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    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n067.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:28:08 CST 2018
0.59/0.80	% done 504 iterations in 0.602s
0.59/0.80	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.59/0.80	% SZS output start Refutation
0.59/0.81	tff(cTHM623_pme, conjecture,
0.59/0.81	  (((![Xn]: (cN(Xn) => cN(cS(Xn)))) & cN(c0) & 
0.59/0.81	    (![Xp:($i > $o),Xq:($i > $o)]:
0.59/0.81	       (((![Xv]: (Xq(Xv) => Xp(cS(Xv)))) & (![Xu]: (Xp(Xu) => Xq(cS(Xu)))) & 
0.59/0.81	         Xp(c0)) =>
0.59/0.81	        ((![Xx]: (cODD(Xx) => Xq(Xx))) & (![Xx]: (cEVEN(Xx) => Xp(Xx))))))) =>
0.59/0.81	   (![Xm]: ((cODD(Xm) | cEVEN(Xm)) => cN(Xm))))).
0.59/0.81	tff(zf_stmt_0, negated_conjecture,
0.59/0.81	  (~
0.59/0.81	    (((![Xn]: (cN(Xn) => cN(cS(Xn)))) & cN(c0) & 
0.59/0.81	      (![Xp:($i > $o),Xq:($i > $o)]:
0.59/0.81	         (((![Xv]: (Xq(Xv) => Xp(cS(Xv)))) & 
0.59/0.81	           (![Xu]: (Xp(Xu) => Xq(cS(Xu)))) & Xp(c0)) =>
0.59/0.81	          ((![Xx]: (cODD(Xx) => Xq(Xx))) & (![Xx]: (cEVEN(Xx) => Xp(Xx))))))) =>
0.59/0.81	     (![Xm]: ((cODD(Xm) | cEVEN(Xm)) => cN(Xm)))))).
0.59/0.81	tff('0', plain, (cODD(sk_Xm) | cEVEN(sk_Xm)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('1', plain, cN(c0), inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('2', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X3]:
0.59/0.81	      (~ X1(c0) | X2(sk_Xv(X2, X1)) | X1(sk_Xu(X2, X1)) | X2(X3) | ~ cODD(X3)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('3', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
0.59/0.81	      X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (X7 != X2
0.59/0.81	       | X6 != X1
0.59/0.81	       | X5 != X1
0.59/0.81	       | X4 != X2
0.59/0.81	       | ~ X1(c0)
0.59/0.81	       | X2(sk_Xv(X4, X5))
0.59/0.81	       | X6(sk_Xu(X4, X5))
0.59/0.81	       | X7(X3)
0.59/0.81	       | ~ cODD(X3)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['2'])).
0.59/0.81	tff('4', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cODD(X0)
0.59/0.81	       | X1(X0)
0.59/0.81	       | X2(sk_Xu(X4, X3))
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | X4 != X5
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != X5),
0.59/0.81	    inference('sup-', [status(thm)], ['1', '3'])).
0.59/0.81	tff('5', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != X5
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | X2(sk_Xu(X4, X3))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cODD(X0)),
0.59/0.81	    inference('simplify', [status(thm)], ['4'])).
0.59/0.81	tff('6', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (X6 != X2
0.59/0.81	       | X1 != X5
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | X6(sk_Xu(X4, X3))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cODD(X0)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['5'])).
0.59/0.81	tff('7', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | X1(sk_Xu(X3, X2))
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | X3 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X0 != X4
0.59/0.81	       | X1 != X5),
0.59/0.81	    inference('sup-', [status(thm)], ['0', '6'])).
0.59/0.81	tff('8', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != X5
0.59/0.81	       | X0 != X4
0.59/0.81	       | X5 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != X4
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | X1(sk_Xu(X3, X2))
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['7'])).
0.59/0.81	tff('9', plain, ~ cN(sk_Xm), inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('10', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xu(X2, X1))
0.59/0.81	       | X3(sk_Xv(X2, X1))
0.59/0.81	       | X2 != X3
0.59/0.81	       | X1 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | cN != X3
0.59/0.81	       | X0 != X4),
0.59/0.81	    inference('sup-', [status(thm)], ['8', '9'])).
0.59/0.81	tff('11', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X0 != X4
0.59/0.81	       | cN != X3
0.59/0.81	       | X4 != cN
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != X3
0.59/0.81	       | X3(sk_Xv(X2, X1))
0.59/0.81	       | X0(sk_Xu(X2, X1))
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['10'])).
0.59/0.81	tff('12', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X5 != X3
0.59/0.81	       | X0 != X4
0.59/0.81	       | cN != X3
0.59/0.81	       | X4 != cN
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != X3
0.59/0.81	       | X5(sk_Xv(X2, X1))
0.59/0.81	       | X0(sk_Xu(X2, X1))
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['11'])).
0.59/0.81	tff('13', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xu(X2, X1))
0.59/0.81	       | X3(sk_Xv(X2, X1))
0.59/0.81	       | X1 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | cN != X2
0.59/0.81	       | X0 != X4
0.59/0.81	       | X3 != X2),
0.59/0.81	    inference('eq_res', [status(thm)], ['12'])).
0.59/0.81	tff('14', plain, ![X0]: (cN(cS(X0)) | ~ cN(X0)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('15', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X3]:
0.59/0.81	      (~ X1(c0)
0.59/0.81	       | X2(sk_Xv(X2, X1))
0.59/0.81	       | ~ X2(cS(sk_Xu(X2, X1)))
0.59/0.81	       | X2(X3)
0.59/0.81	       | ~ cODD(X3)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('16', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
0.59/0.81	      X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (X7 != X2
0.59/0.81	       | X6 != X2
0.59/0.81	       | X5 != X1
0.59/0.81	       | X4 != X2
0.59/0.81	       | ~ X1(c0)
0.59/0.81	       | X2(sk_Xv(X4, X5))
0.59/0.81	       | ~ X6(cS(sk_Xu(X4, X5)))
0.59/0.81	       | X7(X3)
0.59/0.81	       | ~ cODD(X3)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['15'])).
0.59/0.81	tff('17', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cODD(X0)
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | X4 != X5
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != X5
0.59/0.81	       | X1 != X5),
0.59/0.81	    inference('sup-', [status(thm)], ['1', '16'])).
0.59/0.81	tff('18', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != X5
0.59/0.81	       | X2 != X5
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cODD(X0)),
0.59/0.81	    inference('simplify', [status(thm)], ['17'])).
0.59/0.81	tff('19', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | X3 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != X4
0.59/0.81	       | X0 != X4),
0.59/0.81	    inference('sup-', [status(thm)], ['0', '18'])).
0.59/0.81	tff('20', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X0 != X4
0.59/0.81	       | X1 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != X4
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['19'])).
0.59/0.81	tff('21', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | X0(sk_Xv(X3, X2))
0.59/0.81	       | X3 != X0
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != X0),
0.59/0.81	    inference('eq_res', [status(thm)], ['20'])).
0.59/0.81	tff('22', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X4 != X0
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | X3 != X0
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != X0),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['21'])).
0.59/0.81	tff('23', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X0 != X1
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3(sk_Xv(X1, X2))
0.59/0.81	       | ~ X0(cS(sk_Xu(X1, X2)))
0.59/0.81	       | X1(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X3 != X1),
0.59/0.81	    inference('eq_res', [status(thm)], ['22'])).
0.59/0.81	tff('24', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X4 != X1
0.59/0.81	       | X0 != X1
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3(sk_Xv(X1, X2))
0.59/0.81	       | ~ X0(cS(sk_Xu(X1, X2)))
0.59/0.81	       | X4(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X3 != X1),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['23'])).
0.59/0.81	tff('25', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | X2 != X1
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | X2(sk_Xv(X1, X0))
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X3 != X1),
0.59/0.81	    inference('sup-', [status(thm)], ['14', '24'])).
0.59/0.81	tff('26', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X3 != X1
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2(sk_Xv(X1, X0))
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X2 != X1
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['25'])).
0.59/0.81	tff('27', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X3]:
0.59/0.81	      (~ X1(c0)
0.59/0.81	       | ~ X1(cS(sk_Xv(X2, X1)))
0.59/0.81	       | ~ X2(cS(sk_Xu(X2, X1)))
0.59/0.81	       | X2(X3)
0.59/0.81	       | ~ cODD(X3)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('28', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
0.59/0.81	      X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (X7 != X2
0.59/0.81	       | X6 != X2
0.59/0.81	       | X5 != X1
0.59/0.81	       | X4 != X1
0.59/0.81	       | ~ X1(c0)
0.59/0.81	       | ~ X4(cS(sk_Xv(X2, X5)))
0.59/0.81	       | ~ X6(cS(sk_Xu(X2, X5)))
0.59/0.81	       | X7(X3)
0.59/0.81	       | ~ cODD(X3)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['27'])).
0.59/0.81	tff('29', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cODD(X0)
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | ~ X5(cS(sk_Xv(X4, X3)))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != X4
0.59/0.81	       | X1 != X4),
0.59/0.81	    inference('sup-', [status(thm)], ['1', '28'])).
0.59/0.81	tff('30', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != X4
0.59/0.81	       | X2 != X4
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X5(cS(sk_Xv(X4, X3)))
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cODD(X0)),
0.59/0.81	    inference('simplify', [status(thm)], ['29'])).
0.59/0.81	tff('31', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (X6 != X5
0.59/0.81	       | X1 != X4
0.59/0.81	       | X2 != X4
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X6(cS(sk_Xv(X4, X3)))
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cODD(X0)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['30'])).
0.59/0.81	tff('32', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | ~ X4(cS(sk_Xv(X3, X2)))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != X3
0.59/0.81	       | X0 != X3
0.59/0.81	       | X4 != X5),
0.59/0.81	    inference('sup-', [status(thm)], ['0', '31'])).
0.59/0.81	tff('33', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X4 != X5
0.59/0.81	       | X0 != X3
0.59/0.81	       | X1 != X3
0.59/0.81	       | X2 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X4(cS(sk_Xv(X3, X2)))
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['32'])).
0.59/0.81	tff('34', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ X3(cS(sk_Xu(X1, X0)))
0.59/0.81	       | X4 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X3 != X1
0.59/0.81	       | X2 != X1
0.59/0.81	       | cN != X4),
0.59/0.81	    inference('sup-', [status(thm)], ['14', '33'])).
0.59/0.81	tff('35', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X2 != X1
0.59/0.81	       | X3 != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | ~ X3(cS(sk_Xu(X1, X0)))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['34'])).
0.59/0.81	tff('36', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ cN(sk_Xv(X1, X0))
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ X3(cS(sk_Xu(X1, X0)))
0.59/0.81	       | X0 != cN
0.59/0.81	       | X3 != X1
0.59/0.81	       | X2 != X1),
0.59/0.81	    inference('eq_res', [status(thm)], ['35'])).
0.59/0.81	tff('37', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | X2 != X1
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))),
0.59/0.81	    inference('sup-', [status(thm)], ['14', '36'])).
0.59/0.81	tff('38', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (~ cN(sk_Xv(X1, X0))
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X2 != X1
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['37'])).
0.59/0.81	tff('39', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | cN != X1
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X3 != X1
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | X2 != X1
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('sup-', [status(thm)], ['26', '38'])).
0.59/0.81	tff('40', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X2(sk_Xm)
0.59/0.81	       | X2 != X1
0.59/0.81	       | X3 != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | cN != X1
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['39'])).
0.59/0.81	tff('41', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xu(X2, X1))
0.59/0.81	       | cN != X2
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | X1 != cN
0.59/0.81	       | X0 != X2
0.59/0.81	       | X0 != X2),
0.59/0.81	    inference('eq_fact', [status(thm)], ['40'])).
0.59/0.81	tff('42', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (X0 != X2
0.59/0.81	       | X1 != cN
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | cN != X2
0.59/0.81	       | ~ cN(sk_Xu(X2, X1))),
0.59/0.81	    inference('simplify', [status(thm)], ['41'])).
0.59/0.81	tff('43', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X3 != X1
0.59/0.81	       | cN != X4
0.59/0.81	       | cN != X1
0.59/0.81	       | X4 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X3(sk_Xv(X1, X0))
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | cN != X1
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2 != X1),
0.59/0.81	    inference('sup-', [status(thm)], ['13', '42'])).
0.59/0.81	tff('44', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X2 != X1
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X3(sk_Xv(X1, X0))
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | cN != X4
0.59/0.81	       | X3 != X1),
0.59/0.81	    inference('simplify', [status(thm)], ['43'])).
0.59/0.81	tff('45', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X0 != X1
0.59/0.81	       | cN != X2
0.59/0.81	       | cN != X1
0.59/0.81	       | X3 != cN
0.59/0.81	       | X0(sk_Xv(X1, X3))
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | cN != X1),
0.59/0.81	    inference('sup-', [status(thm)], ['44', '9'])).
0.59/0.81	tff('46', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xv(X1, X3))
0.59/0.81	       | X3 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | cN != X2
0.59/0.81	       | X0 != X1),
0.59/0.81	    inference('simplify', [status(thm)], ['45'])).
0.59/0.81	tff('47', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (X0 != X1 | cN != X1 | X2 != cN | X0(sk_Xv(X1, X2)) | cEVEN(sk_Xm)),
0.59/0.81	    inference('eq_res', [status(thm)], ['46'])).
0.59/0.81	tff('48', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X3]:
0.59/0.81	      (~ X1(c0)
0.59/0.81	       | ~ X1(cS(sk_Xv(X2, X1)))
0.59/0.81	       | X1(sk_Xu(X2, X1))
0.59/0.81	       | X2(X3)
0.59/0.81	       | ~ cODD(X3)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('49', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
0.59/0.81	      X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (X7 != X2
0.59/0.81	       | X6 != X1
0.59/0.81	       | X5 != X1
0.59/0.81	       | X4 != X1
0.59/0.81	       | ~ X1(c0)
0.59/0.81	       | ~ X4(cS(sk_Xv(X2, X5)))
0.59/0.81	       | X6(sk_Xu(X2, X5))
0.59/0.81	       | X7(X3)
0.59/0.81	       | ~ cODD(X3)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['48'])).
0.59/0.81	tff('50', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cODD(X0)
0.59/0.81	       | X1(X0)
0.59/0.81	       | X2(sk_Xu(X4, X3))
0.59/0.81	       | ~ X5(cS(sk_Xv(X4, X3)))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != X4),
0.59/0.81	    inference('sup-', [status(thm)], ['1', '49'])).
0.59/0.81	tff('51', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X5(cS(sk_Xv(X4, X3)))
0.59/0.81	       | X2(sk_Xu(X4, X3))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cODD(X0)),
0.59/0.81	    inference('simplify', [status(thm)], ['50'])).
0.59/0.81	tff('52', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (X7 != X2
0.59/0.81	       | X6 != X5
0.59/0.81	       | X1 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X6(cS(sk_Xv(X4, X3)))
0.59/0.81	       | X7(sk_Xu(X4, X3))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cODD(X0)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['51'])).
0.59/0.81	tff('53', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | X1(sk_Xu(X3, X2))
0.59/0.81	       | ~ X4(cS(sk_Xv(X3, X2)))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X6 != cN
0.59/0.81	       | X0 != X3
0.59/0.81	       | X4 != X5
0.59/0.81	       | X1 != X6),
0.59/0.81	    inference('sup-', [status(thm)], ['0', '52'])).
0.59/0.81	tff('54', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (X1 != X6
0.59/0.81	       | X4 != X5
0.59/0.81	       | X0 != X3
0.59/0.81	       | X6 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X4(cS(sk_Xv(X3, X2)))
0.59/0.81	       | X1(sk_Xu(X3, X2))
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['53'])).
0.59/0.81	tff('55', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X3(sk_Xu(X1, X0))
0.59/0.81	       | X4 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X2 != X1
0.59/0.81	       | cN != X4
0.59/0.81	       | X3 != X5),
0.59/0.81	    inference('sup-', [status(thm)], ['14', '54'])).
0.59/0.81	tff('56', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X3 != X5
0.59/0.81	       | X2 != X1
0.59/0.81	       | X5 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | X3(sk_Xu(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['55'])).
0.59/0.81	tff('57', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ cN(sk_Xv(X1, X0))
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X3(sk_Xu(X1, X0))
0.59/0.81	       | X0 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | X2 != X1
0.59/0.81	       | X3 != X4),
0.59/0.81	    inference('eq_res', [status(thm)], ['56'])).
0.59/0.81	tff('58', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | cN != X1
0.59/0.81	       | X2 != X3
0.59/0.81	       | X4 != X1
0.59/0.81	       | X3 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2(sk_Xu(X1, X0))
0.59/0.81	       | X4(sk_Xm)
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('sup-', [status(thm)], ['47', '57'])).
0.59/0.81	tff('59', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X4(sk_Xm)
0.59/0.81	       | X2(sk_Xu(X1, X0))
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X1
0.59/0.81	       | X2 != X3
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['58'])).
0.59/0.81	tff('60', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X2 != X3
0.59/0.81	       | cN != X1
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2(sk_Xu(X1, X0))),
0.59/0.81	    inference('sup-', [status(thm)], ['59', '9'])).
0.59/0.81	tff('61', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X2(sk_Xu(X1, X0))
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != X3
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['60'])).
0.59/0.81	tff('62', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | cN != X3
0.59/0.81	       | X3 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | cEVEN(sk_Xm)
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2 != X1),
0.59/0.81	    inference('sup-', [status(thm)], ['61', '42'])).
0.59/0.81	tff('63', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X2 != X1 | X2(sk_Xm) | cN != X3 | cN != X1 | X0 != cN | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['62'])).
0.59/0.81	tff('64', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (~ $true | cEVEN(sk_Xm) | X0 != cN | cN != X1 | cN != X2 | cN != X1),
0.59/0.81	    inference('sup-', [status(thm)], ['63', '9'])).
0.59/0.81	tff('65', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (cN != X2 | cN != X1 | X0 != cN | cEVEN(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['64'])).
0.59/0.81	tff('66', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o]: (cEVEN(sk_Xm) | cN != X0 | X1 != cN),
0.59/0.81	    inference('condensation', [status(thm)], ['65'])).
0.59/0.81	tff('67', plain, ![X0 : $i > $o]: (cEVEN(sk_Xm) | X0 != cN),
0.59/0.81	    inference('condensation', [status(thm)], ['66'])).
0.59/0.81	tff('68', plain, cEVEN(sk_Xm), inference('eq_res', [status(thm)], ['67'])).
0.59/0.81	tff('69', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X4]:
0.59/0.81	      (~ X1(c0)
0.59/0.81	       | X2(sk_Xv(X2, X1))
0.59/0.81	       | X1(sk_Xu(X2, X1))
0.59/0.81	       | X1(X4)
0.59/0.81	       | ~ cEVEN(X4)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('70', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o, 
0.59/0.81	      X7 : $i > $o, X8 : $i > $o]:
0.59/0.81	      (X8 != X1
0.59/0.81	       | X7 != X1
0.59/0.81	       | X6 != X1
0.59/0.81	       | X5 != X2
0.59/0.81	       | ~ X1(c0)
0.59/0.81	       | X2(sk_Xv(X5, X6))
0.59/0.81	       | X7(sk_Xu(X5, X6))
0.59/0.81	       | X8(X4)
0.59/0.81	       | ~ cEVEN(X4)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['69'])).
0.59/0.81	tff('71', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cEVEN(X0)
0.59/0.81	       | X1(X0)
0.59/0.81	       | X2(sk_Xu(X4, X3))
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | X4 != X5
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != cN),
0.59/0.81	    inference('sup-', [status(thm)], ['1', '70'])).
0.59/0.81	tff('72', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | X2(sk_Xu(X4, X3))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cEVEN(X0)),
0.59/0.81	    inference('simplify', [status(thm)], ['71'])).
0.59/0.81	tff('73', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (X7 != X1
0.59/0.81	       | X6 != X2
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | X6(sk_Xu(X4, X3))
0.59/0.81	       | X7(X0)
0.59/0.81	       | ~ cEVEN(X0)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['72'])).
0.59/0.81	tff('74', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | X1(sk_Xu(X3, X2))
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | X3 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X6 != cN
0.59/0.81	       | X1 != X5
0.59/0.81	       | X0 != X6),
0.59/0.81	    inference('sup-', [status(thm)], ['68', '73'])).
0.59/0.81	tff('75', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (X0 != X6
0.59/0.81	       | X1 != X5
0.59/0.81	       | X6 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != X4
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | X1(sk_Xu(X3, X2))
0.59/0.81	       | X0(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['74'])).
0.59/0.81	tff('76', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X0(sk_Xu(X2, X1))
0.59/0.81	       | X3(sk_Xv(X2, X1))
0.59/0.81	       | X2 != X3
0.59/0.81	       | X1 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X0 != X4
0.59/0.81	       | cN != X5),
0.59/0.81	    inference('sup-', [status(thm)], ['75', '9'])).
0.59/0.81	tff('77', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X0 != X4
0.59/0.81	       | X5 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != X3
0.59/0.81	       | X3(sk_Xv(X2, X1))
0.59/0.81	       | X0(sk_Xu(X2, X1))),
0.59/0.81	    inference('simplify', [status(thm)], ['76'])).
0.59/0.81	tff('78', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X0(sk_Xu(X2, X1))
0.59/0.81	       | X3(sk_Xv(X2, X1))
0.59/0.81	       | X2 != X3
0.59/0.81	       | X1 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | X0 != X4),
0.59/0.81	    inference('eq_res', [status(thm)], ['77'])).
0.59/0.81	tff('79', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X4]:
0.59/0.81	      (~ X1(c0)
0.59/0.81	       | X2(sk_Xv(X2, X1))
0.59/0.81	       | ~ X2(cS(sk_Xu(X2, X1)))
0.59/0.81	       | X1(X4)
0.59/0.81	       | ~ cEVEN(X4)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('80', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o, 
0.59/0.81	      X7 : $i > $o, X8 : $i > $o]:
0.59/0.81	      (X8 != X1
0.59/0.81	       | X7 != X2
0.59/0.81	       | X6 != X1
0.59/0.81	       | X5 != X2
0.59/0.81	       | ~ X1(c0)
0.59/0.81	       | X2(sk_Xv(X5, X6))
0.59/0.81	       | ~ X7(cS(sk_Xu(X5, X6)))
0.59/0.81	       | X8(X4)
0.59/0.81	       | ~ cEVEN(X4)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['79'])).
0.59/0.81	tff('81', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cEVEN(X0)
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | X4 != X5
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != X5
0.59/0.81	       | X1 != cN),
0.59/0.81	    inference('sup-', [status(thm)], ['1', '80'])).
0.59/0.81	tff('82', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != cN
0.59/0.81	       | X2 != X5
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cEVEN(X0)),
0.59/0.81	    inference('simplify', [status(thm)], ['81'])).
0.59/0.81	tff('83', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (X6 != X1
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != X5
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X5(sk_Xv(X4, X3))
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X6(X0)
0.59/0.81	       | ~ cEVEN(X0)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['82'])).
0.59/0.81	tff('84', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | X3 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != X4
0.59/0.81	       | X5 != cN
0.59/0.81	       | X0 != X5),
0.59/0.81	    inference('sup-', [status(thm)], ['68', '83'])).
0.59/0.81	tff('85', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X0 != X5
0.59/0.81	       | X5 != cN
0.59/0.81	       | X1 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != X4
0.59/0.81	       | X4(sk_Xv(X3, X2))
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | X0(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['84'])).
0.59/0.81	tff('86', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X3(sk_Xv(X1, X0))
0.59/0.81	       | X1 != X3
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X3
0.59/0.81	       | X4 != cN
0.59/0.81	       | X2 != X4),
0.59/0.81	    inference('sup-', [status(thm)], ['14', '85'])).
0.59/0.81	tff('87', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X2 != X4
0.59/0.81	       | X4 != cN
0.59/0.81	       | cN != X3
0.59/0.81	       | X0 != cN
0.59/0.81	       | X1 != X3
0.59/0.81	       | X3(sk_Xv(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['86'])).
0.59/0.81	tff('88', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X5 != X3
0.59/0.81	       | X2 != X4
0.59/0.81	       | X4 != cN
0.59/0.81	       | cN != X3
0.59/0.81	       | X0 != cN
0.59/0.81	       | X1 != X3
0.59/0.81	       | X5(sk_Xv(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['87'])).
0.59/0.81	tff('89', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ cN(sk_Xu(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X3(sk_Xv(X1, X0))
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X4 != cN
0.59/0.81	       | X2 != X4
0.59/0.81	       | X3 != X1),
0.59/0.81	    inference('eq_res', [status(thm)], ['88'])).
0.59/0.81	tff('90', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X4]:
0.59/0.81	      (~ X1(c0)
0.59/0.81	       | ~ X1(cS(sk_Xv(X2, X1)))
0.59/0.81	       | ~ X2(cS(sk_Xu(X2, X1)))
0.59/0.81	       | X1(X4)
0.59/0.81	       | ~ cEVEN(X4)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('91', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o, 
0.59/0.81	      X7 : $i > $o, X8 : $i > $o]:
0.59/0.81	      (X8 != X1
0.59/0.81	       | X7 != X2
0.59/0.81	       | X6 != X1
0.59/0.81	       | X5 != X1
0.59/0.81	       | ~ X1(c0)
0.59/0.81	       | ~ X5(cS(sk_Xv(X2, X6)))
0.59/0.81	       | ~ X7(cS(sk_Xu(X2, X6)))
0.59/0.81	       | X8(X4)
0.59/0.81	       | ~ cEVEN(X4)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['90'])).
0.59/0.81	tff('92', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cEVEN(X0)
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | ~ X5(cS(sk_Xv(X4, X3)))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != X4
0.59/0.81	       | X1 != cN),
0.59/0.81	    inference('sup-', [status(thm)], ['1', '91'])).
0.59/0.81	tff('93', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != cN
0.59/0.81	       | X2 != X4
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X5(cS(sk_Xv(X4, X3)))
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cEVEN(X0)),
0.59/0.81	    inference('simplify', [status(thm)], ['92'])).
0.59/0.81	tff('94', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (X7 != X1
0.59/0.81	       | X6 != X5
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != X4
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X6(cS(sk_Xv(X4, X3)))
0.59/0.81	       | ~ X2(cS(sk_Xu(X4, X3)))
0.59/0.81	       | X7(X0)
0.59/0.81	       | ~ cEVEN(X0)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['93'])).
0.59/0.81	tff('95', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | ~ X4(cS(sk_Xv(X3, X2)))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != X3
0.59/0.81	       | X6 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X0 != X6),
0.59/0.81	    inference('sup-', [status(thm)], ['68', '94'])).
0.59/0.81	tff('96', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (X0 != X6
0.59/0.81	       | X4 != X5
0.59/0.81	       | X6 != cN
0.59/0.81	       | X1 != X3
0.59/0.81	       | X2 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X4(cS(sk_Xv(X3, X2)))
0.59/0.81	       | ~ X1(cS(sk_Xu(X3, X2)))
0.59/0.81	       | X0(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['95'])).
0.59/0.81	tff('97', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ X3(cS(sk_Xu(X1, X0)))
0.59/0.81	       | X4 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X3 != X1
0.59/0.81	       | X5 != cN
0.59/0.81	       | cN != X4
0.59/0.81	       | X2 != X5),
0.59/0.81	    inference('sup-', [status(thm)], ['14', '96'])).
0.59/0.81	tff('98', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X2 != X5
0.59/0.81	       | X5 != cN
0.59/0.81	       | X3 != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | ~ X3(cS(sk_Xu(X1, X0)))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['97'])).
0.59/0.81	tff('99', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ cN(sk_Xv(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ X3(cS(sk_Xu(X1, X0)))
0.59/0.81	       | X0 != cN
0.59/0.81	       | X3 != X1
0.59/0.81	       | X4 != cN
0.59/0.81	       | X2 != X4),
0.59/0.81	    inference('eq_res', [status(thm)], ['98'])).
0.59/0.81	tff('100', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | X2 != X3
0.59/0.81	       | X3 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))),
0.59/0.81	    inference('sup-', [status(thm)], ['14', '99'])).
0.59/0.81	tff('101', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ cN(sk_Xv(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != X3
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['100'])).
0.59/0.81	tff('102', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cN != X1
0.59/0.81	       | X4 != X5
0.59/0.81	       | X5 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X4(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | X2 != X3
0.59/0.81	       | X3 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2(sk_Xm)),
0.59/0.81	    inference('sup-', [status(thm)], ['89', '101'])).
0.59/0.81	tff('103', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X2(sk_Xm)
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != X3
0.59/0.81	       | ~ cN(sk_Xu(X1, X0))
0.59/0.81	       | X4(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | cN != X1),
0.59/0.81	    inference('simplify', [status(thm)], ['102'])).
0.59/0.81	tff('104', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cN != X1
0.59/0.81	       | X0 != X2
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xu(X1, X3))
0.59/0.81	       | X0 != X4
0.59/0.81	       | X4 != cN),
0.59/0.81	    inference('eq_fact', [status(thm)], ['103'])).
0.59/0.81	tff('105', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X4 != cN
0.59/0.81	       | X0 != X4
0.59/0.81	       | ~ cN(sk_Xu(X1, X3))
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X0 != X2
0.59/0.81	       | cN != X1),
0.59/0.81	    inference('simplify', [status(thm)], ['104'])).
0.59/0.81	tff('106', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (cN != X0
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xu(X0, X2))
0.59/0.81	       | X1 != X3
0.59/0.81	       | X3 != cN),
0.59/0.81	    inference('eq_res', [status(thm)], ['105'])).
0.59/0.81	tff('107', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X4 != X1
0.59/0.81	       | cN != X0
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X4(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xu(X0, X2))
0.59/0.81	       | X1 != X3
0.59/0.81	       | X3 != cN),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['106'])).
0.59/0.81	tff('108', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X0 != cN
0.59/0.81	       | ~ cN(sk_Xu(X2, X1))
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | X1 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X2
0.59/0.81	       | X3 != X0),
0.59/0.81	    inference('eq_res', [status(thm)], ['107'])).
0.59/0.81	tff('109', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X3 != X0
0.59/0.81	       | cN != X2
0.59/0.81	       | X1 != cN
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xu(X2, X1))
0.59/0.81	       | X0 != cN),
0.59/0.81	    inference('simplify', [status(thm)], ['108'])).
0.59/0.81	tff('110', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cN != X4
0.59/0.81	       | X4 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X1 != X5
0.59/0.81	       | X5(sk_Xv(X1, X0))
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X3 != X2),
0.59/0.81	    inference('sup-', [status(thm)], ['78', '109'])).
0.59/0.81	tff('111', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X3 != X2
0.59/0.81	       | cN != X1
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | X2 != cN
0.59/0.81	       | X5(sk_Xv(X1, X0))
0.59/0.81	       | X1 != X5
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X4),
0.59/0.81	    inference('simplify', [status(thm)], ['110'])).
0.59/0.81	tff('112', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | cN != X0
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != X3
0.59/0.81	       | X3(sk_Xv(X2, X1))
0.59/0.81	       | X4 != cN
0.59/0.81	       | cN != X2
0.59/0.81	       | cN != X4),
0.59/0.81	    inference('sup-', [status(thm)], ['111', '9'])).
0.59/0.81	tff('113', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (cN != X2
0.59/0.81	       | X4 != cN
0.59/0.81	       | X3(sk_Xv(X2, X1))
0.59/0.81	       | X2 != X3
0.59/0.81	       | X1 != cN
0.59/0.81	       | cN != X0),
0.59/0.81	    inference('simplify', [status(thm)], ['112'])).
0.59/0.81	tff('114', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (cN != X0 | X1 != cN | X2 != X3 | X3(sk_Xv(X2, X1)) | cN != X2),
0.59/0.81	    inference('eq_res', [status(thm)], ['113'])).
0.59/0.81	tff('115', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (cN != X0 | X1(sk_Xv(X0, X2)) | X0 != X1 | X2 != cN),
0.59/0.81	    inference('eq_res', [status(thm)], ['114'])).
0.59/0.81	tff('116', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X4]:
0.59/0.81	      (~ X1(c0)
0.59/0.81	       | ~ X1(cS(sk_Xv(X2, X1)))
0.59/0.81	       | X1(sk_Xu(X2, X1))
0.59/0.81	       | X1(X4)
0.59/0.81	       | ~ cEVEN(X4)),
0.59/0.81	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.59/0.81	tff('117', plain,
0.59/0.81	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o, 
0.59/0.81	      X7 : $i > $o, X8 : $i > $o]:
0.59/0.81	      (X8 != X1
0.59/0.81	       | X7 != X1
0.59/0.81	       | X6 != X1
0.59/0.81	       | X5 != X1
0.59/0.81	       | ~ X1(c0)
0.59/0.81	       | ~ X5(cS(sk_Xv(X2, X6)))
0.59/0.81	       | X7(sk_Xu(X2, X6))
0.59/0.81	       | X8(X4)
0.59/0.81	       | ~ cEVEN(X4)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['116'])).
0.59/0.81	tff('118', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cEVEN(X0)
0.59/0.81	       | X1(X0)
0.59/0.81	       | X2(sk_Xu(X4, X3))
0.59/0.81	       | ~ X5(cS(sk_Xv(X4, X3)))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X1 != cN),
0.59/0.81	    inference('sup-', [status(thm)], ['1', '117'])).
0.59/0.81	tff('119', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X1 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X5(cS(sk_Xv(X4, X3)))
0.59/0.81	       | X2(sk_Xu(X4, X3))
0.59/0.81	       | X1(X0)
0.59/0.81	       | ~ cEVEN(X0)),
0.59/0.81	    inference('simplify', [status(thm)], ['118'])).
0.59/0.81	tff('120', plain,
0.59/0.81	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o, X8 : $i > $o]:
0.59/0.81	      (X8 != X1
0.59/0.81	       | X7 != X2
0.59/0.81	       | X6 != X5
0.59/0.81	       | X1 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X6(cS(sk_Xv(X4, X3)))
0.59/0.81	       | X7(sk_Xu(X4, X3))
0.59/0.81	       | X8(X0)
0.59/0.81	       | ~ cEVEN(X0)),
0.59/0.81	    inference('ho.purify_applied_variable', [status(thm)], ['119'])).
0.59/0.81	tff('121', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X0(sk_Xm)
0.59/0.81	       | X1(sk_Xu(X3, X2))
0.59/0.81	       | ~ X4(cS(sk_Xv(X3, X2)))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X6 != cN
0.59/0.81	       | X7 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X1 != X6
0.59/0.81	       | X0 != X7),
0.59/0.81	    inference('sup-', [status(thm)], ['68', '120'])).
0.59/0.81	tff('122', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
0.59/0.81	      (X0 != X7
0.59/0.81	       | X1 != X6
0.59/0.81	       | X4 != X5
0.59/0.81	       | X7 != cN
0.59/0.81	       | X6 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | ~ X4(cS(sk_Xv(X3, X2)))
0.59/0.81	       | X1(sk_Xu(X3, X2))
0.59/0.81	       | X0(sk_Xm)),
0.59/0.81	    inference('simplify', [status(thm)], ['121'])).
0.59/0.81	tff('123', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X3(sk_Xu(X1, X0))
0.59/0.81	       | X4 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X6 != cN
0.59/0.81	       | cN != X4
0.59/0.81	       | X3 != X5
0.59/0.81	       | X2 != X6),
0.59/0.81	    inference('sup-', [status(thm)], ['14', '122'])).
0.59/0.81	tff('124', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o, X6 : $i > $o]:
0.59/0.81	      (X2 != X6
0.59/0.81	       | X3 != X5
0.59/0.81	       | X6 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | X3(sk_Xu(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | ~ cN(sk_Xv(X1, X0))),
0.59/0.81	    inference('simplify', [status(thm)], ['123'])).
0.59/0.81	tff('125', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ cN(sk_Xv(X1, X0))
0.59/0.81	       | X2(sk_Xm)
0.59/0.81	       | X3(sk_Xu(X1, X0))
0.59/0.81	       | X0 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X3 != X4
0.59/0.81	       | X2 != X5),
0.59/0.81	    inference('eq_res', [status(thm)], ['124'])).
0.59/0.81	tff('126', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X0 != cN
0.59/0.81	       | X1 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X2 != X3
0.59/0.81	       | X4 != X5
0.59/0.81	       | X3 != cN
0.59/0.81	       | X5 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X4(sk_Xu(X1, X0))
0.59/0.81	       | X2(sk_Xm)),
0.59/0.81	    inference('sup-', [status(thm)], ['115', '125'])).
0.59/0.81	tff('127', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
0.59/0.81	      X5 : $i > $o]:
0.59/0.81	      (X2(sk_Xm)
0.59/0.81	       | X4(sk_Xu(X1, X0))
0.59/0.81	       | X5 != cN
0.59/0.81	       | X3 != cN
0.59/0.81	       | X4 != X5
0.59/0.81	       | X2 != X3
0.59/0.81	       | X1 != cN
0.59/0.81	       | X0 != cN),
0.59/0.81	    inference('simplify', [status(thm)], ['126'])).
0.59/0.81	tff('128', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X0 != cN
0.59/0.81	       | X1 != cN
0.59/0.81	       | cN != X2
0.59/0.81	       | X3 != X4
0.59/0.81	       | X2 != cN
0.59/0.81	       | X4 != cN
0.59/0.81	       | X3(sk_Xu(X1, X0))),
0.59/0.81	    inference('sup-', [status(thm)], ['127', '9'])).
0.59/0.81	tff('129', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X3(sk_Xu(X1, X0))
0.59/0.81	       | X4 != cN
0.59/0.81	       | X3 != X4
0.59/0.81	       | cN != X2
0.59/0.81	       | X1 != cN
0.59/0.81	       | X0 != cN),
0.59/0.81	    inference('simplify', [status(thm)], ['128'])).
0.59/0.81	tff('130', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X0 != cN | X1 != cN | X2 != X3 | X3 != cN | X2(sk_Xu(X1, X0))),
0.59/0.81	    inference('eq_res', [status(thm)], ['129'])).
0.59/0.81	tff('131', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (~ $true
0.59/0.81	       | X4 != cN
0.59/0.81	       | cN != X4
0.59/0.81	       | X1 != cN
0.59/0.81	       | X0 != cN
0.59/0.81	       | X2 != cN
0.59/0.81	       | X3(sk_Xm)
0.59/0.81	       | X0 != cN
0.59/0.81	       | cN != X1
0.59/0.81	       | X3 != X2),
0.59/0.81	    inference('sup-', [status(thm)], ['130', '109'])).
0.59/0.81	tff('132', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
0.59/0.81	      (X3 != X2 | X3(sk_Xm) | X2 != cN | X0 != cN | X1 != cN | X4 != cN),
0.59/0.81	    inference('simplify', [status(thm)], ['131'])).
0.59/0.81	tff('133', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (~ $true | X0 != cN | X1 != cN | X2 != cN | X3 != cN | cN != X3),
0.59/0.81	    inference('sup-', [status(thm)], ['132', '9'])).
0.59/0.81	tff('134', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
0.59/0.81	      (X3 != cN | X2 != cN | X1 != cN | X0 != cN),
0.59/0.81	    inference('simplify', [status(thm)], ['133'])).
0.59/0.81	tff('135', plain,
0.59/0.81	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
0.59/0.81	      (X0 != cN | X1 != cN | X2 != cN),
0.59/0.81	    inference('eq_res', [status(thm)], ['134'])).
0.59/0.81	tff('136', plain, ![X0 : $i > $o, X1 : $i > $o]: (X0 != cN | X1 != cN),
0.59/0.81	    inference('condensation', [status(thm)], ['135'])).
0.59/0.81	tff('137', plain, ![X0 : $i > $o]: X0 != cN,
0.59/0.81	    inference('condensation', [status(thm)], ['136'])).
0.59/0.81	tff('138', plain, $false, inference('eq_res', [status(thm)], ['137'])).
0.59/0.81	
0.59/0.81	% SZS output end Refutation
0.59/0.81	EOF
