0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : supatvars_int
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-avatar \
0.00/0.01	  --ho \
0.00/0.01	  --force-ho \
0.00/0.01	  --no-ho-elim-pred-var \
0.00/0.01	  --ho-general-ext-pos \
0.00/0.01	  --no-ho-unif \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --sup-at-vars \
0.00/0.01	  --ho-no-ext-pos \
0.00/0.01	  --ho-no-ext-neg \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n185.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:41:24 CST 2018
4.78/4.99	% done 2451 iterations in 4.782s
4.78/4.99	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
4.78/4.99	% SZS output start Refutation
4.78/5.00	tff('thm/sets/EXTENSION_', axiom,
4.78/5.00	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
4.78/5.00	     ((A0 = A1) <=>
4.78/5.00	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
4.78/5.00	tff('0', plain,
4.78/5.00	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
4.78/5.00	      (X13 = X15
4.78/5.00	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
4.78/5.00	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
4.78/5.00	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
4.78/5.00	tff('thm/sets/NOT_IN_EMPTY_', axiom,
4.78/5.00	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
4.78/5.00	tff('1', plain,
4.78/5.00	    ![X8 : $tType, X9 : X8]:
4.78/5.00	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
4.78/5.00	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
4.78/5.00	tff('2', plain,
4.78/5.00	    ![X0 : $tType, X1 : X0 > $o]:
4.78/5.00	      (~ $true
4.78/5.00	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)
4.78/5.00	       | X1 = 'const/sets/EMPTY'(X0)),
4.78/5.00	    inference('sup-', [status(thm)], ['0', '1'])).
4.78/5.00	tff('3', plain,
4.78/5.00	    ![X0 : $tType, X1 : X0 > $o]:
4.78/5.00	      (X1 = 'const/sets/EMPTY'(X0)
4.78/5.00	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)),
4.78/5.01	    inference('simplify', [status(thm)], ['2'])).
4.78/5.01	tff('thm/sets/IN_', axiom,
4.78/5.01	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
4.78/5.01	tff('4', plain,
4.78/5.01	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
4.78/5.01	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
4.78/5.01	    inference('cnf', [status(esa)], [thm/sets/IN_])).
4.78/5.01	tff('thm/sets/REAL_SUP_LE_SUBSET_', conjecture,
4.78/5.01	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
4.78/5.01	     (((?[A1:'type/realax/real']:
4.78/5.01	          (![A2:'type/realax/real']:
4.78/5.01	             ('const/sets/IN'('type/realax/real',A2,A0) =>
4.78/5.01	              'const/realax/real_le'(A2,A1)))) & 
4.78/5.01	       'const/sets/SUBSET'('type/realax/real',A,A0) & 
4.78/5.01	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
4.78/5.01	      'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0))))).
4.78/5.01	tff(zf_stmt_0, negated_conjecture,
4.78/5.01	  (~
4.78/5.01	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
4.78/5.01	       (((?[A1:'type/realax/real']:
4.78/5.01	            (![A2:'type/realax/real']:
4.78/5.01	               ('const/sets/IN'('type/realax/real',A2,A0) =>
4.78/5.01	                'const/realax/real_le'(A2,A1)))) & 
4.78/5.01	         'const/sets/SUBSET'('type/realax/real',A,A0) & 
4.78/5.01	         (A != 'const/sets/EMPTY'('type/realax/real'))) =>
4.78/5.01	        'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0)))))).
4.78/5.01	tff('5', plain, 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A0),
4.78/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.78/5.01	tff('thm/sets/SUBSET_', axiom,
4.78/5.01	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
4.78/5.01	     ('const/sets/SUBSET'(A,A0,A1) <=>
4.78/5.01	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
4.78/5.01	tff('6', plain,
4.78/5.01	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
4.78/5.01	      (~ 'const/sets/IN'(X16, X17, X18)
4.78/5.01	       | 'const/sets/IN'(X16, X17, X19)
4.78/5.01	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
4.78/5.01	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
4.78/5.01	tff('7', plain,
4.78/5.01	    ![X0 : 'type/realax/real']:
4.78/5.01	      (~ $true
4.78/5.01	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
4.78/5.01	    inference('sup-', [status(thm)], ['5', '6'])).
4.78/5.01	tff('8', plain,
4.78/5.01	    ![X0 : 'type/realax/real']:
4.78/5.01	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
4.78/5.01	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)),
4.78/5.01	    inference('simplify', [status(thm)], ['7'])).
4.78/5.01	tff('9', plain,
4.78/5.01	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
4.78/5.01	      (~ $true
4.78/5.01	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
4.78/5.01	       | ~ 'const/sets/IN'(X0, X1, X2)),
4.78/5.01	    inference('sup-', [status(thm)], ['6', '1'])).
4.78/5.01	tff('10', plain,
4.78/5.01	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
4.78/5.01	      (~ 'const/sets/IN'(X0, X1, X2)
4.78/5.01	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))),
4.78/5.01	    inference('simplify', [status(thm)], ['9'])).
4.78/5.01	tff('11', plain,
4.78/5.01	    ![X0 : 'type/realax/real']:
4.78/5.01	      (~ $true
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
4.78/5.01	             'const/sets/EMPTY'('type/realax/real'))),
4.78/5.01	    inference('sup-', [status(thm)], ['8', '10'])).
4.78/5.01	tff('12', plain,
4.78/5.01	    ![X0 : 'type/realax/real']:
4.78/5.01	      (~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
4.78/5.01	           'const/sets/EMPTY'('type/realax/real'))
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
4.78/5.01	    inference('simplify', [status(thm)], ['11'])).
4.78/5.01	tff('13', plain,
4.78/5.01	    ![X0 : 'type/realax/real']:
4.78/5.01	      (~ $true
4.78/5.01	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), 
4.78/5.01	             'const/sets/EMPTY'('type/realax/real'), 
4.78/5.01	             'const/sets/SUBSET'('type/realax/real', sk_A0))
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
4.78/5.01	    inference('sup-', [status(thm)], ['4', '12'])).
4.78/5.01	tff('14', plain,
4.78/5.01	    ![X0 : 'type/realax/real']:
4.78/5.01	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
4.78/5.01	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), 
4.78/5.01	             'const/sets/EMPTY'('type/realax/real'), 
4.78/5.01	             'const/sets/SUBSET'('type/realax/real', sk_A0))),
4.78/5.01	    inference('simplify', [status(thm)], ['13'])).
4.78/5.01	tff('15', plain,
4.78/5.01	    (~ $true
4.78/5.01	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	     | ~ 'const/sets/IN'((> $o, 'type/realax/real'), 
4.78/5.01	           'const/sets/EMPTY'('type/realax/real'), 
4.78/5.01	           'const/sets/SUBSET'('type/realax/real', sk_A0))),
4.78/5.01	    inference('sup-', [status(thm)], ['3', '14'])).
4.78/5.01	tff('16', plain,
4.78/5.01	    (~ 'const/sets/IN'((> $o, 'type/realax/real'), 
4.78/5.01	         'const/sets/EMPTY'('type/realax/real'), 
4.78/5.01	         'const/sets/SUBSET'('type/realax/real', sk_A0))
4.78/5.01	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
4.78/5.01	    inference('simplify', [status(thm)], ['15'])).
4.78/5.01	tff('17', plain, sk_A != 'const/sets/EMPTY'('type/realax/real'),
4.78/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.78/5.01	tff('18', plain,
4.78/5.01	    ~ 'const/sets/IN'((> $o, 'type/realax/real'), 
4.78/5.01	        'const/sets/EMPTY'('type/realax/real'), 
4.78/5.01	        'const/sets/SUBSET'('type/realax/real', sk_A0)),
4.78/5.01	    inference('simplify_reflect-', [status(thm)], ['16', '17'])).
4.78/5.01	tff('thm/sets/SUP_', axiom,
4.78/5.01	  (![A:('type/realax/real' > $o)]:
4.78/5.01	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
4.78/5.01	       (?[A0:'type/realax/real']:
4.78/5.01	          (![A1:'type/realax/real']:
4.78/5.01	             ('const/sets/IN'('type/realax/real',A1,A) =>
4.78/5.01	              'const/realax/real_le'(A1,A0))))) =>
4.78/5.01	      ((![A0:'type/realax/real']:
4.78/5.01	          ('const/sets/IN'('type/realax/real',A0,A) =>
4.78/5.01	           'const/realax/real_le'(A0,'const/sets/sup'(A)))) & 
4.78/5.01	       (![A0:'type/realax/real']:
4.78/5.01	          ((![A1:'type/realax/real']:
4.78/5.01	              ('const/sets/IN'('type/realax/real',A1,A) =>
4.78/5.01	               'const/realax/real_le'(A1,A0))) =>
4.78/5.01	           'const/realax/real_le'('const/sets/sup'(A),A0))))))).
4.78/5.01	tff(zf_stmt_1, axiom,
4.78/5.01	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
4.78/5.01	   zip_tseitin0(A1,A0,A))).
4.78/5.01	tff('19', plain,
4.78/5.01	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
4.78/5.01	      X23 : 'type/realax/real' > $o]:
4.78/5.01	      (zip_tseitin0(X21, X22, X23)
4.78/5.01	       | 'const/sets/IN'('type/realax/real', X21, X23)),
4.78/5.01	    inference('cnf', [status(esa)], [zf_stmt_1])).
4.78/5.01	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
4.78/5.01	tff(zf_stmt_3, axiom,
4.78/5.01	  (zip_tseitin2(A) =>
4.78/5.01	   ((![A0:'type/realax/real']:
4.78/5.01	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
4.78/5.01	        'const/realax/real_le'('const/sets/sup'(A),A0))) & 
4.78/5.01	    (![A0:'type/realax/real']:
4.78/5.01	       ('const/sets/IN'('type/realax/real',A0,A) =>
4.78/5.01	        'const/realax/real_le'(A0,'const/sets/sup'(A))))))).
4.78/5.01	tff(zf_stmt_4, type, zip_tseitin1 :
4.78/5.01	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
4.78/5.01	tff(zf_stmt_5, axiom,
4.78/5.01	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
4.78/5.01	   zip_tseitin1(A1,A0,A))).
4.78/5.01	tff(zf_stmt_6, type, zip_tseitin0 :
4.78/5.01	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
4.78/5.01	tff(zf_stmt_7, axiom,
4.78/5.01	  (![A:('type/realax/real' > $o)]:
4.78/5.01	     (((?[A0:'type/realax/real']:
4.78/5.01	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
4.78/5.01	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
4.78/5.01	      zip_tseitin2(A)))).
4.78/5.01	tff('20', plain,
4.78/5.01	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
4.78/5.01	      (zip_tseitin2(X28)
4.78/5.01	       | X28 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
4.78/5.01	    inference('cnf', [status(esa)], [zf_stmt_7])).
4.78/5.01	tff('21', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
4.78/5.01	      (~ $true
4.78/5.01	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)
4.78/5.01	       | X0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | zip_tseitin2(X0)),
4.78/5.01	    inference('sup-', [status(thm)], ['19', '20'])).
4.78/5.01	tff('22', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
4.78/5.01	      (zip_tseitin2(X0)
4.78/5.01	       | X0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)),
4.78/5.01	    inference('simplify', [status(thm)], ['21'])).
4.78/5.01	tff('23', plain,
4.78/5.01	    ![X30 : 'type/realax/real']:
4.78/5.01	      ('const/realax/real_le'(X30, sk_A13)
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A0)),
4.78/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.78/5.01	tff('24', plain,
4.78/5.01	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
4.78/5.01	      X23 : 'type/realax/real' > $o]:
4.78/5.01	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X21, X22)),
4.78/5.01	    inference('cnf', [status(esa)], [zf_stmt_1])).
4.78/5.01	tff('25', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
4.78/5.01	      (~ $true
4.78/5.01	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)
4.78/5.01	       | X0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | zip_tseitin2(X0)),
4.78/5.01	    inference('sup-', [status(thm)], ['24', '20'])).
4.78/5.01	tff('26', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
4.78/5.01	      (zip_tseitin2(X0)
4.78/5.01	       | X0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)),
4.78/5.01	    inference('simplify', [status(thm)], ['25'])).
4.78/5.01	tff('27', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o]:
4.78/5.01	      (~ $true
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A0)
4.78/5.01	       | X0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | zip_tseitin2(X0)),
4.78/5.01	    inference('sup-', [status(thm)], ['23', '26'])).
4.78/5.01	tff('28', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o]:
4.78/5.01	      (zip_tseitin2(X0)
4.78/5.01	       | X0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A0)),
4.78/5.01	    inference('simplify', [status(thm)], ['27'])).
4.78/5.01	tff('29', plain,
4.78/5.01	    (~ $true
4.78/5.01	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	     | zip_tseitin2(sk_A0)
4.78/5.01	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	     | zip_tseitin2(sk_A0)),
4.78/5.01	    inference('sup-', [status(thm)], ['22', '28'])).
4.78/5.01	tff('30', plain,
4.78/5.01	    (zip_tseitin2(sk_A0) | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
4.78/5.01	    inference('simplify', [status(thm)], ['29'])).
4.78/5.01	tff('thm/sets/REAL_SUP_LE_', axiom,
4.78/5.01	  (![A:('type/realax/real' > $o),A0:'type/realax/real']:
4.78/5.01	     (((![A1:'type/realax/real']:
4.78/5.01	          ('const/sets/IN'('type/realax/real',A1,A) =>
4.78/5.01	           'const/realax/real_le'(A1,A0))) & 
4.78/5.01	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
4.78/5.01	      'const/realax/real_le'('const/sets/sup'(A),A0)))).
4.78/5.01	tff('31', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
4.78/5.01	      (X0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X0)
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
4.78/5.01	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
4.78/5.01	tff('32', plain,
4.78/5.01	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
4.78/5.01	      (~ $true
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
4.78/5.01	       | 'const/sets/IN'('type/realax/real', X0, X1)),
4.78/5.01	    inference('sup-', [status(thm)], ['8', '6'])).
4.78/5.01	tff('33', plain,
4.78/5.01	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
4.78/5.01	      ('const/sets/IN'('type/realax/real', X0, X1)
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
4.78/5.01	    inference('simplify', [status(thm)], ['32'])).
4.78/5.01	tff('34', plain,
4.78/5.01	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
4.78/5.01	      (~ $true
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)
4.78/5.01	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
4.78/5.01	       | 'const/sets/IN'('type/realax/real', sk_A1(X0, sk_A), X1)),
4.78/5.01	    inference('sup-', [status(thm)], ['31', '33'])).
4.78/5.01	tff('35', plain,
4.78/5.01	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
4.78/5.01	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A), X1)
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
4.78/5.01	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)),
4.78/5.01	    inference('simplify', [status(thm)], ['34'])).
4.78/5.01	tff('36', plain,
4.78/5.01	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
4.78/5.01	      ('const/sets/IN'('type/realax/real', sk_A1(X0, sk_A), X1)
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)),
4.78/5.01	    inference('simplify_reflect-', [status(thm)], ['35', '17'])).
4.78/5.01	tff('37', plain,
4.78/5.01	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
4.78/5.01	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
4.78/5.01	       | 'const/realax/real_le'(X27, 'const/sets/sup'(X23))
4.78/5.01	       | ~ zip_tseitin2(X23)),
4.78/5.01	    inference('cnf', [status(esa)], [zf_stmt_3])).
4.78/5.01	tff('38', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
4.78/5.01	      (X0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | ~ 'const/realax/real_le'(sk_A1(X1, X0), X1)
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
4.78/5.01	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
4.78/5.01	tff('39', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
4.78/5.01	      (~ $true
4.78/5.01	       | ~ zip_tseitin2(X0)
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', 
4.78/5.01	             sk_A1('const/sets/sup'(X0), X1), X0)
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
4.78/5.01	       | X1 = 'const/sets/EMPTY'('type/realax/real')),
4.78/5.01	    inference('sup-', [status(thm)], ['37', '38'])).
4.78/5.01	tff('40', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
4.78/5.01	      (X1 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
4.78/5.01	       | ~ 'const/sets/IN'('type/realax/real', 
4.78/5.01	             sk_A1('const/sets/sup'(X0), X1), X0)
4.78/5.01	       | ~ zip_tseitin2(X0)),
4.78/5.01	    inference('simplify', [status(thm)], ['39'])).
4.78/5.01	tff('41', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o]:
4.78/5.01	      (~ $true
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(X0))
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
4.78/5.01	       | ~ zip_tseitin2(X0)
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(X0))
4.78/5.01	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
4.78/5.01	    inference('sup-', [status(thm)], ['36', '40'])).
4.78/5.01	tff('42', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o]:
4.78/5.01	      (sk_A = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	       | ~ zip_tseitin2(X0)
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(X0))),
4.78/5.01	    inference('simplify', [status(thm)], ['41'])).
4.78/5.01	tff('43', plain,
4.78/5.01	    ![X0 : 'type/realax/real' > $o]:
4.78/5.01	      (~ zip_tseitin2(X0)
4.78/5.01	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
4.78/5.01	       | 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(X0))),
4.78/5.01	    inference('simplify_reflect-', [status(thm)], ['42', '17'])).
4.78/5.01	tff('44', plain,
4.78/5.01	    (~ $true
4.78/5.01	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
4.78/5.01	         'const/sets/sup'(sk_A0))
4.78/5.01	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A0)),
4.78/5.01	    inference('sup-', [status(thm)], ['30', '43'])).
4.78/5.01	tff('45', plain,
4.78/5.01	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
4.78/5.01	      ('const/sets/SUBSET'(X16, X18, X20)
4.78/5.01	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
4.78/5.01	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
4.78/5.01	tff('46', plain,
4.78/5.01	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
4.78/5.01	      ('const/sets/SUBSET'(X16, X18, X20)
4.78/5.01	       | ~ 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X20)),
4.78/5.01	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
4.78/5.01	tff('47', plain,
4.78/5.01	    ![X0 : $tType, X1 : X0 > $o]:
4.78/5.01	      (~ $true
4.78/5.01	       | 'const/sets/SUBSET'(X0, X1, X1)
4.78/5.01	       | 'const/sets/SUBSET'(X0, X1, X1)),
4.78/5.01	    inference('sup-', [status(thm)], ['45', '46'])).
4.78/5.01	tff('48', plain,
4.78/5.01	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
4.78/5.01	    inference('simplify', [status(thm)], ['47'])).
4.78/5.01	tff('49', plain,
4.78/5.01	    (~ $true
4.78/5.01	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
4.78/5.01	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
4.78/5.01	         'const/sets/sup'(sk_A0))
4.78/5.01	     | ~ $true),
4.78/5.01	    inference('demod', [status(thm)], ['44', '48'])).
4.78/5.01	tff('50', plain,
4.78/5.01	    ('const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0))
4.78/5.01	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
4.78/5.01	    inference('simplify', [status(thm)], ['49'])).
4.78/5.01	tff('51', plain,
4.78/5.01	    ~ 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0)),
4.78/5.01	    inference('cnf', [status(esa)], [zf_stmt_0])).
4.78/5.01	tff('52', plain, sk_A0 = 'const/sets/EMPTY'('type/realax/real'),
4.78/5.01	    inference('clc', [status(thm)], ['50', '51'])).
4.78/5.01	tff('53', plain,
4.78/5.01	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
4.78/5.01	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
4.78/5.01	    inference('cnf', [status(esa)], [thm/sets/IN_])).
4.78/5.01	tff('54', plain,
4.78/5.01	    ![X0 : $tType, X1 : X0 > $o]:
4.78/5.01	      (~ $true | 'const/sets/IN'((> $o, X0), X1, 'const/sets/SUBSET'(X0, X1))),
4.78/5.01	    inference('sup-', [status(thm)], ['48', '53'])).
4.78/5.01	tff('55', plain,
4.78/5.01	    ![X0 : $tType, X1 : X0 > $o]:
4.78/5.01	      'const/sets/IN'((> $o, X0), X1, 'const/sets/SUBSET'(X0, X1)),
4.78/5.01	    inference('simplify', [status(thm)], ['54'])).
4.78/5.01	tff('56', plain, ~ $true,
4.78/5.01	    inference('demod', [status(thm)], ['18', '52', '55'])).
4.78/5.01	tff('57', plain, $false, inference('simplify', [status(thm)], ['56'])).
4.78/5.01	
4.78/5.01	% SZS output end Refutation
4.78/5.01	EOF
