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    : supatvars_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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --sup-at-vars \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n066.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:44:38 CST 2018
1.77/1.94	% done 1408 iterations in 1.736s
1.77/1.94	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
1.77/1.94	% SZS output start Refutation
1.77/1.94	tff('thm/sets/EXTENSION_', axiom,
1.77/1.94	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
1.77/1.94	     ((A0 = A1) <=>
1.77/1.94	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
1.77/1.94	tff('0', plain,
1.77/1.94	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
1.77/1.94	      (X13 = X15
1.77/1.94	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
1.77/1.94	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
1.77/1.94	tff('thm/sets/NOT_IN_EMPTY_', axiom,
1.77/1.94	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
1.77/1.94	tff('1', plain,
1.77/1.94	    ![X8 : $tType, X9 : X8]:
1.77/1.94	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
1.77/1.94	tff('2', plain,
1.77/1.94	    ![X0 : $tType, X1 : X0 > $o]:
1.77/1.94	      (~ $true
1.77/1.94	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)
1.77/1.94	       | X1 = 'const/sets/EMPTY'(X0)),
1.77/1.94	    inference('sup-', [status(thm)], ['0', '1'])).
1.77/1.94	tff('3', plain,
1.77/1.94	    ![X0 : $tType, X1 : X0 > $o]:
1.77/1.94	      (X1 = 'const/sets/EMPTY'(X0)
1.77/1.94	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)),
1.77/1.94	    inference('simplify', [status(thm)], ['2'])).
1.77/1.94	tff('thm/sets/REAL_LE_INF_SUBSET_', conjecture,
1.77/1.94	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
1.77/1.94	     (((?[A1:'type/realax/real']:
1.77/1.94	          (![A2:'type/realax/real']:
1.77/1.94	             ('const/sets/IN'('type/realax/real',A2,A) =>
1.77/1.94	              'const/realax/real_le'(A1,A2)))) & 
1.77/1.94	       'const/sets/SUBSET'('type/realax/real',A0,A) & 
1.77/1.94	       (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
1.77/1.94	      'const/realax/real_le'('const/sets/inf'(A),'const/sets/inf'(A0))))).
1.77/1.94	tff(zf_stmt_0, negated_conjecture,
1.77/1.94	  (~
1.77/1.94	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
1.77/1.94	       (((?[A1:'type/realax/real']:
1.77/1.94	            (![A2:'type/realax/real']:
1.77/1.94	               ('const/sets/IN'('type/realax/real',A2,A) =>
1.77/1.94	                'const/realax/real_le'(A1,A2)))) & 
1.77/1.94	         'const/sets/SUBSET'('type/realax/real',A0,A) & 
1.77/1.94	         (A0 != 'const/sets/EMPTY'('type/realax/real'))) =>
1.77/1.94	        'const/realax/real_le'('const/sets/inf'(A),'const/sets/inf'(A0)))))).
1.77/1.94	tff('4', plain, 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A),
1.77/1.94	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.77/1.94	tff('thm/sets/SUBSET_', axiom,
1.77/1.94	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
1.77/1.94	     ('const/sets/SUBSET'(A,A0,A1) <=>
1.77/1.94	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
1.77/1.94	tff('5', plain,
1.77/1.94	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
1.77/1.94	      (~ 'const/sets/IN'(X16, X17, X18)
1.77/1.94	       | 'const/sets/IN'(X16, X17, X19)
1.77/1.94	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
1.77/1.94	tff('6', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      (~ $true
1.77/1.94	       | 'const/sets/IN'('type/realax/real', X0, sk_A)
1.77/1.94	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A0)),
1.77/1.94	    inference('sup-', [status(thm)], ['4', '5'])).
1.77/1.94	tff('7', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A0)
1.77/1.94	       | 'const/sets/IN'('type/realax/real', X0, sk_A)),
1.77/1.94	    inference('simplify', [status(thm)], ['6'])).
1.77/1.94	tff('8', plain,
1.77/1.94	    (~ $true
1.77/1.94	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	     | 'const/sets/IN'('type/realax/real', 
1.77/1.94	         sk_A2('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
1.77/1.94	           sk_A0), sk_A)),
1.77/1.94	    inference('sup-', [status(thm)], ['3', '7'])).
1.77/1.94	tff('9', plain,
1.77/1.94	    ('const/sets/IN'('type/realax/real', 
1.77/1.94	       sk_A2('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
1.77/1.94	         sk_A0), sk_A)
1.77/1.94	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
1.77/1.94	    inference('simplify', [status(thm)], ['8'])).
1.77/1.94	tff('10', plain, sk_A0 != 'const/sets/EMPTY'('type/realax/real'),
1.77/1.94	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.77/1.94	tff('11', plain,
1.77/1.94	    'const/sets/IN'('type/realax/real', 
1.77/1.94	      sk_A2('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
1.77/1.94	        sk_A0), sk_A),
1.77/1.94	    inference('simplify_reflect-', [status(thm)], ['9', '10'])).
1.77/1.94	tff('12', plain,
1.77/1.94	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
1.77/1.94	      (~ $true
1.77/1.94	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
1.77/1.94	       | ~ 'const/sets/IN'(X0, X1, X2)),
1.77/1.94	    inference('sup-', [status(thm)], ['5', '1'])).
1.77/1.94	tff('13', plain,
1.77/1.94	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
1.77/1.94	      (~ 'const/sets/IN'(X0, X1, X2)
1.77/1.94	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))),
1.77/1.94	    inference('simplify', [status(thm)], ['12'])).
1.77/1.94	tff('14', plain,
1.77/1.94	    (~ $true
1.77/1.94	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
1.77/1.94	           'const/sets/EMPTY'('type/realax/real'))),
1.77/1.94	    inference('sup-', [status(thm)], ['11', '13'])).
1.77/1.94	tff('15', plain,
1.77/1.94	    ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
1.77/1.94	        'const/sets/EMPTY'('type/realax/real')),
1.77/1.94	    inference('simplify', [status(thm)], ['14'])).
1.77/1.94	tff('16', plain,
1.77/1.94	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
1.77/1.94	      ('const/sets/SUBSET'(X16, X18, X20)
1.77/1.94	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
1.77/1.94	tff('17', plain,
1.77/1.94	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
1.77/1.94	      ('const/sets/SUBSET'(X16, X18, X20)
1.77/1.94	       | ~ 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X20)),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
1.77/1.94	tff('18', plain,
1.77/1.94	    ![X0 : $tType, X1 : X0 > $o]:
1.77/1.94	      (~ $true
1.77/1.94	       | 'const/sets/SUBSET'(X0, X1, X1)
1.77/1.94	       | 'const/sets/SUBSET'(X0, X1, X1)),
1.77/1.94	    inference('sup-', [status(thm)], ['16', '17'])).
1.77/1.94	tff('19', plain,
1.77/1.94	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
1.77/1.94	    inference('simplify', [status(thm)], ['18'])).
1.77/1.94	tff('thm/sets/INF_', axiom,
1.77/1.94	  (![A:('type/realax/real' > $o)]:
1.77/1.94	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
1.77/1.94	       (?[A0:'type/realax/real']:
1.77/1.94	          (![A1:'type/realax/real']:
1.77/1.94	             ('const/sets/IN'('type/realax/real',A1,A) =>
1.77/1.94	              'const/realax/real_le'(A0,A1))))) =>
1.77/1.94	      ((![A0:'type/realax/real']:
1.77/1.94	          ('const/sets/IN'('type/realax/real',A0,A) =>
1.77/1.94	           'const/realax/real_le'('const/sets/inf'(A),A0))) & 
1.77/1.94	       (![A0:'type/realax/real']:
1.77/1.94	          ((![A1:'type/realax/real']:
1.77/1.94	              ('const/sets/IN'('type/realax/real',A1,A) =>
1.77/1.94	               'const/realax/real_le'(A0,A1))) =>
1.77/1.94	           'const/realax/real_le'(A0,'const/sets/inf'(A)))))))).
1.77/1.94	tff(zf_stmt_1, axiom,
1.77/1.94	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A0,A1)) =>
1.77/1.94	   zip_tseitin0(A1,A0,A))).
1.77/1.94	tff('20', plain,
1.77/1.94	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
1.77/1.94	      X23 : 'type/realax/real' > $o]:
1.77/1.94	      (zip_tseitin0(X21, X22, X23)
1.77/1.94	       | 'const/sets/IN'('type/realax/real', X21, X23)),
1.77/1.94	    inference('cnf', [status(esa)], [zf_stmt_1])).
1.77/1.94	tff('thm/sets/IN_', axiom,
1.77/1.94	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
1.77/1.94	tff('21', plain,
1.77/1.94	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
1.77/1.94	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/IN_])).
1.77/1.94	tff('22', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
1.77/1.94	      X2 : 'type/realax/real']: (~ $true | zip_tseitin0(X1, X2, X0) | X0(X1)),
1.77/1.94	    inference('sup-', [status(thm)], ['20', '21'])).
1.77/1.94	tff('23', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
1.77/1.94	      X2 : 'type/realax/real']: (X0(X1) | zip_tseitin0(X1, X2, X0)),
1.77/1.94	    inference('simplify', [status(thm)], ['22'])).
1.77/1.94	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
1.77/1.94	tff(zf_stmt_3, axiom,
1.77/1.94	  (zip_tseitin2(A) =>
1.77/1.94	   ((![A0:'type/realax/real']:
1.77/1.94	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
1.77/1.94	        'const/realax/real_le'(A0,'const/sets/inf'(A)))) & 
1.77/1.94	    (![A0:'type/realax/real']:
1.77/1.94	       ('const/sets/IN'('type/realax/real',A0,A) =>
1.77/1.94	        'const/realax/real_le'('const/sets/inf'(A),A0)))))).
1.77/1.94	tff(zf_stmt_4, type, zip_tseitin1 :
1.77/1.94	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
1.77/1.94	tff(zf_stmt_5, axiom,
1.77/1.94	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A0,A1)) =>
1.77/1.94	   zip_tseitin1(A1,A0,A))).
1.77/1.94	tff(zf_stmt_6, type, zip_tseitin0 :
1.77/1.94	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
1.77/1.94	tff(zf_stmt_7, axiom,
1.77/1.94	  (![A:('type/realax/real' > $o)]:
1.77/1.94	     (((?[A0:'type/realax/real']:
1.77/1.94	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
1.77/1.94	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
1.77/1.94	      zip_tseitin2(A)))).
1.77/1.94	tff('24', plain,
1.77/1.94	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
1.77/1.94	      (zip_tseitin2(X28)
1.77/1.94	       | X28 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
1.77/1.94	    inference('cnf', [status(esa)], [zf_stmt_7])).
1.77/1.94	tff('25', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (~ $true
1.77/1.94	       | X0(sk_A12(X1, X0))
1.77/1.94	       | X0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | zip_tseitin2(X0)),
1.77/1.94	    inference('sup-', [status(thm)], ['23', '24'])).
1.77/1.94	tff('26', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (zip_tseitin2(X0)
1.77/1.94	       | X0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | X0(sk_A12(X1, X0))),
1.77/1.94	    inference('simplify', [status(thm)], ['25'])).
1.77/1.94	tff('27', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (~ 'const/sets/SUBSET'('type/realax/real', sk_A, X0)
1.77/1.94	       | X0(sk_A12(X1, X0))
1.77/1.94	       | zip_tseitin2(X0)),
1.77/1.94	    inference('sup-', [status(thm)], ['26', '15'])).
1.77/1.94	tff('28', plain,
1.77/1.94	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
1.77/1.94	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/IN_])).
1.77/1.94	tff('29', plain,
1.77/1.94	    ![X30 : 'type/realax/real']:
1.77/1.94	      ('const/realax/real_le'(sk_A13, X30)
1.77/1.94	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A)),
1.77/1.94	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.77/1.94	tff('30', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      (~ $true | ~ sk_A(X0) | 'const/realax/real_le'(sk_A13, X0)),
1.77/1.94	    inference('sup-', [status(thm)], ['28', '29'])).
1.77/1.94	tff('31', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      ('const/realax/real_le'(sk_A13, X0) | ~ sk_A(X0)),
1.77/1.94	    inference('simplify', [status(thm)], ['30'])).
1.77/1.94	tff('32', plain,
1.77/1.94	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
1.77/1.94	      (~ $true
1.77/1.94	       | ~ X1(X2)
1.77/1.94	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
1.77/1.94	       | 'const/sets/IN'(X0, X2, X3)),
1.77/1.94	    inference('sup-', [status(thm)], ['28', '5'])).
1.77/1.94	tff('33', plain,
1.77/1.94	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
1.77/1.94	      ('const/sets/IN'(X0, X2, X3)
1.77/1.94	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
1.77/1.94	       | ~ X1(X2)),
1.77/1.94	    inference('simplify', [status(thm)], ['32'])).
1.77/1.94	tff('34', plain,
1.77/1.94	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
1.77/1.94	      (~ $true
1.77/1.94	       | ~ sk_A(X0)
1.77/1.94	       | ~ 'const/sets/SUBSET'('type/realax/real', 
1.77/1.94	             'const/realax/real_le'(sk_A13), X1)
1.77/1.94	       | 'const/sets/IN'('type/realax/real', X0, X1)),
1.77/1.94	    inference('sup-', [status(thm)], ['31', '33'])).
1.77/1.94	tff('35', plain,
1.77/1.94	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
1.77/1.94	      ('const/sets/IN'('type/realax/real', X0, X1)
1.77/1.94	       | ~ 'const/sets/SUBSET'('type/realax/real', 
1.77/1.94	             'const/realax/real_le'(sk_A13), X1)
1.77/1.94	       | ~ sk_A(X0)),
1.77/1.94	    inference('simplify', [status(thm)], ['34'])).
1.77/1.94	tff('36', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (~ $true
1.77/1.94	       | ~ sk_A(X1)
1.77/1.94	       | ~ 'const/sets/SUBSET'('type/realax/real', 
1.77/1.94	             'const/realax/real_le'(sk_A13), X0)
1.77/1.94	       | X0(X1)),
1.77/1.94	    inference('sup-', [status(thm)], ['35', '21'])).
1.77/1.94	tff('37', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (X0(X1)
1.77/1.94	       | ~ 'const/sets/SUBSET'('type/realax/real', 
1.77/1.94	             'const/realax/real_le'(sk_A13), X0)
1.77/1.94	       | ~ sk_A(X1)),
1.77/1.94	    inference('simplify', [status(thm)], ['36'])).
1.77/1.94	tff('38', plain,
1.77/1.94	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
1.77/1.94	      (~ $true
1.77/1.94	       | zip_tseitin2(sk_A)
1.77/1.94	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A)
1.77/1.94	       | ~ 'const/sets/SUBSET'('type/realax/real', 
1.77/1.94	             'const/realax/real_le'(sk_A13), X1)
1.77/1.94	       | X1(sk_A12(X0, sk_A))),
1.77/1.94	    inference('sup-', [status(thm)], ['27', '37'])).
1.77/1.94	tff('39', plain,
1.77/1.94	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
1.77/1.94	      (~ $true
1.77/1.94	       | zip_tseitin2(sk_A)
1.77/1.94	       | ~ $true
1.77/1.94	       | ~ 'const/sets/SUBSET'('type/realax/real', 
1.77/1.94	             'const/realax/real_le'(sk_A13), X1)
1.77/1.94	       | X1(sk_A12(X0, sk_A))),
1.77/1.94	    inference('demod', [status(thm)], ['38', '19'])).
1.77/1.94	tff('40', plain,
1.77/1.94	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
1.77/1.94	      (X1(sk_A12(X0, sk_A))
1.77/1.94	       | ~ 'const/sets/SUBSET'('type/realax/real', 
1.77/1.94	             'const/realax/real_le'(sk_A13), X1)
1.77/1.94	       | zip_tseitin2(sk_A)),
1.77/1.94	    inference('simplify', [status(thm)], ['39'])).
1.77/1.94	tff('thm/sets/REAL_LE_INF_', axiom,
1.77/1.94	  (![A:('type/realax/real' > $o),A0:'type/realax/real']:
1.77/1.94	     (((![A1:'type/realax/real']:
1.77/1.94	          ('const/sets/IN'('type/realax/real',A1,A) =>
1.77/1.94	           'const/realax/real_le'(A0,A1))) & 
1.77/1.94	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
1.77/1.94	      'const/realax/real_le'(A0,'const/sets/inf'(A))))).
1.77/1.94	tff('41', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (X0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X0)
1.77/1.94	       | 'const/realax/real_le'(X1, 'const/sets/inf'(X0))),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/REAL_LE_INF_])).
1.77/1.94	tff('42', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      (~ $true
1.77/1.94	       | 'const/realax/real_le'(X0, 'const/sets/inf'(sk_A0))
1.77/1.94	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | 'const/sets/IN'('type/realax/real', sk_A1(X0, sk_A0), sk_A)),
1.77/1.94	    inference('sup-', [status(thm)], ['41', '7'])).
1.77/1.94	tff('43', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A0), sk_A)
1.77/1.94	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | 'const/realax/real_le'(X0, 'const/sets/inf'(sk_A0))),
1.77/1.94	    inference('simplify', [status(thm)], ['42'])).
1.77/1.94	tff('44', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A0), sk_A)
1.77/1.94	       | 'const/realax/real_le'(X0, 'const/sets/inf'(sk_A0))),
1.77/1.94	    inference('simplify_reflect-', [status(thm)], ['43', '10'])).
1.77/1.94	tff('45', plain,
1.77/1.94	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
1.77/1.94	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
1.77/1.94	       | 'const/realax/real_le'('const/sets/inf'(X23), X27)
1.77/1.94	       | ~ zip_tseitin2(X23)),
1.77/1.94	    inference('cnf', [status(esa)], [zf_stmt_3])).
1.77/1.94	tff('46', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (X0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | ~ 'const/realax/real_le'(X1, sk_A1(X1, X0))
1.77/1.94	       | 'const/realax/real_le'(X1, 'const/sets/inf'(X0))),
1.77/1.94	    inference('cnf', [status(esa)], [thm/sets/REAL_LE_INF_])).
1.77/1.94	tff('47', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
1.77/1.94	      (~ $true
1.77/1.94	       | ~ zip_tseitin2(X1)
1.77/1.94	       | ~ 'const/sets/IN'('type/realax/real', 
1.77/1.94	             sk_A1('const/sets/inf'(X1), X0), X1)
1.77/1.94	       | 'const/realax/real_le'('const/sets/inf'(X1), 'const/sets/inf'(X0))
1.77/1.94	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
1.77/1.94	    inference('sup-', [status(thm)], ['45', '46'])).
1.77/1.94	tff('48', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
1.77/1.94	      (X0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | 'const/realax/real_le'('const/sets/inf'(X1), 'const/sets/inf'(X0))
1.77/1.94	       | ~ 'const/sets/IN'('type/realax/real', 
1.77/1.94	             sk_A1('const/sets/inf'(X1), X0), X1)
1.77/1.94	       | ~ zip_tseitin2(X1)),
1.77/1.94	    inference('simplify', [status(thm)], ['47'])).
1.77/1.94	tff('49', plain,
1.77/1.94	    (~ $true
1.77/1.94	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
1.77/1.94	         'const/sets/inf'(sk_A0))
1.77/1.94	     | ~ zip_tseitin2(sk_A)
1.77/1.94	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
1.77/1.94	         'const/sets/inf'(sk_A0))
1.77/1.94	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
1.77/1.94	    inference('sup-', [status(thm)], ['44', '48'])).
1.77/1.94	tff('50', plain,
1.77/1.94	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	     | ~ zip_tseitin2(sk_A)
1.77/1.94	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
1.77/1.94	         'const/sets/inf'(sk_A0))),
1.77/1.94	    inference('simplify', [status(thm)], ['49'])).
1.77/1.94	tff('51', plain,
1.77/1.94	    (~ zip_tseitin2(sk_A)
1.77/1.94	     | 'const/realax/real_le'('const/sets/inf'(sk_A), 
1.77/1.94	         'const/sets/inf'(sk_A0))),
1.77/1.94	    inference('simplify_reflect-', [status(thm)], ['50', '10'])).
1.77/1.94	tff('52', plain,
1.77/1.94	    ~ 'const/realax/real_le'('const/sets/inf'(sk_A), 'const/sets/inf'(sk_A0)),
1.77/1.94	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.77/1.94	tff('53', plain, ~ zip_tseitin2(sk_A),
1.77/1.94	    inference('clc', [status(thm)], ['51', '52'])).
1.77/1.94	tff('54', plain,
1.77/1.94	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
1.77/1.94	      (~ 'const/sets/SUBSET'('type/realax/real', 
1.77/1.94	           'const/realax/real_le'(sk_A13), X1)
1.77/1.94	       | X1(sk_A12(X0, sk_A))),
1.77/1.94	    inference('clc', [status(thm)], ['40', '53'])).
1.77/1.94	tff('55', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      (~ $true | 'const/realax/real_le'(sk_A13, sk_A12(X0, sk_A))),
1.77/1.94	    inference('sup-', [status(thm)], ['19', '54'])).
1.77/1.94	tff('56', plain,
1.77/1.94	    ![X0 : 'type/realax/real']:
1.77/1.94	      'const/realax/real_le'(sk_A13, sk_A12(X0, sk_A)),
1.77/1.94	    inference('simplify', [status(thm)], ['55'])).
1.77/1.94	tff('57', plain,
1.77/1.94	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
1.77/1.94	      X23 : 'type/realax/real' > $o]:
1.77/1.94	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X22, X21)),
1.77/1.94	    inference('cnf', [status(esa)], [zf_stmt_1])).
1.77/1.94	tff('58', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (~ $true
1.77/1.94	       | ~ 'const/realax/real_le'(X1, sk_A12(X1, X0))
1.77/1.94	       | X0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | zip_tseitin2(X0)),
1.77/1.94	    inference('sup-', [status(thm)], ['57', '24'])).
1.77/1.94	tff('59', plain,
1.77/1.94	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
1.77/1.94	      (zip_tseitin2(X0)
1.77/1.94	       | X0 = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	       | ~ 'const/realax/real_le'(X1, sk_A12(X1, X0))),
1.77/1.94	    inference('simplify', [status(thm)], ['58'])).
1.77/1.94	tff('60', plain,
1.77/1.94	    (~ $true
1.77/1.94	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
1.77/1.94	     | zip_tseitin2(sk_A)),
1.77/1.94	    inference('sup-', [status(thm)], ['56', '59'])).
1.77/1.94	tff('61', plain,
1.77/1.94	    (zip_tseitin2(sk_A) | sk_A = 'const/sets/EMPTY'('type/realax/real')),
1.77/1.94	    inference('simplify', [status(thm)], ['60'])).
1.77/1.94	tff('62', plain, sk_A = 'const/sets/EMPTY'('type/realax/real'),
1.77/1.94	    inference('clc', [status(thm)], ['61', '53'])).
1.77/1.94	tff('63', plain, ~ $true,
1.77/1.94	    inference('demod', [status(thm)], ['15', '62', '19'])).
1.77/1.94	tff('64', plain, $false, inference('simplify', [status(thm)], ['63'])).
1.77/1.94	
1.77/1.94	% SZS output end Refutation
1.77/1.95	EOF
