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    : purification_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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n145.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:39:09 CST 2018
0.00/0.23	% done 34 iterations in 0.030s
0.00/0.23	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.00/0.23	% SZS output start Refutation
0.00/0.24	tff('thm/iterate/NSUM_EQ_0_IFF_', axiom,
0.00/0.24	  (![A:$tType,A0:(A > 'type/nums/num'),A1:(A > $o)]:
0.00/0.24	     ('const/sets/FINITE'(A,A1) =>
0.00/0.24	      (('const/iterate/nsum'(A,A1,A0) = 'const/nums/NUMERAL'('const/nums/_0')) <=>
0.00/0.24	       (![A2:A]:
0.00/0.24	          ('const/sets/IN'(A,A2,A1) =>
0.00/0.24	           (A0(A2) = 'const/nums/NUMERAL'('const/nums/_0')))))))).
0.00/0.24	tff('0', plain,
0.00/0.24	    ![X4 : $tType, X5 : X4 > $o, X6 : X4 > 'type/nums/num']:
0.00/0.24	      ('const/sets/IN'(X4, sk_A2(X4, X5, X6), X5)
0.00/0.24	       | 'const/iterate/nsum'(X4, X5, X6)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/sets/FINITE'(X4, X5)),
0.00/0.24	    inference('cnf', [status(esa)], [thm/iterate/NSUM_EQ_0_IFF_])).
0.00/0.24	tff('thm/iterate/IN_NUMSEG_', axiom,
0.00/0.24	  (![A:'type/nums/num',A0:'type/nums/num',A1:'type/nums/num']:
0.00/0.24	     ('const/sets/IN'('type/nums/num',A1,'const/iterate/..'(A,A0)) <=>
0.00/0.24	      ('const/arith/<='(A1,A0) & 'const/arith/<='(A,A1))))).
0.00/0.24	tff('1', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', X2 : 'type/nums/num']:
0.00/0.24	      ('const/arith/<='(X2, X0)
0.00/0.24	       | ~ 'const/sets/IN'('type/nums/num', X0, 'const/iterate/..'(X2, X1))),
0.00/0.24	    inference('cnf', [status(esa)], [thm/iterate/IN_NUMSEG_])).
0.00/0.24	tff('2', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', 
0.00/0.24	      X2 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ 'const/sets/FINITE'('type/nums/num', 'const/iterate/..'(X1, X0))
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X2)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/arith/<='(X1, 
0.00/0.24	           sk_A2('type/nums/num', 'const/iterate/..'(X1, X0), X2))),
0.00/0.24	    inference('sup-', [status(thm)], ['0', '1'])).
0.00/0.24	tff('thm/iterate/FINITE_NUMSEG_', axiom,
0.00/0.24	  (![A:'type/nums/num',A0:'type/nums/num']:
0.00/0.24	     'const/sets/FINITE'('type/nums/num','const/iterate/..'(A,A0)))).
0.00/0.24	tff('3', plain,
0.00/0.24	    ![X8 : 'type/nums/num', X9 : 'type/nums/num']:
0.00/0.24	      'const/sets/FINITE'('type/nums/num', 'const/iterate/..'(X8, X9)),
0.00/0.24	    inference('cnf', [status(esa)], [thm/iterate/FINITE_NUMSEG_])).
0.00/0.24	tff('4', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', 
0.00/0.24	      X2 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ $true
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X2)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/arith/<='(X1, 
0.00/0.24	           sk_A2('type/nums/num', 'const/iterate/..'(X1, X0), X2))),
0.00/0.24	    inference('demod', [status(thm)], ['2', '3'])).
0.00/0.24	tff('5', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', 
0.00/0.24	      X2 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      ('const/arith/<='(X1, 
0.00/0.24	         sk_A2('type/nums/num', 'const/iterate/..'(X1, X0), X2))
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X2)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('simplify', [status(thm)], ['4'])).
0.00/0.24	tff('6', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', X2 : 'type/nums/num']:
0.00/0.24	      ('const/arith/<='(X0, X1)
0.00/0.24	       | ~ 'const/sets/IN'('type/nums/num', X0, 'const/iterate/..'(X2, X1))),
0.00/0.24	    inference('cnf', [status(esa)], [thm/iterate/IN_NUMSEG_])).
0.00/0.24	tff('7', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', 
0.00/0.24	      X2 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ 'const/sets/FINITE'('type/nums/num', 'const/iterate/..'(X1, X0))
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X2)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/arith/<='(
0.00/0.24	           sk_A2('type/nums/num', 'const/iterate/..'(X1, X0), X2), X0)),
0.00/0.24	    inference('sup-', [status(thm)], ['0', '6'])).
0.00/0.24	tff('8', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', 
0.00/0.24	      X2 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ $true
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X2)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/arith/<='(
0.00/0.24	           sk_A2('type/nums/num', 'const/iterate/..'(X1, X0), X2), X0)),
0.00/0.24	    inference('demod', [status(thm)], ['7', '3'])).
0.00/0.24	tff('9', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', 
0.00/0.24	      X2 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      ('const/arith/<='(
0.00/0.24	         sk_A2('type/nums/num', 'const/iterate/..'(X1, X0), X2), X0)
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X2)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('simplify', [status(thm)], ['8'])).
0.00/0.24	tff('thm/iterate/NSUM_EQ_0_IFF_NUMSEG_', conjecture,
0.00/0.24	  (![A:('type/nums/num' > 'type/nums/num'),A0:'type/nums/num',
0.00/0.24	     A1:'type/nums/num']:
0.00/0.24	     (('const/iterate/nsum'('type/nums/num','const/iterate/..'(A0,A1),A) =
0.00/0.24	       'const/nums/NUMERAL'('const/nums/_0')) <=>
0.00/0.24	      (![A2:'type/nums/num']:
0.00/0.24	         (('const/arith/<='(A2,A1) & 'const/arith/<='(A0,A2)) =>
0.00/0.24	          (A(A2) = 'const/nums/NUMERAL'('const/nums/_0'))))))).
0.00/0.24	tff(zf_stmt_0, negated_conjecture,
0.00/0.24	  (~
0.00/0.24	    (![A:('type/nums/num' > 'type/nums/num'),A0:'type/nums/num',
0.00/0.24	       A1:'type/nums/num']:
0.00/0.24	       (('const/iterate/nsum'('type/nums/num','const/iterate/..'(A0,A1),A) =
0.00/0.24	         'const/nums/NUMERAL'('const/nums/_0')) <=>
0.00/0.24	        (![A2:'type/nums/num']:
0.00/0.24	           (('const/arith/<='(A2,A1) & 'const/arith/<='(A0,A2)) =>
0.00/0.24	            (A(A2) = 'const/nums/NUMERAL'('const/nums/_0')))))))).
0.00/0.24	tff('10', plain,
0.00/0.24	    ![X10 : 'type/nums/num']:
0.00/0.24	      (~ 'const/arith/<='(X10, sk_A1)
0.00/0.24	       | ~ 'const/arith/<='(sk_A0, X10)
0.00/0.24	       | sk_A(X10) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('11', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num', X1 : 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(X1, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | sk_A(sk_A2('type/nums/num', 'const/iterate/..'(X1, sk_A1), X0))
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/arith/<='(sk_A0, 
0.00/0.24	             sk_A2('type/nums/num', 'const/iterate/..'(X1, sk_A1), X0))),
0.00/0.24	    inference('sup-', [status(thm)], ['9', '10'])).
0.00/0.24	tff('12', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num', X1 : 'type/nums/num']:
0.00/0.24	      (~ 'const/arith/<='(sk_A0, 
0.00/0.24	           sk_A2('type/nums/num', 'const/iterate/..'(X1, sk_A1), X0))
0.00/0.24	       | sk_A(sk_A2('type/nums/num', 'const/iterate/..'(X1, sk_A1), X0))
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(X1, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('simplify', [status(thm)], ['11'])).
0.00/0.24	tff('13', plain,
0.00/0.24	    ![X4 : $tType, X5 : X4 > $o, X6 : X4 > 'type/nums/num']:
0.00/0.24	      (X6(sk_A2(X4, X5, X6)) != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'(X4, X5, X6)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/sets/FINITE'(X4, X5)),
0.00/0.24	    inference('cnf', [status(esa)], [thm/iterate/NSUM_EQ_0_IFF_])).
0.00/0.24	tff('14', plain,
0.00/0.24	    ![X4 : $tType, X5 : X4 > $o, X6 : X4 > 'type/nums/num', 
0.00/0.24	      X7 : X4 > 'type/nums/num']:
0.00/0.24	      (X7 != X6
0.00/0.24	       | X6(sk_A2(X4, X5, X7)) != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'(X4, X5, X7)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/sets/FINITE'(X4, X5)),
0.00/0.24	    inference('ho.purify_applied_variable', [status(thm)], ['13'])).
0.00/0.24	tff('15', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num', X1 : 'type/nums/num']:
0.00/0.24	      ('const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	        != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(X1, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/arith/<='(sk_A0, 
0.00/0.24	             sk_A2('type/nums/num', 'const/iterate/..'(X1, sk_A1), X0))
0.00/0.24	       | ~ 'const/sets/FINITE'('type/nums/num', 
0.00/0.24	             'const/iterate/..'(X1, sk_A1))
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(X1, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X0 != sk_A),
0.00/0.24	    inference('sup-', [status(thm)], ['12', '14'])).
0.00/0.24	tff('16', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num', X1 : 'type/nums/num']:
0.00/0.24	      ('const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	        != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(X1, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/arith/<='(sk_A0, 
0.00/0.24	             sk_A2('type/nums/num', 'const/iterate/..'(X1, sk_A1), X0))
0.00/0.24	       | ~ $true
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(X1, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X0 != sk_A),
0.00/0.24	    inference('demod', [status(thm)], ['15', '3'])).
0.00/0.24	tff('17', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num', X1 : 'type/nums/num']:
0.00/0.24	      (X0 != sk_A
0.00/0.24	       | ~ 'const/arith/<='(sk_A0, 
0.00/0.24	             sk_A2('type/nums/num', 'const/iterate/..'(X1, sk_A1), X0))
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(X1, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('simplify', [status(thm)], ['16'])).
0.00/0.24	tff('18', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X0 != sk_A),
0.00/0.24	    inference('sup-', [status(thm)], ['5', '17'])).
0.00/0.24	tff('19', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (X0 != sk_A
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), X0)
0.00/0.24	          = 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('simplify', [status(thm)], ['18'])).
0.00/0.24	tff('20', plain,
0.00/0.24	    ('const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	      != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	     | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	         'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	        = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	     | sk_A != sk_A),
0.00/0.24	    inference('eq_fact', [status(thm)], ['19'])).
0.00/0.24	tff('21', plain,
0.00/0.24	    'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(sk_A0, sk_A1), 
0.00/0.24	      sk_A)
0.00/0.24	     = 'const/nums/NUMERAL'('const/nums/_0'),
0.00/0.24	    inference('simplify', [status(thm)], ['20'])).
0.00/0.24	tff('22', plain,
0.00/0.24	    ('const/arith/<='(sk_A21, sk_A1)
0.00/0.24	     | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	         'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	        != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('23', plain,
0.00/0.24	    ('const/arith/<='(sk_A0, sk_A21)
0.00/0.24	     | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	         'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	        != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('24', plain,
0.00/0.24	    ![X1 : 'type/nums/num', X2 : 'type/nums/num', X3 : 'type/nums/num']:
0.00/0.24	      ('const/sets/IN'('type/nums/num', X3, 'const/iterate/..'(X2, X1))
0.00/0.24	       | ~ 'const/arith/<='(X2, X3)
0.00/0.24	       | ~ 'const/arith/<='(X3, X1)),
0.00/0.24	    inference('cnf', [status(esa)], [thm/iterate/IN_NUMSEG_])).
0.00/0.24	tff('25', plain,
0.00/0.24	    ![X4 : $tType, X5 : X4 > $o, X6 : X4 > 'type/nums/num', X7 : X4]:
0.00/0.24	      ('const/iterate/nsum'(X4, X5, X6)
0.00/0.24	        != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X6(X7) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/sets/IN'(X4, X7, X5)
0.00/0.24	       | ~ 'const/sets/FINITE'(X4, X5)),
0.00/0.24	    inference('cnf', [status(esa)], [thm/iterate/NSUM_EQ_0_IFF_])).
0.00/0.24	tff('26', plain,
0.00/0.24	    ![X4 : $tType, X5 : X4 > $o, X6 : X4 > 'type/nums/num', X7 : X4, 
0.00/0.24	      X8 : X4 > 'type/nums/num']:
0.00/0.24	      (X8 != X6
0.00/0.24	       | 'const/iterate/nsum'(X4, X5, X6)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X8(X7) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/sets/IN'(X4, X7, X5)
0.00/0.24	       | ~ 'const/sets/FINITE'(X4, X5)),
0.00/0.24	    inference('ho.purify_applied_variable', [status(thm)], ['25'])).
0.00/0.24	tff('27', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', X2 : 'type/nums/num', 
0.00/0.24	      X3 : 'type/nums/num' > 'type/nums/num', 
0.00/0.24	      X4 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ 'const/arith/<='(X2, X0)
0.00/0.24	       | ~ 'const/arith/<='(X1, X2)
0.00/0.24	       | ~ 'const/sets/FINITE'('type/nums/num', 'const/iterate/..'(X1, X0))
0.00/0.24	       | X3(X2) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X4)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X3 != X4),
0.00/0.24	    inference('sup-', [status(thm)], ['24', '26'])).
0.00/0.24	tff('28', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', X2 : 'type/nums/num', 
0.00/0.24	      X3 : 'type/nums/num' > 'type/nums/num', 
0.00/0.24	      X4 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | ~ 'const/arith/<='(X2, X0)
0.00/0.24	       | ~ 'const/arith/<='(X1, X2)
0.00/0.24	       | ~ $true
0.00/0.24	       | X3(X2) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X4)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X3 != X4),
0.00/0.24	    inference('demod', [status(thm)], ['27', '3'])).
0.00/0.24	tff('29', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num', X2 : 'type/nums/num', 
0.00/0.24	      X3 : 'type/nums/num' > 'type/nums/num', 
0.00/0.24	      X4 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (X3 != X4
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 'const/iterate/..'(X1, X0), 
0.00/0.24	           X4)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X3(X2) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/arith/<='(X1, X2)
0.00/0.24	       | ~ 'const/arith/<='(X2, X0)),
0.00/0.24	    inference('simplify', [status(thm)], ['28'])).
0.00/0.24	tff('30', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num' > 'type/nums/num', 
0.00/0.24	      X2 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/arith/<='(sk_A21, X0)
0.00/0.24	       | X1(sk_A21) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, X0), X2)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X1 != X2),
0.00/0.24	    inference('sup-', [status(thm)], ['23', '29'])).
0.00/0.24	tff('31', plain,
0.00/0.24	    ![X0 : 'type/nums/num', X1 : 'type/nums/num' > 'type/nums/num', 
0.00/0.24	      X2 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (X1 != X2
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, X0), X2)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X1(sk_A21) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | ~ 'const/arith/<='(sk_A21, X0)
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('simplify', [status(thm)], ['30'])).
0.00/0.24	tff('32', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num', 
0.00/0.24	      X1 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (~ $true
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X0(sk_A21) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), X1)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X0 != X1),
0.00/0.24	    inference('sup-', [status(thm)], ['22', '31'])).
0.00/0.24	tff('33', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num', 
0.00/0.24	      X1 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (X0 != X1
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), X1)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | X0(sk_A21) = 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('simplify', [status(thm)], ['32'])).
0.00/0.24	tff('34', plain,
0.00/0.24	    (sk_A(sk_A21) != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	     | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	         'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	        != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.24	tff('35', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      ('const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	        != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), X0)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | sk_A != X0
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('sup-', [status(thm)], ['33', '34'])).
0.00/0.24	tff('36', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (sk_A != X0
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), X0)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), sk_A)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('simplify', [status(thm)], ['35'])).
0.00/0.24	tff('37', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      (sk_A != X0
0.00/0.24	       | 'const/iterate/nsum'('type/nums/num', 
0.00/0.24	           'const/iterate/..'(sk_A0, sk_A1), X0)
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	          != 'const/nums/NUMERAL'('const/nums/_0')),
0.00/0.24	    inference('demod', [status(thm)], ['36', '21'])).
0.00/0.24	tff('38', plain,
0.00/0.24	    ![X0 : 'type/nums/num' > 'type/nums/num']:
0.00/0.24	      ('const/iterate/nsum'('type/nums/num', 
0.00/0.24	         'const/iterate/..'(sk_A0, sk_A1), X0)
0.00/0.24	        != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	       | sk_A != X0),
0.00/0.24	    inference('simplify', [status(thm)], ['37'])).
0.00/0.24	tff('39', plain,
0.00/0.24	    ('const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	      != 'const/nums/NUMERAL'('const/nums/_0')
0.00/0.24	     | sk_A != sk_A),
0.00/0.24	    inference('sup-', [status(thm)], ['21', '38'])).
0.00/0.24	tff('40', plain, $false, inference('simplify', [status(thm)], ['39'])).
0.00/0.24	
0.00/0.24	% SZS output end Refutation
0.00/0.24	EOF
