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    : supatvars_ext
0.00/0.00	% Ordering    : rpo6
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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --sup-at-vars \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n189.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:41:24 CST 2018
156.92/157.15	% done 18264 iterations in 156.950s
156.92/157.15	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
156.92/157.15	% SZS output start Refutation
156.92/157.16	tff('thm/sets/EXTENSION_', axiom,
156.92/157.16	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
156.92/157.16	     ((A0 = A1) <=>
156.92/157.16	      (![A2:A]: ('const/sets/IN'(A,A2,A0) <=> 'const/sets/IN'(A,A2,A1)))))).
156.92/157.16	tff('0', plain,
156.92/157.16	    ![X10 : $tType, X13 : X10 > $o, X15 : X10 > $o]:
156.92/157.16	      (X13 = X15
156.92/157.16	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X15)
156.92/157.16	       | 'const/sets/IN'(X10, sk_A2(X10, X15, X13), X13)),
156.92/157.16	    inference('cnf', [status(esa)], [thm/sets/EXTENSION_])).
156.92/157.16	tff('thm/sets/SUBSET_', axiom,
156.92/157.16	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
156.92/157.16	     ('const/sets/SUBSET'(A,A0,A1) <=>
156.92/157.16	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
156.92/157.16	tff('1', plain,
156.92/157.16	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
156.92/157.16	      (~ 'const/sets/IN'(X16, X17, X18)
156.92/157.16	       | 'const/sets/IN'(X16, X17, X19)
156.92/157.16	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
156.92/157.16	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
156.92/157.16	tff('thm/sets/NOT_IN_EMPTY_', axiom,
156.92/157.16	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
156.92/157.16	tff('2', plain,
156.92/157.16	    ![X8 : $tType, X9 : X8]:
156.92/157.16	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
156.92/157.16	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
156.92/157.16	tff('3', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
156.92/157.16	       | ~ 'const/sets/IN'(X0, X1, X2)),
156.92/157.16	    inference('sup-', [status(thm)], ['1', '2'])).
156.92/157.16	tff('4', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
156.92/157.16	      (~ 'const/sets/IN'(X0, X1, X2)
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))),
156.92/157.16	    inference('simplify', [status(thm)], ['3'])).
156.92/157.16	tff('5', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)
156.92/157.16	       | X2 = X1
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
156.92/157.16	    inference('sup-', [status(thm)], ['0', '4'])).
156.92/157.16	tff('6', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))
156.92/157.16	       | X2 = X1
156.92/157.16	       | 'const/sets/IN'(X0, sk_A2(X0, X1, X2), X2)),
156.92/157.16	    inference('simplify', [status(thm)], ['5'])).
156.92/157.16	tff('thm/trivia/I_THM_', axiom,
156.92/157.16	  (![A:$tType,A0:A]: ('const/trivia/I'(A,A0) = A0))).
156.92/157.16	tff('7', plain, ![X2 : $tType, X3 : X2]: 'const/trivia/I'(X2, X3) = X3,
156.92/157.16	    inference('cnf', [status(esa)], [thm/trivia/I_THM_])).
156.92/157.16	tff('8', plain,
156.92/157.16	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
156.92/157.16	      ('const/sets/SUBSET'(X16, X18, X20)
156.92/157.16	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
156.92/157.16	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
156.92/157.16	tff('thm/sets/IN_', axiom,
156.92/157.16	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
156.92/157.16	tff('9', plain,
156.92/157.16	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
156.92/157.16	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
156.92/157.16	    inference('cnf', [status(esa)], [thm/sets/IN_])).
156.92/157.16	tff('10', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (~ $true | 'const/sets/SUBSET'(X0, X1, X2) | X1(sk_A21(X0, X2, X1))),
156.92/157.16	    inference('sup-', [status(thm)], ['8', '9'])).
156.92/157.16	tff('11', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (X1(sk_A21(X0, X2, X1)) | 'const/sets/SUBSET'(X0, X1, X2)),
156.92/157.16	    inference('simplify', [status(thm)], ['10'])).
156.92/157.16	tff('12', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      ('const/trivia/I'((> $o, X0), X1, sk_A21(X0, X2, X1))
156.92/157.16	       | 'const/sets/SUBSET'(X0, 'const/trivia/I'((> $o, X0), X1), X2)),
156.92/157.16	    inference('sup+', [status(thm)], ['7', '11'])).
156.92/157.16	tff('13', plain,
156.92/157.16	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
156.92/157.16	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
156.92/157.16	    inference('cnf', [status(esa)], [thm/sets/IN_])).
156.92/157.16	tff('14', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/SUBSET'(X0, 'const/trivia/I'((> $o, X0), X1), X2)
156.92/157.16	       | 'const/sets/IN'(X0, sk_A21(X0, X2, X1), 
156.92/157.16	           'const/trivia/I'((> $o, X0), X1))),
156.92/157.16	    inference('sup-', [status(thm)], ['12', '13'])).
156.92/157.16	tff('15', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      ('const/sets/IN'(X0, sk_A21(X0, X2, X1), 
156.92/157.16	         'const/trivia/I'((> $o, X0), X1))
156.92/157.16	       | 'const/sets/SUBSET'(X0, 'const/trivia/I'((> $o, X0), X1), X2)),
156.92/157.16	    inference('simplify', [status(thm)], ['14'])).
156.92/157.16	tff('16', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      ('const/sets/IN'(X0, sk_A21(X0, X2, X1), X1)
156.92/157.16	       | 'const/sets/SUBSET'(X0, 'const/trivia/I'((> $o, X0), X1), X2)),
156.92/157.16	    inference('sup+', [status(thm)], ['7', '15'])).
156.92/157.16	tff('17', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/SUBSET'(X0, 
156.92/157.16	           'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)), X1)),
156.92/157.16	    inference('sup-', [status(thm)], ['16', '2'])).
156.92/157.16	tff('18', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      'const/sets/SUBSET'(X0, 
156.92/157.16	        'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)), X1),
156.92/157.16	    inference('simplify', [status(thm)], ['17'])).
156.92/157.16	tff('19', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0]:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/sets/IN'(X0, X1, 
156.92/157.16	             'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)))),
156.92/157.16	    inference('sup-', [status(thm)], ['18', '4'])).
156.92/157.16	tff('20', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0]:
156.92/157.16	      ~ 'const/sets/IN'(X0, X1, 
156.92/157.16	          'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0))),
156.92/157.16	    inference('simplify', [status(thm)], ['19'])).
156.92/157.16	tff('21', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)) = X1
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
156.92/157.16	    inference('sup-', [status(thm)], ['6', '20'])).
156.92/157.16	tff('22', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))
156.92/157.16	       | 'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)) = X1),
156.92/157.16	    inference('simplify', [status(thm)], ['21'])).
156.92/157.16	tff('23', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
156.92/157.16	      ('const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0), X2) = X1(X2)
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
156.92/157.16	    inference('ho_complete_eq', [status(thm)], ['22'])).
156.92/157.16	tff('24', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/SUBSET'(X0, 
156.92/157.16	           'const/trivia/I'((> $o, X0), 
156.92/157.16	             'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0))), X1)),
156.92/157.16	    inference('sup-', [status(thm)], ['16', '20'])).
156.92/157.16	tff('25', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      'const/sets/SUBSET'(X0, 
156.92/157.16	        'const/trivia/I'((> $o, X0), 
156.92/157.16	          'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0))), X1),
156.92/157.16	    inference('simplify', [status(thm)], ['24'])).
156.92/157.16	tff('26', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)
156.92/157.16	       | X1 = 'const/sets/EMPTY'(X0)),
156.92/157.16	    inference('sup-', [status(thm)], ['0', '2'])).
156.92/157.16	tff('27', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (X1 = 'const/sets/EMPTY'(X0)
156.92/157.16	       | 'const/sets/IN'(X0, sk_A2(X0, 'const/sets/EMPTY'(X0), X1), X1)),
156.92/157.16	    inference('simplify', [status(thm)], ['26'])).
156.92/157.16	tff('28', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | X1 = 'const/sets/EMPTY'(X0)
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
156.92/157.16	    inference('sup-', [status(thm)], ['27', '4'])).
156.92/157.16	tff('29', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))
156.92/157.16	       | X1 = 'const/sets/EMPTY'(X0)),
156.92/157.16	    inference('simplify', [status(thm)], ['28'])).
156.92/157.16	tff('30', plain,
156.92/157.16	    ![X0 : $tType]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/trivia/I'((> $o, X0), 
156.92/157.16	           'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)))
156.92/157.16	          = 'const/sets/EMPTY'(X0)),
156.92/157.16	    inference('sup-', [status(thm)], ['25', '29'])).
156.92/157.16	tff('31', plain,
156.92/157.16	    ![X0 : $tType]:
156.92/157.16	      'const/trivia/I'((> $o, X0), 
156.92/157.16	        'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)))
156.92/157.16	       = 'const/sets/EMPTY'(X0),
156.92/157.16	    inference('simplify', [status(thm)], ['30'])).
156.92/157.16	tff('32', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0]:
156.92/157.16	      'const/trivia/I'((> $o, X0), 
156.92/157.16	        'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)), X1)
156.92/157.16	       = 'const/sets/EMPTY'(X0, X1),
156.92/157.16	    inference('ho_complete_eq', [status(thm)], ['31'])).
156.92/157.16	tff('33', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0]:
156.92/157.16	      'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0), X1)
156.92/157.16	       = 'const/sets/EMPTY'(X0, X1),
156.92/157.16	    inference('sup+', [status(thm)], ['7', '32'])).
156.92/157.16	tff('34', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0]:
156.92/157.16	      ('const/sets/EMPTY'(X0, X2) = X1(X2)
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
156.92/157.16	    inference('demod', [status(thm)], ['23', '33'])).
156.92/157.16	tff('thm/sets/REAL_SUP_LE_SUBSET_', conjecture,
156.92/157.16	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
156.92/157.16	     (((?[A1:'type/realax/real']:
156.92/157.16	          (![A2:'type/realax/real']:
156.92/157.16	             ('const/sets/IN'('type/realax/real',A2,A0) =>
156.92/157.16	              'const/realax/real_le'(A2,A1)))) & 
156.92/157.16	       'const/sets/SUBSET'('type/realax/real',A,A0) & 
156.92/157.16	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
156.92/157.16	      'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0))))).
156.92/157.16	tff(zf_stmt_0, negated_conjecture,
156.92/157.16	  (~
156.92/157.16	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
156.92/157.16	       (((?[A1:'type/realax/real']:
156.92/157.16	            (![A2:'type/realax/real']:
156.92/157.16	               ('const/sets/IN'('type/realax/real',A2,A0) =>
156.92/157.16	                'const/realax/real_le'(A2,A1)))) & 
156.92/157.16	         'const/sets/SUBSET'('type/realax/real',A,A0) & 
156.92/157.16	         (A != 'const/sets/EMPTY'('type/realax/real'))) =>
156.92/157.16	        'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0)))))).
156.92/157.16	tff('35', plain, sk_A != 'const/sets/EMPTY'('type/realax/real'),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_0])).
156.92/157.16	tff('36', plain,
156.92/157.16	    sk_A('#k1') != 'const/sets/EMPTY'('type/realax/real', '#k1'),
156.92/157.16	    inference('rw_lit', [status(thm)], ['35'])).
156.92/157.16	tff('37', plain,
156.92/157.16	    ('const/sets/EMPTY'('type/realax/real', '#k1')
156.92/157.16	      != 'const/sets/EMPTY'('type/realax/real', '#k1')
156.92/157.16	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
156.92/157.16	           'const/sets/EMPTY'('type/realax/real'))),
156.92/157.16	    inference('sup-', [status(thm)], ['34', '36'])).
156.92/157.16	tff('38', plain,
156.92/157.16	    ~ 'const/sets/SUBSET'('type/realax/real', sk_A, 
156.92/157.16	        'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('simplify', [status(thm)], ['37'])).
156.92/157.16	tff('thm/sets/SUP_', axiom,
156.92/157.16	  (![A:('type/realax/real' > $o)]:
156.92/157.16	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
156.92/157.16	       (?[A0:'type/realax/real']:
156.92/157.16	          (![A1:'type/realax/real']:
156.92/157.16	             ('const/sets/IN'('type/realax/real',A1,A) =>
156.92/157.16	              'const/realax/real_le'(A1,A0))))) =>
156.92/157.16	      ((![A0:'type/realax/real']:
156.92/157.16	          ('const/sets/IN'('type/realax/real',A0,A) =>
156.92/157.16	           'const/realax/real_le'(A0,'const/sets/sup'(A)))) & 
156.92/157.16	       (![A0:'type/realax/real']:
156.92/157.16	          ((![A1:'type/realax/real']:
156.92/157.16	              ('const/sets/IN'('type/realax/real',A1,A) =>
156.92/157.16	               'const/realax/real_le'(A1,A0))) =>
156.92/157.16	           'const/realax/real_le'('const/sets/sup'(A),A0))))))).
156.92/157.16	tff(zf_stmt_1, axiom,
156.92/157.16	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
156.92/157.16	   zip_tseitin0(A1,A0,A))).
156.92/157.16	tff('39', plain,
156.92/157.16	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
156.92/157.16	      X23 : 'type/realax/real' > $o]:
156.92/157.16	      (zip_tseitin0(X21, X22, X23)
156.92/157.16	       | 'const/sets/IN'('type/realax/real', X21, X23)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_1])).
156.92/157.16	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
156.92/157.16	tff(zf_stmt_3, axiom,
156.92/157.16	  (zip_tseitin2(A) =>
156.92/157.16	   ((![A0:'type/realax/real']:
156.92/157.16	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
156.92/157.16	        'const/realax/real_le'('const/sets/sup'(A),A0))) & 
156.92/157.16	    (![A0:'type/realax/real']:
156.92/157.16	       ('const/sets/IN'('type/realax/real',A0,A) =>
156.92/157.16	        'const/realax/real_le'(A0,'const/sets/sup'(A))))))).
156.92/157.16	tff(zf_stmt_4, type, zip_tseitin1 :
156.92/157.16	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
156.92/157.16	tff(zf_stmt_5, axiom,
156.92/157.16	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
156.92/157.16	   zip_tseitin1(A1,A0,A))).
156.92/157.16	tff(zf_stmt_6, type, zip_tseitin0 :
156.92/157.16	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
156.92/157.16	tff(zf_stmt_7, axiom,
156.92/157.16	  (![A:('type/realax/real' > $o)]:
156.92/157.16	     (((?[A0:'type/realax/real']:
156.92/157.16	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
156.92/157.16	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
156.92/157.16	      zip_tseitin2(A)))).
156.92/157.16	tff('40', plain,
156.92/157.16	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
156.92/157.16	      (zip_tseitin2(X28)
156.92/157.16	       | X28 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_7])).
156.92/157.16	tff('41', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | zip_tseitin2(X0)),
156.92/157.16	    inference('sup-', [status(thm)], ['39', '40'])).
156.92/157.16	tff('42', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
156.92/157.16	      (zip_tseitin2(X0)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | 'const/sets/IN'('type/realax/real', sk_A12(X1, X0), X0)),
156.92/157.16	    inference('simplify', [status(thm)], ['41'])).
156.92/157.16	tff('43', plain,
156.92/157.16	    ![X30 : 'type/realax/real']:
156.92/157.16	      ('const/realax/real_le'(X30, sk_A13)
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A0)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_0])).
156.92/157.16	tff('44', plain,
156.92/157.16	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
156.92/157.16	      X23 : 'type/realax/real' > $o]:
156.92/157.16	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X21, X22)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_1])).
156.92/157.16	tff('45', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | zip_tseitin2(X0)),
156.92/157.16	    inference('sup-', [status(thm)], ['44', '40'])).
156.92/157.16	tff('46', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
156.92/157.16	      (zip_tseitin2(X0)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)),
156.92/157.16	    inference('simplify', [status(thm)], ['45'])).
156.92/157.16	tff('47', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A0)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | zip_tseitin2(X0)),
156.92/157.16	    inference('sup-', [status(thm)], ['43', '46'])).
156.92/157.16	tff('48', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o]:
156.92/157.16	      (zip_tseitin2(X0)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), sk_A0)),
156.92/157.16	    inference('simplify', [status(thm)], ['47'])).
156.92/157.16	tff('49', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/sets/SUBSET'('type/realax/real', X1, sk_A0)
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), X1)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | zip_tseitin2(X0)),
156.92/157.16	    inference('sup-', [status(thm)], ['1', '48'])).
156.92/157.16	tff('50', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
156.92/157.16	      (zip_tseitin2(X0)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', sk_A12(sk_A13, X0), X1)
156.92/157.16	       | ~ 'const/sets/SUBSET'('type/realax/real', X1, sk_A0)),
156.92/157.16	    inference('simplify', [status(thm)], ['49'])).
156.92/157.16	tff('51', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | zip_tseitin2(X0)
156.92/157.16	       | ~ 'const/sets/SUBSET'('type/realax/real', X0, sk_A0)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | zip_tseitin2(X0)),
156.92/157.16	    inference('sup-', [status(thm)], ['42', '50'])).
156.92/157.16	tff('52', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o]:
156.92/157.16	      (~ 'const/sets/SUBSET'('type/realax/real', X0, sk_A0)
156.92/157.16	       | zip_tseitin2(X0)
156.92/157.16	       | X0 = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('simplify', [status(thm)], ['51'])).
156.92/157.16	tff('53', plain,
156.92/157.16	    ![X23 : 'type/realax/real' > $o, X24 : 'type/realax/real', 
156.92/157.16	      X25 : 'type/realax/real']:
156.92/157.16	      (zip_tseitin1(X24, X25, X23)
156.92/157.16	       | 'const/sets/IN'('type/realax/real', X24, X23)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_5])).
156.92/157.16	tff('54', plain,
156.92/157.16	    ![X23 : 'type/realax/real' > $o, X26 : 'type/realax/real']:
156.92/157.16	      (~ zip_tseitin1(sk_A11(X26, X23), X26, X23)
156.92/157.16	       | 'const/realax/real_le'('const/sets/sup'(X23), X26)
156.92/157.16	       | ~ zip_tseitin2(X23)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_3])).
156.92/157.16	tff('55', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/IN'('type/realax/real', sk_A11(X1, X0), X0)
156.92/157.16	       | ~ zip_tseitin2(X0)
156.92/157.16	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
156.92/157.16	    inference('sup-', [status(thm)], ['53', '54'])).
156.92/157.16	tff('56', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
156.92/157.16	      ('const/realax/real_le'('const/sets/sup'(X0), X1)
156.92/157.16	       | ~ zip_tseitin2(X0)
156.92/157.16	       | 'const/sets/IN'('type/realax/real', sk_A11(X1, X0), X0)),
156.92/157.16	    inference('simplify', [status(thm)], ['55'])).
156.92/157.16	tff('57', plain, 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A0),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_0])).
156.92/157.16	tff('58', plain,
156.92/157.16	    ![X0 : 'type/realax/real']:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
156.92/157.16	    inference('sup-', [status(thm)], ['57', '1'])).
156.92/157.16	tff('59', plain,
156.92/157.16	    ![X0 : 'type/realax/real']:
156.92/157.16	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
156.92/157.16	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)),
156.92/157.16	    inference('simplify', [status(thm)], ['58'])).
156.92/157.16	tff('60', plain,
156.92/157.16	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
156.92/157.16	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
156.92/157.16	       | 'const/sets/IN'('type/realax/real', X0, X1)),
156.92/157.16	    inference('sup-', [status(thm)], ['59', '1'])).
156.92/157.16	tff('61', plain,
156.92/157.16	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
156.92/157.16	      ('const/sets/IN'('type/realax/real', X0, X1)
156.92/157.16	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
156.92/157.16	    inference('simplify', [status(thm)], ['60'])).
156.92/157.16	tff('62', plain,
156.92/157.16	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ zip_tseitin2(sk_A)
156.92/157.16	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)
156.92/157.16	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
156.92/157.16	       | 'const/sets/IN'('type/realax/real', sk_A11(X0, sk_A), X1)),
156.92/157.16	    inference('sup-', [status(thm)], ['56', '61'])).
156.92/157.16	tff('63', plain,
156.92/157.16	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
156.92/157.16	      ('const/sets/IN'('type/realax/real', sk_A11(X0, sk_A), X1)
156.92/157.16	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
156.92/157.16	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)
156.92/157.16	       | ~ zip_tseitin2(sk_A)),
156.92/157.16	    inference('simplify', [status(thm)], ['62'])).
156.92/157.16	tff('64', plain,
156.92/157.16	    (~ $true
156.92/157.16	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | zip_tseitin2(sk_A0)
156.92/157.16	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | zip_tseitin2(sk_A0)),
156.92/157.16	    inference('sup-', [status(thm)], ['42', '48'])).
156.92/157.16	tff('65', plain,
156.92/157.16	    (zip_tseitin2(sk_A0) | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('simplify', [status(thm)], ['64'])).
156.92/157.16	tff('66', plain,
156.92/157.16	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
156.92/157.16	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
156.92/157.16	       | 'const/realax/real_le'(X27, 'const/sets/sup'(X23))
156.92/157.16	       | ~ zip_tseitin2(X23)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_3])).
156.92/157.16	tff('67', plain,
156.92/157.16	    ![X0 : 'type/realax/real']:
156.92/157.16	      (~ $true
156.92/157.16	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | 'const/realax/real_le'(X0, 'const/sets/sup'(sk_A0))
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A0)),
156.92/157.16	    inference('sup-', [status(thm)], ['65', '66'])).
156.92/157.16	tff('68', plain,
156.92/157.16	    ![X0 : 'type/realax/real']:
156.92/157.16	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A0)
156.92/157.16	       | 'const/realax/real_le'(X0, 'const/sets/sup'(sk_A0))
156.92/157.16	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('simplify', [status(thm)], ['67'])).
156.92/157.16	tff('69', plain,
156.92/157.16	    ![X23 : 'type/realax/real' > $o, X24 : 'type/realax/real', 
156.92/157.16	      X25 : 'type/realax/real']:
156.92/157.16	      (zip_tseitin1(X24, X25, X23) | ~ 'const/realax/real_le'(X24, X25)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_5])).
156.92/157.16	tff('70', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/realax/real_le'(sk_A11(X1, X0), X1)
156.92/157.16	       | ~ zip_tseitin2(X0)
156.92/157.16	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
156.92/157.16	    inference('sup-', [status(thm)], ['69', '54'])).
156.92/157.16	tff('71', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
156.92/157.16	      ('const/realax/real_le'('const/sets/sup'(X0), X1)
156.92/157.16	       | ~ zip_tseitin2(X0)
156.92/157.16	       | ~ 'const/realax/real_le'(sk_A11(X1, X0), X1)),
156.92/157.16	    inference('simplify', [status(thm)], ['70'])).
156.92/157.16	tff('72', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', 
156.92/157.16	             sk_A11('const/sets/sup'(sk_A0), X0), sk_A0)
156.92/157.16	       | ~ zip_tseitin2(X0)
156.92/157.16	       | 'const/realax/real_le'('const/sets/sup'(X0), 
156.92/157.16	           'const/sets/sup'(sk_A0))),
156.92/157.16	    inference('sup-', [status(thm)], ['68', '71'])).
156.92/157.16	tff('73', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o]:
156.92/157.16	      ('const/realax/real_le'('const/sets/sup'(X0), 'const/sets/sup'(sk_A0))
156.92/157.16	       | ~ zip_tseitin2(X0)
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', 
156.92/157.16	             sk_A11('const/sets/sup'(sk_A0), X0), sk_A0)
156.92/157.16	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('simplify', [status(thm)], ['72'])).
156.92/157.16	tff('74', plain,
156.92/157.16	    (~ $true
156.92/157.16	     | ~ zip_tseitin2(sk_A)
156.92/157.16	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
156.92/157.16	         'const/sets/sup'(sk_A0))
156.92/157.16	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A0)
156.92/157.16	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | ~ zip_tseitin2(sk_A)
156.92/157.16	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
156.92/157.16	         'const/sets/sup'(sk_A0))),
156.92/157.16	    inference('sup-', [status(thm)], ['63', '73'])).
156.92/157.16	tff('75', plain,
156.92/157.16	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
156.92/157.16	      ('const/sets/SUBSET'(X16, X18, X20)
156.92/157.16	       | ~ 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X20)),
156.92/157.16	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
156.92/157.16	tff('76', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/SUBSET'(X0, X1, X1)
156.92/157.16	       | 'const/sets/SUBSET'(X0, X1, X1)),
156.92/157.16	    inference('sup-', [status(thm)], ['8', '75'])).
156.92/157.16	tff('77', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
156.92/157.16	    inference('simplify', [status(thm)], ['76'])).
156.92/157.16	tff('78', plain,
156.92/157.16	    (~ $true
156.92/157.16	     | ~ zip_tseitin2(sk_A)
156.92/157.16	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
156.92/157.16	         'const/sets/sup'(sk_A0))
156.92/157.16	     | ~ $true
156.92/157.16	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | ~ zip_tseitin2(sk_A)
156.92/157.16	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
156.92/157.16	         'const/sets/sup'(sk_A0))),
156.92/157.16	    inference('demod', [status(thm)], ['74', '77'])).
156.92/157.16	tff('79', plain,
156.92/157.16	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
156.92/157.16	         'const/sets/sup'(sk_A0))
156.92/157.16	     | ~ zip_tseitin2(sk_A)),
156.92/157.16	    inference('simplify', [status(thm)], ['78'])).
156.92/157.16	tff('80', plain,
156.92/157.16	    ~ 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0)),
156.92/157.16	    inference('cnf', [status(esa)], [zf_stmt_0])).
156.92/157.16	tff('81', plain,
156.92/157.16	    (~ zip_tseitin2(sk_A) | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('clc', [status(thm)], ['79', '80'])).
156.92/157.16	tff('82', plain,
156.92/157.16	    (~ $true
156.92/157.16	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A0)
156.92/157.16	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('sup-', [status(thm)], ['52', '81'])).
156.92/157.16	tff('83', plain,
156.92/157.16	    (~ $true
156.92/157.16	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | ~ $true
156.92/157.16	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('demod', [status(thm)], ['82', '57'])).
156.92/157.16	tff('84', plain,
156.92/157.16	    (sk_A0 = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('simplify', [status(thm)], ['83'])).
156.92/157.16	tff('85', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/SUBSET'(X0, 'const/trivia/I'((> $o, X0), X1), X2)
156.92/157.16	       | X1(sk_A21(X0, X2, X1))),
156.92/157.16	    inference('sup-', [status(thm)], ['16', '9'])).
156.92/157.16	tff('86', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (X1(sk_A21(X0, X2, X1))
156.92/157.16	       | 'const/sets/SUBSET'(X0, 'const/trivia/I'((> $o, X0), X1), X2)),
156.92/157.16	    inference('simplify', [status(thm)], ['85'])).
156.92/157.16	tff('87', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/SUBSET'(X0, X1, X2)
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
156.92/157.16	    inference('sup-', [status(thm)], ['8', '4'])).
156.92/157.16	tff('88', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))
156.92/157.16	       | 'const/sets/SUBSET'(X0, X1, X2)),
156.92/157.16	    inference('simplify', [status(thm)], ['87'])).
156.92/157.16	tff('89', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | X1(sk_A21(X0, 'const/sets/EMPTY'(X0), X1))
156.92/157.16	       | 'const/sets/SUBSET'(X0, 'const/trivia/I'((> $o, X0), X1), X2)),
156.92/157.16	    inference('sup-', [status(thm)], ['86', '88'])).
156.92/157.16	tff('90', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      ('const/sets/SUBSET'(X0, 'const/trivia/I'((> $o, X0), X1), X2)
156.92/157.16	       | X1(sk_A21(X0, 'const/sets/EMPTY'(X0), X1))),
156.92/157.16	    inference('simplify', [status(thm)], ['89'])).
156.92/157.16	tff('91', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      ('const/sets/SUBSET'(X0, X1, X2)
156.92/157.16	       | X1(sk_A21(X0, 'const/sets/EMPTY'(X0), X1))),
156.92/157.16	    inference('sup+', [status(thm)], ['7', '90'])).
156.92/157.16	tff('92', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X2, 
156.92/157.16	             'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)))
156.92/157.16	       | ~ 'const/sets/IN'(X0, X1, X2)),
156.92/157.16	    inference('sup-', [status(thm)], ['1', '20'])).
156.92/157.16	tff('93', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
156.92/157.16	      (~ 'const/sets/IN'(X0, X1, X2)
156.92/157.16	       | ~ 'const/sets/SUBSET'(X0, X2, 
156.92/157.16	             'const/trivia/I'((> $o, X0), 'const/sets/EMPTY'(X0)))),
156.92/157.16	    inference('simplify', [status(thm)], ['92'])).
156.92/157.16	tff('94', plain,
156.92/157.16	    ![X0 : 'type/realax/real']:
156.92/157.16	      (~ $true
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
156.92/157.16	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
156.92/157.16	             'const/trivia/I'((> $o, 'type/realax/real'), 
156.92/157.16	               'const/sets/EMPTY'('type/realax/real')))),
156.92/157.16	    inference('sup-', [status(thm)], ['59', '93'])).
156.92/157.16	tff('95', plain,
156.92/157.16	    ![X0 : 'type/realax/real']:
156.92/157.16	      (~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
156.92/157.16	           'const/trivia/I'((> $o, 'type/realax/real'), 
156.92/157.16	             'const/sets/EMPTY'('type/realax/real')))
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
156.92/157.16	    inference('simplify', [status(thm)], ['94'])).
156.92/157.16	tff('96', plain,
156.92/157.16	    ![X0 : 'type/realax/real']:
156.92/157.16	      (~ $true
156.92/157.16	       | sk_A0(
156.92/157.16	           sk_A21('type/realax/real', 
156.92/157.16	             'const/sets/EMPTY'('type/realax/real'), sk_A0))
156.92/157.16	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
156.92/157.16	    inference('sup-', [status(thm)], ['91', '95'])).
156.92/157.16	tff('97', plain,
156.92/157.16	    ![X0 : 'type/realax/real']:
156.92/157.16	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
156.92/157.16	       | sk_A0(
156.92/157.16	           sk_A21('type/realax/real', 
156.92/157.16	             'const/sets/EMPTY'('type/realax/real'), sk_A0))),
156.92/157.16	    inference('simplify', [status(thm)], ['96'])).
156.92/157.16	tff('98', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/SUBSET'('type/realax/real', 
156.92/157.16	           'const/trivia/I'((> $o, 'type/realax/real'), sk_A), X0)
156.92/157.16	       | sk_A0(
156.92/157.16	           sk_A21('type/realax/real', 
156.92/157.16	             'const/sets/EMPTY'('type/realax/real'), sk_A0))),
156.92/157.16	    inference('sup-', [status(thm)], ['16', '97'])).
156.92/157.16	tff('99', plain,
156.92/157.16	    ![X0 : 'type/realax/real' > $o]:
156.92/157.16	      (sk_A0(
156.92/157.16	         sk_A21('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
156.92/157.16	           sk_A0))
156.92/157.16	       | 'const/sets/SUBSET'('type/realax/real', 
156.92/157.16	           'const/trivia/I'((> $o, 'type/realax/real'), sk_A), X0)),
156.92/157.16	    inference('simplify', [status(thm)], ['98'])).
156.92/157.16	tff('100', plain,
156.92/157.16	    (~ $true
156.92/157.16	     | sk_A0(
156.92/157.16	         sk_A21('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
156.92/157.16	           sk_A0))
156.92/157.16	     | 'const/trivia/I'((> $o, 'type/realax/real'), sk_A)
156.92/157.16	        = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('sup-', [status(thm)], ['99', '29'])).
156.92/157.16	tff('101', plain,
156.92/157.16	    ('const/trivia/I'((> $o, 'type/realax/real'), sk_A)
156.92/157.16	      = 'const/sets/EMPTY'('type/realax/real')
156.92/157.16	     | sk_A0(
156.92/157.16	         sk_A21('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
156.92/157.16	           sk_A0))),
156.92/157.16	    inference('simplify', [status(thm)], ['100'])).
156.92/157.16	tff('102', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
156.92/157.16	      ('const/sets/SUBSET'(X0, X1, X2)
156.92/157.16	       | 'const/sets/IN'(X0, sk_A21(X0, X2, X1), 
156.92/157.16	           'const/trivia/I'((> $o, X0), X1))),
156.92/157.16	    inference('sup+', [status(thm)], ['7', '15'])).
156.92/157.16	tff('103', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      (~ $true
156.92/157.16	       | 'const/sets/SUBSET'(X0, X1, 'const/trivia/I'((> $o, X0), X1))
156.92/157.16	       | 'const/sets/SUBSET'(X0, X1, 'const/trivia/I'((> $o, X0), X1))),
156.92/157.16	    inference('sup-', [status(thm)], ['102', '75'])).
156.92/157.16	tff('104', plain,
156.92/157.16	    ![X0 : $tType, X1 : X0 > $o]:
156.92/157.16	      'const/sets/SUBSET'(X0, X1, 'const/trivia/I'((> $o, X0), X1)),
156.92/157.16	    inference('simplify', [status(thm)], ['103'])).
156.92/157.16	tff('105', plain,
156.92/157.16	    ('const/sets/SUBSET'('type/realax/real', sk_A, 
156.92/157.16	       'const/sets/EMPTY'('type/realax/real'))
156.92/157.16	     | sk_A0(
156.92/157.16	         sk_A21('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
156.92/157.16	           sk_A0))),
156.92/157.16	    inference('sup+', [status(thm)], ['101', '104'])).
156.92/157.16	tff('106', plain,
156.92/157.16	    sk_A0(
156.92/157.16	      sk_A21('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
156.92/157.16	        sk_A0)),
156.92/157.16	    inference('clc', [status(thm)], ['105', '38'])).
156.92/157.16	tff('107', plain,
156.92/157.16	    (~ $true
156.92/157.16	     | 'const/sets/IN'('type/realax/real', 
156.92/157.16	         sk_A21('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
156.92/157.16	           sk_A0), sk_A0)),
156.92/157.16	    inference('sup-', [status(thm)], ['106', '13'])).
156.92/157.16	tff('108', plain,
156.92/157.16	    'const/sets/IN'('type/realax/real', 
156.92/157.16	      sk_A21('type/realax/real', 'const/sets/EMPTY'('type/realax/real'), 
156.92/157.16	        sk_A0), sk_A0),
156.92/157.16	    inference('simplify', [status(thm)], ['107'])).
156.92/157.16	tff('109', plain,
156.92/157.16	    (~ $true
156.92/157.16	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
156.92/157.16	           'const/sets/EMPTY'('type/realax/real'))),
156.92/157.16	    inference('sup-', [status(thm)], ['108', '4'])).
156.92/157.16	tff('110', plain,
156.92/157.16	    ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
156.92/157.16	        'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('simplify', [status(thm)], ['109'])).
156.92/157.16	tff('111', plain,
156.92/157.16	    (~ 'const/sets/SUBSET'('type/realax/real', 
156.92/157.16	         'const/sets/EMPTY'('type/realax/real'), 
156.92/157.16	         'const/sets/EMPTY'('type/realax/real'))
156.92/157.16	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('sup-', [status(thm)], ['84', '110'])).
156.92/157.16	tff('112', plain, (~ $true | sk_A = 'const/sets/EMPTY'('type/realax/real')),
156.92/157.16	    inference('demod', [status(thm)], ['111', '77'])).
156.92/157.16	tff('113', plain, sk_A = 'const/sets/EMPTY'('type/realax/real'),
156.92/157.16	    inference('simplify', [status(thm)], ['112'])).
156.92/157.16	tff('114', plain, ~ $true,
156.92/157.16	    inference('demod', [status(thm)], ['38', '113', '77'])).
156.92/157.16	tff('115', plain, $false, inference('simplify', [status(thm)], ['114'])).
156.92/157.16	
156.92/157.16	% SZS output end Refutation
156.92/157.16	EOF
