0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : purification_int
0.00/0.01	% Ordering    : kbo
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-avatar \
0.00/0.01	  --ho \
0.00/0.01	  --force-ho \
0.00/0.01	  --no-ho-elim-pred-var \
0.00/0.01	  --ho-general-ext-pos \
0.00/0.01	  --no-ho-unif \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --ho-purify int \
0.00/0.01	  --ho-no-ext-pos \
0.00/0.01	  --ho-no-ext-neg \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n172.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:39:09 CST 2018
0.00/0.25	% done 27 iterations in 0.048s
0.00/0.25	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
0.00/0.25	% SZS output start Refutation
0.00/0.26	tff('thm/iterate/nsum_', axiom,
0.00/0.26	  (![A:$tType]:
0.00/0.26	     ('const/iterate/nsum'(A) =
0.00/0.26	      'const/iterate/iterate'(A,'type/nums/num','const/arith/+')))).
0.00/0.26	tff('0', plain,
0.00/0.26	    ![X6 : $tType]:
0.00/0.26	      'const/iterate/nsum'(X6)
0.00/0.26	       = 'const/iterate/iterate'(X6, 'type/nums/num', 'const/arith/+'),
0.00/0.26	    inference('cnf', [status(esa)], [thm/iterate/nsum_])).
0.00/0.26	tff('1', plain,
0.00/0.26	    ![X6 : $tType, X7 : X6 > $o, X8 : X6 > 'type/nums/num']:
0.00/0.26	      'const/iterate/nsum'(X6, X7, X8)
0.00/0.26	       = 'const/iterate/iterate'(X6, 'type/nums/num', 'const/arith/+', X7, 
0.00/0.26	           X8),
0.00/0.26	    inference('ho_complete_eq', [status(thm)], ['0'])).
0.00/0.26	tff('thm/iterate/ITERATE_UNION_NONZERO_', axiom,
0.00/0.26	  (![A:$tType,B:$tType,A0:((B * B) > B)]:
0.00/0.26	     ('const/iterate/monoidal'(B,A0) =>
0.00/0.26	      (![A1:(A > B),A2:(A > $o),A3:(A > $o)]:
0.00/0.26	         (((![A4:A]:
0.00/0.26	              ('const/sets/IN'(A,A4,'const/sets/INTER'(A,A2,A3)) =>
0.00/0.26	               (A1(A4) = 'const/iterate/neutral'(B,A0)))) & 
0.00/0.26	           'const/sets/FINITE'(A,A3) & 'const/sets/FINITE'(A,A2)) =>
0.00/0.26	          ('const/iterate/iterate'(A,B,A0,'const/sets/UNION'(A,A2,A3),A1) =
0.00/0.26	           A0('const/iterate/iterate'(A,B,A0,A2,A1),
0.00/0.26	              'const/iterate/iterate'(A,B,A0,A3,A1)))))))).
0.00/0.26	tff('2', plain,
0.00/0.26	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : $tType, X3 : X2 > $o, 
0.00/0.26	      X4 : X2 > X0, X5 : X2 > $o]:
0.00/0.26	      ('const/iterate/iterate'(X2, X0, X1, 'const/sets/UNION'(X2, X3, X5), 
0.00/0.26	         X4)
0.00/0.26	        = X1('const/iterate/iterate'(X2, X0, X1, X3, X4), 
0.00/0.26	            'const/iterate/iterate'(X2, X0, X1, X5, X4))
0.00/0.26	       | ~ 'const/sets/FINITE'(X2, X5)
0.00/0.26	       | 'const/sets/IN'(X2, sk_A4(X0, X2, X5, X3, X4, X1), 
0.00/0.26	           'const/sets/INTER'(X2, X3, X5))
0.00/0.26	       | ~ 'const/sets/FINITE'(X2, X3)
0.00/0.26	       | ~ 'const/iterate/monoidal'(X0, X1)),
0.00/0.26	    inference('cnf', [status(esa)], [thm/iterate/ITERATE_UNION_NONZERO_])).
0.00/0.26	tff('3', plain,
0.00/0.26	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : $tType, X3 : X2 > $o, 
0.00/0.26	      X4 : X2 > X0, X5 : X2 > $o, X6 : (X0 * X0) > X0]:
0.00/0.26	      (X6 != X1
0.00/0.26	       | 'const/iterate/iterate'(X2, X0, X1, 'const/sets/UNION'(X2, X3, X5), 
0.00/0.26	           X4)
0.00/0.26	          = X6('const/iterate/iterate'(X2, X0, X1, X3, X4), 
0.00/0.26	              'const/iterate/iterate'(X2, X0, X1, X5, X4))
0.00/0.26	       | ~ 'const/sets/FINITE'(X2, X5)
0.00/0.26	       | 'const/sets/IN'(X2, sk_A4(X0, X2, X5, X3, X4, X1), 
0.00/0.26	           'const/sets/INTER'(X2, X3, X5))
0.00/0.26	       | ~ 'const/sets/FINITE'(X2, X3)
0.00/0.26	       | ~ 'const/iterate/monoidal'(X0, X1)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['2'])).
0.00/0.26	tff('thm/iterate/NSUM_UNION_NONZERO_', conjecture,
0.00/0.26	  (![A:$tType,A0:(A > 'type/nums/num'),A1:(A > $o),A2:(A > $o)]:
0.00/0.26	     (((![A3:A]:
0.00/0.26	          ('const/sets/IN'(A,A3,'const/sets/INTER'(A,A1,A2)) =>
0.00/0.26	           (A0(A3) = 'const/nums/NUMERAL'('const/nums/_0')))) & 
0.00/0.26	       'const/sets/FINITE'(A,A2) & 'const/sets/FINITE'(A,A1)) =>
0.00/0.26	      ('const/iterate/nsum'(A,'const/sets/UNION'(A,A1,A2),A0) =
0.00/0.26	       'const/arith/+'('const/iterate/nsum'(A,A1,A0),
0.00/0.26	                       'const/iterate/nsum'(A,A2,A0)))))).
0.00/0.26	tff(zf_stmt_0, negated_conjecture,
0.00/0.26	  (~
0.00/0.26	    (![A:$tType,A0:(A > 'type/nums/num'),A1:(A > $o),A2:(A > $o)]:
0.00/0.26	       (((![A3:A]:
0.00/0.26	            ('const/sets/IN'(A,A3,'const/sets/INTER'(A,A1,A2)) =>
0.00/0.26	             (A0(A3) = 'const/nums/NUMERAL'('const/nums/_0')))) & 
0.00/0.26	         'const/sets/FINITE'(A,A2) & 'const/sets/FINITE'(A,A1)) =>
0.00/0.26	        ('const/iterate/nsum'(A,'const/sets/UNION'(A,A1,A2),A0) =
0.00/0.26	         'const/arith/+'('const/iterate/nsum'(A,A1,A0),
0.00/0.26	                         'const/iterate/nsum'(A,A2,A0))))))).
0.00/0.26	tff('4', plain,
0.00/0.26	    ![X7 : sk_A]:
0.00/0.26	      (sk_A0(X7) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | ~ 'const/sets/IN'(sk_A, X7, 'const/sets/INTER'(sk_A, sk_A1, sk_A2))),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('5', plain,
0.00/0.26	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : sk_A > X0, X3 : (X0 * X0) > X0]:
0.00/0.26	      (~ $true
0.00/0.26	       | ~ 'const/iterate/monoidal'(X0, X1)
0.00/0.26	       | ~ 'const/sets/FINITE'(sk_A, sk_A1)
0.00/0.26	       | ~ 'const/sets/FINITE'(sk_A, sk_A2)
0.00/0.26	       | 'const/iterate/iterate'(sk_A, X0, X1, 
0.00/0.26	           'const/sets/UNION'(sk_A, sk_A1, sk_A2), X2)
0.00/0.26	          = X3('const/iterate/iterate'(sk_A, X0, X1, sk_A1, X2), 
0.00/0.26	              'const/iterate/iterate'(sk_A, X0, X1, sk_A2, X2))
0.00/0.26	       | X3 != X1
0.00/0.26	       | sk_A0(sk_A4(X0, sk_A, sk_A2, sk_A1, X2, X1))
0.00/0.26	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.26	    inference('sup-', [status(thm)], ['3', '4'])).
0.00/0.26	tff('6', plain, 'const/sets/FINITE'(sk_A, sk_A1),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('7', plain, 'const/sets/FINITE'(sk_A, sk_A2),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('8', plain,
0.00/0.26	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : sk_A > X0, X3 : (X0 * X0) > X0]:
0.00/0.26	      (~ $true
0.00/0.26	       | ~ 'const/iterate/monoidal'(X0, X1)
0.00/0.26	       | ~ $true
0.00/0.26	       | ~ $true
0.00/0.26	       | 'const/iterate/iterate'(sk_A, X0, X1, 
0.00/0.26	           'const/sets/UNION'(sk_A, sk_A1, sk_A2), X2)
0.00/0.26	          = X3('const/iterate/iterate'(sk_A, X0, X1, sk_A1, X2), 
0.00/0.26	              'const/iterate/iterate'(sk_A, X0, X1, sk_A2, X2))
0.00/0.26	       | X3 != X1
0.00/0.26	       | sk_A0(sk_A4(X0, sk_A, sk_A2, sk_A1, X2, X1))
0.00/0.26	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.26	    inference('demod', [status(thm)], ['5', '6', '7'])).
0.00/0.26	tff('9', plain,
0.00/0.26	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : sk_A > X0, X3 : (X0 * X0) > X0]:
0.00/0.26	      (sk_A0(sk_A4(X0, sk_A, sk_A2, sk_A1, X2, X1))
0.00/0.26	        = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | X3 != X1
0.00/0.26	       | 'const/iterate/iterate'(sk_A, X0, X1, 
0.00/0.26	           'const/sets/UNION'(sk_A, sk_A1, sk_A2), X2)
0.00/0.26	          = X3('const/iterate/iterate'(sk_A, X0, X1, sk_A1, X2), 
0.00/0.26	              'const/iterate/iterate'(sk_A, X0, X1, sk_A2, X2))
0.00/0.26	       | ~ 'const/iterate/monoidal'(X0, X1)),
0.00/0.26	    inference('simplify', [status(thm)], ['8'])).
0.00/0.26	tff('10', plain,
0.00/0.26	    ![X0 : sk_A > 'type/nums/num', 
0.00/0.26	      X1 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      ('const/iterate/iterate'(sk_A, 'type/nums/num', 'const/arith/+', 
0.00/0.26	         'const/sets/UNION'(sk_A, sk_A1, sk_A2), X0)
0.00/0.26	        = X1('const/iterate/nsum'(sk_A, sk_A1, X0), 
0.00/0.26	            'const/iterate/iterate'(sk_A, 'type/nums/num', 'const/arith/+', 
0.00/0.26	              sk_A2, X0))
0.00/0.26	       | ~ 'const/iterate/monoidal'('type/nums/num', 'const/arith/+')
0.00/0.26	       | X1 != 'const/arith/+'
0.00/0.26	       | sk_A0(
0.00/0.26	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, X0, 'const/arith/+'))
0.00/0.26	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.26	    inference('sup+', [status(thm)], ['1', '9'])).
0.00/0.26	tff('thm/iterate/MONOIDAL_ADD_', axiom,
0.00/0.26	  ('const/iterate/monoidal'('type/nums/num','const/arith/+'))).
0.00/0.26	tff('11', plain, 'const/iterate/monoidal'('type/nums/num', 'const/arith/+'),
0.00/0.26	    inference('cnf', [status(esa)], [thm/iterate/MONOIDAL_ADD_])).
0.00/0.26	tff('12', plain,
0.00/0.26	    ![X0 : sk_A > 'type/nums/num', 
0.00/0.26	      X1 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      ('const/iterate/nsum'(sk_A, 'const/sets/UNION'(sk_A, sk_A1, sk_A2), X0)
0.00/0.26	        = X1('const/iterate/nsum'(sk_A, sk_A1, X0), 
0.00/0.26	            'const/iterate/nsum'(sk_A, sk_A2, X0))
0.00/0.26	       | ~ $true
0.00/0.26	       | X1 != 'const/arith/+'
0.00/0.26	       | sk_A0(
0.00/0.26	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, X0, 'const/arith/+'))
0.00/0.26	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.26	    inference('demod', [status(thm)], ['10', '1', '1', '11'])).
0.00/0.26	tff('13', plain,
0.00/0.26	    ![X0 : sk_A > 'type/nums/num', 
0.00/0.26	      X1 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      (sk_A0(sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, X0, 'const/arith/+'))
0.00/0.26	        = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | X1 != 'const/arith/+'
0.00/0.26	       | 'const/iterate/nsum'(sk_A, 'const/sets/UNION'(sk_A, sk_A1, sk_A2), 
0.00/0.26	           X0)
0.00/0.26	          = X1('const/iterate/nsum'(sk_A, sk_A1, X0), 
0.00/0.26	              'const/iterate/nsum'(sk_A, sk_A2, X0))),
0.00/0.26	    inference('simplify', [status(thm)], ['12'])).
0.00/0.26	tff('14', plain,
0.00/0.26	    ![X0 : sk_A > 'type/nums/num', 
0.00/0.26	      X1 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num', 
0.00/0.26	      X2 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      (X2 != X1
0.00/0.26	       | sk_A0(
0.00/0.26	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, X0, 'const/arith/+'))
0.00/0.26	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | X1 != 'const/arith/+'
0.00/0.26	       | 'const/iterate/nsum'(sk_A, 'const/sets/UNION'(sk_A, sk_A1, sk_A2), 
0.00/0.26	           X0)
0.00/0.26	          = X2('const/iterate/nsum'(sk_A, sk_A1, X0), 
0.00/0.26	              'const/iterate/nsum'(sk_A, sk_A2, X0))),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['13'])).
0.00/0.26	tff('15', plain,
0.00/0.26	    'const/iterate/nsum'(sk_A, 'const/sets/UNION'(sk_A, sk_A1, sk_A2), sk_A0)
0.00/0.26	     != 'const/arith/+'('const/iterate/nsum'(sk_A, sk_A1, sk_A0), 
0.00/0.26	          'const/iterate/nsum'(sk_A, sk_A2, sk_A0)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('16', plain,
0.00/0.26	    ![X0 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      ('const/iterate/nsum'(sk_A, 'const/sets/UNION'(sk_A, sk_A1, sk_A2), 
0.00/0.26	         sk_A0)
0.00/0.26	        != 'const/iterate/nsum'(sk_A, 
0.00/0.26	             'const/sets/UNION'(sk_A, sk_A1, sk_A2), sk_A0)
0.00/0.26	       | X0 != 'const/arith/+'
0.00/0.26	       | sk_A0(
0.00/0.26	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.26	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | 'const/arith/+' != X0),
0.00/0.26	    inference('sup-', [status(thm)], ['14', '15'])).
0.00/0.26	tff('17', plain,
0.00/0.26	    ![X0 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      (sk_A0(
0.00/0.26	         sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.26	        = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | X0 != 'const/arith/+'),
0.00/0.26	    inference('simplify', [status(thm)], ['16'])).
0.00/0.26	tff('18', plain,
0.00/0.26	    sk_A0(sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.26	     = 'const/nums/NUMERAL'('const/nums/_0'),
0.00/0.26	    inference('eq_res', [status(thm)], ['17'])).
0.00/0.26	tff('19', plain,
0.00/0.26	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : $tType, X3 : X2 > $o, 
0.00/0.26	      X4 : X2 > X0, X5 : X2 > $o]:
0.00/0.26	      ('const/iterate/iterate'(X2, X0, X1, 'const/sets/UNION'(X2, X3, X5), 
0.00/0.26	         X4)
0.00/0.26	        = X1('const/iterate/iterate'(X2, X0, X1, X3, X4), 
0.00/0.26	            'const/iterate/iterate'(X2, X0, X1, X5, X4))
0.00/0.26	       | ~ 'const/sets/FINITE'(X2, X5)
0.00/0.26	       | X4(sk_A4(X0, X2, X5, X3, X4, X1)) != 'const/iterate/neutral'(X0, X1)
0.00/0.26	       | ~ 'const/sets/FINITE'(X2, X3)
0.00/0.26	       | ~ 'const/iterate/monoidal'(X0, X1)),
0.00/0.26	    inference('cnf', [status(esa)], [thm/iterate/ITERATE_UNION_NONZERO_])).
0.00/0.26	tff('20', plain,
0.00/0.26	    ![X0 : $tType, X1 : (X0 * X0) > X0, X2 : $tType, X3 : X2 > $o, 
0.00/0.26	      X4 : X2 > X0, X5 : X2 > $o, X6 : (X0 * X0) > X0, X7 : X2 > X0]:
0.00/0.26	      (X7 != X4
0.00/0.26	       | X6 != X1
0.00/0.26	       | 'const/iterate/iterate'(X2, X0, X1, 'const/sets/UNION'(X2, X3, X5), 
0.00/0.26	           X4)
0.00/0.26	          = X6('const/iterate/iterate'(X2, X0, X1, X3, X4), 
0.00/0.26	              'const/iterate/iterate'(X2, X0, X1, X5, X4))
0.00/0.26	       | ~ 'const/sets/FINITE'(X2, X5)
0.00/0.26	       | X7(sk_A4(X0, X2, X5, X3, X4, X1)) != 'const/iterate/neutral'(X0, X1)
0.00/0.26	       | ~ 'const/sets/FINITE'(X2, X3)
0.00/0.26	       | ~ 'const/iterate/monoidal'(X0, X1)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['19'])).
0.00/0.26	tff('21', plain,
0.00/0.26	    ![X0 : $tType, X1 : X0 > 'type/nums/num', X2 : X0 > $o, 
0.00/0.26	      X3 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num', 
0.00/0.26	      X4 : X0 > $o, X5 : X0 > 'type/nums/num']:
0.00/0.26	      ('const/iterate/iterate'(X0, 'type/nums/num', 'const/arith/+', 
0.00/0.26	         'const/sets/UNION'(X0, X2, X4), X1)
0.00/0.26	        = X3('const/iterate/nsum'(X0, X2, X1), 
0.00/0.26	            'const/iterate/iterate'(X0, 'type/nums/num', 'const/arith/+', 
0.00/0.26	              X4, X1))
0.00/0.26	       | ~ 'const/iterate/monoidal'('type/nums/num', 'const/arith/+')
0.00/0.26	       | ~ 'const/sets/FINITE'(X0, X2)
0.00/0.26	       | X5(sk_A4('type/nums/num', X0, X4, X2, X1, 'const/arith/+'))
0.00/0.26	          != 'const/iterate/neutral'('type/nums/num', 'const/arith/+')
0.00/0.26	       | ~ 'const/sets/FINITE'(X0, X4)
0.00/0.26	       | X3 != 'const/arith/+'
0.00/0.26	       | X5 != X1),
0.00/0.26	    inference('sup+', [status(thm)], ['1', '20'])).
0.00/0.26	tff('thm/iterate/NEUTRAL_ADD_', axiom,
0.00/0.26	  ('const/iterate/neutral'('type/nums/num','const/arith/+') =
0.00/0.26	   'const/nums/NUMERAL'('const/nums/_0'))).
0.00/0.26	tff('22', plain,
0.00/0.26	    'const/iterate/neutral'('type/nums/num', 'const/arith/+')
0.00/0.26	     = 'const/nums/NUMERAL'('const/nums/_0'),
0.00/0.26	    inference('cnf', [status(esa)], [thm/iterate/NEUTRAL_ADD_])).
0.00/0.26	tff('23', plain,
0.00/0.26	    ![X0 : $tType, X1 : X0 > 'type/nums/num', X2 : X0 > $o, 
0.00/0.26	      X3 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num', 
0.00/0.26	      X4 : X0 > $o, X5 : X0 > 'type/nums/num']:
0.00/0.26	      ('const/iterate/nsum'(X0, 'const/sets/UNION'(X0, X2, X4), X1)
0.00/0.26	        = X3('const/iterate/nsum'(X0, X2, X1), 
0.00/0.26	            'const/iterate/nsum'(X0, X4, X1))
0.00/0.26	       | ~ $true
0.00/0.26	       | ~ 'const/sets/FINITE'(X0, X2)
0.00/0.26	       | X5(sk_A4('type/nums/num', X0, X4, X2, X1, 'const/arith/+'))
0.00/0.26	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | ~ 'const/sets/FINITE'(X0, X4)
0.00/0.26	       | X3 != 'const/arith/+'
0.00/0.26	       | X5 != X1),
0.00/0.26	    inference('demod', [status(thm)], ['21', '1', '1', '11', '22'])).
0.00/0.26	tff('24', plain,
0.00/0.26	    ![X0 : $tType, X1 : X0 > 'type/nums/num', X2 : X0 > $o, 
0.00/0.26	      X3 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num', 
0.00/0.26	      X4 : X0 > $o, X5 : X0 > 'type/nums/num']:
0.00/0.26	      (X5 != X1
0.00/0.26	       | X3 != 'const/arith/+'
0.00/0.26	       | ~ 'const/sets/FINITE'(X0, X4)
0.00/0.26	       | X5(sk_A4('type/nums/num', X0, X4, X2, X1, 'const/arith/+'))
0.00/0.26	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | ~ 'const/sets/FINITE'(X0, X2)
0.00/0.26	       | 'const/iterate/nsum'(X0, 'const/sets/UNION'(X0, X2, X4), X1)
0.00/0.26	          = X3('const/iterate/nsum'(X0, X2, X1), 
0.00/0.26	              'const/iterate/nsum'(X0, X4, X1))),
0.00/0.26	    inference('simplify', [status(thm)], ['23'])).
0.00/0.26	tff('25', plain,
0.00/0.26	    ![X0 : $tType, X1 : X0 > 'type/nums/num', X2 : X0 > $o, 
0.00/0.26	      X3 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num', 
0.00/0.26	      X4 : X0 > $o, X5 : X0 > 'type/nums/num', 
0.00/0.26	      X6 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      (X6 != X3
0.00/0.26	       | X5 != X1
0.00/0.26	       | X3 != 'const/arith/+'
0.00/0.26	       | ~ 'const/sets/FINITE'(X0, X4)
0.00/0.26	       | X5(sk_A4('type/nums/num', X0, X4, X2, X1, 'const/arith/+'))
0.00/0.26	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | ~ 'const/sets/FINITE'(X0, X2)
0.00/0.26	       | 'const/iterate/nsum'(X0, 'const/sets/UNION'(X0, X2, X4), X1)
0.00/0.26	          = X6('const/iterate/nsum'(X0, X2, X1), 
0.00/0.26	              'const/iterate/nsum'(X0, X4, X1))),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['24'])).
0.00/0.26	tff('26', plain,
0.00/0.26	    ![X0 : sk_A > 'type/nums/num', 
0.00/0.26	      X1 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      ('const/iterate/nsum'(sk_A, 'const/sets/UNION'(sk_A, sk_A1, sk_A2), 
0.00/0.26	         sk_A0)
0.00/0.26	        != 'const/iterate/nsum'(sk_A, 
0.00/0.26	             'const/sets/UNION'(sk_A, sk_A1, sk_A2), sk_A0)
0.00/0.26	       | ~ 'const/sets/FINITE'(sk_A, sk_A1)
0.00/0.26	       | X0(
0.00/0.26	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.26	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | ~ 'const/sets/FINITE'(sk_A, sk_A2)
0.00/0.26	       | X1 != 'const/arith/+'
0.00/0.26	       | X0 != sk_A0
0.00/0.26	       | 'const/arith/+' != X1),
0.00/0.26	    inference('sup-', [status(thm)], ['25', '15'])).
0.00/0.26	tff('27', plain,
0.00/0.26	    ![X0 : sk_A > 'type/nums/num', 
0.00/0.26	      X1 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      ('const/iterate/nsum'(sk_A, 'const/sets/UNION'(sk_A, sk_A1, sk_A2), 
0.00/0.26	         sk_A0)
0.00/0.26	        != 'const/iterate/nsum'(sk_A, 
0.00/0.26	             'const/sets/UNION'(sk_A, sk_A1, sk_A2), sk_A0)
0.00/0.26	       | ~ $true
0.00/0.26	       | X0(
0.00/0.26	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.26	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | ~ $true
0.00/0.26	       | X1 != 'const/arith/+'
0.00/0.26	       | X0 != sk_A0
0.00/0.26	       | 'const/arith/+' != X1),
0.00/0.26	    inference('demod', [status(thm)], ['26', '6', '7'])).
0.00/0.26	tff('28', plain,
0.00/0.26	    ![X0 : sk_A > 'type/nums/num', 
0.00/0.26	      X1 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      (X0 != sk_A0
0.00/0.26	       | X1 != 'const/arith/+'
0.00/0.26	       | X0(
0.00/0.26	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.26	          != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.26	    inference('simplify', [status(thm)], ['27'])).
0.00/0.26	tff('29', plain,
0.00/0.26	    ![X0 : sk_A > 'type/nums/num', 
0.00/0.26	      X1 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num', 
0.00/0.26	      X2 : sk_A > 'type/nums/num']:
0.00/0.26	      (X2 != X0
0.00/0.26	       | X0 != sk_A0
0.00/0.26	       | X1 != 'const/arith/+'
0.00/0.26	       | X2(
0.00/0.26	           sk_A4('type/nums/num', sk_A, sk_A2, sk_A1, sk_A0, 'const/arith/+'))
0.00/0.26	          != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['28'])).
0.00/0.26	tff('30', plain,
0.00/0.26	    ![X0 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num', 
0.00/0.26	      X1 : sk_A > 'type/nums/num']:
0.00/0.26	      ('const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	        != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.26	       | X0 != 'const/arith/+'
0.00/0.26	       | X1 != sk_A0
0.00/0.26	       | sk_A0 != X1),
0.00/0.26	    inference('sup-', [status(thm)], ['18', '29'])).
0.00/0.26	tff('31', plain,
0.00/0.26	    ![X0 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num', 
0.00/0.26	      X1 : sk_A > 'type/nums/num']: (X1 != sk_A0 | X0 != 'const/arith/+'),
0.00/0.26	    inference('simplify', [status(thm)], ['30'])).
0.00/0.26	tff('32', plain,
0.00/0.26	    ![X0 : ('type/nums/num' * 'type/nums/num') > 'type/nums/num']:
0.00/0.26	      X0 != 'const/arith/+',
0.00/0.26	    inference('eq_res', [status(thm)], ['31'])).
0.00/0.26	tff('33', plain, $false, inference('eq_res', [status(thm)], ['32'])).
0.00/0.26	
0.00/0.26	% SZS output end Refutation
0.00/0.26	EOF
