23/11.43	    (~ $true
11.23/11.43	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	     | zip_tseitin2(sk_A0)
11.23/11.43	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	     | zip_tseitin2(sk_A0)),
11.23/11.43	    inference('sup-', [status(thm)], ['22', '25'])).
11.23/11.43	tff('27', plain,
11.23/11.43	    (zip_tseitin2(sk_A0) | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
11.23/11.43	    inference('simplify', [status(thm)], ['26'])).
11.23/11.43	tff('thm/sets/REAL_SUP_LE_', axiom,
11.23/11.43	  (![A:('type/realax/real' > $o),A0:'type/realax/real']:
11.23/11.43	     (((![A1:'type/realax/real']:
11.23/11.43	          ('const/sets/IN'('type/realax/real',A1,A) =>
11.23/11.43	           'const/realax/real_le'(A1,A0))) & 
11.23/11.43	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
11.23/11.43	      'const/realax/real_le'('const/sets/sup'(A),A0)))).
11.23/11.43	tff('28', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
11.23/11.43	      (X0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X0)
11.23/11.43	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
11.23/11.43	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
11.23/11.43	tff('thm/sets/IN_', axiom,
11.23/11.43	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
11.23/11.43	tff('29', plain,
11.23/11.43	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
11.23/11.43	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
11.23/11.43	    inference('cnf', [status(esa)], [thm/sets/IN_])).
11.23/11.43	tff('30', plain,
11.23/11.43	    ![X4 : $tType, X5 : X4 > $o, X6 : X4, X7 : X4 > $o]:
11.23/11.43	      (X7 != X5 | X5(X6) | ~ 'const/sets/IN'(X4, X6, X7)),
11.23/11.43	    inference('ho.purify_applied_variable', [status(thm)], ['29'])).
11.23/11.43	tff('31', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
11.23/11.43	      X2 : 'type/realax/real' > $o]:
11.23/11.43	      (~ $true
11.23/11.43	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)
11.23/11.43	       | X0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | X2(sk_A1(X1, X0))
11.23/11.43	       | X0 != X2),
11.23/11.43	    inference('sup-', [status(thm)], ['28', '30'])).
11.23/11.43	tff('32', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
11.23/11.43	      X2 : 'type/realax/real' > $o]:
11.23/11.43	      (X0 != X2
11.23/11.43	       | X2(sk_A1(X1, X0))
11.23/11.43	       | X0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
11.23/11.43	    inference('simplify', [status(thm)], ['31'])).
11.23/11.43	tff('33', plain,
11.23/11.43	    ~ 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0)),
11.23/11.43	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.23/11.43	tff('34', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      (~ $true
11.23/11.43	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | X0(sk_A1('const/sets/sup'(sk_A0), sk_A))
11.23/11.43	       | sk_A != X0),
11.23/11.43	    inference('sup-', [status(thm)], ['32', '33'])).
11.23/11.43	tff('35', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      (sk_A != X0
11.23/11.43	       | X0(sk_A1('const/sets/sup'(sk_A0), sk_A))
11.23/11.43	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
11.23/11.43	    inference('simplify', [status(thm)], ['34'])).
11.23/11.43	tff('36', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      (sk_A != X0 | X0(sk_A1('const/sets/sup'(sk_A0), sk_A))),
11.23/11.43	    inference('simplify_reflect-', [status(thm)], ['35', '12'])).
11.23/11.43	tff('37', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
11.23/11.43	      (X1 != X0 | sk_A != X0 | X1(sk_A1('const/sets/sup'(sk_A0), sk_A))),
11.23/11.43	    inference('ho.purify_applied_variable', [status(thm)], ['36'])).
11.23/11.43	tff('38', plain,
11.23/11.43	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
11.23/11.43	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
11.23/11.43	    inference('cnf', [status(esa)], [thm/sets/IN_])).
11.23/11.43	tff('39', plain,
11.23/11.43	    ![X4 : $tType, X5 : X4 > $o, X7 : X4, X8 : X4 > $o]:
11.23/11.43	      (X8 != X5 | 'const/sets/IN'(X4, X7, X5) | ~ X8(X7)),
11.23/11.43	    inference('ho.purify_applied_variable', [status(thm)], ['38'])).
11.23/11.43	tff('40', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o, 
11.23/11.43	      X2 : 'type/realax/real' > $o]:
11.23/11.43	      (~ $true
11.23/11.43	       | sk_A != X2
11.23/11.43	       | X0 != X2
11.23/11.43	       | 'const/sets/IN'('type/realax/real', 
11.23/11.43	           sk_A1('const/sets/sup'(sk_A0), sk_A), X1)
11.23/11.43	       | X0 != X1),
11.23/11.43	    inference('sup-', [status(thm)], ['37', '39'])).
11.23/11.43	tff('41', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o, 
11.23/11.43	      X2 : 'type/realax/real' > $o]:
11.23/11.43	      (X0 != X1
11.23/11.43	       | 'const/sets/IN'('type/realax/real', 
11.23/11.43	           sk_A1('const/sets/sup'(sk_A0), sk_A), X1)
11.23/11.43	       | X0 != X2
11.23/11.43	       | sk_A != X2),
11.23/11.43	    inference('simplify', [status(thm)], ['40'])).
11.23/11.43	tff('42', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
11.23/11.43	      (sk_A != X0
11.23/11.43	       | X1 != X0
11.23/11.43	       | 'const/sets/IN'('type/realax/real', 
11.23/11.43	           sk_A1('const/sets/sup'(sk_A0), sk_A), X1)),
11.23/11.43	    inference('eq_res', [status(thm)], ['41'])).
11.23/11.43	tff('43', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      ('const/sets/IN'('type/realax/real', 
11.23/11.43	         sk_A1('const/sets/sup'(sk_A0), sk_A), X0)
11.23/11.43	       | X0 != sk_A),
11.23/11.43	    inference('eq_res', [status(thm)], ['42'])).
11.23/11.43	tff('44', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      (~ $true
11.23/11.43	       | sk_A != sk_A
11.23/11.43	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
11.23/11.43	       | 'const/sets/IN'('type/realax/real', 
11.23/11.43	           sk_A1('const/sets/sup'(sk_A0), sk_A), X0)),
11.23/11.43	    inference('sup-', [status(thm)], ['43', '9'])).
11.23/11.43	tff('45', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o]:
11.23/11.43	      ('const/sets/IN'('type/realax/real', 
11.23/11.43	         sk_A1('const/sets/sup'(sk_A0), sk_A), X0)
11.23/11.43	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)),
11.23/11.43	    inference('simplify', [status(thm)], ['44'])).
11.23/11.43	tff('46', plain,
11.23/11.43	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
11.23/11.43	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
11.23/11.43	       | 'const/realax/real_le'(X27, 'const/sets/sup'(X23))
11.23/11.43	       | ~ zip_tseitin2(X23)),
11.23/11.43	    inference('cnf', [status(esa)], [zf_stmt_3])).
11.23/11.43	tff('47', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
11.23/11.43	      (X0 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | ~ 'const/realax/real_le'(sk_A1(X1, X0), X1)
11.23/11.43	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
11.23/11.43	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
11.23/11.43	tff('48', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
11.23/11.43	      (~ $true
11.23/11.43	       | ~ zip_tseitin2(X0)
11.23/11.43	       | ~ 'const/sets/IN'('type/realax/real', 
11.23/11.43	             sk_A1('const/sets/sup'(X0), X1), X0)
11.23/11.43	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
11.23/11.43	       | X1 = 'const/sets/EMPTY'('type/realax/real')),
11.23/11.43	    inference('sup-', [status(thm)], ['46', '47'])).
11.23/11.43	tff('49', plain,
11.23/11.43	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
11.23/11.43	      (X1 = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
11.23/11.43	       | ~ 'const/sets/IN'('type/realax/real', 
11.23/11.43	             sk_A1('const/sets/sup'(X0), X1), X0)
11.23/11.43	       | ~ zip_tseitin2(X0)),
11.23/11.43	    inference('simplify', [status(thm)], ['48'])).
11.23/11.43	tff('50', plain,
11.23/11.43	    (~ $true
11.23/11.43	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A0)
11.23/11.43	     | ~ zip_tseitin2(sk_A0)
11.23/11.43	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
11.23/11.43	         'const/sets/sup'(sk_A0))
11.23/11.43	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
11.23/11.43	    inference('sup-', [status(thm)], ['45', '49'])).
11.23/11.43	tff('51', plain,
11.23/11.43	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
11.23/11.43	      ('const/sets/SUBSET'(X16, X18, X20)
11.23/11.43	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
11.23/11.43	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
11.23/11.43	tff('52', plain,
11.23/11.43	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
11.23/11.43	      ('const/sets/SUBSET'(X16, X18, X20)
11.23/11.43	       | ~ 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X20)),
11.23/11.43	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
11.23/11.43	tff('53', plain,
11.23/11.43	    ![X0 : $tType, X1 : X0 > $o]:
11.23/11.43	      (~ $true
11.23/11.43	       | 'const/sets/SUBSET'(X0, X1, X1)
11.23/11.43	       | 'const/sets/SUBSET'(X0, X1, X1)),
11.23/11.43	    inference('sup-', [status(thm)], ['51', '52'])).
11.23/11.43	tff('54', plain,
11.23/11.43	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
11.23/11.43	    inference('simplify', [status(thm)], ['53'])).
11.23/11.43	tff('55', plain,
11.23/11.43	    (~ $true
11.23/11.43	     | ~ $true
11.23/11.43	     | ~ zip_tseitin2(sk_A0)
11.23/11.43	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
11.23/11.43	         'const/sets/sup'(sk_A0))
11.23/11.43	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
11.23/11.43	    inference('demod', [status(thm)], ['50', '54'])).
11.23/11.43	tff('56', plain,
11.23/11.43	    (sk_A = 'const/sets/EMPTY'('type/realax/real')
11.23/11.43	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
11.23/11.43	         'const/sets/sup'(sk_A0))
11.23/11.43	     | ~ zip_tseitin2(sk_A0)),
11.23/11.43	    inference('simplify', [status(thm)], ['55'])).
11.23/11.43	tff('57', plain,
11.23/11.43	    ('const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0))
11.23/11.43	     | ~ zip_tseitin2(sk_A0)),
11.23/11.43	    inference('simplify_reflect-', [status(thm)], ['56', '12'])).
11.23/11.43	tff('58', plain, ~ zip_tseitin2(sk_A0),
11.23/11.43	    inference('clc', [status(thm)], ['57', '33'])).
11.23/11.43	tff('59', plain, (~ $true | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
11.23/11.43	    inference('sup-', [status(thm)], ['27', '58'])).
11.23/11.43	tff('60', plain, sk_A0 = 'const/sets/EMPTY'('type/realax/real'),
11.23/11.43	    inference('simplify', [status(thm)], ['59'])).
11.23/11.43	tff('61', plain, ~ $true,
11.23/11.43	    inference('demod', [status(thm)], ['15', '60', '54'])).
11.23/11.43	tff('62', plain, $false, inference('simplify', [status(thm)], ['61'])).
11.23/11.43	
11.23/11.43	% SZS output end Refutation
11.23/11.43	EOF
