0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_int
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-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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n176.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:41:24 CST 2018
31.55/31.75	% done 4243 iterations in 31.549s
31.55/31.75	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
31.55/31.75	% SZS output start Refutation
31.55/31.76	tff('thm/sets/SUBSET_', axiom,
31.55/31.76	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
31.55/31.76	     ('const/sets/SUBSET'(A,A0,A1) <=>
31.55/31.76	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
31.55/31.76	tff('0', plain,
31.55/31.76	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
31.55/31.76	      ('const/sets/SUBSET'(X16, X18, X20)
31.55/31.76	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
31.55/31.76	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
31.55/31.76	tff('1', plain,
31.55/31.76	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
31.55/31.76	      ('const/sets/SUBSET'(X16, X18, X20)
31.55/31.76	       | ~ 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X20)),
31.55/31.76	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
31.55/31.76	tff('2', plain,
31.55/31.76	    ![X0 : $tType, X1 : X0 > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | 'const/sets/SUBSET'(X0, X1, X1)
31.55/31.76	       | 'const/sets/SUBSET'(X0, X1, X1)),
31.55/31.76	    inference('sup-', [status(thm)], ['0', '1'])).
31.55/31.76	tff('3', plain,
31.55/31.76	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
31.55/31.76	    inference('simplify', [status(thm)], ['2'])).
31.55/31.76	tff('thm/sets/EXTENSION_', axiom,
31.55/31.76	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
31.55/31.76	     ((A0 = A1) <=>
31.55/31.76	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
31.55/31.76	tff('4', plain,
31.55/31.76	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
31.55/31.76	      (X13 = X15
31.55/31.76	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
31.55/31.76	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
31.55/31.76	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
31.55/31.76	tff('thm/sets/NOT_IN_EMPTY_', axiom,
31.55/31.76	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
31.55/31.76	tff('5', plain,
31.55/31.76	    ![X8 : $tType, X9 : X8]:
31.55/31.76	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
31.55/31.76	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
31.55/31.76	tff('6', plain,
31.55/31.76	    ![X0 : $tType, X1 : X0 > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)
31.55/31.76	       | X1 = 'const/sets/EMPTY'(X0)),
31.55/31.76	    inference('sup-', [status(thm)], ['4', '5'])).
31.55/31.76	tff('7', plain,
31.55/31.76	    ![X0 : $tType, X1 : X0 > $o]:
31.55/31.76	      (X1 = 'const/sets/EMPTY'(X0)
31.55/31.76	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)),
31.55/31.76	    inference('simplify', [status(thm)], ['6'])).
31.55/31.76	tff('thm/sets/REAL_SUP_LE_SUBSET_', conjecture,
31.55/31.76	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
31.55/31.76	     (((?[A1:'type/realax/real']:
31.55/31.76	          (![A2:'type/realax/real']:
31.55/31.76	             ('const/sets/IN'('type/realax/real',A2,A0) =>
31.55/31.76	              'const/realax/real_le'(A2,A1)))) & 
31.55/31.76	       'const/sets/SUBSET'('type/realax/real',A,A0) & 
31.55/31.76	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
31.55/31.76	      'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0))))).
31.55/31.76	tff(zf_stmt_0, negated_conjecture,
31.55/31.76	  (~
31.55/31.76	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
31.55/31.76	       (((?[A1:'type/realax/real']:
31.55/31.76	            (![A2:'type/realax/real']:
31.55/31.76	               ('const/sets/IN'('type/realax/real',A2,A0) =>
31.55/31.76	                'const/realax/real_le'(A2,A1)))) & 
31.55/31.76	         'const/sets/SUBSET'('type/realax/real',A,A0) & 
31.55/31.76	         (A != 'const/sets/EMPTY'('type/realax/real'))) =>
31.55/31.76	        'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0)))))).
31.55/31.76	tff('8', plain, 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A0),
31.55/31.76	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.55/31.76	tff('9', plain,
31.55/31.76	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
31.55/31.76	      (~ 'const/sets/IN'(X16, X17, X18)
31.55/31.76	       | 'const/sets/IN'(X16, X17, X19)
31.55/31.76	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
31.55/31.76	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
31.55/31.76	tff('10', plain,
31.55/31.76	    ![X0 : 'type/realax/real']:
31.55/31.76	      (~ $true
31.55/31.76	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
31.55/31.76	    inference('sup-', [status(thm)], ['8', '9'])).
31.55/31.76	tff('11', plain,
31.55/31.76	    ![X0 : 'type/realax/real']:
31.55/31.76	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
31.55/31.76	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)),
31.55/31.76	    inference('simplify', [status(thm)], ['10'])).
31.55/31.76	tff('12', plain,
31.55/31.76	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
31.55/31.76	       | ~ 'const/sets/IN'(X0, X1, X2)),
31.55/31.76	    inference('sup-', [status(thm)], ['9', '5'])).
31.55/31.76	tff('13', plain,
31.55/31.76	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
31.55/31.76	      (~ 'const/sets/IN'(X0, X1, X2)
31.55/31.76	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))),
31.55/31.76	    inference('simplify', [status(thm)], ['12'])).
31.55/31.76	tff('14', plain,
31.55/31.76	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | ~ 'const/sets/SUBSET'(X0, X3, X1)
31.55/31.76	       | ~ 'const/sets/IN'(X0, X2, X3)
31.55/31.76	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
31.55/31.76	    inference('sup-', [status(thm)], ['9', '13'])).
31.55/31.76	tff('15', plain,
31.55/31.76	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
31.55/31.76	      (~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))
31.55/31.76	       | ~ 'const/sets/IN'(X0, X2, X3)
31.55/31.76	       | ~ 'const/sets/SUBSET'(X0, X3, X1)),
31.55/31.76	    inference('simplify', [status(thm)], ['14'])).
31.55/31.76	tff('16', plain,
31.55/31.76	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', X1, 
31.55/31.76	             'const/sets/EMPTY'('type/realax/real'))),
31.55/31.76	    inference('sup-', [status(thm)], ['11', '15'])).
31.55/31.76	tff('17', plain,
31.55/31.76	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
31.55/31.76	      (~ 'const/sets/SUBSET'('type/realax/real', X1, 
31.55/31.76	           'const/sets/EMPTY'('type/realax/real'))
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
31.55/31.76	    inference('simplify', [status(thm)], ['16'])).
31.55/31.76	tff('18', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', X0, 
31.55/31.76	             'const/sets/EMPTY'('type/realax/real'))),
31.55/31.76	    inference('sup-', [status(thm)], ['7', '17'])).
31.55/31.76	tff('19', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o]:
31.55/31.76	      (~ 'const/sets/SUBSET'('type/realax/real', X0, 
31.55/31.76	           'const/sets/EMPTY'('type/realax/real'))
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
31.55/31.76	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
31.55/31.76	    inference('simplify', [status(thm)], ['18'])).
31.55/31.76	tff('20', plain, sk_A != 'const/sets/EMPTY'('type/realax/real'),
31.55/31.76	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.55/31.76	tff('21', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o]:
31.55/31.76	      (~ 'const/sets/SUBSET'('type/realax/real', X0, 
31.55/31.76	           'const/sets/EMPTY'('type/realax/real'))
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)),
31.55/31.76	    inference('simplify_reflect-', [status(thm)], ['19', '20'])).
31.55/31.76	tff('22', plain,
31.55/31.76	    (~ $true
31.55/31.76	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
31.55/31.76	           'const/sets/EMPTY'('type/realax/real'))),
31.55/31.76	    inference('sup-', [status(thm)], ['3', '21'])).
31.55/31.76	tff('23', plain,
31.55/31.76	    ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
31.55/31.76	        'const/sets/EMPTY'('type/realax/real')),
31.55/31.76	    inference('simplify', [status(thm)], ['22'])).
31.55/31.76	tff('thm/sets/SUP_', axiom,
31.55/31.76	  (![A:('type/realax/real' > $o)]:
31.55/31.76	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
31.55/31.76	       (?[A0:'type/realax/real']:
31.55/31.76	          (![A1:'type/realax/real']:
31.55/31.76	             ('const/sets/IN'('type/realax/real',A1,A) =>
31.55/31.76	              'const/realax/real_le'(A1,A0))))) =>
31.55/31.76	      ((![A0:'type/realax/real']:
31.55/31.76	          ('const/sets/IN'('type/realax/real',A0,A) =>
31.55/31.76	           'const/realax/real_le'(A0,'const/sets/sup'(A)))) & 
31.55/31.76	       (![A0:'type/realax/real']:
31.55/31.76	          ((![A1:'type/realax/real']:
31.55/31.76	              ('const/sets/IN'('type/realax/real',A1,A) =>
31.55/31.76	               'const/realax/real_le'(A1,A0))) =>
31.55/31.76	           'const/realax/real_le'('const/sets/sup'(A),A0))))))).
31.55/31.76	tff(zf_stmt_1, axiom,
31.55/31.76	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
31.55/31.76	   zip_tseitin0(A1,A0,A))).
31.55/31.76	tff('24', plain,
31.55/31.76	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
31.55/31.76	      X23 : 'type/realax/real' > $o]:
31.55/31.76	      (zip_tseitin0(X21, X22, X23)
31.55/31.76	       | 'const/sets/IN'('type/realax/real', X21, X23)),
31.55/31.76	    inference('cnf', [status(esa)], [zf_stmt_1])).
31.55/31.76	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
31.55/31.76	tff(zf_stmt_3, axiom,
31.55/31.76	  (zip_tseitin2(A) =>
31.55/31.76	   ((![A0:'type/realax/real']:
31.55/31.76	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
31.55/31.76	        'const/realax/real_le'('const/sets/sup'(A),A0))) & 
31.55/31.76	    (![A0:'type/realax/real']:
31.55/31.76	       ('const/sets/IN'('type/realax/real',A0,A) =>
31.55/31.76	        'const/realax/real_le'(A0,'const/sets/sup'(A))))))).
31.55/31.76	tff(zf_stmt_4, type, zip_tseitin1 :
31.55/31.76	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
31.55/31.76	tff(zf_stmt_5, axiom,
31.55/31.76	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
31.55/31.76	   zip_tseitin1(A1,A0,A))).
31.55/31.76	tff(zf_stmt_6, type, zip_tseitin0 :
31.55/31.76	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
31.55/31.76	tff(zf_stmt_7, axiom,
31.55/31.76	  (![A:('type/realax/real' > $o)]:
31.55/31.76	     (((?[A0:'type/realax/real']:
31.55/31.76	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
31.55/31.76	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
31.55/31.76	      zip_tseitin2(A)))).
31.55/31.76	tff('25', plain,
31.55/31.76	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
31.55/31.76	      (zip_tseitin2(X28)
31.55/31.76	       | X28 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
31.55/31.76	    inference('cnf', [status(esa)], [zf_stmt_7])).
31.55/31.76	tff('26', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
31.55/31.76	      (~ $true
31.55/31.76	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)
31.55/31.76	       | X0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | zip_tseitin2(X0)),
31.55/31.76	    inference('sup-', [status(thm)], ['24', '25'])).
31.55/31.76	tff('27', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
31.55/31.76	      (zip_tseitin2(X0)
31.55/31.76	       | X0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)),
31.55/31.76	    inference('simplify', [status(thm)], ['26'])).
31.55/31.76	tff('28', plain,
31.55/31.76	    ![X30 : 'type/realax/real']:
31.55/31.76	      ('const/realax/real_le'(X30, sk_A13)
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A0)),
31.55/31.76	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.55/31.76	tff('29', plain,
31.55/31.76	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
31.55/31.76	      X23 : 'type/realax/real' > $o]:
31.55/31.76	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X21, X22)),
31.55/31.76	    inference('cnf', [status(esa)], [zf_stmt_1])).
31.55/31.76	tff('30', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
31.55/31.76	      (~ $true
31.55/31.76	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)
31.55/31.76	       | X0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | zip_tseitin2(X0)),
31.55/31.76	    inference('sup-', [status(thm)], ['29', '25'])).
31.55/31.76	tff('31', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
31.55/31.76	      (zip_tseitin2(X0)
31.55/31.76	       | X0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)),
31.55/31.76	    inference('simplify', [status(thm)], ['30'])).
31.55/31.76	tff('32', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A0)
31.55/31.76	       | X0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | zip_tseitin2(X0)),
31.55/31.76	    inference('sup-', [status(thm)], ['28', '31'])).
31.55/31.76	tff('33', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o]:
31.55/31.76	      (zip_tseitin2(X0)
31.55/31.76	       | X0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A0)),
31.55/31.76	    inference('simplify', [status(thm)], ['32'])).
31.55/31.76	tff('34', plain,
31.55/31.76	    (~ $true
31.55/31.76	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	     | zip_tseitin2(sk_A0)
31.55/31.76	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	     | zip_tseitin2(sk_A0)),
31.55/31.76	    inference('sup-', [status(thm)], ['27', '33'])).
31.55/31.76	tff('35', plain,
31.55/31.76	    (zip_tseitin2(sk_A0) | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
31.55/31.76	    inference('simplify', [status(thm)], ['34'])).
31.55/31.76	tff('thm/sets/REAL_SUP_LE_', axiom,
31.55/31.76	  (![A:('type/realax/real' > $o),A0:'type/realax/real']:
31.55/31.76	     (((![A1:'type/realax/real']:
31.55/31.76	          ('const/sets/IN'('type/realax/real',A1,A) =>
31.55/31.76	           'const/realax/real_le'(A1,A0))) & 
31.55/31.76	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
31.55/31.76	      'const/realax/real_le'('const/sets/sup'(A),A0)))).
31.55/31.76	tff('36', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
31.55/31.76	      (X0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X0)
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
31.55/31.76	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
31.55/31.76	tff('37', plain,
31.55/31.76	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
31.55/31.76	       | 'const/sets/IN'('type/realax/real', X0, X1)),
31.55/31.76	    inference('sup-', [status(thm)], ['11', '9'])).
31.55/31.76	tff('38', plain,
31.55/31.76	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
31.55/31.76	      ('const/sets/IN'('type/realax/real', X0, X1)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
31.55/31.76	    inference('simplify', [status(thm)], ['37'])).
31.55/31.76	tff('39', plain,
31.55/31.76	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)
31.55/31.76	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
31.55/31.76	       | 'const/sets/IN'('type/realax/real', sk_A1(X0, sk_A), X1)),
31.55/31.76	    inference('sup-', [status(thm)], ['36', '38'])).
31.55/31.76	tff('40', plain,
31.55/31.76	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
31.55/31.76	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A), X1)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
31.55/31.76	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)),
31.55/31.76	    inference('simplify', [status(thm)], ['39'])).
31.55/31.76	tff('41', plain,
31.55/31.76	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
31.55/31.76	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A), X1)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)),
31.55/31.76	    inference('simplify_reflect-', [status(thm)], ['40', '20'])).
31.55/31.76	tff('42', plain,
31.55/31.76	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
31.55/31.76	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
31.55/31.76	       | 'const/realax/real_le'(X27, 'const/sets/sup'(X23))
31.55/31.76	       | ~ zip_tseitin2(X23)),
31.55/31.76	    inference('cnf', [status(esa)], [zf_stmt_3])).
31.55/31.76	tff('43', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
31.55/31.76	      (X0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | ~ 'const/realax/real_le'(sk_A1(X1, X0), X1)
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
31.55/31.76	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
31.55/31.76	tff('44', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | ~ zip_tseitin2(X0)
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', 
31.55/31.76	             sk_A1('const/sets/sup'(X0), X1), X0)
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
31.55/31.76	       | X1 = 'const/sets/EMPTY'('type/realax/real')),
31.55/31.76	    inference('sup-', [status(thm)], ['42', '43'])).
31.55/31.76	tff('45', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
31.55/31.76	      (X1 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
31.55/31.76	       | ~ 'const/sets/IN'('type/realax/real', 
31.55/31.76	             sk_A1('const/sets/sup'(X0), X1), X0)
31.55/31.76	       | ~ zip_tseitin2(X0)),
31.55/31.76	    inference('simplify', [status(thm)], ['44'])).
31.55/31.76	tff('46', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o]:
31.55/31.76	      (~ $true
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(X0))
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
31.55/31.76	       | ~ zip_tseitin2(X0)
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(X0))
31.55/31.76	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
31.55/31.76	    inference('sup-', [status(thm)], ['41', '45'])).
31.55/31.76	tff('47', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o]:
31.55/31.76	      (sk_A = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	       | ~ zip_tseitin2(X0)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(X0))),
31.55/31.76	    inference('simplify', [status(thm)], ['46'])).
31.55/31.76	tff('48', plain,
31.55/31.76	    ![X0 : 'type/realax/real' > $o]:
31.55/31.76	      (~ zip_tseitin2(X0)
31.55/31.76	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
31.55/31.76	       | 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(X0))),
31.55/31.76	    inference('simplify_reflect-', [status(thm)], ['47', '20'])).
31.55/31.76	tff('49', plain,
31.55/31.76	    (~ $true
31.55/31.76	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
31.55/31.76	         'const/sets/sup'(sk_A0))
31.55/31.76	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A0)),
31.55/31.76	    inference('sup-', [status(thm)], ['35', '48'])).
31.55/31.76	tff('50', plain,
31.55/31.76	    (~ $true
31.55/31.76	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
31.55/31.76	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
31.55/31.76	         'const/sets/sup'(sk_A0))
31.55/31.76	     | ~ $true),
31.55/31.76	    inference('demod', [status(thm)], ['49', '3'])).
31.55/31.76	tff('51', plain,
31.55/31.76	    ('const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0))
31.55/31.76	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
31.55/31.76	    inference('simplify', [status(thm)], ['50'])).
31.55/31.76	tff('52', plain,
31.55/31.76	    ~ 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0)),
31.55/31.76	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.55/31.76	tff('53', plain, sk_A0 = 'const/sets/EMPTY'('type/realax/real'),
31.55/31.76	    inference('clc', [status(thm)], ['51', '52'])).
31.55/31.76	tff('54', plain, ~ $true,
31.55/31.76	    inference('demod', [status(thm)], ['23', '53', '3'])).
31.55/31.76	tff('55', plain, $false, inference('simplify', [status(thm)], ['54'])).
31.55/31.76	
31.55/31.76	% SZS output end Refutation
31.55/31.76	EOF
