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_ext
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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n124.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:43:09 CST 2018
13.71/13.90	% done 2584 iterations in 13.700s
13.71/13.90	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
13.71/13.90	% SZS output start Refutation
13.71/13.90	tff('thm/sets/EXTENSION_', axiom,
13.71/13.90	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
13.71/13.90	     ((A0 = A1) <=>
13.71/13.90	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
13.71/13.90	tff('0', plain,
13.71/13.90	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
13.71/13.90	      (X13 = X15
13.71/13.90	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
13.71/13.90	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
13.71/13.90	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
13.71/13.90	tff('thm/sets/NOT_IN_EMPTY_', axiom,
13.71/13.90	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
13.71/13.90	tff('1', plain,
13.71/13.90	    ![X8 : $tType, X9 : X8]:
13.71/13.90	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
13.71/13.90	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
13.71/13.90	tff('2', plain,
13.71/13.90	    ![X0 : $tType, X1 : X0 > $o]:
13.71/13.90	      (~ $true
13.71/13.90	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)
13.71/13.90	       | X1 = 'const/sets/EMPTY'(X0)),
13.71/13.90	    inference('sup-', [status(thm)], ['0', '1'])).
13.71/13.90	tff('3', plain,
13.71/13.90	    ![X0 : $tType, X1 : X0 > $o]:
13.71/13.90	      (X1 = 'const/sets/EMPTY'(X0)
13.71/13.90	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)),
13.71/13.90	    inference('simplify', [status(thm)], ['2'])).
13.71/13.90	tff('thm/sets/SUBSET_', axiom,
13.71/13.90	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
13.71/13.90	     ('const/sets/SUBSET'(A,A0,A1) <=>
13.71/13.90	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
13.71/13.90	tff('4', plain,
13.71/13.90	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
13.71/13.90	      ('const/sets/SUBSET'(X16, X18, X20)
13.71/13.90	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
13.71/13.90	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
13.71/13.90	tff('thm/sets/REAL_LE_INF_SUBSET_', conjecture,
13.71/13.90	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
13.71/13.90	     (((?[A1:'type/realax/real']:
13.71/13.90	          (![A2:'type/realax/real']:
13.71/13.90	             ('const/sets/IN'('type/realax/real',A2,A) =>
13.71/13.90	              'const/realax/real_le'(A1,A2)))) & 
13.71/13.90	       'const/sets/SUBSET'('type/realax/real',A0,A) & 
13.71/13.90	       (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
13.71/13.90	      'const/realax/real_le'('const/sets/inf'(A),'const/sets/inf'(A0))))).
13.71/13.90	tff(zf_stmt_0, negated_conjecture,
13.71/13.90	  (~
13.71/13.90	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
13.71/13.90	       (((?[A1:'type/realax/real']:
13.71/13.90	            (![A2:'type/realax/real']:
13.71/13.90	               ('const/sets/IN'('type/realax/real',A2,A) =>
13.71/13.90	                'const/realax/real_le'(A1,A2)))) & 
13.71/13.90	         'const/sets/SUBSET'('type/realax/real',A0,A) & 
13.71/13.90	         (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
13.71/13.90	        'const/realax/real_le'('const/sets/inf'(A),'const/sets/inf'(A0)))))).
13.71/13.90	tff('5', plain, 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A),
13.71/13.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
13.71/13.90	tff('6', plain,
13.71/13.90	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
13.71/13.90	      (~ 'const/sets/IN'(X16, X17, X18)
13.71/13.90	       | 'const/sets/IN'(X16, X17, X19)
13.71/13.90	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
13.71/13.90	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
13.71/13.90	tff('7', plain,
13.71/13.90	    ![X0 : 'type/realax/real']:
13.71/13.90	      (~ $true
13.71/13.90	       | 'const/sets/IN'('type/realax/real', X0, sk_A)
13.71/13.90	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A0)),
13.71/13.90	    inference('sup-', [status(thm)], ['5', '6'])).
13.71/13.90	tff('8', plain,
13.71/13.90	    ![X0 : 'type/realax/real']:
13.71/13.90	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A0)
13.71/13.90	       | 'const/sets/IN'('type/realax/real', X0, sk_A)),
13.71/13.90	    inference('simplify', [status(thm)], ['7'])).
13.71/13.90	tff('9', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o]:
13.71/13.90	      (~ $true
13.71/13.90	       | 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
13.71/13.90	       | 'const/sets/IN'('type/realax/real', 
13.71/13.90	           sk_A21('type/realax/real', X0, sk_A0), sk_A)),
13.71/13.90	    inference('sup-', [status(thm)], ['4', '8'])).
13.71/13.90	tff('10', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o]:
13.71/13.90	      ('const/sets/IN'('type/realax/real', 
13.71/13.90	         sk_A21('type/realax/real', X0, sk_A0), sk_A)
13.71/13.90	       | 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)),
13.71/13.90	    inference('simplify', [status(thm)], ['9'])).
13.71/13.90	tff('11', plain,
13.71/13.90	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
13.71/13.90	      (~ $true
13.71/13.90	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
13.71/13.90	       | ~ 'const/sets/IN'(X0, X1, X2)),
13.71/13.90	    inference('sup-', [status(thm)], ['6', '1'])).
13.71/13.90	tff('12', plain,
13.71/13.90	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
13.71/13.90	      (~ 'const/sets/IN'(X0, X1, X2)
13.71/13.90	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))),
13.71/13.90	    inference('simplify', [status(thm)], ['11'])).
13.71/13.90	tff('13', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o]:
13.71/13.90	      (~ $true
13.71/13.90	       | 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
13.71/13.90	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	             'const/sets/EMPTY'('type/realax/real'))),
13.71/13.90	    inference('sup-', [status(thm)], ['10', '12'])).
13.71/13.90	tff('14', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o]:
13.71/13.90	      (~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	           'const/sets/EMPTY'('type/realax/real'))
13.71/13.90	       | 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)),
13.71/13.90	    inference('simplify', [status(thm)], ['13'])).
13.71/13.90	tff('15', plain,
13.71/13.90	    ![X0 : 'type/realax/real']:
13.71/13.90	      (~ $true
13.71/13.90	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	             'const/sets/EMPTY'('type/realax/real'))
13.71/13.90	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A0)),
13.71/13.90	    inference('sup-', [status(thm)], ['14', '12'])).
13.71/13.90	tff('16', plain,
13.71/13.90	    ![X0 : 'type/realax/real']:
13.71/13.90	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A0)
13.71/13.90	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	             'const/sets/EMPTY'('type/realax/real'))),
13.71/13.90	    inference('simplify', [status(thm)], ['15'])).
13.71/13.90	tff('17', plain,
13.71/13.90	    (~ $true
13.71/13.90	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	           'const/sets/EMPTY'('type/realax/real'))),
13.71/13.90	    inference('sup-', [status(thm)], ['3', '16'])).
13.71/13.90	tff('18', plain,
13.71/13.90	    (~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	         'const/sets/EMPTY'('type/realax/real'))
13.71/13.90	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('simplify', [status(thm)], ['17'])).
13.71/13.90	tff('19', plain,
13.71/13.90	    ![X1 : 'type/realax/real']:
13.71/13.90	      (sk_A0(X1) = 'const/sets/EMPTY'('type/realax/real', X1)
13.71/13.90	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	             'const/sets/EMPTY'('type/realax/real'))),
13.71/13.90	    inference('ho_complete_eq', [status(thm)], ['18'])).
13.71/13.90	tff('20', plain, sk_A0 != 'const/sets/EMPTY'('type/realax/real'),
13.71/13.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
13.71/13.90	tff('21', plain,
13.71/13.90	    sk_A0('#k1') != 'const/sets/EMPTY'('type/realax/real', '#k1'),
13.71/13.90	    inference('rw_lit', [status(thm)], ['20'])).
13.71/13.90	tff('22', plain,
13.71/13.90	    ('const/sets/EMPTY'('type/realax/real', '#k1')
13.71/13.90	      != 'const/sets/EMPTY'('type/realax/real', '#k1')
13.71/13.90	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	           'const/sets/EMPTY'('type/realax/real'))),
13.71/13.90	    inference('sup-', [status(thm)], ['19', '21'])).
13.71/13.90	tff('23', plain,
13.71/13.90	    ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
13.71/13.90	        'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('simplify', [status(thm)], ['22'])).
13.71/13.90	tff('thm/sets/INF_', axiom,
13.71/13.90	  (![A:('type/realax/real' > $o)]:
13.71/13.90	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
13.71/13.90	       (?[A0:'type/realax/real']:
13.71/13.90	          (![A1:'type/realax/real']:
13.71/13.90	             ('const/sets/IN'('type/realax/real',A1,A) =>
13.71/13.90	              'const/realax/real_le'(A0,A1))))) =>
13.71/13.90	      ((![A0:'type/realax/real']:
13.71/13.90	          ('const/sets/IN'('type/realax/real',A0,A) =>
13.71/13.90	           'const/realax/real_le'('const/sets/inf'(A),A0))) & 
13.71/13.90	       (![A0:'type/realax/real']:
13.71/13.90	          ((![A1:'type/realax/real']:
13.71/13.90	              ('const/sets/IN'('type/realax/real',A1,A) =>
13.71/13.90	               'const/realax/real_le'(A0,A1))) =>
13.71/13.90	           'const/realax/real_le'(A0,'const/sets/inf'(A)))))))).
13.71/13.90	tff(zf_stmt_1, axiom,
13.71/13.90	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A0,A1)) =>
13.71/13.90	   zip_tseitin0(A1,A0,A))).
13.71/13.90	tff('24', plain,
13.71/13.90	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
13.71/13.90	      X23 : 'type/realax/real' > $o]:
13.71/13.90	      (zip_tseitin0(X21, X22, X23)
13.71/13.90	       | 'const/sets/IN'('type/realax/real', X21, X23)),
13.71/13.90	    inference('cnf', [status(esa)], [zf_stmt_1])).
13.71/13.90	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
13.71/13.90	tff(zf_stmt_3, axiom,
13.71/13.90	  (zip_tseitin2(A) =>
13.71/13.90	   ((![A0:'type/realax/real']:
13.71/13.90	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
13.71/13.90	        'const/realax/real_le'(A0,'const/sets/inf'(A)))) & 
13.71/13.90	    (![A0:'type/realax/real']:
13.71/13.90	       ('const/sets/IN'('type/realax/real',A0,A) =>
13.71/13.90	        'const/realax/real_le'('const/sets/inf'(A),A0)))))).
13.71/13.90	tff(zf_stmt_4, type, zip_tseitin1 :
13.71/13.90	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
13.71/13.90	tff(zf_stmt_5, axiom,
13.71/13.90	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A0,A1)) =>
13.71/13.90	   zip_tseitin1(A1,A0,A))).
13.71/13.90	tff(zf_stmt_6, type, zip_tseitin0 :
13.71/13.90	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
13.71/13.90	tff(zf_stmt_7, axiom,
13.71/13.90	  (![A:('type/realax/real' > $o)]:
13.71/13.90	     (((?[A0:'type/realax/real']:
13.71/13.90	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
13.71/13.90	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
13.71/13.90	      zip_tseitin2(A)))).
13.71/13.90	tff('25', plain,
13.71/13.90	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
13.71/13.90	      (zip_tseitin2(X28)
13.71/13.90	       | X28 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
13.71/13.90	    inference('cnf', [status(esa)], [zf_stmt_7])).
13.71/13.90	tff('26', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
13.71/13.90	      (~ $true
13.71/13.90	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)
13.71/13.90	       | X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | zip_tseitin2(X0)),
13.71/13.90	    inference('sup-', [status(thm)], ['24', '25'])).
13.71/13.90	tff('27', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
13.71/13.90	      (zip_tseitin2(X0)
13.71/13.90	       | X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)),
13.71/13.90	    inference('simplify', [status(thm)], ['26'])).
13.71/13.90	tff('28', plain,
13.71/13.90	    ![X30 : 'type/realax/real']:
13.71/13.90	      ('const/realax/real_le'(sk_A13, X30)
13.71/13.90	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A)),
13.71/13.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
13.71/13.90	tff('29', plain,
13.71/13.90	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
13.71/13.90	      X23 : 'type/realax/real' > $o]:
13.71/13.90	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X22, X21)),
13.71/13.90	    inference('cnf', [status(esa)], [zf_stmt_1])).
13.71/13.90	tff('30', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
13.71/13.90	      (~ $true
13.71/13.90	       | ~ 'const/realax/real_le'(X1, sk_A12(X1, X0))
13.71/13.90	       | X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | zip_tseitin2(X0)),
13.71/13.90	    inference('sup-', [status(thm)], ['29', '25'])).
13.71/13.90	tff('31', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
13.71/13.90	      (zip_tseitin2(X0)
13.71/13.90	       | X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | ~ 'const/realax/real_le'(X1, sk_A12(X1, X0))),
13.71/13.90	    inference('simplify', [status(thm)], ['30'])).
13.71/13.90	tff('32', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o]:
13.71/13.90	      (~ $true
13.71/13.90	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A)
13.71/13.90	       | X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | zip_tseitin2(X0)),
13.71/13.90	    inference('sup-', [status(thm)], ['28', '31'])).
13.71/13.90	tff('33', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o]:
13.71/13.90	      (zip_tseitin2(X0)
13.71/13.90	       | X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A)),
13.71/13.90	    inference('simplify', [status(thm)], ['32'])).
13.71/13.90	tff('34', plain,
13.71/13.90	    (~ $true
13.71/13.90	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	     | zip_tseitin2(sk_A)
13.71/13.90	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	     | zip_tseitin2(sk_A)),
13.71/13.90	    inference('sup-', [status(thm)], ['27', '33'])).
13.71/13.90	tff('35', plain,
13.71/13.90	    (zip_tseitin2(sk_A) | sk_A = 'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('simplify', [status(thm)], ['34'])).
13.71/13.90	tff('thm/sets/REAL_LE_INF_', axiom,
13.71/13.90	  (![A:('type/realax/real' > $o),A0:'type/realax/real']:
13.71/13.90	     (((![A1:'type/realax/real']:
13.71/13.90	          ('const/sets/IN'('type/realax/real',A1,A) =>
13.71/13.90	           'const/realax/real_le'(A0,A1))) & 
13.71/13.90	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
13.71/13.90	      'const/realax/real_le'(A0,'const/sets/inf'(A))))).
13.71/13.90	tff('36', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
13.71/13.90	      (X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X0)
13.71/13.90	       | 'const/realax/real_le'(X1, 'const/sets/inf'(X0))),
13.71/13.90	    inference('cnf', [status(esa)], [thm/sets/REAL_LE_INF_])).
13.71/13.90	tff('37', plain,
13.71/13.90	    ![X0 : 'type/realax/real']:
13.71/13.90	      (~ $true
13.71/13.90	       | 'const/realax/real_le'(X0, 'const/sets/inf'(sk_A0))
13.71/13.90	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | 'const/sets/IN'('type/realax/real', sk_A1(X0, sk_A0), sk_A)),
13.71/13.90	    inference('sup-', [status(thm)], ['36', '8'])).
13.71/13.90	tff('38', plain,
13.71/13.90	    ![X0 : 'type/realax/real']:
13.71/13.90	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A0), sk_A)
13.71/13.90	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | 'const/realax/real_le'(X0, 'const/sets/inf'(sk_A0))),
13.71/13.90	    inference('simplify', [status(thm)], ['37'])).
13.71/13.90	tff('39', plain,
13.71/13.90	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
13.71/13.90	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
13.71/13.90	       | 'const/realax/real_le'('const/sets/inf'(X23), X27)
13.71/13.90	       | ~ zip_tseitin2(X23)),
13.71/13.90	    inference('cnf', [status(esa)], [zf_stmt_3])).
13.71/13.90	tff('40', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
13.71/13.90	      (X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | ~ 'const/realax/real_le'(X1, sk_A1(X1, X0))
13.71/13.90	       | 'const/realax/real_le'(X1, 'const/sets/inf'(X0))),
13.71/13.90	    inference('cnf', [status(esa)], [thm/sets/REAL_LE_INF_])).
13.71/13.90	tff('41', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
13.71/13.90	      (~ $true
13.71/13.90	       | ~ zip_tseitin2(X1)
13.71/13.90	       | ~ 'const/sets/IN'('type/realax/real', 
13.71/13.90	             sk_A1('const/sets/inf'(X1), X0), X1)
13.71/13.90	       | 'const/realax/real_le'('const/sets/inf'(X1), 'const/sets/inf'(X0))
13.71/13.90	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('sup-', [status(thm)], ['39', '40'])).
13.71/13.90	tff('42', plain,
13.71/13.90	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
13.71/13.90	      (X0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	       | 'const/realax/real_le'('const/sets/inf'(X1), 'const/sets/inf'(X0))
13.71/13.90	       | ~ 'const/sets/IN'('type/realax/real', 
13.71/13.90	             sk_A1('const/sets/inf'(X1), X0), X1)
13.71/13.90	       | ~ zip_tseitin2(X1)),
13.71/13.90	    inference('simplify', [status(thm)], ['41'])).
13.71/13.90	tff('43', plain,
13.71/13.90	    (~ $true
13.71/13.90	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
13.71/13.90	         'const/sets/inf'(sk_A0))
13.71/13.90	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	     | ~ zip_tseitin2(sk_A)
13.71/13.90	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
13.71/13.90	         'const/sets/inf'(sk_A0))
13.71/13.90	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('sup-', [status(thm)], ['38', '42'])).
13.71/13.90	tff('44', plain,
13.71/13.90	    (~ zip_tseitin2(sk_A)
13.71/13.90	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
13.71/13.90	         'const/sets/inf'(sk_A0))),
13.71/13.90	    inference('simplify', [status(thm)], ['43'])).
13.71/13.90	tff('45', plain,
13.71/13.90	    ~ 'const/realax/real_le'('const/sets/inf'(sk_A), 'const/sets/inf'(sk_A0)),
13.71/13.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
13.71/13.90	tff('46', plain,
13.71/13.90	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real') | ~ zip_tseitin2(sk_A)),
13.71/13.90	    inference('clc', [status(thm)], ['44', '45'])).
13.71/13.90	tff('47', plain,
13.71/13.90	    (~ $true
13.71/13.90	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('sup-', [status(thm)], ['35', '46'])).
13.71/13.90	tff('48', plain,
13.71/13.90	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
13.71/13.90	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('simplify', [status(thm)], ['47'])).
13.71/13.90	tff('49', plain,
13.71/13.90	    ![X1 : 'type/realax/real']:
13.71/13.90	      (sk_A0(X1) = 'const/sets/EMPTY'('type/realax/real', X1)
13.71/13.90	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('ho_complete_eq', [status(thm)], ['48'])).
13.71/13.90	tff('50', plain,
13.71/13.90	    ('const/sets/EMPTY'('type/realax/real', '#k1')
13.71/13.90	      != 'const/sets/EMPTY'('type/realax/real', '#k1')
13.71/13.90	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
13.71/13.90	    inference('sup-', [status(thm)], ['49', '21'])).
13.71/13.90	tff('51', plain, sk_A = 'const/sets/EMPTY'('type/realax/real'),
13.71/13.90	    inference('simplify', [status(thm)], ['50'])).
13.71/13.90	tff('52', plain,
13.71/13.90	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
13.71/13.90	      ('const/sets/SUBSET'(X16, X18, X20)
13.71/13.90	       | ~ 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X20)),
13.71/13.90	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
13.71/13.90	tff('53', plain,
13.71/13.90	    ![X0 : $tType, X1 : X0 > $o]:
13.71/13.90	      (~ $true
13.71/13.90	       | 'const/sets/SUBSET'(X0, X1, X1)
13.71/13.90	       | 'const/sets/SUBSET'(X0, X1, X1)),
13.71/13.90	    inference('sup-', [status(thm)], ['4', '52'])).
13.71/13.90	tff('54', plain,
13.71/13.90	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
13.71/13.90	    inference('simplify', [status(thm)], ['53'])).
13.71/13.90	tff('55', plain, ~ $true,
13.71/13.90	    inference('demod', [status(thm)], ['23', '51', '54'])).
13.71/13.90	tff('56', plain, $false, inference('simplify', [status(thm)], ['55'])).
13.71/13.90	
13.71/13.90	% SZS output end Refutation
13.71/13.91	EOF
