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_ext
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	  --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   : n163.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
103.24/103.41	% done 15339 iterations in 103.198s
103.24/103.41	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
103.24/103.41	% SZS output start Refutation
103.24/103.41	tff('thm/sets/REAL_SUP_LE_SUBSET_', conjecture,
103.24/103.41	  (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
103.24/103.41	     (((?[A1:'type/realax/real']:
103.24/103.41	          (![A2:'type/realax/real']:
103.24/103.41	             ('const/sets/IN'('type/realax/real',A2,A0) =>
103.24/103.41	              'const/realax/real_le'(A2,A1)))) & 
103.24/103.41	       'const/sets/SUBSET'('type/realax/real',A,A0) & 
103.24/103.41	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
103.24/103.41	      'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0))))).
103.24/103.41	tff(zf_stmt_0, negated_conjecture,
103.24/103.41	  (~
103.24/103.41	    (![A:('type/realax/real' > $o),A0:('type/realax/real' > $o)]:
103.24/103.41	       (((?[A1:'type/realax/real']:
103.24/103.41	            (![A2:'type/realax/real']:
103.24/103.41	               ('const/sets/IN'('type/realax/real',A2,A0) =>
103.24/103.41	                'const/realax/real_le'(A2,A1)))) & 
103.24/103.41	         'const/sets/SUBSET'('type/realax/real',A,A0) & 
103.24/103.41	         (A != 'const/sets/EMPTY'('type/realax/real'))) =>
103.24/103.41	        'const/realax/real_le'('const/sets/sup'(A),'const/sets/sup'(A0)))))).
103.24/103.41	tff('0', plain, sk_A != 'const/sets/EMPTY'('type/realax/real'),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
103.24/103.41	tff('1', plain, sk_A('#k1') != 'const/sets/EMPTY'('type/realax/real', '#k1'),
103.24/103.41	    inference('rw_lit', [status(thm)], ['0'])).
103.24/103.41	tff('thm/sets/SUP_', axiom,
103.24/103.41	  (![A:('type/realax/real' > $o)]:
103.24/103.41	     (((A != 'const/sets/EMPTY'('type/realax/real')) & 
103.24/103.41	       (?[A0:'type/realax/real']:
103.24/103.41	          (![A1:'type/realax/real']:
103.24/103.41	             ('const/sets/IN'('type/realax/real',A1,A) =>
103.24/103.41	              'const/realax/real_le'(A1,A0))))) =>
103.24/103.41	      ((![A0:'type/realax/real']:
103.24/103.41	          ('const/sets/IN'('type/realax/real',A0,A) =>
103.24/103.41	           'const/realax/real_le'(A0,'const/sets/sup'(A)))) & 
103.24/103.41	       (![A0:'type/realax/real']:
103.24/103.41	          ((![A1:'type/realax/real']:
103.24/103.41	              ('const/sets/IN'('type/realax/real',A1,A) =>
103.24/103.41	               'const/realax/real_le'(A1,A0))) =>
103.24/103.41	           'const/realax/real_le'('const/sets/sup'(A),A0))))))).
103.24/103.41	tff(zf_stmt_1, axiom,
103.24/103.41	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
103.24/103.41	   zip_tseitin0(A1,A0,A))).
103.24/103.41	tff('2', plain,
103.24/103.41	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
103.24/103.41	      X23 : 'type/realax/real' > $o]:
103.24/103.41	      (zip_tseitin0(X21, X22, X23)
103.24/103.41	       | 'const/sets/IN'('type/realax/real', X21, X23)),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_1])).
103.24/103.41	tff('3', plain,
103.24/103.41	    ![X30 : 'type/realax/real']:
103.24/103.41	      ('const/realax/real_le'(X30, sk_A13)
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', X30, sk_A0)),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
103.24/103.41	tff('4', plain,
103.24/103.41	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
103.24/103.41	      (~ $true
103.24/103.41	       | zip_tseitin0(X0, X1, sk_A0)
103.24/103.41	       | 'const/realax/real_le'(X0, sk_A13)),
103.24/103.41	    inference('sup-', [status(thm)], ['2', '3'])).
103.24/103.41	tff('5', plain,
103.24/103.41	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
103.24/103.41	      ('const/realax/real_le'(X0, sk_A13) | zip_tseitin0(X0, X1, sk_A0)),
103.24/103.41	    inference('simplify', [status(thm)], ['4'])).
103.24/103.41	tff(zf_stmt_2, type, zip_tseitin2 : 'type/realax/real' > $o > $o).
103.24/103.41	tff(zf_stmt_3, axiom,
103.24/103.41	  (zip_tseitin2(A) =>
103.24/103.41	   ((![A0:'type/realax/real']:
103.24/103.41	       ((![A1:'type/realax/real']: zip_tseitin1(A1,A0,A)) =>
103.24/103.41	        'const/realax/real_le'('const/sets/sup'(A),A0))) & 
103.24/103.41	    (![A0:'type/realax/real']:
103.24/103.41	       ('const/sets/IN'('type/realax/real',A0,A) =>
103.24/103.41	        'const/realax/real_le'(A0,'const/sets/sup'(A))))))).
103.24/103.41	tff(zf_stmt_4, type, zip_tseitin1 :
103.24/103.41	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
103.24/103.41	tff(zf_stmt_5, axiom,
103.24/103.41	  (('const/sets/IN'('type/realax/real',A1,A) => 'const/realax/real_le'(A1,A0)) =>
103.24/103.41	   zip_tseitin1(A1,A0,A))).
103.24/103.41	tff(zf_stmt_6, type, zip_tseitin0 :
103.24/103.41	    ('type/realax/real' * 'type/realax/real' * 'type/realax/real' > $o) > $o).
103.24/103.41	tff(zf_stmt_7, axiom,
103.24/103.41	  (![A:('type/realax/real' > $o)]:
103.24/103.41	     (((?[A0:'type/realax/real']:
103.24/103.41	          (![A1:'type/realax/real']: zip_tseitin0(A1,A0,A))) & 
103.24/103.41	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
103.24/103.41	      zip_tseitin2(A)))).
103.24/103.41	tff('6', plain,
103.24/103.41	    ![X28 : 'type/realax/real' > $o, X29 : 'type/realax/real']:
103.24/103.41	      (zip_tseitin2(X28)
103.24/103.41	       | X28 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | ~ zip_tseitin0(sk_A12(X29, X28), X29, X28)),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_7])).
103.24/103.41	tff('7', plain,
103.24/103.41	    ![X0 : 'type/realax/real']:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/realax/real_le'(sk_A12(X0, sk_A0), sk_A13)
103.24/103.41	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | zip_tseitin2(sk_A0)),
103.24/103.41	    inference('sup-', [status(thm)], ['5', '6'])).
103.24/103.41	tff('8', plain,
103.24/103.41	    ![X0 : 'type/realax/real']:
103.24/103.41	      (zip_tseitin2(sk_A0)
103.24/103.41	       | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | 'const/realax/real_le'(sk_A12(X0, sk_A0), sk_A13)),
103.24/103.41	    inference('simplify', [status(thm)], ['7'])).
103.24/103.41	tff('9', plain,
103.24/103.41	    ![X21 : 'type/realax/real', X22 : 'type/realax/real', 
103.24/103.41	      X23 : 'type/realax/real' > $o]:
103.24/103.41	      (zip_tseitin0(X21, X22, X23) | ~ 'const/realax/real_le'(X21, X22)),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_1])).
103.24/103.41	tff('10', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)
103.24/103.41	       | X0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | zip_tseitin2(X0)),
103.24/103.41	    inference('sup-', [status(thm)], ['9', '6'])).
103.24/103.41	tff('11', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.41	      (zip_tseitin2(X0)
103.24/103.41	       | X0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | ~ 'const/realax/real_le'(sk_A12(X1, X0), X1)),
103.24/103.41	    inference('simplify', [status(thm)], ['10'])).
103.24/103.41	tff('12', plain,
103.24/103.41	    (~ $true
103.24/103.41	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	     | zip_tseitin2(sk_A0)
103.24/103.41	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	     | zip_tseitin2(sk_A0)),
103.24/103.41	    inference('sup-', [status(thm)], ['8', '11'])).
103.24/103.41	tff('13', plain,
103.24/103.41	    (zip_tseitin2(sk_A0) | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('simplify', [status(thm)], ['12'])).
103.24/103.41	tff('thm/sets/SUBSET_', axiom,
103.24/103.41	  (![A:$tType,A0:(A > $o),A1:(A > $o)]:
103.24/103.41	     ('const/sets/SUBSET'(A,A0,A1) <=>
103.24/103.41	      (![A2:A]: ('const/sets/IN'(A,A2,A0) => 'const/sets/IN'(A,A2,A1)))))).
103.24/103.41	tff('14', plain,
103.24/103.41	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
103.24/103.41	      ('const/sets/SUBSET'(X16, X18, X20)
103.24/103.41	       | 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X18)),
103.24/103.41	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
103.24/103.41	tff('15', plain,
103.24/103.41	    ![X16 : $tType, X18 : X16 > $o, X20 : X16 > $o]:
103.24/103.41	      ('const/sets/SUBSET'(X16, X18, X20)
103.24/103.41	       | ~ 'const/sets/IN'(X16, sk_A21(X16, X20, X18), X20)),
103.24/103.41	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
103.24/103.41	tff('16', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/SUBSET'(X0, X1, X1)
103.24/103.41	       | 'const/sets/SUBSET'(X0, X1, X1)),
103.24/103.41	    inference('sup-', [status(thm)], ['14', '15'])).
103.24/103.41	tff('17', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o]: 'const/sets/SUBSET'(X0, X1, X1),
103.24/103.41	    inference('simplify', [status(thm)], ['16'])).
103.24/103.41	tff('thm/sets/IN_', axiom,
103.24/103.41	  (![A:$tType,P:(A > $o),A0:A]: ('const/sets/IN'(A,A0,P) <=> P(A0)))).
103.24/103.41	tff('18', plain,
103.24/103.41	    ![X4 : $tType, X5 : X4 > $o, X7 : X4]:
103.24/103.41	      ('const/sets/IN'(X4, X7, X5) | ~ X5(X7)),
103.24/103.41	    inference('cnf', [status(esa)], [thm/sets/IN_])).
103.24/103.41	tff('19', plain,
103.24/103.41	    ![X16 : $tType, X17 : X16, X18 : X16 > $o, X19 : X16 > $o]:
103.24/103.41	      (~ 'const/sets/IN'(X16, X17, X18)
103.24/103.41	       | 'const/sets/IN'(X16, X17, X19)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X16, X18, X19)),
103.24/103.41	    inference('cnf', [status(esa)], [thm/sets/SUBSET_])).
103.24/103.41	tff('20', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ X1(X2)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
103.24/103.41	       | 'const/sets/IN'(X0, X2, X3)),
103.24/103.41	    inference('sup-', [status(thm)], ['18', '19'])).
103.24/103.41	tff('21', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
103.24/103.41	      ('const/sets/IN'(X0, X2, X3)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
103.24/103.41	       | ~ X1(X2)),
103.24/103.41	    inference('simplify', [status(thm)], ['20'])).
103.24/103.41	tff('22', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ 'const/sets/SUBSET'((> $o, X0), 'const/sets/SUBSET'(X0, X1), X2)
103.24/103.41	       | 'const/sets/IN'((> $o, X0), X1, X2)),
103.24/103.41	    inference('sup-', [status(thm)], ['17', '21'])).
103.24/103.41	tff('23', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
103.24/103.41	      ('const/sets/IN'((> $o, X0), X1, X2)
103.24/103.41	       | ~ 'const/sets/SUBSET'((> $o, X0), 'const/sets/SUBSET'(X0, X1), X2)),
103.24/103.41	    inference('simplify', [status(thm)], ['22'])).
103.24/103.41	tff('24', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o]:
103.24/103.41	      (~ $true | 'const/sets/IN'((> $o, X0), X1, 'const/sets/SUBSET'(X0, X1))),
103.24/103.41	    inference('sup-', [status(thm)], ['17', '23'])).
103.24/103.41	tff('25', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o]:
103.24/103.41	      'const/sets/IN'((> $o, X0), X1, 'const/sets/SUBSET'(X0, X1)),
103.24/103.41	    inference('simplify', [status(thm)], ['24'])).
103.24/103.41	tff('thm/sets/REAL_SUP_LE_', axiom,
103.24/103.41	  (![A:('type/realax/real' > $o),A0:'type/realax/real']:
103.24/103.41	     (((![A1:'type/realax/real']:
103.24/103.41	          ('const/sets/IN'('type/realax/real',A1,A) =>
103.24/103.41	           'const/realax/real_le'(A1,A0))) & 
103.24/103.41	       (A != 'const/sets/EMPTY'('type/realax/real'))) =>
103.24/103.41	      'const/realax/real_le'('const/sets/sup'(A),A0)))).
103.24/103.41	tff('26', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.41	      (X0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | 'const/sets/IN'('type/realax/real', sk_A1(X1, X0), X0)
103.24/103.41	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
103.24/103.41	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
103.24/103.41	tff('27', plain,
103.24/103.41	    ![X4 : $tType, X5 : X4 > $o, X6 : X4]:
103.24/103.41	      (X5(X6) | ~ 'const/sets/IN'(X4, X6, X5)),
103.24/103.41	    inference('cnf', [status(esa)], [thm/sets/IN_])).
103.24/103.41	tff('28', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X3, X1)
103.24/103.41	       | ~ 'const/sets/IN'(X0, X2, X3)
103.24/103.41	       | X1(X2)),
103.24/103.41	    inference('sup-', [status(thm)], ['19', '27'])).
103.24/103.41	tff('29', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0, X3 : X0 > $o]:
103.24/103.41	      (X1(X2)
103.24/103.41	       | ~ 'const/sets/IN'(X0, X2, X3)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X3, X1)),
103.24/103.41	    inference('simplify', [status(thm)], ['28'])).
103.24/103.41	tff('30', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
103.24/103.41	      X2 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)
103.24/103.41	       | X0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', X0, X2)
103.24/103.41	       | X2(sk_A1(X1, X0))),
103.24/103.41	    inference('sup-', [status(thm)], ['26', '29'])).
103.24/103.41	tff('31', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
103.24/103.41	      X2 : 'type/realax/real' > $o]:
103.24/103.41	      (X2(sk_A1(X1, X0))
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', X0, X2)
103.24/103.41	       | X0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
103.24/103.41	    inference('simplify', [status(thm)], ['30'])).
103.24/103.41	tff('32', plain,
103.24/103.41	    ~ 'const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0)),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
103.24/103.41	tff('33', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, X0)
103.24/103.41	       | X0(sk_A1('const/sets/sup'(sk_A0), sk_A))),
103.24/103.41	    inference('sup-', [status(thm)], ['31', '32'])).
103.24/103.41	tff('34', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      (X0(sk_A1('const/sets/sup'(sk_A0), sk_A))
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, X0)
103.24/103.41	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('simplify', [status(thm)], ['33'])).
103.24/103.41	tff('35', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
103.24/103.41	      (~ $true | 'const/sets/SUBSET'(X0, X1, X2) | X1(sk_A21(X0, X2, X1))),
103.24/103.41	    inference('sup-', [status(thm)], ['14', '27'])).
103.24/103.41	tff('36', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
103.24/103.41	      (X1(sk_A21(X0, X2, X1)) | 'const/sets/SUBSET'(X0, X1, X2)),
103.24/103.41	    inference('simplify', [status(thm)], ['35'])).
103.24/103.41	tff('37', plain, 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A0),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_0])).
103.24/103.41	tff('38', plain,
103.24/103.41	    ![X0 : 'type/realax/real']:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
103.24/103.41	    inference('sup-', [status(thm)], ['37', '19'])).
103.24/103.41	tff('39', plain,
103.24/103.41	    ![X0 : 'type/realax/real']:
103.24/103.41	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
103.24/103.41	       | 'const/sets/IN'('type/realax/real', X0, sk_A0)),
103.24/103.41	    inference('simplify', [status(thm)], ['38'])).
103.24/103.41	tff('40', plain,
103.24/103.41	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
103.24/103.41	       | X1(X0)),
103.24/103.41	    inference('sup-', [status(thm)], ['39', '29'])).
103.24/103.41	tff('41', plain,
103.24/103.41	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
103.24/103.41	      (X1(X0)
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
103.24/103.41	    inference('simplify', [status(thm)], ['40'])).
103.24/103.41	tff('42', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/SUBSET'('type/realax/real', sk_A, X0)
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
103.24/103.41	       | X1(sk_A21('type/realax/real', X0, sk_A))),
103.24/103.41	    inference('sup-', [status(thm)], ['14', '41'])).
103.24/103.41	tff('43', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
103.24/103.41	      (X1(sk_A21('type/realax/real', X0, sk_A))
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
103.24/103.41	       | 'const/sets/SUBSET'('type/realax/real', sk_A, X0)),
103.24/103.41	    inference('simplify', [status(thm)], ['42'])).
103.24/103.41	tff('44', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
103.24/103.41	      (~ $true | ~ X1(sk_A21(X0, X1, X2)) | 'const/sets/SUBSET'(X0, X2, X1)),
103.24/103.41	    inference('sup-', [status(thm)], ['18', '15'])).
103.24/103.41	tff('45', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
103.24/103.41	      ('const/sets/SUBSET'(X0, X2, X1) | ~ X1(sk_A21(X0, X1, X2))),
103.24/103.41	    inference('simplify', [status(thm)], ['44'])).
103.24/103.41	tff('46', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/SUBSET'('type/realax/real', sk_A, X0)
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
103.24/103.41	       | 'const/sets/SUBSET'('type/realax/real', sk_A, X0)),
103.24/103.41	    inference('sup-', [status(thm)], ['43', '45'])).
103.24/103.41	tff('47', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      (~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
103.24/103.41	       | 'const/sets/SUBSET'('type/realax/real', sk_A, X0)),
103.24/103.41	    inference('simplify', [status(thm)], ['46'])).
103.24/103.41	tff('48', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.41	           'const/sets/SUBSET'('type/realax/real', sk_A0), X0)
103.24/103.41	       | 'const/sets/SUBSET'('type/realax/real', sk_A, 
103.24/103.41	           sk_A21((> $o, 'type/realax/real'), X0, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0)))),
103.24/103.41	    inference('sup-', [status(thm)], ['36', '47'])).
103.24/103.41	tff('49', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o > $o]:
103.24/103.41	      ('const/sets/SUBSET'('type/realax/real', sk_A, 
103.24/103.41	         sk_A21((> $o, 'type/realax/real'), X0, 
103.24/103.41	           'const/sets/SUBSET'('type/realax/real', sk_A0)))
103.24/103.41	       | 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.41	           'const/sets/SUBSET'('type/realax/real', sk_A0), X0)),
103.24/103.41	    inference('simplify', [status(thm)], ['48'])).
103.24/103.41	tff('50', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0, X2 : X0 > $o > $o, X3 : X0 > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X3, 
103.24/103.41	             sk_A21((> $o, X0), 'const/sets/IN'(X0, X1), X2))
103.24/103.41	       | ~ 'const/sets/IN'(X0, X1, X3)
103.24/103.41	       | 'const/sets/SUBSET'((> $o, X0), X2, 'const/sets/IN'(X0, X1))),
103.24/103.41	    inference('sup-', [status(thm)], ['19', '45'])).
103.24/103.41	tff('51', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0, X2 : X0 > $o > $o, X3 : X0 > $o]:
103.24/103.41	      ('const/sets/SUBSET'((> $o, X0), X2, 'const/sets/IN'(X0, X1))
103.24/103.41	       | ~ 'const/sets/IN'(X0, X1, X3)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X3, 
103.24/103.41	             sk_A21((> $o, X0), 'const/sets/IN'(X0, X1), X2))),
103.24/103.41	    inference('simplify', [status(thm)], ['50'])).
103.24/103.41	tff('52', plain,
103.24/103.41	    ![X0 : 'type/realax/real']:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.41	           'const/sets/SUBSET'('type/realax/real', sk_A0), 
103.24/103.41	           'const/sets/IN'('type/realax/real', X0))
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
103.24/103.41	       | 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.41	           'const/sets/SUBSET'('type/realax/real', sk_A0), 
103.24/103.41	           'const/sets/IN'('type/realax/real', X0))),
103.24/103.41	    inference('sup-', [status(thm)], ['49', '51'])).
103.24/103.41	tff('53', plain,
103.24/103.41	    ![X0 : 'type/realax/real']:
103.24/103.41	      (~ 'const/sets/IN'('type/realax/real', X0, sk_A)
103.24/103.41	       | 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.41	           'const/sets/SUBSET'('type/realax/real', sk_A0), 
103.24/103.41	           'const/sets/IN'('type/realax/real', X0))),
103.24/103.41	    inference('simplify', [status(thm)], ['52'])).
103.24/103.41	tff('54', plain,
103.24/103.41	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X1, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | 'const/sets/IN'('type/realax/real', X0, X1)),
103.24/103.41	    inference('sup-', [status(thm)], ['53', '29'])).
103.24/103.41	tff('55', plain,
103.24/103.41	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
103.24/103.41	      ('const/sets/IN'('type/realax/real', X0, X1)
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X1, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', X0, sk_A)),
103.24/103.41	    inference('simplify', [status(thm)], ['54'])).
103.24/103.41	tff('56', plain,
103.24/103.41	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ sk_A(X0)
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X1, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | 'const/sets/IN'('type/realax/real', X0, X1)),
103.24/103.41	    inference('sup-', [status(thm)], ['18', '55'])).
103.24/103.41	tff('57', plain,
103.24/103.41	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
103.24/103.41	      ('const/sets/IN'('type/realax/real', X0, X1)
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X1, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | ~ sk_A(X0)),
103.24/103.41	    inference('simplify', [status(thm)], ['56'])).
103.24/103.41	tff('58', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ sk_A(X1)
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X0, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | X0(X1)),
103.24/103.41	    inference('sup-', [status(thm)], ['57', '27'])).
103.24/103.41	tff('59', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.41	      (X0(X1)
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X0, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | ~ sk_A(X1)),
103.24/103.41	    inference('simplify', [status(thm)], ['58'])).
103.24/103.41	tff('60', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A, sk_A)
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X0, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | X0(sk_A1('const/sets/sup'(sk_A0), sk_A))),
103.24/103.41	    inference('sup-', [status(thm)], ['34', '59'])).
103.24/103.41	tff('61', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | ~ $true
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X0, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | X0(sk_A1('const/sets/sup'(sk_A0), sk_A))),
103.24/103.41	    inference('demod', [status(thm)], ['60', '17'])).
103.24/103.41	tff('62', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      (X0(sk_A1('const/sets/sup'(sk_A0), sk_A))
103.24/103.41	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), X0, 
103.24/103.41	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.41	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('simplify', [status(thm)], ['61'])).
103.24/103.41	tff('63', plain,
103.24/103.41	    (~ $true
103.24/103.41	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	     | sk_A0(sk_A1('const/sets/sup'(sk_A0), sk_A))),
103.24/103.41	    inference('sup-', [status(thm)], ['25', '62'])).
103.24/103.41	tff('64', plain,
103.24/103.41	    (sk_A0(sk_A1('const/sets/sup'(sk_A0), sk_A))
103.24/103.41	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('simplify', [status(thm)], ['63'])).
103.24/103.41	tff('65', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | sk_A = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
103.24/103.41	       | 'const/sets/IN'('type/realax/real', 
103.24/103.41	           sk_A1('const/sets/sup'(sk_A0), sk_A), X0)),
103.24/103.41	    inference('sup-', [status(thm)], ['64', '21'])).
103.24/103.41	tff('66', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o]:
103.24/103.41	      ('const/sets/IN'('type/realax/real', 
103.24/103.41	         sk_A1('const/sets/sup'(sk_A0), sk_A), X0)
103.24/103.41	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
103.24/103.41	       | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('simplify', [status(thm)], ['65'])).
103.24/103.41	tff('67', plain,
103.24/103.41	    ![X23 : 'type/realax/real' > $o, X27 : 'type/realax/real']:
103.24/103.41	      (~ 'const/sets/IN'('type/realax/real', X27, X23)
103.24/103.41	       | 'const/realax/real_le'(X27, 'const/sets/sup'(X23))
103.24/103.41	       | ~ zip_tseitin2(X23)),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_3])).
103.24/103.41	tff('68', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.41	      (X0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | ~ 'const/realax/real_le'(sk_A1(X1, X0), X1)
103.24/103.41	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
103.24/103.41	    inference('cnf', [status(esa)], [thm/sets/REAL_SUP_LE_])).
103.24/103.41	tff('69', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ zip_tseitin2(X0)
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', 
103.24/103.41	             sk_A1('const/sets/sup'(X0), X1), X0)
103.24/103.41	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
103.24/103.41	       | X1 = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('sup-', [status(thm)], ['67', '68'])).
103.24/103.41	tff('70', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real' > $o]:
103.24/103.41	      (X1 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	       | 'const/realax/real_le'('const/sets/sup'(X1), 'const/sets/sup'(X0))
103.24/103.41	       | ~ 'const/sets/IN'('type/realax/real', 
103.24/103.41	             sk_A1('const/sets/sup'(X0), X1), X0)
103.24/103.41	       | ~ zip_tseitin2(X0)),
103.24/103.41	    inference('simplify', [status(thm)], ['69'])).
103.24/103.41	tff('71', plain,
103.24/103.41	    (~ $true
103.24/103.41	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A0)
103.24/103.41	     | ~ zip_tseitin2(sk_A0)
103.24/103.41	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
103.24/103.41	         'const/sets/sup'(sk_A0))
103.24/103.41	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('sup-', [status(thm)], ['66', '70'])).
103.24/103.41	tff('72', plain,
103.24/103.41	    (~ $true
103.24/103.41	     | sk_A = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	     | ~ $true
103.24/103.41	     | ~ zip_tseitin2(sk_A0)
103.24/103.41	     | 'const/realax/real_le'('const/sets/sup'(sk_A), 
103.24/103.41	         'const/sets/sup'(sk_A0))
103.24/103.41	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('demod', [status(thm)], ['71', '17'])).
103.24/103.41	tff('73', plain,
103.24/103.41	    ('const/realax/real_le'('const/sets/sup'(sk_A), 'const/sets/sup'(sk_A0))
103.24/103.41	     | ~ zip_tseitin2(sk_A0)
103.24/103.41	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('simplify', [status(thm)], ['72'])).
103.24/103.41	tff('74', plain,
103.24/103.41	    (sk_A = 'const/sets/EMPTY'('type/realax/real') | ~ zip_tseitin2(sk_A0)),
103.24/103.41	    inference('clc', [status(thm)], ['73', '32'])).
103.24/103.41	tff('75', plain,
103.24/103.41	    (~ $true
103.24/103.41	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('sup-', [status(thm)], ['13', '74'])).
103.24/103.41	tff('76', plain,
103.24/103.41	    (sk_A = 'const/sets/EMPTY'('type/realax/real')
103.24/103.41	     | sk_A0 = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.41	    inference('simplify', [status(thm)], ['75'])).
103.24/103.41	tff('77', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/SUBSET'(X0, X1, X2)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
103.24/103.41	       | 'const/sets/IN'(X0, sk_A21(X0, X2, X1), X3)),
103.24/103.41	    inference('sup-', [status(thm)], ['14', '19'])).
103.24/103.41	tff('78', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
103.24/103.41	      ('const/sets/IN'(X0, sk_A21(X0, X2, X1), X3)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X1, X3)
103.24/103.41	       | 'const/sets/SUBSET'(X0, X1, X2)),
103.24/103.41	    inference('simplify', [status(thm)], ['77'])).
103.24/103.41	tff('thm/sets/NOT_IN_EMPTY_', axiom,
103.24/103.41	  (![A:$tType,A0:A]: (~'const/sets/IN'(A,A0,'const/sets/EMPTY'(A))))).
103.24/103.41	tff('79', plain,
103.24/103.41	    ![X8 : $tType, X9 : X8]:
103.24/103.41	      ~ 'const/sets/IN'(X8, X9, 'const/sets/EMPTY'(X8)),
103.24/103.41	    inference('cnf', [status(esa)], [thm/sets/NOT_IN_EMPTY_])).
103.24/103.41	tff('80', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))
103.24/103.41	       | ~ 'const/sets/IN'(X0, X1, X2)),
103.24/103.41	    inference('sup-', [status(thm)], ['19', '79'])).
103.24/103.41	tff('81', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0, X2 : X0 > $o]:
103.24/103.41	      (~ 'const/sets/IN'(X0, X1, X2)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X2, 'const/sets/EMPTY'(X0))),
103.24/103.41	    inference('simplify', [status(thm)], ['80'])).
103.24/103.41	tff('82', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/SUBSET'(X0, X2, X3)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
103.24/103.41	    inference('sup-', [status(thm)], ['78', '81'])).
103.24/103.41	tff('83', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o, X3 : X0 > $o]:
103.24/103.41	      (~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X2, X1)
103.24/103.41	       | 'const/sets/SUBSET'(X0, X2, X3)),
103.24/103.41	    inference('simplify', [status(thm)], ['82'])).
103.24/103.41	tff('84', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | 'const/sets/SUBSET'(X0, X1, X2)
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
103.24/103.41	    inference('sup-', [status(thm)], ['14', '81'])).
103.24/103.41	tff('85', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o]:
103.24/103.41	      (~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))
103.24/103.41	       | 'const/sets/SUBSET'(X0, X1, X2)),
103.24/103.41	    inference('simplify', [status(thm)], ['84'])).
103.24/103.41	tff('86', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
103.24/103.41	      (~ $true
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))
103.24/103.41	       | 'const/sets/SUBSET'((> $o, X0), X2, 'const/sets/SUBSET'(X0, X1))),
103.24/103.41	    inference('sup-', [status(thm)], ['85', '45'])).
103.24/103.41	tff('87', plain,
103.24/103.41	    ![X0 : $tType, X1 : X0 > $o, X2 : X0 > $o > $o]:
103.24/103.41	      ('const/sets/SUBSET'((> $o, X0), X2, 'const/sets/SUBSET'(X0, X1))
103.24/103.41	       | ~ 'const/sets/SUBSET'(X0, X1, 'const/sets/EMPTY'(X0))),
103.24/103.41	    inference('simplify', [status(thm)], ['86'])).
103.24/103.41	tff('88', plain,
103.24/103.41	    ![X23 : 'type/realax/real' > $o, X24 : 'type/realax/real', 
103.24/103.41	      X25 : 'type/realax/real']:
103.24/103.41	      (zip_tseitin1(X24, X25, X23)
103.24/103.41	       | 'const/sets/IN'('type/realax/real', X24, X23)),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_5])).
103.24/103.41	tff('89', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
103.24/103.41	      X2 : 'type/realax/real']: (~ $true | zip_tseitin1(X1, X2, X0) | X0(X1)),
103.24/103.41	    inference('sup-', [status(thm)], ['88', '27'])).
103.24/103.41	tff('90', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
103.24/103.41	      X2 : 'type/realax/real']: (X0(X1) | zip_tseitin1(X1, X2, X0)),
103.24/103.41	    inference('simplify', [status(thm)], ['89'])).
103.24/103.41	tff('91', plain,
103.24/103.41	    ![X23 : 'type/realax/real' > $o, X26 : 'type/realax/real']:
103.24/103.41	      (~ zip_tseitin1(sk_A11(X26, X23), X26, X23)
103.24/103.41	       | 'const/realax/real_le'('const/sets/sup'(X23), X26)
103.24/103.41	       | ~ zip_tseitin2(X23)),
103.24/103.41	    inference('cnf', [status(esa)], [zf_stmt_3])).
103.24/103.41	tff('92', plain,
103.24/103.41	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.41	      (~ $true
103.24/103.42	       | X0(sk_A11(X1, X0))
103.24/103.42	       | ~ zip_tseitin2(X0)
103.24/103.42	       | 'const/realax/real_le'('const/sets/sup'(X0), X1)),
103.24/103.42	    inference('sup-', [status(thm)], ['90', '91'])).
103.24/103.42	tff('93', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.42	      ('const/realax/real_le'('const/sets/sup'(X0), X1)
103.24/103.42	       | ~ zip_tseitin2(X0)
103.24/103.42	       | X0(sk_A11(X1, X0))),
103.24/103.42	    inference('simplify', [status(thm)], ['92'])).
103.24/103.42	tff('94', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
103.24/103.42	      (~ $true | zip_tseitin0(X0, X1, 'const/sets/EMPTY'('type/realax/real'))),
103.24/103.42	    inference('sup-', [status(thm)], ['2', '79'])).
103.24/103.42	tff('95', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real']:
103.24/103.42	      zip_tseitin0(X0, X1, 'const/sets/EMPTY'('type/realax/real')),
103.24/103.42	    inference('simplify', [status(thm)], ['94'])).
103.24/103.42	tff('96', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real' > $o > $o]:
103.24/103.42	      (~ $true
103.24/103.42	       | ~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	             zip_tseitin0(X1, X0), X2)
103.24/103.42	       | 'const/sets/IN'((> $o, 'type/realax/real'), 
103.24/103.42	           'const/sets/EMPTY'('type/realax/real'), X2)),
103.24/103.42	    inference('sup-', [status(thm)], ['95', '21'])).
103.24/103.42	tff('97', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real' > $o > $o]:
103.24/103.42	      ('const/sets/IN'((> $o, 'type/realax/real'), 
103.24/103.42	         'const/sets/EMPTY'('type/realax/real'), X2)
103.24/103.42	       | ~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	             zip_tseitin0(X1, X0), X2)),
103.24/103.42	    inference('simplify', [status(thm)], ['96'])).
103.24/103.42	tff('98', plain,
103.24/103.42	    ![X0 : 'type/realax/real']:
103.24/103.42	      (~ $true
103.24/103.42	       | ~ sk_A(X0)
103.24/103.42	       | ~ 'const/sets/IN'((> $o, 'type/realax/real'), 
103.24/103.42	             'const/sets/EMPTY'('type/realax/real'), 
103.24/103.42	             'const/sets/SUBSET'('type/realax/real', sk_A0))),
103.24/103.42	    inference('sup-', [status(thm)], ['57', '79'])).
103.24/103.42	tff('99', plain,
103.24/103.42	    ![X0 : 'type/realax/real']:
103.24/103.42	      (~ 'const/sets/IN'((> $o, 'type/realax/real'), 
103.24/103.42	           'const/sets/EMPTY'('type/realax/real'), 
103.24/103.42	           'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.42	       | ~ sk_A(X0)),
103.24/103.42	    inference('simplify', [status(thm)], ['98'])).
103.24/103.42	tff('100', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real']:
103.24/103.42	      (~ $true
103.24/103.42	       | ~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	             zip_tseitin0(X2, X1), 
103.24/103.42	             'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.42	       | ~ sk_A(X0)),
103.24/103.42	    inference('sup-', [status(thm)], ['97', '99'])).
103.24/103.42	tff('101', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real']:
103.24/103.42	      (~ sk_A(X0)
103.24/103.42	       | ~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	             zip_tseitin0(X2, X1), 
103.24/103.42	             'const/sets/SUBSET'('type/realax/real', sk_A0))),
103.24/103.42	    inference('simplify', [status(thm)], ['100'])).
103.24/103.42	tff('102', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real']:
103.24/103.42	      (~ $true
103.24/103.42	       | ~ zip_tseitin2(sk_A)
103.24/103.42	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)
103.24/103.42	       | ~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	             zip_tseitin0(X2, X1), 
103.24/103.42	             'const/sets/SUBSET'('type/realax/real', sk_A0))),
103.24/103.42	    inference('sup-', [status(thm)], ['93', '101'])).
103.24/103.42	tff('103', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real']:
103.24/103.42	      (~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	           zip_tseitin0(X2, X1), 
103.24/103.42	           'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.42	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)
103.24/103.42	       | ~ zip_tseitin2(sk_A)),
103.24/103.42	    inference('simplify', [status(thm)], ['102'])).
103.24/103.42	tff('104', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real']: (~ $true | zip_tseitin0(X1, X2, X0) | X0(X1)),
103.24/103.42	    inference('sup-', [status(thm)], ['2', '27'])).
103.24/103.42	tff('105', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real']: (X0(X1) | zip_tseitin0(X1, X2, X0)),
103.24/103.42	    inference('simplify', [status(thm)], ['104'])).
103.24/103.42	tff('106', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.42	      (~ $true
103.24/103.42	       | X0(sk_A12(X1, X0))
103.24/103.42	       | X0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.42	       | zip_tseitin2(X0)),
103.24/103.42	    inference('sup-', [status(thm)], ['105', '6'])).
103.24/103.42	tff('107', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.42	      (zip_tseitin2(X0)
103.24/103.42	       | X0 = 'const/sets/EMPTY'('type/realax/real')
103.24/103.42	       | X0(sk_A12(X1, X0))),
103.24/103.42	    inference('simplify', [status(thm)], ['106'])).
103.24/103.42	tff('108', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real']:
103.24/103.42	      (X0(X2) = 'const/sets/EMPTY'('type/realax/real', X2)
103.24/103.42	       | X0(sk_A12(X1, X0))
103.24/103.42	       | zip_tseitin2(X0)),
103.24/103.42	    inference('ho_complete_eq', [status(thm)], ['107'])).
103.24/103.42	tff('109', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o, X1 : 'type/realax/real']:
103.24/103.42	      (sk_A('#k1') != X0('#k1') | zip_tseitin2(X0) | X0(sk_A12(X1, X0))),
103.24/103.42	    inference('sup-', [status(thm)], ['108', '1'])).
103.24/103.42	tff('110', plain,
103.24/103.42	    ![X1 : 'type/realax/real', X2 : 'type/realax/real']:
103.24/103.42	      (~ $true
103.24/103.42	       | zip_tseitin2(sk_A)
103.24/103.42	       | sk_A('#k1') != sk_A('#k1')
103.24/103.42	       | ~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	             zip_tseitin0(X2, X1), 
103.24/103.42	             'const/sets/SUBSET'('type/realax/real', sk_A0))),
103.24/103.42	    inference('sup-', [status(thm)], ['109', '101'])).
103.24/103.42	tff('111', plain,
103.24/103.42	    ![X1 : 'type/realax/real', X2 : 'type/realax/real']:
103.24/103.42	      (~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	           zip_tseitin0(X2, X1), 
103.24/103.42	           'const/sets/SUBSET'('type/realax/real', sk_A0))
103.24/103.42	       | zip_tseitin2(sk_A)),
103.24/103.42	    inference('simplify', [status(thm)], ['110'])).
103.24/103.42	tff('112', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real', 
103.24/103.42	      X2 : 'type/realax/real']:
103.24/103.42	      ('const/realax/real_le'('const/sets/sup'(sk_A), X0)
103.24/103.42	       | ~ 'const/sets/SUBSET'((> $o, 'type/realax/real'), 
103.24/103.42	             zip_tseitin0(X2, X1), 
103.24/103.42	             'const/sets/SUBSET'('type/realax/real', sk_A0))),
103.24/103.42	    inference('clc', [status(thm)], ['103', '111'])).
103.24/103.42	tff('113', plain,
103.24/103.42	    ![X2 : 'type/realax/real']:
103.24/103.42	      (~ $true
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
103.24/103.42	             'const/sets/EMPTY'('type/realax/real'))
103.24/103.42	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X2)),
103.24/103.42	    inference('sup-', [status(thm)], ['87', '112'])).
103.24/103.42	tff('114', plain,
103.24/103.42	    ![X2 : 'type/realax/real']:
103.24/103.42	      ('const/realax/real_le'('const/sets/sup'(sk_A), X2)
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
103.24/103.42	             'const/sets/EMPTY'('type/realax/real'))),
103.24/103.42	    inference('simplify', [status(thm)], ['113'])).
103.24/103.42	tff('115', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
103.24/103.42	      (~ $true
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', X1, 
103.24/103.42	             'const/sets/EMPTY'('type/realax/real'))
103.24/103.42	       | 'const/realax/real_le'('const/sets/sup'(sk_A), X0)),
103.24/103.42	    inference('sup-', [status(thm)], ['83', '114'])).
103.24/103.42	tff('116', plain,
103.24/103.42	    ![X0 : 'type/realax/real', X1 : 'type/realax/real' > $o]:
103.24/103.42	      ('const/realax/real_le'('const/sets/sup'(sk_A), X0)
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', X1, 
103.24/103.42	             'const/sets/EMPTY'('type/realax/real'))
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X1)),
103.24/103.42	    inference('simplify', [status(thm)], ['115'])).
103.24/103.42	tff('117', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o]:
103.24/103.42	      (~ $true
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', X0, 
103.24/103.42	             'const/sets/EMPTY'('type/realax/real'))),
103.24/103.42	    inference('sup-', [status(thm)], ['116', '32'])).
103.24/103.42	tff('118', plain,
103.24/103.42	    ![X0 : 'type/realax/real' > $o]:
103.24/103.42	      (~ 'const/sets/SUBSET'('type/realax/real', X0, 
103.24/103.42	           'const/sets/EMPTY'('type/realax/real'))
103.24/103.42	       | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, X0)),
103.24/103.42	    inference('simplify', [status(thm)], ['117'])).
103.24/103.42	tff('119', plain,
103.24/103.42	    (~ $true
103.24/103.42	     | ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
103.24/103.42	           'const/sets/EMPTY'('type/realax/real'))),
103.24/103.42	    inference('sup-', [status(thm)], ['17', '118'])).
103.24/103.42	tff('120', plain,
103.24/103.42	    ~ 'const/sets/SUBSET'('type/realax/real', sk_A0, 
103.24/103.42	        'const/sets/EMPTY'('type/realax/real')),
103.24/103.42	    inference('simplify', [status(thm)], ['119'])).
103.24/103.42	tff('121', plain,
103.24/103.42	    (~ 'const/sets/SUBSET'('type/realax/real', sk_A0, sk_A0)
103.24/103.42	     | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.42	    inference('sup-', [status(thm)], ['76', '120'])).
103.24/103.42	tff('122', plain, (~ $true | sk_A = 'const/sets/EMPTY'('type/realax/real')),
103.24/103.42	    inference('demod', [status(thm)], ['121', '17'])).
103.24/103.42	tff('123', plain, sk_A = 'const/sets/EMPTY'('type/realax/real'),
103.24/103.42	    inference('simplify', [status(thm)], ['122'])).
103.24/103.42	tff('124', plain,
103.24/103.42	    ![X1 : 'type/realax/real']:
103.24/103.42	      sk_A(X1) = 'const/sets/EMPTY'('type/realax/real', X1),
103.24/103.42	    inference('ho_complete_eq', [status(thm)], ['123'])).
103.24/103.42	tff('125', plain, sk_A('#k1') != sk_A('#k1'),
103.24/103.42	    inference('demod', [status(thm)], ['1', '124'])).
103.24/103.42	tff('126', plain, $false, inference('simplify', [status(thm)], ['125'])).
103.24/103.42	
103.24/103.42	% SZS output end Refutation
103.24/103.42	EOF
