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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n171.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:29:23 CST 2018
0.00/0.39	% done 142 iterations in 0.191s
0.00/0.39	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.00/0.39	% SZS output start Refutation
0.00/0.40	tff(cTHM623_pme, conjecture,
0.00/0.40	  (((![Xn]: (cN(Xn) => cN(cS(Xn)))) & cN(c0) & 
0.00/0.40	    (![Xp:($i > $o),Xq:($i > $o)]:
0.00/0.40	       (((![Xv]: (Xq(Xv) => Xp(cS(Xv)))) & (![Xu]: (Xp(Xu) => Xq(cS(Xu)))) & 
0.00/0.40	         Xp(c0)) =>
0.00/0.40	        ((![Xx]: (cODD(Xx) => Xq(Xx))) & (![Xx]: (cEVEN(Xx) => Xp(Xx))))))) =>
0.00/0.40	   (![Xm]: ((cODD(Xm) | cEVEN(Xm)) => cN(Xm))))).
0.00/0.40	tff(zf_stmt_0, negated_conjecture,
0.00/0.40	  (~
0.00/0.40	    (((![Xn]: (cN(Xn) => cN(cS(Xn)))) & cN(c0) & 
0.00/0.40	      (![Xp:($i > $o),Xq:($i > $o)]:
0.00/0.40	         (((![Xv]: (Xq(Xv) => Xp(cS(Xv)))) & 
0.00/0.40	           (![Xu]: (Xp(Xu) => Xq(cS(Xu)))) & Xp(c0)) =>
0.00/0.40	          ((![Xx]: (cODD(Xx) => Xq(Xx))) & (![Xx]: (cEVEN(Xx) => Xp(Xx))))))) =>
0.00/0.40	     (![Xm]: ((cODD(Xm) | cEVEN(Xm)) => cN(Xm)))))).
0.00/0.40	tff('0', plain, (cODD(sk_Xm) | cEVEN(sk_Xm)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('1', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X3]:
0.00/0.40	      (~ X1(c0) | X2(sk_Xv(X2, X1)) | X1(sk_Xu(X2, X1)) | X2(X3) | ~ cODD(X3)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('2', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o]:
0.00/0.40	      (X5 != X1
0.00/0.40	       | X4 != X2
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | X2(sk_Xv(X4, X5))
0.00/0.40	       | X1(sk_Xu(X4, X5))
0.00/0.40	       | X2(X3)
0.00/0.40	       | ~ cODD(X3)),
0.00/0.40	    inference('ho.purify_applied_variable', [status(thm)], ['1'])).
0.00/0.40	tff('3', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | X1(sk_Xu(X3, X2))
0.00/0.40	       | X0(sk_Xv(X3, X2))
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | X3 != X0
0.00/0.40	       | X2 != X1),
0.00/0.40	    inference('sup-', [status(thm)], ['0', '2'])).
0.00/0.40	tff('4', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (X2 != X1
0.00/0.40	       | X3 != X0
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | X0(sk_Xv(X3, X2))
0.00/0.40	       | X1(sk_Xu(X3, X2))
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | cEVEN(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['3'])).
0.00/0.40	tff('5', plain, ~ cN(sk_Xm), inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('6', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X0(sk_Xu(X2, X1))
0.00/0.40	       | cN(sk_Xv(X2, X1))
0.00/0.40	       | ~ X0(c0)
0.00/0.40	       | X2 != cN
0.00/0.40	       | X1 != X0),
0.00/0.40	    inference('sup-', [status(thm)], ['4', '5'])).
0.00/0.40	tff('7', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (X1 != X0
0.00/0.40	       | X2 != cN
0.00/0.40	       | ~ X0(c0)
0.00/0.40	       | cN(sk_Xv(X2, X1))
0.00/0.40	       | X0(sk_Xu(X2, X1))
0.00/0.40	       | cEVEN(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['6'])).
0.00/0.40	tff('8', plain, ![X0]: (cN(cS(X0)) | ~ cN(X0)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('9', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X3]:
0.00/0.40	      (~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X2, X1)))
0.00/0.40	       | X1(sk_Xu(X2, X1))
0.00/0.40	       | X2(X3)
0.00/0.40	       | ~ cODD(X3)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('10', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o]:
0.00/0.40	      (X5 != X2
0.00/0.40	       | X4 != X1
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X2, X4)))
0.00/0.40	       | X1(sk_Xu(X2, X4))
0.00/0.40	       | X5(X3)
0.00/0.40	       | ~ cODD(X3)),
0.00/0.40	    inference('ho.purify_applied_variable', [status(thm)], ['9'])).
0.00/0.40	tff('11', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | X1(sk_Xu(X3, X2))
0.00/0.40	       | ~ X1(cS(sk_Xv(X3, X2)))
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | X2 != X1
0.00/0.40	       | X0 != X3),
0.00/0.40	    inference('sup-', [status(thm)], ['0', '10'])).
0.00/0.40	tff('12', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (X0 != X3
0.00/0.40	       | X2 != X1
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X3, X2)))
0.00/0.40	       | X1(sk_Xu(X3, X2))
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | cEVEN(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['11'])).
0.00/0.40	tff('13', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X2(sk_Xm)
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | ~ cN(c0)
0.00/0.40	       | X0 != cN
0.00/0.40	       | X2 != X1),
0.00/0.40	    inference('sup-', [status(thm)], ['8', '12'])).
0.00/0.40	tff('14', plain, cN(c0), inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('15', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X2(sk_Xm)
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | ~ $true
0.00/0.40	       | X0 != cN
0.00/0.40	       | X2 != X1),
0.00/0.40	    inference('demod', [status(thm)], ['13', '14'])).
0.00/0.40	tff('16', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (X2 != X1
0.00/0.40	       | X0 != cN
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X2(sk_Xm)
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['15'])).
0.00/0.40	tff('17', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X0 != cN
0.00/0.40	       | cN != X1),
0.00/0.40	    inference('sup-', [status(thm)], ['16', '5'])).
0.00/0.40	tff('18', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (cN != X1
0.00/0.40	       | X0 != cN
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['17'])).
0.00/0.40	tff('19', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X2(sk_Xu(X1, X0))
0.00/0.40	       | ~ X2(c0)
0.00/0.40	       | X1 != cN
0.00/0.40	       | X0 != X2
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X0 != cN
0.00/0.40	       | cN != X1),
0.00/0.40	    inference('sup-', [status(thm)], ['7', '18'])).
0.00/0.40	tff('20', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (X0 != cN
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X0 != X2
0.00/0.40	       | X1 != cN
0.00/0.40	       | ~ X2(c0)
0.00/0.40	       | X2(sk_Xu(X1, X0))
0.00/0.40	       | cEVEN(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['19'])).
0.00/0.40	tff('21', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | ~ cN(c0)
0.00/0.40	       | X1 != cN
0.00/0.40	       | X0 != cN
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X0 != cN),
0.00/0.40	    inference('eq_fact', [status(thm)], ['20'])).
0.00/0.40	tff('22', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (cN(sk_Xu(X1, X0)) | X0 != cN | X1 != cN | ~ cN(c0) | cEVEN(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['21'])).
0.00/0.40	tff('23', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (cN(sk_Xu(X1, X0)) | X0 != cN | X1 != cN | ~ $true | cEVEN(sk_Xm)),
0.00/0.40	    inference('demod', [status(thm)], ['22', '14'])).
0.00/0.40	tff('24', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (cEVEN(sk_Xm) | X1 != cN | X0 != cN | cN(sk_Xu(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['23'])).
0.00/0.40	tff('25', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X3]:
0.00/0.40	      (~ X1(c0)
0.00/0.40	       | X2(sk_Xv(X2, X1))
0.00/0.40	       | ~ X2(cS(sk_Xu(X2, X1)))
0.00/0.40	       | X2(X3)
0.00/0.40	       | ~ cODD(X3)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('26', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o]:
0.00/0.40	      (X5 != X1
0.00/0.40	       | X4 != X2
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | X2(sk_Xv(X4, X5))
0.00/0.40	       | ~ X2(cS(sk_Xu(X4, X5)))
0.00/0.40	       | X2(X3)
0.00/0.40	       | ~ cODD(X3)),
0.00/0.40	    inference('ho.purify_applied_variable', [status(thm)], ['25'])).
0.00/0.40	tff('27', plain,
0.00/0.40	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cODD(X0)
0.00/0.40	       | X1(X0)
0.00/0.40	       | ~ X1(cS(sk_Xu(X3, X2)))
0.00/0.40	       | X1(sk_Xv(X3, X2))
0.00/0.40	       | X3 != X1
0.00/0.40	       | X2 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['14', '26'])).
0.00/0.40	tff('28', plain,
0.00/0.40	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (X2 != cN
0.00/0.40	       | X3 != X1
0.00/0.40	       | X1(sk_Xv(X3, X2))
0.00/0.40	       | ~ X1(cS(sk_Xu(X3, X2)))
0.00/0.40	       | X1(X0)
0.00/0.40	       | ~ cODD(X0)),
0.00/0.40	    inference('simplify', [status(thm)], ['27'])).
0.00/0.40	tff('29', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | ~ X0(cS(sk_Xu(X2, X1)))
0.00/0.40	       | X0(sk_Xv(X2, X1))
0.00/0.40	       | X2 != X0
0.00/0.40	       | X1 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['0', '28'])).
0.00/0.40	tff('30', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (X1 != cN
0.00/0.40	       | X2 != X0
0.00/0.40	       | X0(sk_Xv(X2, X1))
0.00/0.40	       | ~ X0(cS(sk_Xu(X2, X1)))
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | cEVEN(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['29'])).
0.00/0.40	tff('31', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (cEVEN(sk_Xm)
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | ~ X0(cS(sk_Xu(X1, cN)))
0.00/0.40	       | X0(sk_Xv(X1, cN))
0.00/0.40	       | X1 != X0),
0.00/0.40	    inference('eq_res', [status(thm)], ['30'])).
0.00/0.40	tff('32', plain,
0.00/0.40	    ![X0 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X0 != cN
0.00/0.40	       | cN(sk_Xv(X0, cN))
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | cEVEN(sk_Xm)),
0.00/0.40	    inference('sup-', [status(thm)], ['31', '5'])).
0.00/0.40	tff('33', plain,
0.00/0.40	    ![X0 : $i > $o]:
0.00/0.40	      (cEVEN(sk_Xm) | ~ cN(cS(sk_Xu(X0, cN))) | cN(sk_Xv(X0, cN)) | X0 != cN),
0.00/0.40	    inference('simplify', [status(thm)], ['32'])).
0.00/0.40	tff('34', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X4]:
0.00/0.40	      (~ X1(c0)
0.00/0.40	       | X2(sk_Xv(X2, X1))
0.00/0.40	       | ~ X2(cS(sk_Xu(X2, X1)))
0.00/0.40	       | X1(X4)
0.00/0.40	       | ~ cEVEN(X4)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('35', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o]:
0.00/0.40	      (X6 != X1
0.00/0.40	       | X5 != X2
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | X2(sk_Xv(X5, X6))
0.00/0.40	       | ~ X2(cS(sk_Xu(X5, X6)))
0.00/0.40	       | X1(X4)
0.00/0.40	       | ~ cEVEN(X4)),
0.00/0.40	    inference('ho.purify_applied_variable', [status(thm)], ['34'])).
0.00/0.40	tff('36', plain,
0.00/0.40	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cEVEN(X0)
0.00/0.40	       | cN(X0)
0.00/0.40	       | ~ X1(cS(sk_Xu(X3, X2)))
0.00/0.40	       | X1(sk_Xv(X3, X2))
0.00/0.40	       | X3 != X1
0.00/0.40	       | X2 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['14', '35'])).
0.00/0.40	tff('37', plain,
0.00/0.40	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (X2 != cN
0.00/0.40	       | X3 != X1
0.00/0.40	       | X1(sk_Xv(X3, X2))
0.00/0.40	       | ~ X1(cS(sk_Xu(X3, X2)))
0.00/0.40	       | cN(X0)
0.00/0.40	       | ~ cEVEN(X0)),
0.00/0.40	    inference('simplify', [status(thm)], ['36'])).
0.00/0.40	tff('38', plain,
0.00/0.40	    ![X0, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ cEVEN(X0)
0.00/0.40	       | cN(X0)
0.00/0.40	       | ~ X1(cS(sk_Xu(X2, cN)))
0.00/0.40	       | X1(sk_Xv(X2, cN))
0.00/0.40	       | X2 != X1),
0.00/0.40	    inference('eq_res', [status(thm)], ['37'])).
0.00/0.40	tff('39', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X0 != X1
0.00/0.40	       | X1(sk_Xv(X0, cN))
0.00/0.40	       | ~ X1(cS(sk_Xu(X0, cN)))
0.00/0.40	       | ~ cEVEN(sk_Xm)),
0.00/0.40	    inference('sup-', [status(thm)], ['38', '5'])).
0.00/0.40	tff('40', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ cEVEN(sk_Xm)
0.00/0.40	       | ~ X1(cS(sk_Xu(X0, cN)))
0.00/0.40	       | X1(sk_Xv(X0, cN))
0.00/0.40	       | X0 != X1),
0.00/0.40	    inference('simplify', [status(thm)], ['39'])).
0.00/0.40	tff('41', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X2 != cN
0.00/0.40	       | cN(sk_Xv(X2, cN))
0.00/0.40	       | ~ cN(cS(sk_Xu(X2, cN)))
0.00/0.40	       | X0 != X1
0.00/0.40	       | X1(sk_Xv(X0, cN))
0.00/0.40	       | ~ X1(cS(sk_Xu(X0, cN)))),
0.00/0.40	    inference('sup-', [status(thm)], ['33', '40'])).
0.00/0.40	tff('42', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ X1(cS(sk_Xu(X0, cN)))
0.00/0.40	       | X1(sk_Xv(X0, cN))
0.00/0.40	       | X0 != X1
0.00/0.40	       | ~ cN(cS(sk_Xu(X2, cN)))
0.00/0.40	       | cN(sk_Xv(X2, cN))
0.00/0.40	       | X2 != cN),
0.00/0.40	    inference('simplify', [status(thm)], ['41'])).
0.00/0.40	tff('43', plain,
0.00/0.40	    ![X0 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X0 != cN
0.00/0.40	       | cN(sk_Xv(X0, cN))
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | X0 != cN
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))),
0.00/0.40	    inference('eq_fact', [status(thm)], ['42'])).
0.00/0.40	tff('44', plain,
0.00/0.40	    ![X0 : $i > $o]: (~ cN(cS(sk_Xu(X0, cN))) | cN(sk_Xv(X0, cN)) | X0 != cN),
0.00/0.40	    inference('simplify', [status(thm)], ['43'])).
0.00/0.40	tff('45', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X3]:
0.00/0.40	      (~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X2, X1)))
0.00/0.40	       | ~ X2(cS(sk_Xu(X2, X1)))
0.00/0.40	       | X2(X3)
0.00/0.40	       | ~ cODD(X3)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('46', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
0.00/0.40	      X6 : $i > $o]:
0.00/0.40	      (X6 != X2
0.00/0.40	       | X5 != X2
0.00/0.40	       | X4 != X1
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X2, X4)))
0.00/0.40	       | ~ X5(cS(sk_Xu(X2, X4)))
0.00/0.40	       | X6(X3)
0.00/0.40	       | ~ cODD(X3)),
0.00/0.40	    inference('ho.purify_applied_variable', [status(thm)], ['45'])).
0.00/0.40	tff('47', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | ~ X1(cS(sk_Xu(X3, X2)))
0.00/0.40	       | ~ X4(cS(sk_Xv(X3, X2)))
0.00/0.40	       | ~ X4(c0)
0.00/0.40	       | X2 != X4
0.00/0.40	       | X1 != X3
0.00/0.40	       | X0 != X3),
0.00/0.40	    inference('sup-', [status(thm)], ['0', '46'])).
0.00/0.40	tff('48', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.00/0.40	      (X0 != X3
0.00/0.40	       | X1 != X3
0.00/0.40	       | X2 != X4
0.00/0.40	       | ~ X4(c0)
0.00/0.40	       | ~ X4(cS(sk_Xv(X3, X2)))
0.00/0.40	       | ~ X1(cS(sk_Xu(X3, X2)))
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | cEVEN(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['47'])).
0.00/0.40	tff('49', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X2(sk_Xm)
0.00/0.40	       | ~ X3(cS(sk_Xu(X1, X0)))
0.00/0.40	       | ~ cN(c0)
0.00/0.40	       | X0 != cN
0.00/0.40	       | X3 != X1
0.00/0.40	       | X2 != X1),
0.00/0.40	    inference('sup-', [status(thm)], ['8', '48'])).
0.00/0.40	tff('50', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | X2(sk_Xm)
0.00/0.40	       | ~ X3(cS(sk_Xu(X1, X0)))
0.00/0.40	       | ~ $true
0.00/0.40	       | X0 != cN
0.00/0.40	       | X3 != X1
0.00/0.40	       | X2 != X1),
0.00/0.40	    inference('demod', [status(thm)], ['49', '14'])).
0.00/0.40	tff('51', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (X2 != X1
0.00/0.40	       | X3 != X1
0.00/0.40	       | X0 != cN
0.00/0.40	       | ~ X3(cS(sk_Xu(X1, X0)))
0.00/0.40	       | X2(sk_Xm)
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['50'])).
0.00/0.40	tff('52', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | ~ X2(cS(sk_Xu(X1, X0)))
0.00/0.40	       | X0 != cN
0.00/0.40	       | X2 != X1
0.00/0.40	       | cN != X1),
0.00/0.40	    inference('sup-', [status(thm)], ['51', '5'])).
0.00/0.40	tff('53', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (cN != X1
0.00/0.40	       | X2 != X1
0.00/0.40	       | X0 != cN
0.00/0.40	       | ~ X2(cS(sk_Xu(X1, X0)))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['52'])).
0.00/0.40	tff('54', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X0 != cN
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | ~ X1(cS(sk_Xu(X0, cN)))
0.00/0.40	       | cN != cN
0.00/0.40	       | X1 != X0
0.00/0.40	       | cN != X0),
0.00/0.40	    inference('sup-', [status(thm)], ['44', '53'])).
0.00/0.40	tff('55', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (X1 != X0
0.00/0.40	       | ~ X1(cS(sk_Xu(X0, cN)))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | X0 != cN),
0.00/0.40	    inference('simplify', [status(thm)], ['54'])).
0.00/0.40	tff('56', plain,
0.00/0.40	    ![X0 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xu(X0, cN))
0.00/0.40	       | X0 != cN
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | cEVEN(sk_Xm)
0.00/0.40	       | cN != X0),
0.00/0.40	    inference('sup-', [status(thm)], ['8', '55'])).
0.00/0.40	tff('57', plain,
0.00/0.40	    ![X0 : $i > $o]:
0.00/0.40	      (cEVEN(sk_Xm)
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | X0 != cN
0.00/0.40	       | ~ cN(sk_Xu(X0, cN))),
0.00/0.40	    inference('simplify', [status(thm)], ['56'])).
0.00/0.40	tff('58', plain,
0.00/0.40	    ![X0 : $i > $o]: (~ cN(sk_Xu(X0, cN)) | X0 != cN | cEVEN(sk_Xm)),
0.00/0.40	    inference('clc', [status(thm)], ['57', '8'])).
0.00/0.40	tff('59', plain,
0.00/0.40	    ![X0 : $i > $o]:
0.00/0.40	      (~ $true | cN != cN | X0 != cN | cEVEN(sk_Xm) | cEVEN(sk_Xm) | X0 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['24', '58'])).
0.00/0.40	tff('60', plain, ![X0 : $i > $o]: (cEVEN(sk_Xm) | X0 != cN),
0.00/0.40	    inference('simplify', [status(thm)], ['59'])).
0.00/0.40	tff('61', plain, cEVEN(sk_Xm), inference('eq_res', [status(thm)], ['60'])).
0.00/0.40	tff('62', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X4]:
0.00/0.40	      (~ X1(c0)
0.00/0.40	       | X2(sk_Xv(X2, X1))
0.00/0.40	       | X1(sk_Xu(X2, X1))
0.00/0.40	       | X1(X4)
0.00/0.40	       | ~ cEVEN(X4)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('63', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o]:
0.00/0.40	      (X6 != X1
0.00/0.40	       | X5 != X2
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | X2(sk_Xv(X5, X6))
0.00/0.40	       | X1(sk_Xu(X5, X6))
0.00/0.40	       | X1(X4)
0.00/0.40	       | ~ cEVEN(X4)),
0.00/0.40	    inference('ho.purify_applied_variable', [status(thm)], ['62'])).
0.00/0.40	tff('64', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | X0(sk_Xu(X2, X1))
0.00/0.40	       | X3(sk_Xv(X2, X1))
0.00/0.40	       | ~ X0(c0)
0.00/0.40	       | X2 != X3
0.00/0.40	       | X1 != X0),
0.00/0.40	    inference('sup-', [status(thm)], ['61', '63'])).
0.00/0.40	tff('65', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (X1 != X0
0.00/0.40	       | X2 != X3
0.00/0.40	       | ~ X0(c0)
0.00/0.40	       | X3(sk_Xv(X2, X1))
0.00/0.40	       | X0(sk_Xu(X2, X1))
0.00/0.40	       | X0(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['64'])).
0.00/0.40	tff('66', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X2(sk_Xv(X1, X0))
0.00/0.40	       | ~ cN(c0)
0.00/0.40	       | X1 != X2
0.00/0.40	       | X0 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['65', '5'])).
0.00/0.40	tff('67', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X2(sk_Xv(X1, X0))
0.00/0.40	       | ~ $true
0.00/0.40	       | X1 != X2
0.00/0.40	       | X0 != cN),
0.00/0.40	    inference('demod', [status(thm)], ['66', '14'])).
0.00/0.40	tff('68', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (X0 != cN | X1 != X2 | X2(sk_Xv(X1, X0)) | cN(sk_Xu(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['67'])).
0.00/0.40	tff('69', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X4]:
0.00/0.40	      (~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X2, X1)))
0.00/0.40	       | X1(sk_Xu(X2, X1))
0.00/0.40	       | X1(X4)
0.00/0.40	       | ~ cEVEN(X4)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('70', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o]:
0.00/0.40	      (X5 != X1
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X2, X5)))
0.00/0.40	       | X1(sk_Xu(X2, X5))
0.00/0.40	       | X1(X4)
0.00/0.40	       | ~ cEVEN(X4)),
0.00/0.40	    inference('ho.purify_applied_variable', [status(thm)], ['69'])).
0.00/0.40	tff('71', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | X0(sk_Xu(X2, X1))
0.00/0.40	       | ~ X0(cS(sk_Xv(X2, X1)))
0.00/0.40	       | ~ X0(c0)
0.00/0.40	       | X1 != X0),
0.00/0.40	    inference('sup-', [status(thm)], ['61', '70'])).
0.00/0.40	tff('72', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (X1 != X0
0.00/0.40	       | ~ X0(c0)
0.00/0.40	       | ~ X0(cS(sk_Xv(X2, X1)))
0.00/0.40	       | X0(sk_Xu(X2, X1))
0.00/0.40	       | X0(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['71'])).
0.00/0.40	tff('73', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | ~ cN(cS(sk_Xv(X1, X0)))
0.00/0.40	       | ~ cN(c0)
0.00/0.40	       | X0 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['72', '5'])).
0.00/0.40	tff('74', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | ~ cN(cS(sk_Xv(X1, X0)))
0.00/0.40	       | ~ $true
0.00/0.40	       | X0 != cN),
0.00/0.40	    inference('demod', [status(thm)], ['73', '14'])).
0.00/0.40	tff('75', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (X0 != cN | ~ cN(cS(sk_Xv(X1, X0))) | cN(sk_Xu(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['74'])).
0.00/0.40	tff('76', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true | ~ cN(sk_Xv(X1, X0)) | cN(sk_Xu(X1, X0)) | X0 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['8', '75'])).
0.00/0.40	tff('77', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (X0 != cN | cN(sk_Xu(X1, X0)) | ~ cN(sk_Xv(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['76'])).
0.00/0.40	tff('78', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X1 != cN
0.00/0.40	       | X0 != cN
0.00/0.40	       | cN(sk_Xu(X1, X0))
0.00/0.40	       | X0 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['68', '77'])).
0.00/0.40	tff('79', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]: (X0 != cN | X1 != cN | cN(sk_Xu(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['78'])).
0.00/0.40	tff('80', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true | X0 != X1 | X1(sk_Xv(X0, cN)) | ~ X1(cS(sk_Xu(X0, cN)))),
0.00/0.40	    inference('sup-', [status(thm)], ['61', '40'])).
0.00/0.40	tff('81', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ X1(cS(sk_Xu(X0, cN))) | X1(sk_Xv(X0, cN)) | X0 != X1),
0.00/0.40	    inference('simplify', [status(thm)], ['80'])).
0.00/0.40	tff('82', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X4]:
0.00/0.40	      (~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X2, X1)))
0.00/0.40	       | ~ X2(cS(sk_Xu(X2, X1)))
0.00/0.40	       | X1(X4)
0.00/0.40	       | ~ cEVEN(X4)),
0.00/0.40	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.40	tff('83', plain,
0.00/0.40	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o]:
0.00/0.40	      (X6 != X2
0.00/0.40	       | X5 != X1
0.00/0.40	       | ~ X1(c0)
0.00/0.40	       | ~ X1(cS(sk_Xv(X2, X5)))
0.00/0.40	       | ~ X6(cS(sk_Xu(X2, X5)))
0.00/0.40	       | X1(X4)
0.00/0.40	       | ~ cEVEN(X4)),
0.00/0.40	    inference('ho.purify_applied_variable', [status(thm)], ['82'])).
0.00/0.40	tff('84', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X0(sk_Xm)
0.00/0.40	       | ~ X1(cS(sk_Xu(X3, X2)))
0.00/0.40	       | ~ X0(cS(sk_Xv(X3, X2)))
0.00/0.40	       | ~ X0(c0)
0.00/0.40	       | X2 != X0
0.00/0.40	       | X1 != X3),
0.00/0.40	    inference('sup-', [status(thm)], ['61', '83'])).
0.00/0.40	tff('85', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.00/0.40	      (X1 != X3
0.00/0.40	       | X2 != X0
0.00/0.40	       | ~ X0(c0)
0.00/0.40	       | ~ X0(cS(sk_Xv(X3, X2)))
0.00/0.40	       | ~ X1(cS(sk_Xu(X3, X2)))
0.00/0.40	       | X0(sk_Xm)),
0.00/0.40	    inference('simplify', [status(thm)], ['84'])).
0.00/0.40	tff('86', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ X0(cS(sk_Xu(X2, X1)))
0.00/0.40	       | ~ cN(cS(sk_Xv(X2, X1)))
0.00/0.40	       | ~ cN(c0)
0.00/0.40	       | X1 != cN
0.00/0.40	       | X0 != X2),
0.00/0.40	    inference('sup-', [status(thm)], ['85', '5'])).
0.00/0.40	tff('87', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ X0(cS(sk_Xu(X2, X1)))
0.00/0.40	       | ~ cN(cS(sk_Xv(X2, X1)))
0.00/0.40	       | ~ $true
0.00/0.40	       | X1 != cN
0.00/0.40	       | X0 != X2),
0.00/0.40	    inference('demod', [status(thm)], ['86', '14'])).
0.00/0.40	tff('88', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (X0 != X2
0.00/0.40	       | X1 != cN
0.00/0.40	       | ~ cN(cS(sk_Xv(X2, X1)))
0.00/0.40	       | ~ X0(cS(sk_Xu(X2, X1)))),
0.00/0.40	    inference('simplify', [status(thm)], ['87'])).
0.00/0.40	tff('89', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xv(X1, X0))
0.00/0.40	       | ~ X2(cS(sk_Xu(X1, X0)))
0.00/0.40	       | X0 != cN
0.00/0.40	       | X2 != X1),
0.00/0.40	    inference('sup-', [status(thm)], ['8', '88'])).
0.00/0.40	tff('90', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.00/0.40	      (X2 != X1 | X0 != cN | ~ X2(cS(sk_Xu(X1, X0))) | ~ cN(sk_Xv(X1, X0))),
0.00/0.40	    inference('simplify', [status(thm)], ['89'])).
0.00/0.40	tff('91', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | X0 != cN
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | ~ X1(cS(sk_Xu(X0, cN)))
0.00/0.40	       | cN != cN
0.00/0.40	       | X1 != X0),
0.00/0.40	    inference('sup-', [status(thm)], ['81', '90'])).
0.00/0.40	tff('92', plain,
0.00/0.40	    ![X0 : $i > $o, X1 : $i > $o]:
0.00/0.40	      (X1 != X0
0.00/0.40	       | ~ X1(cS(sk_Xu(X0, cN)))
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | X0 != cN),
0.00/0.40	    inference('simplify', [status(thm)], ['91'])).
0.00/0.40	tff('93', plain,
0.00/0.40	    ![X0 : $i > $o]:
0.00/0.40	      (~ $true
0.00/0.40	       | ~ cN(sk_Xu(X0, cN))
0.00/0.40	       | X0 != cN
0.00/0.40	       | ~ cN(cS(sk_Xu(X0, cN)))
0.00/0.40	       | cN != X0),
0.00/0.40	    inference('sup-', [status(thm)], ['8', '92'])).
0.00/0.40	tff('94', plain,
0.00/0.40	    ![X0 : $i > $o]:
0.00/0.40	      (~ cN(cS(sk_Xu(X0, cN))) | X0 != cN | ~ cN(sk_Xu(X0, cN))),
0.00/0.40	    inference('simplify', [status(thm)], ['93'])).
0.00/0.40	tff('95', plain, ![X0 : $i > $o]: (~ cN(sk_Xu(X0, cN)) | X0 != cN),
0.00/0.40	    inference('clc', [status(thm)], ['94', '8'])).
0.00/0.40	tff('96', plain, ![X0 : $i > $o]: (~ $true | X0 != cN | cN != cN | X0 != cN),
0.00/0.40	    inference('sup-', [status(thm)], ['79', '95'])).
0.00/0.40	tff('97', plain, ![X0 : $i > $o]: X0 != cN,
0.00/0.40	    inference('simplify', [status(thm)], ['96'])).
0.00/0.40	tff('98', plain, $false, inference('eq_res', [status(thm)], ['97'])).
0.00/0.40	
0.00/0.40	% SZS output end Refutation
0.00/0.40	EOF
