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_ext
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 $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --ho-purify ext \
0.00/0.01	  --ho-ext-axiom \
0.00/0.01	  --restrict-hidden-sup-at-vars \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n115.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:29:08 CST 2018
15.81/16.07	% done 1976 iterations in 15.865s
15.81/16.07	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
15.81/16.07	% SZS output start Refutation
15.81/16.07	tff('thm/sets/EMPTY_UNIONS_', conjecture,
15.81/16.07	  (![A:$tType,A0:(A > $o > $o)]:
15.81/16.07	     (('const/sets/UNIONS'(A,A0) = 'const/sets/EMPTY'(A)) <=>
15.81/16.07	      (![A1:(A > $o)]:
15.81/16.07	         ('const/sets/IN'(A > $o,A1,A0) => (A1 = 'const/sets/EMPTY'(A))))))).
15.81/16.07	tff(zf_stmt_0, negated_conjecture,
15.81/16.07	  (~
15.81/16.07	    (![A:$tType,A0:(A > $o > $o)]:
15.81/16.07	       (('const/sets/UNIONS'(A,A0) = 'const/sets/EMPTY'(A)) <=>
15.81/16.07	        (![A1:(A > $o)]:
15.81/16.07	           ('const/sets/IN'(A > $o,A1,A0) => (A1 = 'const/sets/EMPTY'(A)))))))).
15.81/16.07	tff('0', plain,
15.81/16.07	    (sk_A1 != 'const/sets/EMPTY'(sk_A)
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
15.81/16.07	tff('1', plain,
15.81/16.07	    (sk_A1('#k1') != 'const/sets/EMPTY'(sk_A, '#k1')
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0, '#k2')
15.81/16.07	        != 'const/sets/EMPTY'(sk_A, '#k2')),
15.81/16.07	    inference('rw_lit', [status(thm)], ['0'])).
15.81/16.07	tff('thm/sets/EXTENSION_', axiom,
15.81/16.07	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
15.81/16.07	     ((A0 = A1) <=>
15.81/16.07	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
15.81/16.07	tff('2', plain,
15.81/16.07	    ![X13 : $tType, X16 : X13 > $o, X18 : X13 > $o]:
15.81/16.07	      (X16 = X18
15.81/16.07	       | 'const/sets/IN'(X13, sk_A21(X13, X18, X16), X18)
15.81/16.07	       | 'const/sets/IN'(X13, sk_A21(X13, X18, X16), X16)),
15.81/16.07	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
15.81/16.07	tff('thm/sets/NOT_IN_EMPTY_', axiom,
15.81/16.07	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
15.81/16.07	tff('3', plain,
15.81/16.07	    ![X2 : $tType, X3 : X2]:
15.81/16.07	      ~ 'const/sets/IN'(X2, X3, 'const/sets/EMPTY'(X2)),
15.81/16.07	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
15.81/16.07	tff('4', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X1), X1)
15.81/16.07	       | X1 = 'const/sets/EMPTY'(X0)),
15.81/16.07	    inference('sup-', [status(thm)], ['2', '3'])).
15.81/16.07	tff('5', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o]:
15.81/16.07	      (X1 = 'const/sets/EMPTY'(X0)
15.81/16.07	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X1), X1)),
15.81/16.07	    inference('simplify', [status(thm)], ['4'])).
15.81/16.07	tff('thm/sets/IN_UNIONS_', axiom,
15.81/16.07	  (![A:$tType,A0:(A > $o > $o),A1:A]:
15.81/16.07	     ('const/sets/IN'(A,A1,'const/sets/UNIONS'(A,A0)) <=>
15.81/16.07	      (?[A2:(A > $o)]:
15.81/16.07	         ('const/sets/IN'(A,A1,A2) & 'const/sets/IN'(A > $o,A2,A0)))))).
15.81/16.07	tff('6', plain,
15.81/16.07	    ![X8 : $tType, X9 : X8, X10 : X8 > $o > $o]:
15.81/16.07	      ('const/sets/IN'((> $o, X8), sk_A2(X8, X9, X10), X10)
15.81/16.07	       | ~ 'const/sets/IN'(X8, X9, 'const/sets/UNIONS'(X8, X10))),
15.81/16.07	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
15.81/16.07	tff('7', plain,
15.81/16.07	    ![X19 : sk_A > $o]:
15.81/16.07	      (~ 'const/sets/IN'((> $o, sk_A), X19, sk_A0)
15.81/16.07	       | X19 = 'const/sets/EMPTY'(sk_A)
15.81/16.07	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
15.81/16.07	tff('8', plain,
15.81/16.07	    ![X0 : sk_A]:
15.81/16.07	      (~ $true
15.81/16.07	       | ~ 'const/sets/IN'(sk_A, X0, 'const/sets/UNIONS'(sk_A, sk_A0))
15.81/16.07	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
15.81/16.07	       | sk_A2(sk_A, X0, sk_A0) = 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('sup-', [status(thm)], ['6', '7'])).
15.81/16.07	tff('9', plain,
15.81/16.07	    ![X0 : sk_A]:
15.81/16.07	      (sk_A2(sk_A, X0, sk_A0) = 'const/sets/EMPTY'(sk_A)
15.81/16.07	       | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
15.81/16.07	       | ~ 'const/sets/IN'(sk_A, X0, 'const/sets/UNIONS'(sk_A, sk_A0))),
15.81/16.07	    inference('simplify', [status(thm)], ['8'])).
15.81/16.07	tff('10', plain,
15.81/16.07	    (~ $true
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
15.81/16.07	     | sk_A2(sk_A, 
15.81/16.07	         sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
15.81/16.07	           'const/sets/UNIONS'(sk_A, sk_A0)), sk_A0)
15.81/16.07	        = 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('sup-', [status(thm)], ['5', '9'])).
15.81/16.07	tff('11', plain,
15.81/16.07	    (sk_A2(sk_A, 
15.81/16.07	       sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
15.81/16.07	         'const/sets/UNIONS'(sk_A, sk_A0)), sk_A0)
15.81/16.07	      = 'const/sets/EMPTY'(sk_A)
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('simplify', [status(thm)], ['10'])).
15.81/16.07	tff('12', plain,
15.81/16.07	    ![X8 : $tType, X9 : X8, X10 : X8 > $o > $o]:
15.81/16.07	      ('const/sets/IN'(X8, X9, sk_A2(X8, X9, X10))
15.81/16.07	       | ~ 'const/sets/IN'(X8, X9, 'const/sets/UNIONS'(X8, X10))),
15.81/16.07	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
15.81/16.07	tff('13', plain,
15.81/16.07	    ('const/sets/IN'(sk_A, 
15.81/16.07	       sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
15.81/16.07	         'const/sets/UNIONS'(sk_A, sk_A0)), 'const/sets/EMPTY'(sk_A))
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)
15.81/16.07	     | ~ 'const/sets/IN'(sk_A, 
15.81/16.07	           sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
15.81/16.07	             'const/sets/UNIONS'(sk_A, sk_A0)), 
15.81/16.07	           'const/sets/UNIONS'(sk_A, sk_A0))),
15.81/16.07	    inference('sup+', [status(thm)], ['11', '12'])).
15.81/16.07	tff('14', plain,
15.81/16.07	    (~ 'const/sets/IN'(sk_A, 
15.81/16.07	         sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), 
15.81/16.07	           'const/sets/UNIONS'(sk_A, sk_A0)), 
15.81/16.07	         'const/sets/UNIONS'(sk_A, sk_A0))
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('clc', [status(thm)], ['13', '3'])).
15.81/16.07	tff('15', plain, 'const/sets/UNIONS'(sk_A, sk_A0) = 'const/sets/EMPTY'(sk_A),
15.81/16.07	    inference('clc', [status(thm)], ['14', '5'])).
15.81/16.07	tff('16', plain,
15.81/16.07	    ![X1 : sk_A]:
15.81/16.07	      'const/sets/UNIONS'(sk_A, sk_A0, X1) = 'const/sets/EMPTY'(sk_A, X1),
15.81/16.07	    inference('ho_complete_eq', [status(thm)], ['15'])).
15.81/16.07	tff('17', plain,
15.81/16.07	    (sk_A1('#k1') != 'const/sets/EMPTY'(sk_A, '#k1')
15.81/16.07	     | 'const/sets/EMPTY'(sk_A, '#k2') != 'const/sets/EMPTY'(sk_A, '#k2')),
15.81/16.07	    inference('demod', [status(thm)], ['1', '16'])).
15.81/16.07	tff('18', plain, sk_A1('#k1') != 'const/sets/EMPTY'(sk_A, '#k1'),
15.81/16.07	    inference('simplify', [status(thm)], ['17'])).
15.81/16.07	tff('19', plain,
15.81/16.07	    ('const/sets/IN'((> $o, sk_A), sk_A1, sk_A0)
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0) != 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('cnf', [status(esa)], [zf_stmt_0])).
15.81/16.07	tff('20', plain,
15.81/16.07	    ('const/sets/IN'((> $o, sk_A), sk_A1, sk_A0)
15.81/16.07	     | 'const/sets/UNIONS'(sk_A, sk_A0, '#k2')
15.81/16.07	        != 'const/sets/EMPTY'(sk_A, '#k2')),
15.81/16.07	    inference('rw_lit', [status(thm)], ['19'])).
15.81/16.07	tff('21', plain,
15.81/16.07	    ('const/sets/IN'((> $o, sk_A), sk_A1, sk_A0)
15.81/16.07	     | 'const/sets/EMPTY'(sk_A, '#k2') != 'const/sets/EMPTY'(sk_A, '#k2')),
15.81/16.07	    inference('demod', [status(thm)], ['20', '16'])).
15.81/16.07	tff('22', plain, 'const/sets/IN'((> $o, sk_A), sk_A1, sk_A0),
15.81/16.07	    inference('simplify', [status(thm)], ['21'])).
15.81/16.07	tff('23', plain,
15.81/16.07	    ![X8 : $tType, X10 : X8 > $o > $o, X11 : X8, X12 : X8 > $o]:
15.81/16.07	      ('const/sets/IN'(X8, X11, 'const/sets/UNIONS'(X8, X10))
15.81/16.07	       | ~ 'const/sets/IN'((> $o, X8), X12, X10)
15.81/16.07	       | ~ 'const/sets/IN'(X8, X11, X12)),
15.81/16.07	    inference('cnf', [status(esa)], [thm/sets/IN_UNIONS_])).
15.81/16.07	tff('thm/sets/IN_', axiom,
15.81/16.07	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
15.81/16.07	tff('24', plain,
15.81/16.07	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
15.81/16.07	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
15.81/16.07	    inference('cnf', [status(esa)], [thm/sets/IN_])).
15.81/16.07	tff('25', plain,
15.81/16.07	    ![X4 : $tType, X5 : X4 > $o, X6 : X4, X7 : X4 > $o]:
15.81/16.07	      (X7 != X5 | X5(X6) | ~ 'const/sets/IN'(X4, X6, X7)),
15.81/16.07	    inference('ho.purify_applied_variable', [status(thm)], ['24'])).
15.81/16.07	tff('26', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0]:
15.81/16.07	      (~ $true
15.81/16.07	       | ~ 'const/sets/IN'(X0, X1, 
15.81/16.07	             'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0))))),
15.81/16.07	    inference('sup-', [status(thm)], ['6', '3'])).
15.81/16.07	tff('27', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0]:
15.81/16.07	      ~ 'const/sets/IN'(X0, X1, 
15.81/16.07	          'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))),
15.81/16.07	    inference('simplify', [status(thm)], ['26'])).
15.81/16.07	tff('28', plain,
15.81/16.07	    ![X0 : $tType]:
15.81/16.07	      (~ $true
15.81/16.07	       | 'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))
15.81/16.07	          = 'const/sets/EMPTY'(X0)),
15.81/16.07	    inference('sup-', [status(thm)], ['5', '27'])).
15.81/16.07	tff('29', plain,
15.81/16.07	    ![X0 : $tType]:
15.81/16.07	      'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))
15.81/16.07	       = 'const/sets/EMPTY'(X0),
15.81/16.07	    inference('simplify', [status(thm)], ['28'])).
15.81/16.07	tff('30', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0]:
15.81/16.07	      'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)), X1)
15.81/16.07	       = 'const/sets/EMPTY'(X0, X1),
15.81/16.07	    inference('ho_complete_eq', [status(thm)], ['29'])).
15.81/16.07	tff('31', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
15.81/16.07	      ($true = 'const/sets/EMPTY'(X0, X1)
15.81/16.07	       | ~ 'const/sets/IN'(X0, X1, X2)
15.81/16.07	       | X2 != 'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))),
15.81/16.07	    inference('sup+', [status(thm)], ['25', '30'])).
15.81/16.07	tff('32', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
15.81/16.07	      ($true = 'const/sets/EMPTY'(X0, X1)
15.81/16.07	       | ~ 'const/sets/IN'(X0, X1, X2)
15.81/16.07	       | X2 != 'const/sets/EMPTY'(X0)),
15.81/16.07	    inference('demod', [status(thm)], ['31', '29'])).
15.81/16.07	tff('33', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | ~ 'const/sets/IN'(X0, X2, X3)
15.81/16.07	       | ~ 'const/sets/IN'((> $o, X0), X3, X1)
15.81/16.07	       | 'const/sets/UNIONS'(X0, X1) != 'const/sets/EMPTY'(X0)
15.81/16.07	       | 'const/sets/EMPTY'(X0, X2)),
15.81/16.07	    inference('sup-', [status(thm)], ['23', '32'])).
15.81/16.07	tff('34', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o]:
15.81/16.07	      ('const/sets/EMPTY'(X0, X2)
15.81/16.07	       | 'const/sets/UNIONS'(X0, X1) != 'const/sets/EMPTY'(X0)
15.81/16.07	       | ~ 'const/sets/IN'((> $o, X0), X3, X1)
15.81/16.07	       | ~ 'const/sets/IN'(X0, X2, X3)),
15.81/16.07	    inference('simplify', [status(thm)], ['33'])).
15.81/16.07	tff('35', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o]:
15.81/16.07	      ('const/sets/EMPTY'(X0, X2)
15.81/16.07	       | 'const/sets/UNIONS'(X0, X1, '#k33'(X0, X1))
15.81/16.07	          != 'const/sets/EMPTY'(X0, '#k33'(X0, X1))
15.81/16.07	       | ~ 'const/sets/IN'((> $o, X0), X3, X1)
15.81/16.07	       | ~ 'const/sets/IN'(X0, X2, X3)),
15.81/16.07	    inference('rw_lit', [status(thm)], ['34'])).
15.81/16.07	tff('36', plain,
15.81/16.07	    ![X0 : sk_A > $o, X1 : sk_A]:
15.81/16.07	      ('const/sets/EMPTY'(sk_A, '#k33'(sk_A, sk_A0))
15.81/16.07	        != 'const/sets/EMPTY'(sk_A, '#k33'(sk_A, sk_A0))
15.81/16.07	       | ~ 'const/sets/IN'(sk_A, X1, X0)
15.81/16.07	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A0)
15.81/16.07	       | 'const/sets/EMPTY'(sk_A, X1)),
15.81/16.07	    inference('sup-', [status(thm)], ['16', '35'])).
15.81/16.07	tff('37', plain,
15.81/16.07	    ![X0 : sk_A > $o, X1 : sk_A]:
15.81/16.07	      ('const/sets/EMPTY'(sk_A, X1)
15.81/16.07	       | ~ 'const/sets/IN'((> $o, sk_A), X0, sk_A0)
15.81/16.07	       | ~ 'const/sets/IN'(sk_A, X1, X0)),
15.81/16.07	    inference('simplify', [status(thm)], ['36'])).
15.81/16.07	tff('38', plain,
15.81/16.07	    ![X0 : sk_A]:
15.81/16.07	      (~ $true
15.81/16.07	       | ~ 'const/sets/IN'(sk_A, X0, sk_A1)
15.81/16.07	       | 'const/sets/EMPTY'(sk_A, X0)),
15.81/16.07	    inference('sup-', [status(thm)], ['22', '37'])).
15.81/16.07	tff('39', plain,
15.81/16.07	    ![X0 : sk_A]:
15.81/16.07	      ('const/sets/EMPTY'(sk_A, X0) | ~ 'const/sets/IN'(sk_A, X0, sk_A1)),
15.81/16.07	    inference('simplify', [status(thm)], ['38'])).
15.81/16.07	tff('40', plain,
15.81/16.07	    (~ $true
15.81/16.07	     | sk_A1 = 'const/sets/EMPTY'(sk_A)
15.81/16.07	     | 'const/sets/EMPTY'(sk_A, 
15.81/16.07	         sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1))),
15.81/16.07	    inference('sup-', [status(thm)], ['5', '39'])).
15.81/16.07	tff('41', plain,
15.81/16.07	    ('const/sets/EMPTY'(sk_A, sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1))
15.81/16.07	     | sk_A1 = 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('simplify', [status(thm)], ['40'])).
15.81/16.07	tff('42', plain,
15.81/16.07	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
15.81/16.07	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
15.81/16.07	    inference('cnf', [status(esa)], [thm/sets/IN_])).
15.81/16.07	tff('43', plain,
15.81/16.07	    ![X4 : $tType, X5 : X4 > $o, X7 : X4, X8 : X4 > $o]:
15.81/16.07	      (X8 != X5 | 'const/sets/IN'(X4, X7, X5) | ~ X8(X7)),
15.81/16.07	    inference('ho.purify_applied_variable', [status(thm)], ['42'])).
15.81/16.07	tff('44', plain,
15.81/16.07	    ![X0 : sk_A > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | sk_A1 = 'const/sets/EMPTY'(sk_A)
15.81/16.07	       | 'const/sets/IN'(sk_A, 
15.81/16.07	           sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1), X0)
15.81/16.07	       | 'const/sets/EMPTY'(sk_A) != X0),
15.81/16.07	    inference('sup-', [status(thm)], ['41', '43'])).
15.81/16.07	tff('45', plain,
15.81/16.07	    ![X0 : sk_A > $o]:
15.81/16.07	      ('const/sets/EMPTY'(sk_A) != X0
15.81/16.07	       | 'const/sets/IN'(sk_A, 
15.81/16.07	           sk_A21(sk_A, 'const/sets/EMPTY'(sk_A), sk_A1), X0)
15.81/16.07	       | sk_A1 = 'const/sets/EMPTY'(sk_A)),
15.81/16.07	    inference('simplify', [status(thm)], ['44'])).
15.81/16.07	tff('46', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | X1 = 'const/sets/EMPTY'(X0)
15.81/16.07	       | X2(sk_A21(X0, 'const/sets/EMPTY'(X0), X1))
15.81/16.07	       | X1 != X2),
15.81/16.07	    inference('sup-', [status(thm)], ['5', '25'])).
15.81/16.07	tff('47', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
15.81/16.07	      (X1 != X2
15.81/16.07	       | X2(sk_A21(X0, 'const/sets/EMPTY'(X0), X1))
15.81/16.07	       | X1 = 'const/sets/EMPTY'(X0)),
15.81/16.07	    inference('simplify', [status(thm)], ['46'])).
15.81/16.07	tff('48', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | X2 = 'const/sets/EMPTY'(X0)
15.81/16.07	       | X2 != X1
15.81/16.07	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X2), X3)
15.81/16.07	       | X1 != X3),
15.81/16.07	    inference('sup-', [status(thm)], ['47', '43'])).
15.81/16.07	tff('49', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
15.81/16.07	      (X1 != X3
15.81/16.07	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X2), X3)
15.81/16.07	       | X2 != X1
15.81/16.07	       | X2 = 'const/sets/EMPTY'(X0)),
15.81/16.07	    inference('simplify', [status(thm)], ['48'])).
15.81/16.07	tff('50', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
15.81/16.07	      (X1 = 'const/sets/EMPTY'(X0)
15.81/16.07	       | X1 != X2
15.81/16.07	       | 'const/sets/IN'(X0, sk_A21(X0, 'const/sets/EMPTY'(X0), X1), X2)),
15.81/16.07	    inference('eq_res', [status(thm)], ['49'])).
15.81/16.07	tff('51', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | ~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))
15.81/16.07	       | X3(sk_A2(X0, X2, X1))
15.81/16.07	       | X1 != X3),
15.81/16.07	    inference('sup-', [status(thm)], ['6', '25'])).
15.81/16.07	tff('52', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o > $o]:
15.81/16.07	      (X1 != X3
15.81/16.07	       | X3(sk_A2(X0, X2, X1))
15.81/16.07	       | ~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))),
15.81/16.07	    inference('simplify', [status(thm)], ['51'])).
15.81/16.07	tff('53', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o > $o, X3 : X0, 
15.81/16.07	      X4 : X0 > $o > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | ~ 'const/sets/IN'(X0, X3, 'const/sets/UNIONS'(X0, X2))
15.81/16.07	       | X2 != X1
15.81/16.07	       | 'const/sets/IN'((> $o, X0), sk_A2(X0, X3, X2), X4)
15.81/16.07	       | X1 != X4),
15.81/16.07	    inference('sup-', [status(thm)], ['52', '43'])).
15.81/16.07	tff('54', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o > $o, X3 : X0, 
15.81/16.07	      X4 : X0 > $o > $o]:
15.81/16.07	      (X1 != X4
15.81/16.07	       | 'const/sets/IN'((> $o, X0), sk_A2(X0, X3, X2), X4)
15.81/16.07	       | X2 != X1
15.81/16.07	       | ~ 'const/sets/IN'(X0, X3, 'const/sets/UNIONS'(X0, X2))),
15.81/16.07	    inference('simplify', [status(thm)], ['53'])).
15.81/16.07	tff('55', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | ~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))
15.81/16.07	       | X1 != X3
15.81/16.07	       | X3 != 'const/sets/EMPTY'((> $o, X0))),
15.81/16.07	    inference('sup-', [status(thm)], ['54', '3'])).
15.81/16.07	tff('56', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0, X3 : X0 > $o > $o]:
15.81/16.07	      (X3 != 'const/sets/EMPTY'((> $o, X0))
15.81/16.07	       | X1 != X3
15.81/16.07	       | ~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))),
15.81/16.07	    inference('simplify', [status(thm)], ['55'])).
15.81/16.07	tff('57', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0]:
15.81/16.07	      (~ 'const/sets/IN'(X0, X2, 'const/sets/UNIONS'(X0, X1))
15.81/16.07	       | X1 != 'const/sets/EMPTY'((> $o, X0))),
15.81/16.07	    inference('eq_res', [status(thm)], ['56'])).
15.81/16.07	tff('58', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o]:
15.81/16.07	      (~ $true
15.81/16.07	       | X2 != 'const/sets/UNIONS'(X0, X1)
15.81/16.07	       | X2 = 'const/sets/EMPTY'(X0)
15.81/16.07	       | X1 != 'const/sets/EMPTY'((> $o, X0))),
15.81/16.07	    inference('sup-', [status(thm)], ['50', '57'])).
15.81/16.07	tff('59', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o > $o, X2 : X0 > $o]:
15.81/16.07	      (X1 != 'const/sets/EMPTY'((> $o, X0))
15.81/16.07	       | X2 = 'const/sets/EMPTY'(X0)
15.81/16.07	       | X2 != 'const/sets/UNIONS'(X0, X1)),
15.81/16.07	    inference('simplify', [status(thm)], ['58'])).
15.81/16.07	tff('60', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o > $o]:
15.81/16.07	      (~ 'const/sets/IN'(X0, X2, X1)
15.81/16.07	       | X1 != 'const/sets/UNIONS'(X0, X3)
15.81/16.07	       | X3 != 'const/sets/EMPTY'((> $o, X0))),
15.81/16.07	    inference('sup-', [status(thm)], ['59', '3'])).
15.81/16.07	tff('61', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
15.81/16.07	      (X1 != 'const/sets/UNIONS'(X0, 'const/sets/EMPTY'((> $o, X0)))
15.81/16.07	       | ~ 'const/sets/IN'(X0, X2, X1)),
15.81/16.07	    inference('eq_res', [status(thm)], ['60'])).
15.81/16.07	tff('62', plain,
15.81/16.07	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
15.81/16.07	      (X1 != 'const/sets/EMPTY'(X0) | ~ 'const/sets/IN'(X0, X2, X1)),
15.81/16.07	    inference('demod', [status(thm)], ['61', '29'])).
15.81/16.07	tff('63', plain,
15.81/16.07	    ![X0 : sk_A > $o]:
15.81/16.07	      (sk_A1 = 'const/sets/EMPTY'(sk_A) | 'const/sets/EMPTY'(sk_A) != X0),
15.81/16.07	    inference('clc', [status(thm)], ['45', '62'])).
15.81/16.07	tff('64', plain, sk_A1 = 'const/sets/EMPTY'(sk_A),
15.81/16.07	    inference('eq_res', [status(thm)], ['63'])).
15.81/16.07	tff('65', plain, ![X1 : sk_A]: sk_A1(X1) = 'const/sets/EMPTY'(sk_A, X1),
15.81/16.07	    inference('ho_complete_eq', [status(thm)], ['64'])).
15.81/16.07	tff('66', plain, sk_A1('#k1') != sk_A1('#k1'),
15.81/16.07	    inference('demod', [status(thm)], ['18', '65'])).
15.81/16.07	tff('67', plain, $false, inference('simplify', [status(thm)], ['66'])).
15.81/16.07	
15.81/16.07	% SZS output end Refutation
15.81/16.08	EOF
