0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_int
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n119.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 18:52:39 CST 2018
9.16/9.39	% done 1541 iterations in 9.195s
9.16/9.39	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
9.16/9.39	% SZS output start Refutation
9.16/9.40	tff('thm/sets/EXTENSION_', axiom,
9.16/9.40	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
9.16/9.40	     ((A0 = A1) <=>
9.16/9.40	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
9.16/9.40	tff('0', plain,
9.16/9.40	    ![X13 : $tType, X16 : X13 > $o, X18 : X13 > $o]:
9.16/9.40	      (X16 = X18
9.16/9.40	       | 'const/sets/IN'(X13, sk_A21(X13, X18, X16), X18)
9.16/9.40	       | 'const/sets/IN'(X13, sk_A21(X13, X18, X16), X16)),
9.16/9.40	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
9.16/9.40	tff('thm/sets/NOT_IN_EMPTY_', axiom,
9.16/9.40	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
9.16/9.40	tff('1', plain,
9.16/9.40	    ![X2 : $tType, X3 : X2]:
9.16/9.40	      ~ 'const/sets/IN'(X2, X3, 'const/sets/EMPTY'(X2)),
9.16/9.40	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
9.16/9.40	tff('2', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0 > $o]:
9.16/9.40	      (~ $true
9.16/9.40	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X1), X1)
9.16/9.40	       | X1 = 'const/sets/EMPTY'(X0)),
9.16/9.40	    inference('sup-', [status(thm)], ['0', '1'])).
9.16/9.40	tff('3', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0 > $o]:
9.16/9.40	      (X1 = 'const/sets/EMPTY'(X0)
9.16/9.40	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X1), X1)),
9.16/9.40	    inference('simplify', [status(thm)], ['2'])).
9.16/9.40	tff('thm/sets/EMPTY_UNIONS_', conjecture,
9.16/9.40	  (![A:$tType,A0:(A > $o > $o)]:
9.16/9.40	     (('const/sets/UNIONS'(A,A0) = 'const/sets/EMPTY'(A)) <=>
9.16/9.40	      (![A1:(A > $o)]:
9.16/9.40	         ('const/sets/IN'(A > $o,A1,A0) => (A1 = 'const/sets/EMPTY'(A))))))).
9.16/9.40	tff(zf_stmt_0, negated_conjecture,
9.16/9.40	  (~
9.16/9.40	    (![A:$tType,A0:(A > $o > $o)]:
9.16/9.40	       (('const/sets/UNIONS'(A,A0) = 'const/sets/EMPTY'(A)) <=>
9.16/9.40	        (![A1:(A > $o)]:
9.16/9.40	           ('const/sets/IN'(A > $o,A1,A0) => (A1 = 'const/sets/EMPTY'(A)))))))).
9.16/9.40	tff('4', plain,
9.16/9.40	    ('const/sets/IN'((> $o, sk_A), sk_A1, sk_A0)
9.16/9.40	     | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.16/9.40	tff('thm/sets/IN_UNIONS_', axiom,
9.16/9.40	  (![A:$tType,A0:(A > $o > $o),A1:A]:
9.16/9.40	     ('const/sets/IN'(A,A1,'const/sets/UNIONS'(A,A0)) <=>
9.16/9.40	      (?[A2:(A > $o)]:
9.16/9.40	         ('const/sets/IN'(A,A1,A2) & 'const/sets/IN'(A > $o,A2,A0)))))).
9.16/9.40	tff('5', plain,
9.16/9.40	    ![X8 : $tType, X9 : X8, X10 : X8 > $o > $o]:
9.16/9.40	      ('const/sets/IN'((> $o, X8), sk_A2(X8, X9, X10), X10)
9.16/9.40	       | ~ 'const/sets/IN'(X8, X9, 'const/sets/UNIONS'(X8, X10))),
9.16/9.40	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
9.16/9.40	tff('6', plain,
9.16/9.40	    ![X19 : sk_A > $o]:
9.16/9.40	      (~ 'const/sets/IN'((> $o, sk_A), X19, sk_A0)
9.16/9.40	       | X19 = 'const/sets/EMPTY'(sk_A)
9.16/9.40	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.16/9.40	tff('7', plain,
9.16/9.40	    ![X0 : sk_A]:
9.16/9.40	      (~ $true
9.16/9.40	       | ~ 'const/sets/IN'(sk_A, X0, 'const/sets/UNIONS'(sk_A, sk_A0))
9.16/9.40	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
9.16/9.40	       | sk_A2(sk_A, X0, sk_A0) = 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('sup-', [status(thm)], ['5', '6'])).
9.16/9.40	tff('8', plain,
9.16/9.40	    ![X0 : sk_A]:
9.16/9.40	      (sk_A2(sk_A, X0, sk_A0) = 'const/sets/EMPTY'(sk_A)
9.16/9.40	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
9.16/9.40	       | ~ 'const/sets/IN'(sk_A, X0, 'const/sets/UNIONS'(sk_A, sk_A0))),
9.16/9.40	    inference('simplify', [status(thm)], ['7'])).
9.16/9.40	tff('9', plain,
9.16/9.40	    (~ $true
9.16/9.40	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
9.16/9.40	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
9.16/9.40	     | sk_A2(sk_A, 
9.16/9.40	         sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
9.16/9.40	           'const/sets/UNIONS'(sk_A, sk_A0)), sk_A0)
9.16/9.40	        = 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('sup-', [status(thm)], ['3', '8'])).
9.16/9.40	tff('10', plain,
9.16/9.40	    (sk_A2(sk_A, 
9.16/9.40	       sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
9.16/9.40	         'const/sets/UNIONS'(sk_A, sk_A0)), sk_A0)
9.16/9.40	      = 'const/sets/EMPTY'(sk_A)
9.16/9.40	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('simplify', [status(thm)], ['9'])).
9.16/9.40	tff('11', plain,
9.16/9.40	    ![X8 : $tType, X9 : X8, X10 : X8 > $o > $o]:
9.16/9.40	      ('const/sets/IN'(X8, X9, sk_A2(X8, X9, X10))
9.16/9.40	       | ~ 'const/sets/IN'(X8, X9, 'const/sets/UNIONS'(X8, X10))),
9.16/9.40	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
9.16/9.40	tff('12', plain,
9.16/9.40	    ('const/sets/IN'(sk_A, 
9.16/9.40	       sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
9.16/9.40	         'const/sets/UNIONS'(sk_A, sk_A0)), 'const/sets/EMPTY'(sk_A))
9.16/9.40	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
9.16/9.40	     | ~ 'const/sets/IN'(sk_A, 
9.16/9.40	           sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
9.16/9.40	             'const/sets/UNIONS'(sk_A, sk_A0)), 
9.16/9.40	           'const/sets/UNIONS'(sk_A, sk_A0))),
9.16/9.40	    inference('sup+', [status(thm)], ['10', '11'])).
9.16/9.40	tff('13', plain,
9.16/9.40	    (~ 'const/sets/IN'(sk_A, 
9.16/9.40	         sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
9.16/9.40	           'const/sets/UNIONS'(sk_A, sk_A0)), 
9.16/9.40	         'const/sets/UNIONS'(sk_A, sk_A0))
9.16/9.40	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('clc', [status(thm)], ['12', '1'])).
9.16/9.40	tff('14', plain, 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A),
9.16/9.40	    inference('clc', [status(thm)], ['13', '3'])).
9.16/9.40	tff('15', plain,
9.16/9.40	    ('const/sets/IN'((> $o, sk_A), sk_A1, sk_A0)
9.16/9.40	     | 'const/sets/EMPTY'(sk_A) != 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('demod', [status(thm)], ['4', '14'])).
9.16/9.40	tff('16', plain, 'const/sets/IN'((> $o, sk_A), sk_A1, sk_A0),
9.16/9.40	    inference('simplify', [status(thm)], ['15'])).
9.16/9.40	tff('17', plain,
9.16/9.40	    ![X8 : $tType, X10 : X8 > $o > $o, X11 : X8, X12 : X8 > $o]:
9.16/9.40	      ('const/sets/IN'(X8, X11, 'const/sets/UNIONS'(X8, X10))
9.16/9.40	       | ~ 'const/sets/IN'((> $o, X8), X12, X10)
9.16/9.40	       | ~ 'const/sets/IN'(X8, X11, X12)),
9.16/9.40	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
9.16/9.40	tff('thm/sets/IN_', axiom,
9.16/9.40	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
9.16/9.40	tff('18', plain,
9.16/9.40	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
9.16/9.40	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
9.16/9.40	    inference('cnf', [status(esa)], [thm/sets/IN_])).
9.16/9.40	tff('19', plain,
9.16/9.40	    ![X4 : $tType, X5 : X4 > $o, X6 : X4, X7 : X4 > $o]:
9.16/9.40	      (X7 != X5 | X5(X6) | ~ 'const/sets/IN'(X4, X6, X7)),
9.16/9.40	    inference('ho.purify_applied_variable', [status(thm)], ['18'])).
9.16/9.40	tff('20', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0]:
9.16/9.40	      (~ $true
9.16/9.40	       | ~ 'const/sets/IN'(X0, X1, 
9.16/9.40	             'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0))))),
9.16/9.40	    inference('sup-', [status(thm)], ['5', '1'])).
9.16/9.40	tff('21', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0]:
9.16/9.40	      ~ 'const/sets/IN'(X0, X1, 
9.16/9.40	          'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))),
9.16/9.40	    inference('simplify', [status(thm)], ['20'])).
9.16/9.40	tff('22', plain,
9.16/9.40	    ![X0 : $tType]:
9.16/9.40	      (~ $true
9.16/9.40	       | 'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))
9.16/9.40	          = 'const/sets/EMPTY'(X0)),
9.16/9.40	    inference('sup-', [status(thm)], ['3', '21'])).
9.16/9.40	tff('23', plain,
9.16/9.40	    ![X0 : $tType]:
9.16/9.40	      'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))
9.16/9.40	       = 'const/sets/EMPTY'(X0),
9.16/9.40	    inference('simplify', [status(thm)], ['22'])).
9.16/9.40	tff('24', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0]:
9.16/9.40	      'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)), X1)
9.16/9.40	       = 'const/sets/EMPTY'(X0, X1),
9.16/9.40	    inference('ho_complete_eq', [status(thm)], ['23'])).
9.16/9.40	tff('25', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
9.16/9.40	      ($true = 'const/sets/EMPTY'(X0, X1)
9.16/9.40	       | ~ 'const/sets/IN'(X0, X1, X2)
9.16/9.40	       | X2 != 'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))),
9.16/9.40	    inference('sup+', [status(thm)], ['19', '24'])).
9.16/9.40	tff('26', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
9.16/9.40	      ($true = 'const/sets/EMPTY'(X0, X1)
9.16/9.40	       | ~ 'const/sets/IN'(X0, X1, X2)
9.16/9.40	       | X2 != 'const/sets/EMPTY'(X0)),
9.16/9.40	    inference('demod', [status(thm)], ['25', '23'])).
9.16/9.40	tff('27', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o]:
9.16/9.40	      (~ $true
9.16/9.40	       | ~ 'const/sets/IN'(X0, X2, X3)
9.16/9.40	       | ~ 'const/sets/IN'((> $o, X0), X3, X1)
9.16/9.40	       | 'const/sets/UNIONS'(X0, X1) != 'const/sets/EMPTY'(X0)
9.16/9.40	       | 'const/sets/EMPTY'(X0, X2)),
9.16/9.40	    inference('sup-', [status(thm)], ['17', '26'])).
9.16/9.40	tff('28', plain,
9.16/9.40	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o]:
9.16/9.40	      ('const/sets/EMPTY'(X0, X2)
9.16/9.40	       | 'const/sets/UNIONS'(X0, X1) != 'const/sets/EMPTY'(X0)
9.16/9.40	       | ~ 'const/sets/IN'((> $o, X0), X3, X1)
9.16/9.40	       | ~ 'const/sets/IN'(X0, X2, X3)),
9.16/9.40	    inference('simplify', [status(thm)], ['27'])).
9.16/9.40	tff('29', plain,
9.16/9.40	    ![X0 : sk_A]:
9.16/9.40	      (~ $true
9.16/9.40	       | ~ 'const/sets/IN'(sk_A, X0, sk_A1)
9.16/9.40	       | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)
9.16/9.40	       | 'const/sets/EMPTY'(sk_A, X0)),
9.16/9.40	    inference('sup-', [status(thm)], ['16', '28'])).
9.16/9.40	tff('30', plain,
9.16/9.40	    ![X0 : sk_A]:
9.16/9.40	      (~ $true
9.16/9.40	       | ~ 'const/sets/IN'(sk_A, X0, sk_A1)
9.16/9.40	       | 'const/sets/EMPTY'(sk_A) != 'const/sets/EMPTY'(sk_A)
9.16/9.40	       | 'const/sets/EMPTY'(sk_A, X0)),
9.16/9.40	    inference('demod', [status(thm)], ['29', '14'])).
9.16/9.40	tff('31', plain,
9.16/9.40	    ![X0 : sk_A]:
9.16/9.40	      ('const/sets/EMPTY'(sk_A, X0) | ~ 'const/sets/IN'(sk_A, X0, sk_A1)),
9.16/9.40	    inference('simplify', [status(thm)], ['30'])).
9.16/9.40	tff('32', plain,
9.16/9.40	    (~ $true
9.16/9.40	     | sk_A1 = 'const/sets/EMPTY'(sk_A)
9.16/9.40	     | 'const/sets/EMPTY'(sk_A, 
9.16/9.40	         sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1))),
9.16/9.40	    inference('sup-', [status(thm)], ['3', '31'])).
9.16/9.40	tff('33', plain,
9.16/9.40	    ('const/sets/EMPTY'(sk_A, sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1))
9.16/9.40	     | sk_A1 = 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('simplify', [status(thm)], ['32'])).
9.16/9.40	tff('34', plain,
9.16/9.40	    (sk_A1 != 'const/sets/EMPTY'(sk_A)
9.16/9.40	     | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
9.16/9.40	tff('35', plain,
9.16/9.40	    (sk_A1 != 'const/sets/EMPTY'(sk_A)
9.16/9.40	     | 'const/sets/EMPTY'(sk_A) != 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('demod', [status(thm)], ['34', '14'])).
9.16/9.40	tff('36', plain, sk_A1 != 'const/sets/EMPTY'(sk_A),
9.16/9.40	    inference('simplify', [status(thm)], ['35'])).
9.16/9.40	tff('37', plain,
9.16/9.40	    'const/sets/EMPTY'(sk_A, sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1)),
9.16/9.40	    inference('simplify_reflect-', [status(thm)], ['33', '36'])).
9.16/9.40	tff('38', plain,
9.16/9.40	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
9.16/9.40	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
9.16/9.40	    inference('cnf', [status(esa)], [thm/sets/IN_])).
9.16/9.40	tff('39', plain,
9.16/9.40	    ![X4 : $tType, X5 : X4 > $o, X7 : X4, X8 : X4 > $o]:
9.16/9.40	      (X8 != X5 | 'const/sets/IN'(X4, X7, X5) | ~ X8(X7)),
9.16/9.40	    inference('ho.purify_applied_variable', [status(thm)], ['38'])).
9.16/9.40	tff('40', plain,
9.16/9.40	    ![X0 : sk_A > $o]:
9.16/9.40	      (~ $true
9.16/9.40	       | 'const/sets/IN'(sk_A, 
9.16/9.40	           sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1), X0)
9.16/9.40	       | 'const/sets/EMPTY'(sk_A) != X0),
9.16/9.40	    inference('sup-', [status(thm)], ['37', '39'])).
9.16/9.40	tff('41', plain,
9.16/9.40	    ![X0 : sk_A > $o]:
9.16/9.40	      ('const/sets/EMPTY'(sk_A) != X0
9.16/9.40	       | 'const/sets/IN'(sk_A, 
9.16/9.40	           sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1), X0)),
9.16/9.40	    inference('simplify', [status(thm)], ['40'])).
9.16/9.40	tff('42', plain,
9.16/9.40	    (~ $true | 'const/sets/EMPTY'(sk_A) != 'const/sets/EMPTY'(sk_A)),
9.16/9.40	    inference('sup-', [status(thm)], ['41', '1'])).
9.16/9.40	tff('43', plain, $false, inference('simplify', [status(thm)], ['42'])).
9.16/9.40	
9.16/9.40	% SZS output end Refutation
9.16/9.40	EOF
