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    : 
0.00/0.01	#!/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 $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --sup-at-vars \
0.00/0.01	  --ho-no-ext-pos \
0.00/0.01	  --ho-no-ext-neg \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n069.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:51:53 CST 2018
0.00/0.42	% done 192 iterations in 0.217s
0.00/0.42	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.00/0.42	% SZS output start Refutation
0.00/0.42	tff('thm/sets/EXTENSION_', axiom,
0.00/0.42	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
0.00/0.42	     ((A0 = A1) <=>
0.00/0.42	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
0.00/0.42	tff('0', plain,
0.00/0.42	    ![X13 : $tType, X16 : X13 > $o, X18 : X13 > $o]:
0.00/0.42	      (X16 = X18
0.00/0.42	       | 'const/sets/IN'(X13, sk_A21(X13, X18, X16), X18)
0.00/0.42	       | 'const/sets/IN'(X13, sk_A21(X13, X18, X16), X16)),
0.00/0.42	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
0.00/0.42	tff('thm/sets/NOT_IN_EMPTY_', axiom,
0.00/0.42	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
0.00/0.42	tff('1', plain,
0.00/0.42	    ![X2 : $tType, X3 : X2]:
0.00/0.42	      ~ 'const/sets/IN'(X2, X3, 'const/sets/EMPTY'(X2)),
0.00/0.42	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
0.00/0.42	tff('2', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o]:
0.00/0.42	      (~ $true
0.00/0.42	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X1), X1)
0.00/0.42	       | X1 = 'const/sets/EMPTY'(X0)),
0.00/0.42	    inference('sup-', [status(thm)], ['0', '1'])).
0.00/0.42	tff('3', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o]:
0.00/0.42	      (X1 = 'const/sets/EMPTY'(X0)
0.00/0.42	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X1), X1)),
0.00/0.42	    inference('simplify', [status(thm)], ['2'])).
0.00/0.42	tff('thm/sets/IN_', axiom,
0.00/0.42	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
0.00/0.42	tff('4', plain,
0.00/0.42	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
0.00/0.42	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
0.00/0.42	    inference('cnf', [status(esa)], [thm/sets/IN_])).
0.00/0.42	tff('5', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o]:
0.00/0.42	      (~ $true
0.00/0.42	       | X1 = 'const/sets/EMPTY'(X0)
0.00/0.42	       | X1(sk_A21(X0, 'const/sets/EMPTY'(X0), X1))),
0.00/0.42	    inference('sup-', [status(thm)], ['3', '4'])).
0.00/0.42	tff('6', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o]:
0.00/0.42	      (X1(sk_A21(X0, 'const/sets/EMPTY'(X0), X1))
0.00/0.42	       | X1 = 'const/sets/EMPTY'(X0)),
0.00/0.42	    inference('simplify', [status(thm)], ['5'])).
0.00/0.42	tff('7', plain,
0.00/0.42	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
0.00/0.42	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
0.00/0.42	    inference('cnf', [status(esa)], [thm/sets/IN_])).
0.00/0.42	tff('thm/sets/IN_UNIONS_', axiom,
0.00/0.42	  (![A:$tType,A0:(A > $o > $o),A1:A]:
0.00/0.42	     ('const/sets/IN'(A,A1,'const/sets/UNIONS'(A,A0)) <=>
0.00/0.42	      (?[A2:(A > $o)]:
0.00/0.42	         ('const/sets/IN'(A,A1,A2) & 'const/sets/IN'(A > $o,A2,A0)))))).
0.00/0.42	tff('8', plain,
0.00/0.42	    ![X8 : $tType, X9 : X8, X10 : X8 > $o > $o]:
0.00/0.42	      ('const/sets/IN'((> $o, X8), sk_A2(X8, X9, X10), X10)
0.00/0.42	       | ~ 'const/sets/IN'(X8, X9, 'const/sets/UNIONS'(X8, X10))),
0.00/0.42	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
0.00/0.42	tff('9', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
0.00/0.42	      (~ $true
0.00/0.42	       | ~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))
0.00/0.42	       | X1(sk_A2(X0, X2, X1))),
0.00/0.42	    inference('sup-', [status(thm)], ['8', '4'])).
0.00/0.42	tff('10', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
0.00/0.42	      (X1(sk_A2(X0, X2, X1))
0.00/0.42	       | ~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))),
0.00/0.42	    inference('simplify', [status(thm)], ['9'])).
0.00/0.42	tff('11', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
0.00/0.42	      (~ $true | ~ 'const/sets/UNIONS'(X0, X1, X2) | X1(sk_A2(X0, X2, X1))),
0.00/0.42	    inference('sup-', [status(thm)], ['7', '10'])).
0.00/0.42	tff('12', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
0.00/0.42	      (X1(sk_A2(X0, X2, X1)) | ~ 'const/sets/UNIONS'(X0, X1, X2)),
0.00/0.42	    inference('simplify', [status(thm)], ['11'])).
0.00/0.42	tff('13', plain,
0.00/0.42	    ![X8 : $tType, X9 : X8, X10 : X8 > $o > $o]:
0.00/0.42	      ('const/sets/IN'(X8, X9, sk_A2(X8, X9, X10))
0.00/0.42	       | ~ 'const/sets/IN'(X8, X9, 'const/sets/UNIONS'(X8, X10))),
0.00/0.42	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
0.00/0.42	tff('14', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
0.00/0.42	      (~ $true
0.00/0.42	       | ~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))
0.00/0.42	       | sk_A2(X0, X2, X1, X2)),
0.00/0.42	    inference('sup-', [status(thm)], ['13', '4'])).
0.00/0.42	tff('15', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
0.00/0.42	      (sk_A2(X0, X2, X1, X2)
0.00/0.42	       | ~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))),
0.00/0.42	    inference('simplify', [status(thm)], ['14'])).
0.00/0.42	tff('16', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
0.00/0.42	      (~ $true | ~ 'const/sets/UNIONS'(X0, X1, X2) | sk_A2(X0, X2, X1, X2)),
0.00/0.42	    inference('sup-', [status(thm)], ['7', '15'])).
0.00/0.42	tff('17', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
0.00/0.42	      (sk_A2(X0, X2, X1, X2) | ~ 'const/sets/UNIONS'(X0, X1, X2)),
0.00/0.42	    inference('simplify', [status(thm)], ['16'])).
0.00/0.42	tff('thm/sets/EMPTY_UNIONS_', conjecture,
0.00/0.42	  (![A:$tType,A0:(A > $o > $o)]:
0.00/0.42	     (('const/sets/UNIONS'(A,A0) = 'const/sets/EMPTY'(A)) <=>
0.00/0.42	      (![A1:(A > $o)]:
0.00/0.42	         ('const/sets/IN'(A > $o,A1,A0) => (A1 = 'const/sets/EMPTY'(A))))))).
0.00/0.42	tff(zf_stmt_0, negated_conjecture,
0.00/0.42	  (~
0.00/0.42	    (![A:$tType,A0:(A > $o > $o)]:
0.00/0.42	       (('const/sets/UNIONS'(A,A0) = 'const/sets/EMPTY'(A)) <=>
0.00/0.42	        (![A1:(A > $o)]:
0.00/0.42	           ('const/sets/IN'(A > $o,A1,A0) => (A1 = 'const/sets/EMPTY'(A)))))))).
0.00/0.42	tff('18', plain,
0.00/0.42	    ![X19 : sk_A > $o]:
0.00/0.42	      (~ 'const/sets/IN'((> $o, sk_A), X19, sk_A0)
0.00/0.42	       | X19 = 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.42	tff('19', plain,
0.00/0.42	    ![X0 : sk_A > $o]:
0.00/0.42	      (~ $true
0.00/0.42	       | ~ sk_A0(X0)
0.00/0.42	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | X0 = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('sup-', [status(thm)], ['7', '18'])).
0.00/0.42	tff('20', plain,
0.00/0.42	    ![X0 : sk_A > $o]:
0.00/0.42	      (X0 = 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | ~ sk_A0(X0)),
0.00/0.42	    inference('simplify', [status(thm)], ['19'])).
0.00/0.42	tff('21', plain,
0.00/0.42	    ('const/sets/IN'((> $o, sk_A), sk_A1, sk_A0)
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.42	tff('22', plain,
0.00/0.42	    (~ $true
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)
0.00/0.42	     | sk_A0(sk_A1)),
0.00/0.42	    inference('sup-', [status(thm)], ['21', '4'])).
0.00/0.42	tff('23', plain,
0.00/0.42	    (sk_A0(sk_A1)
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('simplify', [status(thm)], ['22'])).
0.00/0.42	tff('24', plain,
0.00/0.42	    ![X0 : sk_A > $o]:
0.00/0.42	      ('const/sets/EMPTY'(sk_A) != 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | ~ sk_A0(X0)
0.00/0.42	       | X0 = 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | sk_A0(sk_A1)),
0.00/0.42	    inference('sup-', [status(thm)], ['20', '23'])).
0.00/0.42	tff('25', plain,
0.00/0.42	    ![X0 : sk_A > $o]:
0.00/0.42	      (sk_A0(sk_A1) | X0 = 'const/sets/EMPTY'(sk_A) | ~ sk_A0(X0)),
0.00/0.42	    inference('simplify', [status(thm)], ['24'])).
0.00/0.42	tff('26', plain,
0.00/0.42	    ![X0 : sk_A > $o, X1 : sk_A]:
0.00/0.42	      (X0(X1) = 'const/sets/EMPTY'(sk_A, X1) | ~ sk_A0(X0) | sk_A0(sk_A1)),
0.00/0.42	    inference('ho_complete_eq', [status(thm)], ['25'])).
0.00/0.42	tff('27', plain,
0.00/0.42	    ![X0 : sk_A, X1 : sk_A > $o > $o]:
0.00/0.42	      ($true = 'const/sets/EMPTY'(sk_A, X0)
0.00/0.42	       | ~ 'const/sets/UNIONS'(sk_A, X1, X0)
0.00/0.42	       | sk_A0(sk_A1)
0.00/0.42	       | ~ sk_A0(sk_A2(sk_A, X0, X1))),
0.00/0.42	    inference('sup+', [status(thm)], ['17', '26'])).
0.00/0.42	tff('28', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0]: (~ $true | ~ 'const/sets/EMPTY'(X0, X1)),
0.00/0.42	    inference('sup-', [status(thm)], ['7', '1'])).
0.00/0.42	tff('29', plain, ![X0 : $tType, X1 : X0]: ~ 'const/sets/EMPTY'(X0, X1),
0.00/0.42	    inference('simplify', [status(thm)], ['28'])).
0.00/0.42	tff('30', plain,
0.00/0.42	    ![X0 : sk_A, X1 : sk_A > $o > $o]:
0.00/0.42	      (~ 'const/sets/UNIONS'(sk_A, X1, X0)
0.00/0.42	       | sk_A0(sk_A1)
0.00/0.42	       | ~ sk_A0(sk_A2(sk_A, X0, X1))),
0.00/0.42	    inference('simplify_reflect-', [status(thm)], ['27', '29'])).
0.00/0.42	tff('31', plain,
0.00/0.42	    ![X0 : sk_A]:
0.00/0.42	      (~ $true
0.00/0.42	       | ~ 'const/sets/UNIONS'(sk_A, sk_A0, X0)
0.00/0.42	       | sk_A0(sk_A1)
0.00/0.42	       | ~ 'const/sets/UNIONS'(sk_A, sk_A0, X0)),
0.00/0.42	    inference('sup-', [status(thm)], ['12', '30'])).
0.00/0.42	tff('32', plain,
0.00/0.42	    ![X0 : sk_A]: (sk_A0(sk_A1) | ~ 'const/sets/UNIONS'(sk_A, sk_A0, X0)),
0.00/0.42	    inference('simplify', [status(thm)], ['31'])).
0.00/0.42	tff('33', plain,
0.00/0.42	    (~ $true
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
0.00/0.42	     | sk_A0(sk_A1)),
0.00/0.42	    inference('sup-', [status(thm)], ['6', '32'])).
0.00/0.42	tff('34', plain,
0.00/0.42	    (sk_A0(sk_A1)
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('simplify', [status(thm)], ['33'])).
0.00/0.42	tff('35', plain, sk_A0(sk_A1), inference('clc', [status(thm)], ['34', '23'])).
0.00/0.42	tff('36', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o]:
0.00/0.42	      (~ $true
0.00/0.42	       | 'const/sets/UNIONS'(X0, X1) = 'const/sets/EMPTY'(X0)
0.00/0.42	       | X1(
0.00/0.42	           sk_A2(X0, 
0.00/0.42	             sk_A21(X0, 'const/sets/EMPTY'(X0), 'const/sets/UNIONS'(X0, X1)), 
0.00/0.42	             X1))),
0.00/0.42	    inference('sup-', [status(thm)], ['3', '10'])).
0.00/0.42	tff('37', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o]:
0.00/0.42	      (X1(
0.00/0.42	         sk_A2(X0, 
0.00/0.42	           sk_A21(X0, 'const/sets/EMPTY'(X0), 'const/sets/UNIONS'(X0, X1)), 
0.00/0.42	           X1))
0.00/0.42	       | 'const/sets/UNIONS'(X0, X1) = 'const/sets/EMPTY'(X0)),
0.00/0.42	    inference('simplify', [status(thm)], ['36'])).
0.00/0.42	tff('38', plain,
0.00/0.42	    ![X0 : sk_A > $o, X1 : sk_A]:
0.00/0.42	      (X0(X1) = 'const/sets/EMPTY'(sk_A, X1)
0.00/0.42	       | ~ sk_A0(X0)
0.00/0.42	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('ho_complete_eq', [status(thm)], ['20'])).
0.00/0.42	tff('39', plain,
0.00/0.42	    ![X0 : sk_A]:
0.00/0.42	      (~ $true
0.00/0.42	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | sk_A2(sk_A, 
0.00/0.42	           sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
0.00/0.42	             'const/sets/UNIONS'(sk_A, sk_A0)), sk_A0, X0)
0.00/0.42	          = 'const/sets/EMPTY'(sk_A, X0)),
0.00/0.42	    inference('sup-', [status(thm)], ['37', '38'])).
0.00/0.42	tff('40', plain,
0.00/0.42	    ![X0 : sk_A]:
0.00/0.42	      (sk_A2(sk_A, 
0.00/0.42	         sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
0.00/0.42	           'const/sets/UNIONS'(sk_A, sk_A0)), sk_A0, X0)
0.00/0.42	        = 'const/sets/EMPTY'(sk_A, X0)
0.00/0.42	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('simplify', [status(thm)], ['39'])).
0.00/0.42	tff('41', plain,
0.00/0.42	    ($true
0.00/0.42	      = 'const/sets/EMPTY'(sk_A, 
0.00/0.42	          sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
0.00/0.42	            'const/sets/UNIONS'(sk_A, sk_A0)))
0.00/0.42	     | ~ 'const/sets/UNIONS'(sk_A, sk_A0, 
0.00/0.42	           sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
0.00/0.42	             'const/sets/UNIONS'(sk_A, sk_A0)))
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('sup+', [status(thm)], ['17', '40'])).
0.00/0.42	tff('42', plain,
0.00/0.42	    (~ 'const/sets/UNIONS'(sk_A, sk_A0, 
0.00/0.42	         sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
0.00/0.42	           'const/sets/UNIONS'(sk_A, sk_A0)))
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('simplify_reflect-', [status(thm)], ['41', '29'])).
0.00/0.42	tff('43', plain, 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A),
0.00/0.42	    inference('clc', [status(thm)], ['42', '6'])).
0.00/0.42	tff('44', plain,
0.00/0.42	    ![X8 : $tType, X10 : X8 > $o > $o, X11 : X8, X12 : X8 > $o]:
0.00/0.42	      ('const/sets/IN'(X8, X11, 'const/sets/UNIONS'(X8, X10))
0.00/0.42	       | ~ 'const/sets/IN'((> $o, X8), X12, X10)
0.00/0.42	       | ~ 'const/sets/IN'(X8, X11, X12)),
0.00/0.42	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
0.00/0.42	tff('45', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0]:
0.00/0.42	      (~ $true
0.00/0.42	       | ~ X1(X2)
0.00/0.42	       | ~ 'const/sets/IN'(X0, X3, X2)
0.00/0.42	       | 'const/sets/IN'(X0, X3, 'const/sets/UNIONS'(X0, X1))),
0.00/0.42	    inference('sup-', [status(thm)], ['7', '44'])).
0.00/0.42	tff('46', plain,
0.00/0.42	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o, X3 : X0]:
0.00/0.42	      ('const/sets/IN'(X0, X3, 'const/sets/UNIONS'(X0, X1))
0.00/0.42	       | ~ 'const/sets/IN'(X0, X3, X2)
0.00/0.42	       | ~ X1(X2)),
0.00/0.42	    inference('simplify', [status(thm)], ['45'])).
0.00/0.42	tff('47', plain,
0.00/0.42	    ![X0 : sk_A, X1 : sk_A > $o]:
0.00/0.42	      ('const/sets/IN'(sk_A, X0, 'const/sets/EMPTY'(sk_A))
0.00/0.42	       | ~ sk_A0(X1)
0.00/0.42	       | ~ 'const/sets/IN'(sk_A, X0, X1)),
0.00/0.42	    inference('sup+', [status(thm)], ['43', '46'])).
0.00/0.42	tff('48', plain,
0.00/0.42	    ![X0 : sk_A, X1 : sk_A > $o]:
0.00/0.42	      (~ 'const/sets/IN'(sk_A, X0, X1) | ~ sk_A0(X1)),
0.00/0.42	    inference('clc', [status(thm)], ['47', '1'])).
0.00/0.42	tff('49', plain,
0.00/0.42	    ![X0 : sk_A > $o]:
0.00/0.42	      (~ $true | X0 = 'const/sets/EMPTY'(sk_A) | ~ sk_A0(X0)),
0.00/0.42	    inference('sup-', [status(thm)], ['3', '48'])).
0.00/0.42	tff('50', plain,
0.00/0.42	    ![X0 : sk_A > $o]: (~ sk_A0(X0) | X0 = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('simplify', [status(thm)], ['49'])).
0.00/0.42	tff('51', plain, (~ $true | sk_A1 = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('sup-', [status(thm)], ['35', '50'])).
0.00/0.42	tff('52', plain, sk_A1 = 'const/sets/EMPTY'(sk_A),
0.00/0.42	    inference('simplify', [status(thm)], ['51'])).
0.00/0.42	tff('53', plain,
0.00/0.42	    (sk_A1 != 'const/sets/EMPTY'(sk_A)
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.42	tff('54', plain,
0.00/0.42	    ![X0 : sk_A > $o, X1 : sk_A]:
0.00/0.42	      ('const/sets/EMPTY'(sk_A) != 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | ~ sk_A0(X0)
0.00/0.42	       | X0(X1) = 'const/sets/EMPTY'(sk_A, X1)
0.00/0.42	       | sk_A1 != 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('sup-', [status(thm)], ['38', '53'])).
0.00/0.42	tff('55', plain,
0.00/0.42	    ![X0 : sk_A > $o, X1 : sk_A]:
0.00/0.42	      (sk_A1 != 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | X0(X1) = 'const/sets/EMPTY'(sk_A, X1)
0.00/0.42	       | ~ sk_A0(X0)),
0.00/0.42	    inference('simplify', [status(thm)], ['54'])).
0.00/0.42	tff('56', plain,
0.00/0.42	    ![X0 : sk_A, X1 : sk_A > $o > $o]:
0.00/0.42	      ($true = 'const/sets/EMPTY'(sk_A, X0)
0.00/0.42	       | ~ 'const/sets/UNIONS'(sk_A, X1, X0)
0.00/0.42	       | ~ sk_A0(sk_A2(sk_A, X0, X1))
0.00/0.42	       | sk_A1 != 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('sup+', [status(thm)], ['17', '55'])).
0.00/0.42	tff('57', plain,
0.00/0.42	    ![X0 : sk_A, X1 : sk_A > $o > $o]:
0.00/0.42	      (~ 'const/sets/UNIONS'(sk_A, X1, X0)
0.00/0.42	       | ~ sk_A0(sk_A2(sk_A, X0, X1))
0.00/0.42	       | sk_A1 != 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('simplify_reflect-', [status(thm)], ['56', '29'])).
0.00/0.42	tff('58', plain,
0.00/0.42	    ![X0 : sk_A]:
0.00/0.42	      (~ $true
0.00/0.42	       | ~ 'const/sets/UNIONS'(sk_A, sk_A0, X0)
0.00/0.42	       | sk_A1 != 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | ~ 'const/sets/UNIONS'(sk_A, sk_A0, X0)),
0.00/0.42	    inference('sup-', [status(thm)], ['12', '57'])).
0.00/0.42	tff('59', plain,
0.00/0.42	    ![X0 : sk_A]:
0.00/0.42	      (sk_A1 != 'const/sets/EMPTY'(sk_A)
0.00/0.42	       | ~ 'const/sets/UNIONS'(sk_A, sk_A0, X0)),
0.00/0.42	    inference('simplify', [status(thm)], ['58'])).
0.00/0.42	tff('60', plain,
0.00/0.42	    (~ $true
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
0.00/0.42	     | sk_A1 != 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('sup-', [status(thm)], ['6', '59'])).
0.00/0.42	tff('61', plain,
0.00/0.42	    (sk_A1 != 'const/sets/EMPTY'(sk_A)
0.00/0.42	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
0.00/0.42	    inference('simplify', [status(thm)], ['60'])).
0.00/0.42	tff('62', plain, sk_A1 != 'const/sets/EMPTY'(sk_A),
0.00/0.42	    inference('clc', [status(thm)], ['61', '53'])).
0.00/0.42	tff('63', plain, $false,
0.00/0.42	    inference('simplify_reflect-', [status(thm)], ['52', '62'])).
0.00/0.42	
0.00/0.42	% SZS output end Refutation
0.00/0.42	EOF
