0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n143.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 07:31:08 CST 2018
11.29/11.48	% done 3952 iterations in 11.280s
11.29/11.48	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
11.29/11.48	% SZS output start Refutation
11.29/11.49	tff(cTHM623_pme, conjecture,
11.29/11.49	  (((![Xn]: (cN(Xn) => cN(cS(Xn)))) & cN(c0) & 
11.29/11.49	    (![Xp:($i > $o),Xq:($i > $o)]:
11.29/11.49	       (((![Xv]: (Xq(Xv) => Xp(cS(Xv)))) & (![Xu]: (Xp(Xu) => Xq(cS(Xu)))) & 
11.29/11.49	         Xp(c0)) =>
11.29/11.49	        ((![Xx]: (cODD(Xx) => Xq(Xx))) & (![Xx]: (cEVEN(Xx) => Xp(Xx))))))) =>
11.29/11.49	   (![Xm]: ((cODD(Xm) | cEVEN(Xm)) => cN(Xm))))).
11.29/11.49	tff(zf_stmt_0, negated_conjecture,
11.29/11.49	  (~
11.29/11.49	    (((![Xn]: (cN(Xn) => cN(cS(Xn)))) & cN(c0) & 
11.29/11.49	      (![Xp:($i > $o),Xq:($i > $o)]:
11.29/11.49	         (((![Xv]: (Xq(Xv) => Xp(cS(Xv)))) & 
11.29/11.49	           (![Xu]: (Xp(Xu) => Xq(cS(Xu)))) & Xp(c0)) =>
11.29/11.49	          ((![Xx]: (cODD(Xx) => Xq(Xx))) & (![Xx]: (cEVEN(Xx) => Xp(Xx))))))) =>
11.29/11.49	     (![Xm]: ((cODD(Xm) | cEVEN(Xm)) => cN(Xm)))))).
11.29/11.49	tff('0', plain, (cODD(sk_Xm) | cEVEN(sk_Xm)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('1', plain, cN(c0), inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('2', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X3]:
11.29/11.49	      (~ X1(c0) | X2(sk_Xv(X2, X1)) | X1(sk_Xu(X2, X1)) | X2(X3) | ~ cODD(X3)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('3', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
11.29/11.49	      X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (X7 != X2
11.29/11.49	       | X6 != X1
11.29/11.49	       | X5 != X1
11.29/11.49	       | X4 != X2
11.29/11.49	       | ~ X1(c0)
11.29/11.49	       | X2(sk_Xv(X4, X5))
11.29/11.49	       | X6(sk_Xu(X4, X5))
11.29/11.49	       | X7(X3)
11.29/11.49	       | ~ cODD(X3)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['2'])).
11.29/11.49	tff('4', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cODD(X0)
11.29/11.49	       | X1(X0)
11.29/11.49	       | X2(sk_Xu(X4, X3))
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | X4 != X5
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != X5),
11.29/11.49	    inference('sup-', [status(thm)], ['1', '3'])).
11.29/11.49	tff('5', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != X5
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | X2(sk_Xu(X4, X3))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cODD(X0)),
11.29/11.49	    inference('simplify', [status(thm)], ['4'])).
11.29/11.49	tff('6', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (X6 != X2
11.29/11.49	       | X1 != X5
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | X6(sk_Xu(X4, X3))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cODD(X0)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['5'])).
11.29/11.49	tff('7', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | X1(sk_Xu(X3, X2))
11.29/11.49	       | X4(sk_Xv(X3, X2))
11.29/11.49	       | X3 != X4
11.29/11.49	       | X2 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | X0 != X4
11.29/11.49	       | X1 != X5),
11.29/11.49	    inference('sup-', [status(thm)], ['0', '6'])).
11.29/11.49	tff('8', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != X5
11.29/11.49	       | X0 != X4
11.29/11.49	       | X5 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != X4
11.29/11.49	       | X4(sk_Xv(X3, X2))
11.29/11.49	       | X1(sk_Xu(X3, X2))
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['7'])).
11.29/11.49	tff('9', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (cEVEN(sk_Xm)
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | X1(sk_Xu(X2, cN))
11.29/11.49	       | X3(sk_Xv(X2, cN))
11.29/11.49	       | X2 != X3
11.29/11.49	       | X4 != cN
11.29/11.49	       | X0 != X3
11.29/11.49	       | X1 != X4),
11.29/11.49	    inference('eq_res', [status(thm)], ['8'])).
11.29/11.49	tff('10', plain, ~ cN(sk_Xm), inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('11', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X0 != X1
11.29/11.49	       | cN != X2
11.29/11.49	       | X1 != cN
11.29/11.49	       | X3 != X2
11.29/11.49	       | X2(sk_Xv(X3, cN))
11.29/11.49	       | X0(sk_Xu(X3, cN))
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('sup-', [status(thm)], ['9', '10'])).
11.29/11.49	tff('12', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (cEVEN(sk_Xm)
11.29/11.49	       | X0(sk_Xu(X3, cN))
11.29/11.49	       | X2(sk_Xv(X3, cN))
11.29/11.49	       | X3 != X2
11.29/11.49	       | X1 != cN
11.29/11.49	       | cN != X2
11.29/11.49	       | X0 != X1),
11.29/11.49	    inference('simplify', [status(thm)], ['11'])).
11.29/11.49	tff('13', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X4 != X2
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X0(sk_Xu(X3, cN))
11.29/11.49	       | X2(sk_Xv(X3, cN))
11.29/11.49	       | X3 != X2
11.29/11.49	       | X1 != cN
11.29/11.49	       | cN != X4
11.29/11.49	       | X0 != X1),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['12'])).
11.29/11.49	tff('14', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X0 != X1
11.29/11.49	       | cN != X2
11.29/11.49	       | X1 != cN
11.29/11.49	       | X3 != X2
11.29/11.49	       | X2(sk_Xv(X3, cN))
11.29/11.49	       | X0(sk_Xu(X3, cN))
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('eq_res', [status(thm)], ['13'])).
11.29/11.49	tff('15', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X4 != X2
11.29/11.49	       | X0 != X1
11.29/11.49	       | cN != X2
11.29/11.49	       | X1 != cN
11.29/11.49	       | X3 != X2
11.29/11.49	       | X4(sk_Xv(X3, cN))
11.29/11.49	       | X0(sk_Xu(X3, cN))
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['14'])).
11.29/11.49	tff('16', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (cEVEN(sk_Xm)
11.29/11.49	       | X0(sk_Xu(X1, cN))
11.29/11.49	       | X2(sk_Xv(X1, cN))
11.29/11.49	       | X3 != cN
11.29/11.49	       | cN != X1
11.29/11.49	       | X0 != X3
11.29/11.49	       | X2 != X1),
11.29/11.49	    inference('eq_res', [status(thm)], ['15'])).
11.29/11.49	tff('17', plain, ![X0]: (cN(cS(X0)) | ~ cN(X0)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('18', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X3]:
11.29/11.49	      (~ X1(c0)
11.29/11.49	       | X2(sk_Xv(X2, X1))
11.29/11.49	       | ~ X2(cS(sk_Xu(X2, X1)))
11.29/11.49	       | X2(X3)
11.29/11.49	       | ~ cODD(X3)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('19', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
11.29/11.49	      X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (X7 != X2
11.29/11.49	       | X6 != X2
11.29/11.49	       | X5 != X1
11.29/11.49	       | X4 != X2
11.29/11.49	       | ~ X1(c0)
11.29/11.49	       | X2(sk_Xv(X4, X5))
11.29/11.49	       | ~ X6(cS(sk_Xu(X4, X5)))
11.29/11.49	       | X7(X3)
11.29/11.49	       | ~ cODD(X3)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['18'])).
11.29/11.49	tff('20', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cODD(X0)
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | X4 != X5
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != X5
11.29/11.49	       | X1 != X5),
11.29/11.49	    inference('sup-', [status(thm)], ['1', '19'])).
11.29/11.49	tff('21', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != X5
11.29/11.49	       | X2 != X5
11.29/11.49	       | X3 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cODD(X0)),
11.29/11.49	    inference('simplify', [status(thm)], ['20'])).
11.29/11.49	tff('22', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | ~ X1(cS(sk_Xu(X3, X2)))
11.29/11.49	       | X4(sk_Xv(X3, X2))
11.29/11.49	       | X3 != X4
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != X4
11.29/11.49	       | X0 != X4),
11.29/11.49	    inference('sup-', [status(thm)], ['0', '21'])).
11.29/11.49	tff('23', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X0 != X4
11.29/11.49	       | X1 != X4
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != X4
11.29/11.49	       | X4(sk_Xv(X3, X2))
11.29/11.49	       | ~ X1(cS(sk_Xu(X3, X2)))
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['22'])).
11.29/11.49	tff('24', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | ~ X0(cS(sk_Xu(X2, X1)))
11.29/11.49	       | X3(sk_Xv(X2, X1))
11.29/11.49	       | X2 != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X0 != X3
11.29/11.49	       | cN != X3),
11.29/11.49	    inference('sup-', [status(thm)], ['23', '10'])).
11.29/11.49	tff('25', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (cN != X3
11.29/11.49	       | X0 != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != X3
11.29/11.49	       | X3(sk_Xv(X2, X1))
11.29/11.49	       | ~ X0(cS(sk_Xu(X2, X1)))
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['24'])).
11.29/11.49	tff('26', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X4 != X3
11.29/11.49	       | cN != X3
11.29/11.49	       | X0 != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != X3
11.29/11.49	       | X4(sk_Xv(X2, X1))
11.29/11.49	       | ~ X0(cS(sk_Xu(X2, X1)))
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['25'])).
11.29/11.49	tff('27', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cN(sk_Xu(X1, X0))
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X2(sk_Xv(X1, X0))
11.29/11.49	       | X1 != X3
11.29/11.49	       | X0 != cN
11.29/11.49	       | cN != X3
11.29/11.49	       | cN != X3
11.29/11.49	       | X2 != X3),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '26'])).
11.29/11.49	tff('28', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X2 != X3
11.29/11.49	       | cN != X3
11.29/11.49	       | X0 != cN
11.29/11.49	       | X1 != X3
11.29/11.49	       | X2(sk_Xv(X1, X0))
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | ~ cN(sk_Xu(X1, X0))),
11.29/11.49	    inference('simplify', [status(thm)], ['27'])).
11.29/11.49	tff('29', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ cN(sk_Xu(X1, X0))
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X2(sk_Xv(X1, X0))
11.29/11.49	       | X0 != cN
11.29/11.49	       | cN != X1
11.29/11.49	       | X2 != X1),
11.29/11.49	    inference('eq_res', [status(thm)], ['28'])).
11.29/11.49	tff('30', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X2 != X0
11.29/11.49	       | cN != X3
11.29/11.49	       | cN != X0
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2(sk_Xv(X0, cN))
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X1 != X0
11.29/11.49	       | cN != X0
11.29/11.49	       | cN != cN
11.29/11.49	       | X1(sk_Xv(X0, cN))
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('sup-', [status(thm)], ['16', '29'])).
11.29/11.49	tff('31', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X1(sk_Xv(X0, cN))
11.29/11.49	       | X1 != X0
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X2(sk_Xv(X0, cN))
11.29/11.49	       | cN != X0
11.29/11.49	       | cN != X3
11.29/11.49	       | X2 != X0),
11.29/11.49	    inference('simplify', [status(thm)], ['30'])).
11.29/11.49	tff('32', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X0 != X1
11.29/11.49	       | cN != X2
11.29/11.49	       | cN != X1
11.29/11.49	       | X0(sk_Xv(X1, cN))
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X0 != X1),
11.29/11.49	    inference('eq_fact', [status(thm)], ['31'])).
11.29/11.49	tff('33', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (cEVEN(sk_Xm) | X0(sk_Xv(X1, cN)) | cN != X1 | cN != X2 | X0 != X1),
11.29/11.49	    inference('simplify', [status(thm)], ['32'])).
11.29/11.49	tff('34', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]:
11.29/11.49	      (cEVEN(sk_Xm) | X0(sk_Xv(X1, cN)) | X0 != X1 | cN != X1),
11.29/11.49	    inference('condensation', [status(thm)], ['33'])).
11.29/11.49	tff('35', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X3]:
11.29/11.49	      (~ X1(c0)
11.29/11.49	       | ~ X1(cS(sk_Xv(X2, X1)))
11.29/11.49	       | X1(sk_Xu(X2, X1))
11.29/11.49	       | X2(X3)
11.29/11.49	       | ~ cODD(X3)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('36', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
11.29/11.49	      X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (X7 != X2
11.29/11.49	       | X6 != X1
11.29/11.49	       | X5 != X1
11.29/11.49	       | X4 != X1
11.29/11.49	       | ~ X1(c0)
11.29/11.49	       | ~ X4(cS(sk_Xv(X2, X5)))
11.29/11.49	       | X6(sk_Xu(X2, X5))
11.29/11.49	       | X7(X3)
11.29/11.49	       | ~ cODD(X3)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['35'])).
11.29/11.49	tff('37', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cODD(X0)
11.29/11.49	       | X1(X0)
11.29/11.49	       | X2(sk_Xu(X4, X3))
11.29/11.49	       | ~ X5(cS(sk_Xv(X4, X3)))
11.29/11.49	       | X5 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != X4),
11.29/11.49	    inference('sup-', [status(thm)], ['1', '36'])).
11.29/11.49	tff('38', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != X4
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X5(cS(sk_Xv(X4, X3)))
11.29/11.49	       | X2(sk_Xu(X4, X3))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cODD(X0)),
11.29/11.49	    inference('simplify', [status(thm)], ['37'])).
11.29/11.49	tff('39', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (X7 != X2
11.29/11.49	       | X6 != X5
11.29/11.49	       | X1 != X4
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X6(cS(sk_Xv(X4, X3)))
11.29/11.49	       | X7(sk_Xu(X4, X3))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cODD(X0)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['38'])).
11.29/11.49	tff('40', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | X1(sk_Xu(X3, X2))
11.29/11.49	       | ~ X4(cS(sk_Xv(X3, X2)))
11.29/11.49	       | X5 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X6 != cN
11.29/11.49	       | X0 != X3
11.29/11.49	       | X4 != X5
11.29/11.49	       | X1 != X6),
11.29/11.49	    inference('sup-', [status(thm)], ['0', '39'])).
11.29/11.49	tff('41', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (X1 != X6
11.29/11.49	       | X4 != X5
11.29/11.49	       | X0 != X3
11.29/11.49	       | X6 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X4(cS(sk_Xv(X3, X2)))
11.29/11.49	       | X1(sk_Xu(X3, X2))
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['40'])).
11.29/11.49	tff('42', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X3]:
11.29/11.49	      (~ X1(c0)
11.29/11.49	       | ~ X1(cS(sk_Xv(X2, X1)))
11.29/11.49	       | ~ X2(cS(sk_Xu(X2, X1)))
11.29/11.49	       | X2(X3)
11.29/11.49	       | ~ cODD(X3)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('43', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X3, X4 : $i > $o, X5 : $i > $o, 
11.29/11.49	      X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (X7 != X2
11.29/11.49	       | X6 != X2
11.29/11.49	       | X5 != X1
11.29/11.49	       | X4 != X1
11.29/11.49	       | ~ X1(c0)
11.29/11.49	       | ~ X4(cS(sk_Xv(X2, X5)))
11.29/11.49	       | ~ X6(cS(sk_Xu(X2, X5)))
11.29/11.49	       | X7(X3)
11.29/11.49	       | ~ cODD(X3)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['42'])).
11.29/11.49	tff('44', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cODD(X0)
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | ~ X5(cS(sk_Xv(X4, X3)))
11.29/11.49	       | X5 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != X4
11.29/11.49	       | X1 != X4),
11.29/11.49	    inference('sup-', [status(thm)], ['1', '43'])).
11.29/11.49	tff('45', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != X4
11.29/11.49	       | X2 != X4
11.29/11.49	       | X3 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X5(cS(sk_Xv(X4, X3)))
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cODD(X0)),
11.29/11.49	    inference('simplify', [status(thm)], ['44'])).
11.29/11.49	tff('46', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (X6 != X5
11.29/11.49	       | X1 != X4
11.29/11.49	       | X2 != X4
11.29/11.49	       | X3 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X6(cS(sk_Xv(X4, X3)))
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cODD(X0)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['45'])).
11.29/11.49	tff('47', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | ~ X1(cS(sk_Xu(X3, X2)))
11.29/11.49	       | ~ X4(cS(sk_Xv(X3, X2)))
11.29/11.49	       | X5 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != X3
11.29/11.49	       | X0 != X3
11.29/11.49	       | X4 != X5),
11.29/11.49	    inference('sup-', [status(thm)], ['0', '46'])).
11.29/11.49	tff('48', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X4 != X5
11.29/11.49	       | X0 != X3
11.29/11.49	       | X1 != X3
11.29/11.49	       | X2 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X4(cS(sk_Xv(X3, X2)))
11.29/11.49	       | ~ X1(cS(sk_Xu(X3, X2)))
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['47'])).
11.29/11.49	tff('49', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cN(sk_Xv(X1, X0))
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X2(sk_Xm)
11.29/11.49	       | ~ X3(cS(sk_Xu(X1, X0)))
11.29/11.49	       | X4 != cN
11.29/11.49	       | X0 != cN
11.29/11.49	       | X3 != X1
11.29/11.49	       | X2 != X1
11.29/11.49	       | cN != X4),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '48'])).
11.29/11.49	tff('50', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X2 != X1
11.29/11.49	       | X3 != X1
11.29/11.49	       | X0 != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | ~ X3(cS(sk_Xu(X1, X0)))
11.29/11.49	       | X2(sk_Xm)
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | ~ cN(sk_Xv(X1, X0))),
11.29/11.49	    inference('simplify', [status(thm)], ['49'])).
11.29/11.49	tff('51', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cN != X0
11.29/11.49	       | cN != X0
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X1(sk_Xm)
11.29/11.49	       | ~ X2(cS(sk_Xu(X0, cN)))
11.29/11.49	       | X3 != cN
11.29/11.49	       | cN != cN
11.29/11.49	       | X2 != X0
11.29/11.49	       | X1 != X0),
11.29/11.49	    inference('sup-', [status(thm)], ['34', '50'])).
11.29/11.49	tff('52', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X1 != X0
11.29/11.49	       | X2 != X0
11.29/11.49	       | X3 != cN
11.29/11.49	       | ~ X2(cS(sk_Xu(X0, cN)))
11.29/11.49	       | X1(sk_Xm)
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | cN != X0),
11.29/11.49	    inference('simplify', [status(thm)], ['51'])).
11.29/11.49	tff('53', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cN != X0
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | ~ X1(cS(sk_Xu(X0, cN)))
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != X0
11.29/11.49	       | cN != X0),
11.29/11.49	    inference('sup-', [status(thm)], ['52', '10'])).
11.29/11.49	tff('54', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (X1 != X0
11.29/11.49	       | X2 != cN
11.29/11.49	       | ~ X1(cS(sk_Xu(X0, cN)))
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | cN != X0),
11.29/11.49	    inference('simplify', [status(thm)], ['53'])).
11.29/11.49	tff('55', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]:
11.29/11.49	      (X0 != X1 | cN != X1 | ~ X0(cS(sk_Xu(X1, cN))) | cEVEN(sk_Xm)),
11.29/11.49	    inference('condensation', [status(thm)], ['54'])).
11.29/11.49	tff('56', plain,
11.29/11.49	    ![X0 : $i > $o]:
11.29/11.49	      (~ $true | ~ cN(sk_Xu(X0, cN)) | cEVEN(sk_Xm) | cN != X0 | cN != X0),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '55'])).
11.29/11.49	tff('57', plain,
11.29/11.49	    ![X0 : $i > $o]: (cN != X0 | cEVEN(sk_Xm) | ~ cN(sk_Xu(X0, cN))),
11.29/11.49	    inference('simplify', [status(thm)], ['56'])).
11.29/11.49	tff('58', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X1(sk_Xm)
11.29/11.49	       | ~ X2(cS(sk_Xv(X0, cN)))
11.29/11.49	       | X3 != cN
11.29/11.49	       | cN != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | X1 != X0
11.29/11.49	       | X2 != X3
11.29/11.49	       | cN != X4
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | cN != X0),
11.29/11.49	    inference('sup-', [status(thm)], ['41', '57'])).
11.29/11.49	tff('59', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (cN != X0
11.29/11.49	       | X2 != X3
11.29/11.49	       | X1 != X0
11.29/11.49	       | X4 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | ~ X2(cS(sk_Xv(X0, cN)))
11.29/11.49	       | X1(sk_Xm)
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['58'])).
11.29/11.49	tff('60', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | ~ X0(cS(sk_Xv(X1, cN)))
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | cN != X1
11.29/11.49	       | X0 != X2
11.29/11.49	       | cN != X1),
11.29/11.49	    inference('sup-', [status(thm)], ['59', '10'])).
11.29/11.49	tff('61', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X0 != X2
11.29/11.49	       | cN != X1
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | ~ X0(cS(sk_Xv(X1, cN)))
11.29/11.49	       | cEVEN(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['60'])).
11.29/11.49	tff('62', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cN(sk_Xv(X0, cN))
11.29/11.49	       | cEVEN(sk_Xm)
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | cN != X0
11.29/11.49	       | cN != X1),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '61'])).
11.29/11.49	tff('63', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (cN != X0 | X2 != cN | X1 != cN | cEVEN(sk_Xm) | ~ cN(sk_Xv(X0, cN))),
11.29/11.49	    inference('simplify', [status(thm)], ['62'])).
11.29/11.49	tff('64', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]:
11.29/11.49	      (cN != X0 | ~ cN(sk_Xv(X0, cN)) | X1 != cN | cEVEN(sk_Xm)),
11.29/11.49	    inference('condensation', [status(thm)], ['63'])).
11.29/11.49	tff('65', plain,
11.29/11.49	    ![X0 : $i > $o]: (cEVEN(sk_Xm) | ~ cN(sk_Xv(X0, cN)) | X0 != cN),
11.29/11.49	    inference('condensation', [status(thm)], ['64'])).
11.29/11.49	tff('66', plain,
11.29/11.49	    ![X0 : $i > $o]:
11.29/11.49	      (~ $true | cN != X0 | cN != X0 | cEVEN(sk_Xm) | X0 != cN | cEVEN(sk_Xm)),
11.29/11.49	    inference('sup-', [status(thm)], ['34', '65'])).
11.29/11.49	tff('67', plain, ![X0 : $i > $o]: (cEVEN(sk_Xm) | cN != X0),
11.29/11.49	    inference('simplify', [status(thm)], ['66'])).
11.29/11.49	tff('68', plain, cEVEN(sk_Xm), inference('eq_res', [status(thm)], ['67'])).
11.29/11.49	tff('69', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X4]:
11.29/11.49	      (~ X1(c0)
11.29/11.49	       | X2(sk_Xv(X2, X1))
11.29/11.49	       | X1(sk_Xu(X2, X1))
11.29/11.49	       | X1(X4)
11.29/11.49	       | ~ cEVEN(X4)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('70', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o, 
11.29/11.49	      X7 : $i > $o, X8 : $i > $o]:
11.29/11.49	      (X8 != X1
11.29/11.49	       | X7 != X1
11.29/11.49	       | X6 != X1
11.29/11.49	       | X5 != X2
11.29/11.49	       | ~ X1(c0)
11.29/11.49	       | X2(sk_Xv(X5, X6))
11.29/11.49	       | X7(sk_Xu(X5, X6))
11.29/11.49	       | X8(X4)
11.29/11.49	       | ~ cEVEN(X4)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['69'])).
11.29/11.49	tff('71', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cEVEN(X0)
11.29/11.49	       | X1(X0)
11.29/11.49	       | X2(sk_Xu(X4, X3))
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | X4 != X5
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['1', '70'])).
11.29/11.49	tff('72', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | X2(sk_Xu(X4, X3))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cEVEN(X0)),
11.29/11.49	    inference('simplify', [status(thm)], ['71'])).
11.29/11.49	tff('73', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (X7 != X1
11.29/11.49	       | X6 != X2
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | X6(sk_Xu(X4, X3))
11.29/11.49	       | X7(X0)
11.29/11.49	       | ~ cEVEN(X0)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['72'])).
11.29/11.49	tff('74', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | X1(sk_Xu(X3, X2))
11.29/11.49	       | X4(sk_Xv(X3, X2))
11.29/11.49	       | X3 != X4
11.29/11.49	       | X2 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | X6 != cN
11.29/11.49	       | X1 != X5
11.29/11.49	       | X0 != X6),
11.29/11.49	    inference('sup-', [status(thm)], ['68', '73'])).
11.29/11.49	tff('75', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (X0 != X6
11.29/11.49	       | X1 != X5
11.29/11.49	       | X6 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != X4
11.29/11.49	       | X4(sk_Xv(X3, X2))
11.29/11.49	       | X1(sk_Xu(X3, X2))
11.29/11.49	       | X0(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['74'])).
11.29/11.49	tff('76', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X0(sk_Xu(X2, X1))
11.29/11.49	       | X3(sk_Xv(X2, X1))
11.29/11.49	       | X2 != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | X0 != X4
11.29/11.49	       | cN != X5),
11.29/11.49	    inference('sup-', [status(thm)], ['75', '10'])).
11.29/11.49	tff('77', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X0 != X4
11.29/11.49	       | X5 != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != X3
11.29/11.49	       | X3(sk_Xv(X2, X1))
11.29/11.49	       | X0(sk_Xu(X2, X1))),
11.29/11.49	    inference('simplify', [status(thm)], ['76'])).
11.29/11.49	tff('78', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X0(sk_Xu(X2, X1))
11.29/11.49	       | X3(sk_Xv(X2, X1))
11.29/11.49	       | X2 != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | X0 != X4),
11.29/11.49	    inference('eq_res', [status(thm)], ['77'])).
11.29/11.49	tff('79', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X4]:
11.29/11.49	      (~ X1(c0)
11.29/11.49	       | X2(sk_Xv(X2, X1))
11.29/11.49	       | ~ X2(cS(sk_Xu(X2, X1)))
11.29/11.49	       | X1(X4)
11.29/11.49	       | ~ cEVEN(X4)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('80', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o, 
11.29/11.49	      X7 : $i > $o, X8 : $i > $o]:
11.29/11.49	      (X8 != X1
11.29/11.49	       | X7 != X2
11.29/11.49	       | X6 != X1
11.29/11.49	       | X5 != X2
11.29/11.49	       | ~ X1(c0)
11.29/11.49	       | X2(sk_Xv(X5, X6))
11.29/11.49	       | ~ X7(cS(sk_Xu(X5, X6)))
11.29/11.49	       | X8(X4)
11.29/11.49	       | ~ cEVEN(X4)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['79'])).
11.29/11.49	tff('81', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cEVEN(X0)
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | X4 != X5
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != X5
11.29/11.49	       | X1 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['1', '80'])).
11.29/11.49	tff('82', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != cN
11.29/11.49	       | X2 != X5
11.29/11.49	       | X3 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cEVEN(X0)),
11.29/11.49	    inference('simplify', [status(thm)], ['81'])).
11.29/11.49	tff('83', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (X6 != X1
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != X5
11.29/11.49	       | X3 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X5(sk_Xv(X4, X3))
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X6(X0)
11.29/11.49	       | ~ cEVEN(X0)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['82'])).
11.29/11.49	tff('84', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | ~ X1(cS(sk_Xu(X3, X2)))
11.29/11.49	       | X4(sk_Xv(X3, X2))
11.29/11.49	       | X3 != X4
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != X4
11.29/11.49	       | X5 != cN
11.29/11.49	       | X0 != X5),
11.29/11.49	    inference('sup-', [status(thm)], ['68', '83'])).
11.29/11.49	tff('85', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X0 != X5
11.29/11.49	       | X5 != cN
11.29/11.49	       | X1 != X4
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != X4
11.29/11.49	       | X4(sk_Xv(X3, X2))
11.29/11.49	       | ~ X1(cS(sk_Xu(X3, X2)))
11.29/11.49	       | X0(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['84'])).
11.29/11.49	tff('86', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ X0(cS(sk_Xu(X2, X1)))
11.29/11.49	       | X3(sk_Xv(X2, X1))
11.29/11.49	       | X2 != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X0 != X3
11.29/11.49	       | X4 != cN
11.29/11.49	       | cN != X4),
11.29/11.49	    inference('sup-', [status(thm)], ['85', '10'])).
11.29/11.49	tff('87', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X4 != cN
11.29/11.49	       | X0 != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != X3
11.29/11.49	       | X3(sk_Xv(X2, X1))
11.29/11.49	       | ~ X0(cS(sk_Xu(X2, X1)))),
11.29/11.49	    inference('simplify', [status(thm)], ['86'])).
11.29/11.49	tff('88', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ X0(cS(sk_Xu(X2, X1)))
11.29/11.49	       | X3(sk_Xv(X2, X1))
11.29/11.49	       | X2 != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X0 != X3),
11.29/11.49	    inference('eq_res', [status(thm)], ['87'])).
11.29/11.49	tff('89', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cN(sk_Xu(X1, X0))
11.29/11.49	       | cN != X2
11.29/11.49	       | X0 != cN
11.29/11.49	       | X1 != X2
11.29/11.49	       | X2(sk_Xv(X1, X0))),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '88'])).
11.29/11.49	tff('90', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (X2(sk_Xv(X1, X0))
11.29/11.49	       | X1 != X2
11.29/11.49	       | X0 != cN
11.29/11.49	       | cN != X2
11.29/11.49	       | ~ cN(sk_Xu(X1, X0))),
11.29/11.49	    inference('simplify', [status(thm)], ['89'])).
11.29/11.49	tff('91', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X3 != X2
11.29/11.49	       | X2(sk_Xv(X1, X0))
11.29/11.49	       | X1 != X2
11.29/11.49	       | X0 != cN
11.29/11.49	       | cN != X3
11.29/11.49	       | ~ cN(sk_Xu(X1, X0))),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['90'])).
11.29/11.49	tff('92', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ cN(sk_Xu(X1, X0))
11.29/11.49	       | cN != X2
11.29/11.49	       | X0 != cN
11.29/11.49	       | X1 != X2
11.29/11.49	       | X2(sk_Xv(X1, X0))),
11.29/11.49	    inference('eq_res', [status(thm)], ['91'])).
11.29/11.49	tff('93', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X3 != X2
11.29/11.49	       | ~ cN(sk_Xu(X1, X0))
11.29/11.49	       | cN != X2
11.29/11.49	       | X0 != cN
11.29/11.49	       | X1 != X2
11.29/11.49	       | X3(sk_Xv(X1, X0))),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['92'])).
11.29/11.49	tff('94', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (X0(sk_Xv(X2, X1))
11.29/11.49	       | X1 != cN
11.29/11.49	       | cN != X2
11.29/11.49	       | ~ cN(sk_Xu(X2, X1))
11.29/11.49	       | X0 != X2),
11.29/11.49	    inference('eq_res', [status(thm)], ['93'])).
11.29/11.49	tff('95', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cN != X3
11.29/11.49	       | X3 != cN
11.29/11.49	       | X0 != cN
11.29/11.49	       | X1 != X4
11.29/11.49	       | X4(sk_Xv(X1, X0))
11.29/11.49	       | X2 != X1
11.29/11.49	       | cN != X1
11.29/11.49	       | X0 != cN
11.29/11.49	       | X2(sk_Xv(X1, X0))),
11.29/11.49	    inference('sup-', [status(thm)], ['78', '94'])).
11.29/11.49	tff('96', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X2(sk_Xv(X1, X0))
11.29/11.49	       | cN != X1
11.29/11.49	       | X2 != X1
11.29/11.49	       | X4(sk_Xv(X1, X0))
11.29/11.49	       | X1 != X4
11.29/11.49	       | X0 != cN
11.29/11.49	       | cN != X3),
11.29/11.49	    inference('simplify', [status(thm)], ['95'])).
11.29/11.49	tff('97', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cN != X3
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != X0
11.29/11.49	       | X0(sk_Xv(X2, X1))
11.29/11.49	       | X0 != X2
11.29/11.49	       | cN != X2),
11.29/11.49	    inference('eq_fact', [status(thm)], ['96'])).
11.29/11.49	tff('98', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (cN != X2 | X0(sk_Xv(X2, X1)) | X2 != X0 | X1 != cN | cN != X3),
11.29/11.49	    inference('simplify', [status(thm)], ['97'])).
11.29/11.49	tff('99', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (X0 != cN | X1 != X2 | X2(sk_Xv(X1, X0)) | cN != X1),
11.29/11.49	    inference('eq_res', [status(thm)], ['98'])).
11.29/11.49	tff('100', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X4]:
11.29/11.49	      (~ X1(c0)
11.29/11.49	       | ~ X1(cS(sk_Xv(X2, X1)))
11.29/11.49	       | X1(sk_Xu(X2, X1))
11.29/11.49	       | X1(X4)
11.29/11.49	       | ~ cEVEN(X4)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('101', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o, 
11.29/11.49	      X7 : $i > $o, X8 : $i > $o]:
11.29/11.49	      (X8 != X1
11.29/11.49	       | X7 != X1
11.29/11.49	       | X6 != X1
11.29/11.49	       | X5 != X1
11.29/11.49	       | ~ X1(c0)
11.29/11.49	       | ~ X5(cS(sk_Xv(X2, X6)))
11.29/11.49	       | X7(sk_Xu(X2, X6))
11.29/11.49	       | X8(X4)
11.29/11.49	       | ~ cEVEN(X4)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['100'])).
11.29/11.49	tff('102', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cEVEN(X0)
11.29/11.49	       | X1(X0)
11.29/11.49	       | X2(sk_Xu(X4, X3))
11.29/11.49	       | ~ X5(cS(sk_Xv(X4, X3)))
11.29/11.49	       | X5 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['1', '101'])).
11.29/11.49	tff('103', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X5(cS(sk_Xv(X4, X3)))
11.29/11.49	       | X2(sk_Xu(X4, X3))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cEVEN(X0)),
11.29/11.49	    inference('simplify', [status(thm)], ['102'])).
11.29/11.49	tff('104', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o, X8 : $i > $o]:
11.29/11.49	      (X8 != X1
11.29/11.49	       | X7 != X2
11.29/11.49	       | X6 != X5
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X6(cS(sk_Xv(X4, X3)))
11.29/11.49	       | X7(sk_Xu(X4, X3))
11.29/11.49	       | X8(X0)
11.29/11.49	       | ~ cEVEN(X0)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['103'])).
11.29/11.49	tff('105', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | X1(sk_Xu(X3, X2))
11.29/11.49	       | ~ X4(cS(sk_Xv(X3, X2)))
11.29/11.49	       | X5 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X6 != cN
11.29/11.49	       | X7 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X1 != X6
11.29/11.49	       | X0 != X7),
11.29/11.49	    inference('sup-', [status(thm)], ['68', '104'])).
11.29/11.49	tff('106', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (X0 != X7
11.29/11.49	       | X1 != X6
11.29/11.49	       | X4 != X5
11.29/11.49	       | X7 != cN
11.29/11.49	       | X6 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X4(cS(sk_Xv(X3, X2)))
11.29/11.49	       | X1(sk_Xu(X3, X2))
11.29/11.49	       | X0(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['105'])).
11.29/11.49	tff('107', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (X0 != X1 | X2 != X1 | X1(sk_Xv(X2, cN)) | ~ X0(cS(sk_Xu(X2, cN)))),
11.29/11.49	    inference('eq_res', [status(thm)], ['88'])).
11.29/11.49	tff('108', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cN(sk_Xu(X0, cN))
11.29/11.49	       | X1(sk_Xv(X0, cN))
11.29/11.49	       | X0 != X1
11.29/11.49	       | cN != X1),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '107'])).
11.29/11.49	tff('109', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]:
11.29/11.49	      (cN != X1 | X0 != X1 | X1(sk_Xv(X0, cN)) | ~ cN(sk_Xu(X0, cN))),
11.29/11.49	    inference('simplify', [status(thm)], ['108'])).
11.29/11.49	tff('110', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (X2 != X1
11.29/11.49	       | cN != X1
11.29/11.49	       | X0 != X1
11.29/11.49	       | X2(sk_Xv(X0, cN))
11.29/11.49	       | ~ cN(sk_Xu(X0, cN))),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['109'])).
11.29/11.49	tff('111', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]:
11.29/11.49	      (~ cN(sk_Xu(X0, cN)) | X1(sk_Xv(X0, cN)) | cN != X0 | X1 != X0),
11.29/11.49	    inference('eq_res', [status(thm)], ['110'])).
11.29/11.49	tff('112', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cN != X2
11.29/11.49	       | X2 != cN
11.29/11.49	       | cN != cN
11.29/11.49	       | X0 != X3
11.29/11.49	       | X3(sk_Xv(X0, cN))
11.29/11.49	       | X1 != X0
11.29/11.49	       | cN != X0
11.29/11.49	       | X1(sk_Xv(X0, cN))),
11.29/11.49	    inference('sup-', [status(thm)], ['78', '111'])).
11.29/11.49	tff('113', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X1(sk_Xv(X0, cN))
11.29/11.49	       | cN != X0
11.29/11.49	       | X1 != X0
11.29/11.49	       | X3(sk_Xv(X0, cN))
11.29/11.49	       | X0 != X3
11.29/11.49	       | cN != X2),
11.29/11.49	    inference('simplify', [status(thm)], ['112'])).
11.29/11.49	tff('114', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | cN != X2
11.29/11.49	       | X1 != X0
11.29/11.49	       | X0(sk_Xv(X1, cN))
11.29/11.49	       | X0 != X1
11.29/11.49	       | cN != X1),
11.29/11.49	    inference('eq_fact', [status(thm)], ['113'])).
11.29/11.49	tff('115', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (cN != X1 | X0(sk_Xv(X1, cN)) | X1 != X0 | cN != X2),
11.29/11.49	    inference('simplify', [status(thm)], ['114'])).
11.29/11.49	tff('116', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]: (cN != X0 | X1(sk_Xv(X0, cN)) | X0 != X1),
11.29/11.49	    inference('condensation', [status(thm)], ['115'])).
11.29/11.49	tff('117', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X4]:
11.29/11.49	      (~ X1(c0)
11.29/11.49	       | ~ X1(cS(sk_Xv(X2, X1)))
11.29/11.49	       | ~ X2(cS(sk_Xu(X2, X1)))
11.29/11.49	       | X1(X4)
11.29/11.49	       | ~ cEVEN(X4)),
11.29/11.49	    inference('cnf', [status(esa)], [zf_stmt_0])).
11.29/11.49	tff('118', plain,
11.29/11.49	    ![X1 : $i > $o, X2 : $i > $o, X4, X5 : $i > $o, X6 : $i > $o, 
11.29/11.49	      X7 : $i > $o, X8 : $i > $o]:
11.29/11.49	      (X8 != X1
11.29/11.49	       | X7 != X2
11.29/11.49	       | X6 != X1
11.29/11.49	       | X5 != X1
11.29/11.49	       | ~ X1(c0)
11.29/11.49	       | ~ X5(cS(sk_Xv(X2, X6)))
11.29/11.49	       | ~ X7(cS(sk_Xu(X2, X6)))
11.29/11.49	       | X8(X4)
11.29/11.49	       | ~ cEVEN(X4)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['117'])).
11.29/11.49	tff('119', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cEVEN(X0)
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | ~ X5(cS(sk_Xv(X4, X3)))
11.29/11.49	       | X5 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != X4
11.29/11.49	       | X1 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['1', '118'])).
11.29/11.49	tff('120', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X1 != cN
11.29/11.49	       | X2 != X4
11.29/11.49	       | X3 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X5(cS(sk_Xv(X4, X3)))
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X1(X0)
11.29/11.49	       | ~ cEVEN(X0)),
11.29/11.49	    inference('simplify', [status(thm)], ['119'])).
11.29/11.49	tff('121', plain,
11.29/11.49	    ![X0, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o, X7 : $i > $o]:
11.29/11.49	      (X7 != X1
11.29/11.49	       | X6 != X5
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != X4
11.29/11.49	       | X3 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X6(cS(sk_Xv(X4, X3)))
11.29/11.49	       | ~ X2(cS(sk_Xu(X4, X3)))
11.29/11.49	       | X7(X0)
11.29/11.49	       | ~ cEVEN(X0)),
11.29/11.49	    inference('ho.purify_applied_variable', [status(thm)], ['120'])).
11.29/11.49	tff('122', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X0(sk_Xm)
11.29/11.49	       | ~ X1(cS(sk_Xu(X3, X2)))
11.29/11.49	       | ~ X4(cS(sk_Xv(X3, X2)))
11.29/11.49	       | X5 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X1 != X3
11.29/11.49	       | X6 != cN
11.29/11.49	       | X4 != X5
11.29/11.49	       | X0 != X6),
11.29/11.49	    inference('sup-', [status(thm)], ['68', '121'])).
11.29/11.49	tff('123', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o, X6 : $i > $o]:
11.29/11.49	      (X0 != X6
11.29/11.49	       | X4 != X5
11.29/11.49	       | X6 != cN
11.29/11.49	       | X1 != X3
11.29/11.49	       | X2 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | ~ X4(cS(sk_Xv(X3, X2)))
11.29/11.49	       | ~ X1(cS(sk_Xu(X3, X2)))
11.29/11.49	       | X0(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['122'])).
11.29/11.49	tff('124', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ X0(cS(sk_Xu(X2, X1)))
11.29/11.49	       | ~ X3(cS(sk_Xv(X2, X1)))
11.29/11.49	       | X4 != cN
11.29/11.49	       | X1 != cN
11.29/11.49	       | X0 != X2
11.29/11.49	       | X5 != cN
11.29/11.49	       | X3 != X4
11.29/11.49	       | cN != X5),
11.29/11.49	    inference('sup-', [status(thm)], ['123', '10'])).
11.29/11.49	tff('125', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X3 != X4
11.29/11.49	       | X5 != cN
11.29/11.49	       | X0 != X2
11.29/11.49	       | X1 != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | ~ X3(cS(sk_Xv(X2, X1)))
11.29/11.49	       | ~ X0(cS(sk_Xu(X2, X1)))),
11.29/11.49	    inference('simplify', [status(thm)], ['124'])).
11.29/11.49	tff('126', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cN(sk_Xv(X1, X0))
11.29/11.49	       | ~ X2(cS(sk_Xu(X1, X0)))
11.29/11.49	       | X3 != cN
11.29/11.49	       | X0 != cN
11.29/11.49	       | X2 != X1
11.29/11.49	       | X4 != cN
11.29/11.49	       | cN != X3),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '125'])).
11.29/11.49	tff('127', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X4 != cN
11.29/11.49	       | X2 != X1
11.29/11.49	       | X0 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | ~ X2(cS(sk_Xu(X1, X0)))
11.29/11.49	       | ~ cN(sk_Xv(X1, X0))),
11.29/11.49	    inference('simplify', [status(thm)], ['126'])).
11.29/11.49	tff('128', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X0 != cN
11.29/11.49	       | cN != X0
11.29/11.49	       | ~ X1(cS(sk_Xu(X0, cN)))
11.29/11.49	       | X2 != cN
11.29/11.49	       | cN != cN
11.29/11.49	       | X1 != X0
11.29/11.49	       | X3 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['116', '127'])).
11.29/11.49	tff('129', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X3 != cN | X1 != X0 | X2 != cN | ~ X1(cS(sk_Xu(X0, cN))) | X0 != cN),
11.29/11.49	    inference('simplify', [status(thm)], ['128'])).
11.29/11.49	tff('130', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cN(sk_Xu(X0, cN))
11.29/11.49	       | X0 != cN
11.29/11.49	       | X1 != cN
11.29/11.49	       | cN != X0
11.29/11.49	       | X2 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '129'])).
11.29/11.49	tff('131', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (X2 != cN | X1 != cN | X0 != cN | ~ cN(sk_Xu(X0, cN))),
11.29/11.49	    inference('simplify', [status(thm)], ['130'])).
11.29/11.49	tff('132', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]:
11.29/11.49	      (~ cN(sk_Xu(X0, cN)) | X1 != cN | X0 != cN),
11.29/11.49	    inference('condensation', [status(thm)], ['131'])).
11.29/11.49	tff('133', plain, ![X0 : $i > $o]: (~ cN(sk_Xu(X0, cN)) | X0 != cN),
11.29/11.49	    inference('condensation', [status(thm)], ['132'])).
11.29/11.49	tff('134', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | X1(sk_Xm)
11.29/11.49	       | ~ X2(cS(sk_Xv(X0, cN)))
11.29/11.49	       | X3 != cN
11.29/11.49	       | cN != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | X5 != cN
11.29/11.49	       | X2 != X3
11.29/11.49	       | cN != X4
11.29/11.49	       | X1 != X5
11.29/11.49	       | X0 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['106', '133'])).
11.29/11.49	tff('135', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o, 
11.29/11.49	      X5 : $i > $o]:
11.29/11.49	      (X0 != cN
11.29/11.49	       | X1 != X5
11.29/11.49	       | X2 != X3
11.29/11.49	       | X5 != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | ~ X2(cS(sk_Xv(X0, cN)))
11.29/11.49	       | X1(sk_Xm)),
11.29/11.49	    inference('simplify', [status(thm)], ['134'])).
11.29/11.49	tff('136', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ X0(cS(sk_Xv(X1, cN)))
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X4 != cN
11.29/11.49	       | X0 != X2
11.29/11.49	       | cN != X4
11.29/11.49	       | X1 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['135', '10'])).
11.29/11.49	tff('137', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o, X4 : $i > $o]:
11.29/11.49	      (X1 != cN
11.29/11.49	       | X0 != X2
11.29/11.49	       | X4 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | ~ X0(cS(sk_Xv(X1, cN)))),
11.29/11.49	    inference('simplify', [status(thm)], ['136'])).
11.29/11.49	tff('138', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (~ $true
11.29/11.49	       | ~ cN(sk_Xv(X0, cN))
11.29/11.49	       | X1 != cN
11.29/11.49	       | X2 != cN
11.29/11.49	       | X3 != cN
11.29/11.49	       | cN != X1
11.29/11.49	       | X0 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['17', '137'])).
11.29/11.49	tff('139', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o, X3 : $i > $o]:
11.29/11.49	      (X0 != cN | X3 != cN | X2 != cN | X1 != cN | ~ cN(sk_Xv(X0, cN))),
11.29/11.49	    inference('simplify', [status(thm)], ['138'])).
11.29/11.49	tff('140', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o, X2 : $i > $o]:
11.29/11.49	      (~ cN(sk_Xv(X0, cN)) | X1 != cN | X2 != cN | X0 != cN),
11.29/11.49	    inference('eq_res', [status(thm)], ['139'])).
11.29/11.49	tff('141', plain,
11.29/11.49	    ![X0 : $i > $o, X1 : $i > $o]:
11.29/11.49	      (~ cN(sk_Xv(X0, cN)) | X0 != cN | X1 != cN),
11.29/11.49	    inference('condensation', [status(thm)], ['140'])).
11.29/11.49	tff('142', plain, ![X0 : $i > $o]: (~ cN(sk_Xv(X0, cN)) | X0 != cN),
11.29/11.49	    inference('condensation', [status(thm)], ['141'])).
11.29/11.49	tff('143', plain,
11.29/11.49	    ![X0 : $i > $o]: (~ $true | cN != X0 | X0 != cN | cN != cN | X0 != cN),
11.29/11.49	    inference('sup-', [status(thm)], ['99', '142'])).
11.29/11.49	tff('144', plain, ![X0 : $i > $o]: cN != X0,
11.29/11.49	    inference('simplify', [status(thm)], ['143'])).
11.29/11.49	tff('145', plain, $false, inference('eq_res', [status(thm)], ['144'])).
11.29/11.49	
11.29/11.49	% SZS output end Refutation
11.29/11.49	EOF
