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_int
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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n087.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 18:39:24 CST 2018
0.00/0.34	% done 127 iterations in 0.139s
0.00/0.34	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.00/0.34	% SZS output start Refutation
0.00/0.34	tff('thm/iterate/SUM_LT_ALL_', conjecture,
0.00/0.34	  (![A:$tType,A0:(A > 'type/realax/real'),A1:(A > 'type/realax/real'),
0.00/0.34	     A2:(A > $o)]:
0.00/0.34	     (((![A3:A]:
0.00/0.34	          ('const/sets/IN'(A,A3,A2) => 'const/realax/real_lt'(A0(A3),A1(A3)))) & 
0.00/0.34	       (A2 != 'const/sets/EMPTY'(A)) & 'const/sets/FINITE'(A,A2)) =>
0.00/0.34	      'const/realax/real_lt'('const/iterate/sum'(A,A2,A0),
0.00/0.34	                             'const/iterate/sum'(A,A2,A1))))).
0.00/0.34	tff(zf_stmt_0, negated_conjecture,
0.00/0.34	  (~
0.00/0.34	    (![A:$tType,A0:(A > 'type/realax/real'),A1:(A > 'type/realax/real'),
0.00/0.34	       A2:(A > $o)]:
0.00/0.34	       (((![A3:A]:
0.00/0.34	            ('const/sets/IN'(A,A3,A2) =>
0.00/0.34	             'const/realax/real_lt'(A0(A3),A1(A3)))) & 
0.00/0.34	         (A2 != 'const/sets/EMPTY'(A)) & 'const/sets/FINITE'(A,A2)) =>
0.00/0.34	        'const/realax/real_lt'('const/iterate/sum'(A,A2,A0),
0.00/0.34	                               'const/iterate/sum'(A,A2,A1)))))).
0.00/0.34	tff('0', plain,
0.00/0.34	    ![X13 : sk_A]:
0.00/0.34	      ('const/realax/real_lt'(sk_A0(X13), sk_A11(X13))
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X13, sk_A2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('thm/realarith/REAL_LT_IMP_LE_', axiom,
0.00/0.34	  (![A:'type/realax/real',A0:'type/realax/real']:
0.00/0.34	     ('const/realax/real_lt'(A,A0) => 'const/realax/real_le'(A,A0)))).
0.00/0.34	tff('1', plain,
0.00/0.34	    ![X7 : 'type/realax/real', X8 : 'type/realax/real']:
0.00/0.34	      ('const/realax/real_le'(X7, X8) | ~ 'const/realax/real_lt'(X7, X8)),
0.00/0.34	    inference('cnf', [status(esa)], [thm/realarith/REAL_LT_IMP_LE_])).
0.00/0.34	tff('thm/sets/MEMBER_NOT_EMPTY_', axiom,
0.00/0.34	  (![A:$tType,A0:(A > $o)]:
0.00/0.34	     ((?[A1:A]: 'const/sets/IN'(A,A1,A0)) <=> (A0 != 'const/sets/EMPTY'(A))))).
0.00/0.34	tff('2', plain,
0.00/0.34	    ![X9 : $tType, X12 : X9 > $o]:
0.00/0.34	      ('const/sets/IN'(X9, sk_A1(X9, X12), X12)
0.00/0.34	       | X12 = 'const/sets/EMPTY'(X9)),
0.00/0.34	    inference('cnf', [status(esa)], [thm/sets/MEMBER_NOT_EMPTY_])).
0.00/0.34	tff('thm/iterate/SUM_LT_', axiom,
0.00/0.34	  (![A:$tType,A0:(A > 'type/realax/real'),A1:(A > 'type/realax/real'),
0.00/0.34	     A2:(A > $o)]:
0.00/0.34	     (((?[A3:A]:
0.00/0.34	          ('const/realax/real_lt'(A0(A3),A1(A3)) & 'const/sets/IN'(A,A3,A2))) & 
0.00/0.34	       (![A3:A]:
0.00/0.34	          ('const/sets/IN'(A,A3,A2) => 'const/realax/real_le'(A0(A3),A1(A3)))) & 
0.00/0.34	       'const/sets/FINITE'(A,A2)) =>
0.00/0.34	      'const/realax/real_lt'('const/iterate/sum'(A,A2,A0),
0.00/0.34	                             'const/iterate/sum'(A,A2,A1))))).
0.00/0.34	tff('3', plain,
0.00/0.34	    ![X2 : $tType, X3 : X2 > $o, X4 : X2 > 'type/realax/real', 
0.00/0.34	      X5 : X2 > 'type/realax/real', X6 : X2]:
0.00/0.34	      ('const/realax/real_lt'('const/iterate/sum'(X2, X3, X4), 
0.00/0.34	         'const/iterate/sum'(X2, X3, X5))
0.00/0.34	       | ~ 'const/sets/FINITE'(X2, X3)
0.00/0.34	       | ~ 'const/realax/real_le'(X4(sk_A3(X2, X3, X5, X4)), 
0.00/0.34	             X5(sk_A3(X2, X3, X5, X4)))
0.00/0.34	       | ~ 'const/sets/IN'(X2, X6, X3)
0.00/0.34	       | ~ 'const/realax/real_lt'(X4(X6), X5(X6))),
0.00/0.34	    inference('cnf', [status(esa)], [thm/iterate/SUM_LT_])).
0.00/0.34	tff('4', plain,
0.00/0.34	    ![X2 : $tType, X3 : X2 > $o, X4 : X2 > 'type/realax/real', 
0.00/0.34	      X5 : X2 > 'type/realax/real', X6 : X2, X7 : X2 > 'type/realax/real', 
0.00/0.34	      X8 : X2 > 'type/realax/real', X9 : X2 > 'type/realax/real', 
0.00/0.34	      X10 : X2 > 'type/realax/real']:
0.00/0.34	      (X10 != X5
0.00/0.34	       | X9 != X4
0.00/0.34	       | X8 != X5
0.00/0.34	       | X7 != X4
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(X2, X3, X4), 
0.00/0.34	           'const/iterate/sum'(X2, X3, X5))
0.00/0.34	       | ~ 'const/sets/FINITE'(X2, X3)
0.00/0.34	       | ~ 'const/realax/real_le'(X7(sk_A3(X2, X3, X5, X4)), 
0.00/0.34	             X8(sk_A3(X2, X3, X5, X4)))
0.00/0.34	       | ~ 'const/sets/IN'(X2, X6, X3)
0.00/0.34	       | ~ 'const/realax/real_lt'(X9(X6), X10(X6))),
0.00/0.34	    inference('ho.purify_applied_variable', [status(thm)], ['3'])).
0.00/0.34	tff('5', plain,
0.00/0.34	    ![X0 : sk_A, X1 : sk_A > $o, X2 : sk_A > 'type/realax/real', 
0.00/0.34	      X3 : sk_A > 'type/realax/real', X4 : sk_A > 'type/realax/real', 
0.00/0.34	      X5 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X0, sk_A2)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X0, X1)
0.00/0.34	       | ~ 'const/realax/real_le'(X5(sk_A3(sk_A, X1, X4, X3)), 
0.00/0.34	             X2(sk_A3(sk_A, X1, X4, X3)))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X1)
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X1, X3), 
0.00/0.34	           'const/iterate/sum'(sk_A, X1, X4))
0.00/0.34	       | X5 != X3
0.00/0.34	       | X2 != X4
0.00/0.34	       | sk_A0 != X3
0.00/0.34	       | sk_A11 != X4),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '4'])).
0.00/0.34	tff('6', plain,
0.00/0.34	    ![X0 : sk_A, X1 : sk_A > $o, X2 : sk_A > 'type/realax/real', 
0.00/0.34	      X3 : sk_A > 'type/realax/real', X4 : sk_A > 'type/realax/real', 
0.00/0.34	      X5 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X4
0.00/0.34	       | sk_A0 != X3
0.00/0.34	       | X2 != X4
0.00/0.34	       | X5 != X3
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X1, X3), 
0.00/0.34	           'const/iterate/sum'(sk_A, X1, X4))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X1)
0.00/0.34	       | ~ 'const/realax/real_le'(X5(sk_A3(sk_A, X1, X4, X3)), 
0.00/0.34	             X2(sk_A3(sk_A, X1, X4, X3)))
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X0, X1)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X0, sk_A2)),
0.00/0.34	    inference('simplify', [status(thm)], ['5'])).
0.00/0.34	tff('7', plain,
0.00/0.34	    ![X0 : sk_A > $o, X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real', 
0.00/0.34	      X4 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, sk_A1(sk_A, sk_A2), X0)
0.00/0.34	       | ~ 'const/realax/real_le'(X4(sk_A3(sk_A, X0, X3, X2)), 
0.00/0.34	             X1(sk_A3(sk_A, X0, X3, X2)))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X0)
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X0, X2), 
0.00/0.34	           'const/iterate/sum'(sk_A, X0, X3))
0.00/0.34	       | X4 != X2
0.00/0.34	       | X1 != X3
0.00/0.34	       | sk_A0 != X2
0.00/0.34	       | sk_A11 != X3),
0.00/0.34	    inference('sup-', [status(thm)], ['2', '6'])).
0.00/0.34	tff('8', plain,
0.00/0.34	    ![X0 : sk_A > $o, X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real', 
0.00/0.34	      X4 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X3
0.00/0.34	       | sk_A0 != X2
0.00/0.34	       | X1 != X3
0.00/0.34	       | X4 != X2
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X0, X2), 
0.00/0.34	           'const/iterate/sum'(sk_A, X0, X3))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X0)
0.00/0.34	       | ~ 'const/realax/real_le'(X4(sk_A3(sk_A, X0, X3, X2)), 
0.00/0.34	             X1(sk_A3(sk_A, X0, X3, X2)))
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, sk_A1(sk_A, sk_A2), X0)
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('simplify', [status(thm)], ['7'])).
0.00/0.34	tff('9', plain, sk_A2 != 'const/sets/EMPTY'(sk_A),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('10', plain,
0.00/0.34	    ![X0 : sk_A > $o, X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real', 
0.00/0.34	      X4 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X3
0.00/0.34	       | sk_A0 != X2
0.00/0.34	       | X1 != X3
0.00/0.34	       | X4 != X2
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X0, X2), 
0.00/0.34	           'const/iterate/sum'(sk_A, X0, X3))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X0)
0.00/0.34	       | ~ 'const/realax/real_le'(X4(sk_A3(sk_A, X0, X3, X2)), 
0.00/0.34	             X1(sk_A3(sk_A, X0, X3, X2)))
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, sk_A1(sk_A, sk_A2), X0)),
0.00/0.34	    inference('simplify_reflect-', [status(thm)], ['8', '9'])).
0.00/0.34	tff('11', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)
0.00/0.34	       | ~ 'const/realax/real_le'(X3(sk_A3(sk_A, sk_A2, X2, X1)), 
0.00/0.34	             X0(sk_A3(sk_A, sk_A2, X2, X1)))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, sk_A2)
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X2))
0.00/0.34	       | X3 != X1
0.00/0.34	       | X0 != X2
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | sk_A11 != X2),
0.00/0.34	    inference('sup-', [status(thm)], ['2', '10'])).
0.00/0.34	tff('12', plain, 'const/sets/FINITE'(sk_A, sk_A2),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('13', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)
0.00/0.34	       | ~ 'const/realax/real_le'(X3(sk_A3(sk_A, sk_A2, X2, X1)), 
0.00/0.34	             X0(sk_A3(sk_A, sk_A2, X2, X1)))
0.00/0.34	       | ~ $true
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X2))
0.00/0.34	       | X3 != X1
0.00/0.34	       | X0 != X2
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | sk_A11 != X2),
0.00/0.34	    inference('demod', [status(thm)], ['11', '12'])).
0.00/0.34	tff('14', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X2
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | X0 != X2
0.00/0.34	       | X3 != X1
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X2))
0.00/0.34	       | ~ 'const/realax/real_le'(X3(sk_A3(sk_A, sk_A2, X2, X1)), 
0.00/0.34	             X0(sk_A3(sk_A, sk_A2, X2, X1)))
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('simplify', [status(thm)], ['13'])).
0.00/0.34	tff('15', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X2
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | X0 != X2
0.00/0.34	       | X3 != X1
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X2))
0.00/0.34	       | ~ 'const/realax/real_le'(X3(sk_A3(sk_A, sk_A2, X2, X1)), 
0.00/0.34	             X0(sk_A3(sk_A, sk_A2, X2, X1)))),
0.00/0.34	    inference('simplify_reflect-', [status(thm)], ['14', '9'])).
0.00/0.34	tff('16', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ 'const/realax/real_lt'(X3(sk_A3(sk_A, sk_A2, X2, X1)), 
0.00/0.34	             X0(sk_A3(sk_A, sk_A2, X2, X1)))
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X2))
0.00/0.34	       | X3 != X1
0.00/0.34	       | X0 != X2
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | sk_A11 != X2),
0.00/0.34	    inference('sup-', [status(thm)], ['1', '15'])).
0.00/0.34	tff('17', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real', X3 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X2
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | X0 != X2
0.00/0.34	       | X3 != X1
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X2))
0.00/0.34	       | ~ 'const/realax/real_lt'(X3(sk_A3(sk_A, sk_A2, X2, X1)), 
0.00/0.34	             X0(sk_A3(sk_A, sk_A2, X2, X1)))),
0.00/0.34	    inference('simplify', [status(thm)], ['16'])).
0.00/0.34	tff('18', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, sk_A3(sk_A, sk_A2, X1, X0), sk_A2)
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X0), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X1))
0.00/0.34	       | sk_A0 != X0
0.00/0.34	       | sk_A11 != X1
0.00/0.34	       | sk_A0 != X0
0.00/0.34	       | sk_A11 != X1),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '17'])).
0.00/0.34	tff('19', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X1
0.00/0.34	       | sk_A0 != X0
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X0), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X1))
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, sk_A3(sk_A, sk_A2, X1, X0), sk_A2)),
0.00/0.34	    inference('simplify', [status(thm)], ['18'])).
0.00/0.34	tff('20', plain,
0.00/0.34	    ![X2 : $tType, X3 : X2 > $o, X4 : X2 > 'type/realax/real', 
0.00/0.34	      X5 : X2 > 'type/realax/real', X6 : X2]:
0.00/0.34	      ('const/realax/real_lt'('const/iterate/sum'(X2, X3, X4), 
0.00/0.34	         'const/iterate/sum'(X2, X3, X5))
0.00/0.34	       | ~ 'const/sets/FINITE'(X2, X3)
0.00/0.34	       | 'const/sets/IN'(X2, sk_A3(X2, X3, X5, X4), X3)
0.00/0.34	       | ~ 'const/sets/IN'(X2, X6, X3)
0.00/0.34	       | ~ 'const/realax/real_lt'(X4(X6), X5(X6))),
0.00/0.34	    inference('cnf', [status(esa)], [thm/iterate/SUM_LT_])).
0.00/0.34	tff('21', plain,
0.00/0.34	    ![X2 : $tType, X3 : X2 > $o, X4 : X2 > 'type/realax/real', 
0.00/0.34	      X5 : X2 > 'type/realax/real', X6 : X2, X7 : X2 > 'type/realax/real', 
0.00/0.34	      X8 : X2 > 'type/realax/real']:
0.00/0.34	      (X8 != X5
0.00/0.34	       | X7 != X4
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(X2, X3, X4), 
0.00/0.34	           'const/iterate/sum'(X2, X3, X5))
0.00/0.34	       | ~ 'const/sets/FINITE'(X2, X3)
0.00/0.34	       | 'const/sets/IN'(X2, sk_A3(X2, X3, X5, X4), X3)
0.00/0.34	       | ~ 'const/sets/IN'(X2, X6, X3)
0.00/0.34	       | ~ 'const/realax/real_lt'(X7(X6), X8(X6))),
0.00/0.34	    inference('ho.purify_applied_variable', [status(thm)], ['20'])).
0.00/0.34	tff('22', plain,
0.00/0.34	    ![X0 : sk_A, X1 : sk_A > $o, X2 : sk_A > 'type/realax/real', 
0.00/0.34	      X3 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X0, sk_A2)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X0, X1)
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, X1, X3, X2), X1)
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X1)
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X1, X2), 
0.00/0.34	           'const/iterate/sum'(sk_A, X1, X3))
0.00/0.34	       | sk_A0 != X2
0.00/0.34	       | sk_A11 != X3),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '21'])).
0.00/0.34	tff('23', plain,
0.00/0.34	    ![X0 : sk_A, X1 : sk_A > $o, X2 : sk_A > 'type/realax/real', 
0.00/0.34	      X3 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X3
0.00/0.34	       | sk_A0 != X2
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X1, X2), 
0.00/0.34	           'const/iterate/sum'(sk_A, X1, X3))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X1)
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, X1, X3, X2), X1)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X0, X1)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, X0, sk_A2)),
0.00/0.34	    inference('simplify', [status(thm)], ['22'])).
0.00/0.34	tff('24', plain,
0.00/0.34	    ![X0 : sk_A > $o, X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, sk_A1(sk_A, sk_A2), X0)
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, X0, X2, X1), X0)
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X0)
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X0, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, X0, X2))
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | sk_A11 != X2),
0.00/0.34	    inference('sup-', [status(thm)], ['2', '23'])).
0.00/0.34	tff('25', plain,
0.00/0.34	    ![X0 : sk_A > $o, X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X2
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X0, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, X0, X2))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X0)
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, X0, X2, X1), X0)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, sk_A1(sk_A, sk_A2), X0)
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('simplify', [status(thm)], ['24'])).
0.00/0.34	tff('26', plain,
0.00/0.34	    ![X0 : sk_A > $o, X1 : sk_A > 'type/realax/real', 
0.00/0.34	      X2 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X2
0.00/0.34	       | sk_A0 != X1
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, X0, X1), 
0.00/0.34	           'const/iterate/sum'(sk_A, X0, X2))
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, X0)
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, X0, X2, X1), X0)
0.00/0.34	       | ~ 'const/sets/IN'(sk_A, sk_A1(sk_A, sk_A2), X0)),
0.00/0.34	    inference('simplify_reflect-', [status(thm)], ['25', '9'])).
0.00/0.34	tff('27', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, sk_A2, X1, X0), sk_A2)
0.00/0.34	       | ~ 'const/sets/FINITE'(sk_A, sk_A2)
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X0), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X1))
0.00/0.34	       | sk_A0 != X0
0.00/0.34	       | sk_A11 != X1),
0.00/0.34	    inference('sup-', [status(thm)], ['2', '26'])).
0.00/0.34	tff('28', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real']:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, sk_A2, X1, X0), sk_A2)
0.00/0.34	       | ~ $true
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X0), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X1))
0.00/0.34	       | sk_A0 != X0
0.00/0.34	       | sk_A11 != X1),
0.00/0.34	    inference('demod', [status(thm)], ['27', '12'])).
0.00/0.34	tff('29', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X1
0.00/0.34	       | sk_A0 != X0
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X0), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X1))
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, sk_A2, X1, X0), sk_A2)
0.00/0.34	       | sk_A2 = 'const/sets/EMPTY'(sk_A)),
0.00/0.34	    inference('simplify', [status(thm)], ['28'])).
0.00/0.34	tff('30', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real']:
0.00/0.34	      (sk_A11 != X1
0.00/0.34	       | sk_A0 != X0
0.00/0.34	       | 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X0), 
0.00/0.34	           'const/iterate/sum'(sk_A, sk_A2, X1))
0.00/0.34	       | 'const/sets/IN'(sk_A, sk_A3(sk_A, sk_A2, X1, X0), sk_A2)),
0.00/0.34	    inference('simplify_reflect-', [status(thm)], ['29', '9'])).
0.00/0.34	tff('31', plain,
0.00/0.34	    ![X0 : sk_A > 'type/realax/real', X1 : sk_A > 'type/realax/real']:
0.00/0.34	      ('const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, X0), 
0.00/0.34	         'const/iterate/sum'(sk_A, sk_A2, X1))
0.00/0.34	       | sk_A0 != X0
0.00/0.34	       | sk_A11 != X1),
0.00/0.34	    inference('clc', [status(thm)], ['19', '30'])).
0.00/0.34	tff('32', plain,
0.00/0.34	    ~ 'const/realax/real_lt'('const/iterate/sum'(sk_A, sk_A2, sk_A0), 
0.00/0.34	        'const/iterate/sum'(sk_A, sk_A2, sk_A11)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('33', plain, (~ $true | sk_A11 != sk_A11 | sk_A0 != sk_A0),
0.00/0.34	    inference('sup-', [status(thm)], ['31', '32'])).
0.00/0.34	tff('34', plain, $false, inference('simplify', [status(thm)], ['33'])).
0.00/0.34	
0.00/0.34	% SZS output end Refutation
0.00/0.34	EOF
