0.00/0.00	% File    : /export/starexec/sandbox2/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   : n066.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 17:51:38 CST 2018
133.70/133.90	% done 6794 iterations in 133.699s
133.70/133.90	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
133.70/133.90	% SZS output start Refutation
133.70/133.90	tff(cTHM150_pme, conjecture,
133.70/133.90	  (![Xr:((a * a) > $o),Xx:a,Xy:a,Xz:a]:
133.70/133.90	     (((![Xq:(a > $o)]:
133.70/133.90	          (((![Xu:a,Xv:a]: ((Xr(Xu,Xv) & Xq(Xu)) => Xq(Xv))) & 
133.70/133.90	            (![Xw:a]: (Xr(Xy,Xw) => Xq(Xw)))) =>
133.70/133.90	           Xq(Xz))) & 
133.70/133.90	       (![Xq:(a > $o)]:
133.70/133.90	          (((![Xu:a,Xv:a]: ((Xr(Xu,Xv) & Xq(Xu)) => Xq(Xv))) & 
133.70/133.90	            (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
133.70/133.90	           Xq(Xy)))) =>
133.70/133.90	      (![Xq:(a > $o)]:
133.70/133.90	         (((![Xu:a,Xv:a]: ((Xr(Xu,Xv) & Xq(Xu)) => Xq(Xv))) & 
133.70/133.90	           (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
133.70/133.90	          Xq(Xz)))))).
133.70/133.90	tff(zf_stmt_0, negated_conjecture,
133.70/133.90	  (~
133.70/133.90	    (![Xr:((a * a) > $o),Xx:a,Xy:a,Xz:a]:
133.70/133.90	       (((![Xq:(a > $o)]:
133.70/133.90	            (((![Xu:a,Xv:a]: ((Xr(Xu,Xv) & Xq(Xu)) => Xq(Xv))) & 
133.70/133.90	              (![Xw:a]: (Xr(Xy,Xw) => Xq(Xw)))) =>
133.70/133.90	             Xq(Xz))) & 
133.70/133.90	         (![Xq:(a > $o)]:
133.70/133.90	            (((![Xu:a,Xv:a]: ((Xr(Xu,Xv) & Xq(Xu)) => Xq(Xv))) & 
133.70/133.90	              (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
133.70/133.90	             Xq(Xy)))) =>
133.70/133.90	        (![Xq:(a > $o)]:
133.70/133.90	           (((![Xu:a,Xv:a]: ((Xr(Xu,Xv) & Xq(Xu)) => Xq(Xv))) & 
133.70/133.91	             (![Xw:a]: (Xr(Xx,Xw) => Xq(Xw)))) =>
133.70/133.91	            Xq(Xz))))))).
133.70/133.91	tff('0', plain,
133.70/133.91	    ![X4 : a > $o]:
133.70/133.91	      (X4(sk_Xy) | sk_Xr(sk_Xx, sk_Xw(X4)) | sk_Xr(sk_Xu(X4), sk_Xv(X4))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('1', plain,
133.70/133.91	    ![X4 : a > $o, X5 : a > $o]:
133.70/133.91	      (X5 != X4
133.70/133.91	       | X4(sk_Xy)
133.70/133.91	       | sk_Xr(sk_Xx, sk_Xw(X5))
133.70/133.91	       | sk_Xr(sk_Xu(X5), sk_Xv(X5))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['0'])).
133.70/133.91	tff('2', plain,
133.70/133.91	    ![X0 : a, X1 : a]: (~ sk_Xq(X0) | ~ sk_Xr(X0, X1) | sk_Xq(X1)),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('3', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | sk_Xr(sk_Xx, sk_Xw(X0))
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | X0 != X1
133.70/133.91	       | sk_Xq(sk_Xv(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu(X0))),
133.70/133.91	    inference('sup-', [status(thm)], ['1', '2'])).
133.70/133.91	tff('4', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ sk_Xq(sk_Xu(X0))
133.70/133.91	       | sk_Xq(sk_Xv(X0))
133.70/133.91	       | X0 != X1
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | sk_Xr(sk_Xx, sk_Xw(X0))),
133.70/133.91	    inference('simplify', [status(thm)], ['3'])).
133.70/133.91	tff('5', plain, ![X2 : a]: (sk_Xq(X2) | ~ sk_Xr(sk_Xx, X2)),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('6', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | X0 != X1
133.70/133.91	       | sk_Xq(sk_Xv(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu(X0))
133.70/133.91	       | sk_Xq(sk_Xw(X0))),
133.70/133.91	    inference('sup-', [status(thm)], ['4', '5'])).
133.70/133.91	tff('7', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (sk_Xq(sk_Xw(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu(X0))
133.70/133.91	       | sk_Xq(sk_Xv(X0))
133.70/133.91	       | X0 != X1
133.70/133.91	       | X1(sk_Xy)),
133.70/133.91	    inference('simplify', [status(thm)], ['6'])).
133.70/133.91	tff('8', plain,
133.70/133.91	    ![X4 : a > $o]: (X4(sk_Xy) | sk_Xr(sk_Xx, sk_Xw(X4)) | ~ X4(sk_Xv(X4))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('9', plain,
133.70/133.91	    ![X4 : a > $o, X5 : a > $o, X6 : a > $o]:
133.70/133.91	      (X6 != X4
133.70/133.91	       | X5 != X4
133.70/133.91	       | X4(sk_Xy)
133.70/133.91	       | sk_Xr(sk_Xx, sk_Xw(X5))
133.70/133.91	       | ~ X6(sk_Xv(X5))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['8'])).
133.70/133.91	tff('10', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | ~ X1(sk_Xv(X0))
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | X0 != X2
133.70/133.91	       | X1 != X2
133.70/133.91	       | sk_Xq(sk_Xw(X0))),
133.70/133.91	    inference('sup-', [status(thm)], ['9', '5'])).
133.70/133.91	tff('11', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (sk_Xq(sk_Xw(X0)) | X1 != X2 | X0 != X2 | X2(sk_Xy) | ~ X1(sk_Xv(X0))),
133.70/133.91	    inference('simplify', [status(thm)], ['10'])).
133.70/133.91	tff('12', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ X0(sk_Xv(X1)) | X1(sk_Xy) | X0 != X1 | sk_Xq(sk_Xw(X1))),
133.70/133.91	    inference('eq_res', [status(thm)], ['11'])).
133.70/133.91	tff('13', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X2 != X1 | ~ X0(sk_Xv(X1)) | X2(sk_Xy) | X0 != X1 | sk_Xq(sk_Xw(X1))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['12'])).
133.70/133.91	tff('14', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | X0 != X2
133.70/133.91	       | ~ sk_Xq(sk_Xu(X0))
133.70/133.91	       | sk_Xq(sk_Xw(X0))
133.70/133.91	       | sk_Xq(sk_Xw(X0))
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['7', '13'])).
133.70/133.91	tff('15', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X1 != X0
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | sk_Xq(sk_Xw(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu(X0))
133.70/133.91	       | X0 != X2
133.70/133.91	       | X2(sk_Xy)),
133.70/133.91	    inference('simplify', [status(thm)], ['14'])).
133.70/133.91	tff('16', plain,
133.70/133.91	    ![X4 : a > $o]: (X4(sk_Xy) | sk_Xr(sk_Xx, sk_Xw(X4)) | X4(sk_Xu(X4))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('17', plain,
133.70/133.91	    ![X4 : a > $o, X5 : a > $o, X6 : a > $o]:
133.70/133.91	      (X6 != X4
133.70/133.91	       | X5 != X4
133.70/133.91	       | X4(sk_Xy)
133.70/133.91	       | sk_Xr(sk_Xx, sk_Xw(X5))
133.70/133.91	       | X6(sk_Xu(X5))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['16'])).
133.70/133.91	tff('18', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X1(sk_Xu(X0))
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | X0 != X2
133.70/133.91	       | X1 != X2
133.70/133.91	       | sk_Xq(sk_Xw(X0))),
133.70/133.91	    inference('sup-', [status(thm)], ['17', '5'])).
133.70/133.91	tff('19', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (sk_Xq(sk_Xw(X0)) | X1 != X2 | X0 != X2 | X2(sk_Xy) | X1(sk_Xu(X0))),
133.70/133.91	    inference('simplify', [status(thm)], ['18'])).
133.70/133.91	tff('20', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (X0(sk_Xu(X1)) | X1(sk_Xy) | X0 != X1 | sk_Xq(sk_Xw(X1))),
133.70/133.91	    inference('eq_res', [status(thm)], ['19'])).
133.70/133.91	tff('21', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X2 != X1 | X0(sk_Xu(X1)) | X2(sk_Xy) | X0 != X1 | sk_Xq(sk_Xw(X1))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['20'])).
133.70/133.91	tff('22', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X2(sk_Xy)
133.70/133.91	       | X0 != X2
133.70/133.91	       | sk_Xq(sk_Xw(X0))
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('clc', [status(thm)], ['15', '21'])).
133.70/133.91	tff('23', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X0 != X1
133.70/133.91	       | X0(sk_Xy)
133.70/133.91	       | sk_Xq != X1
133.70/133.91	       | sk_Xq(sk_Xw(X1))
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('eq_fact', [status(thm)], ['22'])).
133.70/133.91	tff('24', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (sk_Xq(sk_Xw(X1)) | sk_Xq != X1 | X0(sk_Xy) | X0 != X1),
133.70/133.91	    inference('simplify', [status(thm)], ['23'])).
133.70/133.91	tff('25', plain,
133.70/133.91	    ![X4 : a > $o]:
133.70/133.91	      (X4(sk_Xy) | ~ X4(sk_Xw(X4)) | sk_Xr(sk_Xu(X4), sk_Xv(X4))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('26', plain,
133.70/133.91	    ![X4 : a > $o, X5 : a > $o, X6 : a > $o]:
133.70/133.91	      (X6 != X4
133.70/133.91	       | X5 != X4
133.70/133.91	       | X4(sk_Xy)
133.70/133.91	       | ~ X5(sk_Xw(X6))
133.70/133.91	       | sk_Xr(sk_Xu(X6), sk_Xv(X6))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['25'])).
133.70/133.91	tff('27', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | ~ X1(sk_Xw(X0))
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | X1 != X2
133.70/133.91	       | X0 != X2
133.70/133.91	       | sk_Xq(sk_Xv(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu(X0))),
133.70/133.91	    inference('sup-', [status(thm)], ['26', '2'])).
133.70/133.91	tff('28', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ sk_Xq(sk_Xu(X0))
133.70/133.91	       | sk_Xq(sk_Xv(X0))
133.70/133.91	       | X0 != X2
133.70/133.91	       | X1 != X2
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | ~ X1(sk_Xw(X0))),
133.70/133.91	    inference('simplify', [status(thm)], ['27'])).
133.70/133.91	tff('29', plain,
133.70/133.91	    ![X4 : a > $o]: (X4(sk_Xy) | ~ X4(sk_Xw(X4)) | ~ X4(sk_Xv(X4))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('30', plain,
133.70/133.91	    ![X4 : a > $o, X5 : a > $o, X6 : a > $o, X7 : a > $o]:
133.70/133.91	      (X7 != X4
133.70/133.91	       | X6 != X4
133.70/133.91	       | X5 != X4
133.70/133.91	       | X4(sk_Xy)
133.70/133.91	       | ~ X5(sk_Xw(X6))
133.70/133.91	       | ~ X7(sk_Xv(X6))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['29'])).
133.70/133.91	tff('31', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ X0(sk_Xv(X1)) | ~ X2(sk_Xw(X1)) | X1(sk_Xy) | X2 != X1 | X0 != X1),
133.70/133.91	    inference('eq_res', [status(thm)], ['30'])).
133.70/133.91	tff('32', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (X3 != X1
133.70/133.91	       | ~ X0(sk_Xv(X1))
133.70/133.91	       | ~ X2(sk_Xw(X1))
133.70/133.91	       | X3(sk_Xy)
133.70/133.91	       | X2 != X1
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['31'])).
133.70/133.91	tff('33', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X3 != X0
133.70/133.91	       | X3(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X1 != X0
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | ~ X1(sk_Xv(X0))
133.70/133.91	       | X2 != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['24', '32'])).
133.70/133.91	tff('34', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (X2 != X0
133.70/133.91	       | ~ X1(sk_Xv(X0))
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | X1 != X0
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X3(sk_Xy)
133.70/133.91	       | X3 != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['33'])).
133.70/133.91	tff('35', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X0 != X1
133.70/133.91	       | X0(sk_Xy)
133.70/133.91	       | sk_Xq != X1
133.70/133.91	       | X2 != X1
133.70/133.91	       | ~ X2(sk_Xv(X1))
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('eq_fact', [status(thm)], ['34'])).
133.70/133.91	tff('36', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ X2(sk_Xv(X1)) | X2 != X1 | sk_Xq != X1 | X0(sk_Xy) | X0 != X1),
133.70/133.91	    inference('simplify', [status(thm)], ['35'])).
133.70/133.91	tff('37', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | ~ X2(sk_Xw(X0))
133.70/133.91	       | X3(sk_Xy)
133.70/133.91	       | X2 != X3
133.70/133.91	       | X0 != X3
133.70/133.91	       | ~ sk_Xq(sk_Xu(X0))
133.70/133.91	       | X1 != X0
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | sk_Xq != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['28', '36'])).
133.70/133.91	tff('38', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (sk_Xq != X0
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | X1 != X0
133.70/133.91	       | ~ sk_Xq(sk_Xu(X0))
133.70/133.91	       | X0 != X3
133.70/133.91	       | X2 != X3
133.70/133.91	       | X3(sk_Xy)
133.70/133.91	       | ~ X2(sk_Xw(X0))),
133.70/133.91	    inference('simplify', [status(thm)], ['37'])).
133.70/133.91	tff('39', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | ~ X1(sk_Xw(X2))
133.70/133.91	       | X0(sk_Xy)
133.70/133.91	       | X1 != X0
133.70/133.91	       | X2 != X0
133.70/133.91	       | ~ sk_Xq(sk_Xu(X2))
133.70/133.91	       | X0 != X2
133.70/133.91	       | sk_Xq != X2),
133.70/133.91	    inference('eq_fact', [status(thm)], ['38'])).
133.70/133.91	tff('40', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (sk_Xq != X2
133.70/133.91	       | ~ sk_Xq(sk_Xu(X2))
133.70/133.91	       | X2 != X0
133.70/133.91	       | X1 != X0
133.70/133.91	       | X0(sk_Xy)
133.70/133.91	       | ~ X1(sk_Xw(X2))),
133.70/133.91	    inference('simplify', [status(thm)], ['39'])).
133.70/133.91	tff('41', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ X0(sk_Xw(X1))
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | X0 != X1
133.70/133.91	       | ~ sk_Xq(sk_Xu(X1))
133.70/133.91	       | sk_Xq != X1),
133.70/133.91	    inference('eq_res', [status(thm)], ['40'])).
133.70/133.91	tff('42', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X2 != X1
133.70/133.91	       | ~ X0(sk_Xw(X1))
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | X0 != X1
133.70/133.91	       | ~ sk_Xq(sk_Xu(X1))
133.70/133.91	       | sk_Xq != X1),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['41'])).
133.70/133.91	tff('43', plain,
133.70/133.91	    ![X4 : a > $o]: (X4(sk_Xy) | ~ X4(sk_Xw(X4)) | X4(sk_Xu(X4))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('44', plain,
133.70/133.91	    ![X4 : a > $o, X5 : a > $o, X6 : a > $o, X7 : a > $o]:
133.70/133.91	      (X7 != X4
133.70/133.91	       | X6 != X4
133.70/133.91	       | X5 != X4
133.70/133.91	       | X4(sk_Xy)
133.70/133.91	       | ~ X5(sk_Xw(X6))
133.70/133.91	       | X7(sk_Xu(X6))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['43'])).
133.70/133.91	tff('45', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X0(sk_Xu(X1)) | ~ X2(sk_Xw(X1)) | X1(sk_Xy) | X2 != X1 | X0 != X1),
133.70/133.91	    inference('eq_res', [status(thm)], ['44'])).
133.70/133.91	tff('46', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (X3 != X1
133.70/133.91	       | X0(sk_Xu(X1))
133.70/133.91	       | ~ X2(sk_Xw(X1))
133.70/133.91	       | X3(sk_Xy)
133.70/133.91	       | X2 != X1
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['45'])).
133.70/133.91	tff('47', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (sk_Xq != X1 | X0 != X1 | X2(sk_Xy) | ~ X0(sk_Xw(X1)) | X2 != X1),
133.70/133.91	    inference('clc', [status(thm)], ['42', '46'])).
133.70/133.91	tff('48', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X2 != X0
133.70/133.91	       | X2(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X1 != X0
133.70/133.91	       | X1(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | sk_Xq != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['24', '47'])).
133.70/133.91	tff('49', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X1(sk_Xy) | X1 != X0 | sk_Xq != X0 | X2(sk_Xy) | X2 != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['48'])).
133.70/133.91	tff('50', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true | X0 != X1 | X0(sk_Xy) | sk_Xq != X1 | X0 != X1),
133.70/133.91	    inference('eq_fact', [status(thm)], ['49'])).
133.70/133.91	tff('51', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]: (sk_Xq != X1 | X0(sk_Xy) | X0 != X1),
133.70/133.91	    inference('simplify', [status(thm)], ['50'])).
133.70/133.91	tff('52', plain,
133.70/133.91	    ![X3 : a > $o]:
133.70/133.91	      (X3(sk_Xz) | sk_Xr(sk_Xy, sk_Xw1(X3)) | sk_Xr(sk_Xu1(X3), sk_Xv1(X3))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('53', plain,
133.70/133.91	    ![X3 : a > $o, X4 : a > $o]:
133.70/133.91	      (X4 != X3
133.70/133.91	       | X3(sk_Xz)
133.70/133.91	       | sk_Xr(sk_Xy, sk_Xw1(X4))
133.70/133.91	       | sk_Xr(sk_Xu1(X4), sk_Xv1(X4))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['52'])).
133.70/133.91	tff('54', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | sk_Xr(sk_Xy, sk_Xw1(X0))
133.70/133.91	       | X1(sk_Xz)
133.70/133.91	       | X0 != X1
133.70/133.91	       | sk_Xq(sk_Xv1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu1(X0))),
133.70/133.91	    inference('sup-', [status(thm)], ['53', '2'])).
133.70/133.91	tff('55', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ sk_Xq(sk_Xu1(X0))
133.70/133.91	       | sk_Xq(sk_Xv1(X0))
133.70/133.91	       | X0 != X1
133.70/133.91	       | X1(sk_Xz)
133.70/133.91	       | sk_Xr(sk_Xy, sk_Xw1(X0))),
133.70/133.91	    inference('simplify', [status(thm)], ['54'])).
133.70/133.91	tff('56', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X1(sk_Xz)
133.70/133.91	       | X0 != X1
133.70/133.91	       | sk_Xq(sk_Xv1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu1(X0))
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xy)),
133.70/133.91	    inference('sup-', [status(thm)], ['55', '2'])).
133.70/133.91	tff('57', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu1(X0))
133.70/133.91	       | sk_Xq(sk_Xv1(X0))
133.70/133.91	       | X0 != X1
133.70/133.91	       | X1(sk_Xz)),
133.70/133.91	    inference('simplify', [status(thm)], ['56'])).
133.70/133.91	tff('58', plain,
133.70/133.91	    ![X3 : a > $o]: (X3(sk_Xz) | sk_Xr(sk_Xy, sk_Xw1(X3)) | ~ X3(sk_Xv1(X3))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('59', plain,
133.70/133.91	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
133.70/133.91	      (X5 != X3
133.70/133.91	       | X4 != X3
133.70/133.91	       | X3(sk_Xz)
133.70/133.91	       | sk_Xr(sk_Xy, sk_Xw1(X4))
133.70/133.91	       | ~ X5(sk_Xv1(X4))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['58'])).
133.70/133.91	tff('60', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ X0(sk_Xv1(X1)) | sk_Xr(sk_Xy, sk_Xw1(X1)) | X1(sk_Xz) | X0 != X1),
133.70/133.91	    inference('eq_res', [status(thm)], ['59'])).
133.70/133.91	tff('61', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X2 != X1
133.70/133.91	       | ~ X0(sk_Xv1(X1))
133.70/133.91	       | sk_Xr(sk_Xy, sk_Xw1(X1))
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['60'])).
133.70/133.91	tff('62', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X1 != X0
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | ~ X1(sk_Xv1(X0))
133.70/133.91	       | X2 != X0
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xy)),
133.70/133.91	    inference('sup-', [status(thm)], ['61', '2'])).
133.70/133.91	tff('63', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | X2 != X0
133.70/133.91	       | ~ X1(sk_Xv1(X0))
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['62'])).
133.70/133.91	tff('64', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X0 != X2
133.70/133.91	       | ~ sk_Xq(sk_Xu1(X0))
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X1(sk_Xz)
133.70/133.91	       | X1 != X0
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xy)),
133.70/133.91	    inference('sup-', [status(thm)], ['57', '63'])).
133.70/133.91	tff('65', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X1 != X0
133.70/133.91	       | X1(sk_Xz)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | ~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu1(X0))
133.70/133.91	       | X0 != X2
133.70/133.91	       | X2(sk_Xz)),
133.70/133.91	    inference('simplify', [status(thm)], ['64'])).
133.70/133.91	tff('66', plain,
133.70/133.91	    ![X3 : a > $o]: (X3(sk_Xz) | sk_Xr(sk_Xy, sk_Xw1(X3)) | X3(sk_Xu1(X3))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('67', plain,
133.70/133.91	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
133.70/133.91	      (X5 != X3
133.70/133.91	       | X4 != X3
133.70/133.91	       | X3(sk_Xz)
133.70/133.91	       | sk_Xr(sk_Xy, sk_Xw1(X4))
133.70/133.91	       | X5(sk_Xu1(X4))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['66'])).
133.70/133.91	tff('68', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (X0(sk_Xu1(X1)) | sk_Xr(sk_Xy, sk_Xw1(X1)) | X1(sk_Xz) | X0 != X1),
133.70/133.91	    inference('eq_res', [status(thm)], ['67'])).
133.70/133.91	tff('69', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X2 != X1
133.70/133.91	       | X0(sk_Xu1(X1))
133.70/133.91	       | sk_Xr(sk_Xy, sk_Xw1(X1))
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['68'])).
133.70/133.91	tff('70', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X1 != X0
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X1(sk_Xu1(X0))
133.70/133.91	       | X2 != X0
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xy)),
133.70/133.91	    inference('sup-', [status(thm)], ['69', '2'])).
133.70/133.91	tff('71', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | X2 != X0
133.70/133.91	       | X1(sk_Xu1(X0))
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['70'])).
133.70/133.91	tff('72', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X2(sk_Xz)
133.70/133.91	       | X0 != X2
133.70/133.91	       | sk_Xq(sk_Xw1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X1(sk_Xz)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('clc', [status(thm)], ['65', '71'])).
133.70/133.91	tff('73', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X0 != X1
133.70/133.91	       | X0(sk_Xz)
133.70/133.91	       | sk_Xq != X1
133.70/133.91	       | ~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq(sk_Xw1(X1))
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('eq_fact', [status(thm)], ['72'])).
133.70/133.91	tff('74', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (sk_Xq(sk_Xw1(X1))
133.70/133.91	       | ~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq != X1
133.70/133.91	       | X0(sk_Xz)
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('simplify', [status(thm)], ['73'])).
133.70/133.91	tff('75', plain,
133.70/133.91	    ![X3 : a > $o]:
133.70/133.91	      (X3(sk_Xz) | ~ X3(sk_Xw1(X3)) | sk_Xr(sk_Xu1(X3), sk_Xv1(X3))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('76', plain,
133.70/133.91	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
133.70/133.91	      (X5 != X3
133.70/133.91	       | X4 != X3
133.70/133.91	       | X3(sk_Xz)
133.70/133.91	       | ~ X4(sk_Xw1(X5))
133.70/133.91	       | sk_Xr(sk_Xu1(X5), sk_Xv1(X5))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['75'])).
133.70/133.91	tff('77', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (sk_Xr(sk_Xu1(X0), sk_Xv1(X0))
133.70/133.91	       | ~ X1(sk_Xw1(X0))
133.70/133.91	       | X0(sk_Xz)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('eq_res', [status(thm)], ['76'])).
133.70/133.91	tff('78', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X2 != X0
133.70/133.91	       | sk_Xr(sk_Xu1(X0), sk_Xv1(X0))
133.70/133.91	       | ~ X1(sk_Xw1(X0))
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['77'])).
133.70/133.91	tff('79', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X1 != X0
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | ~ X1(sk_Xw1(X0))
133.70/133.91	       | X2 != X0
133.70/133.91	       | sk_Xq(sk_Xv1(X0))
133.70/133.91	       | ~ sk_Xq(sk_Xu1(X0))),
133.70/133.91	    inference('sup-', [status(thm)], ['78', '2'])).
133.70/133.91	tff('80', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ sk_Xq(sk_Xu1(X0))
133.70/133.91	       | sk_Xq(sk_Xv1(X0))
133.70/133.91	       | X2 != X0
133.70/133.91	       | ~ X1(sk_Xw1(X0))
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['79'])).
133.70/133.91	tff('81', plain,
133.70/133.91	    ![X3 : a > $o]: (X3(sk_Xz) | ~ X3(sk_Xw1(X3)) | ~ X3(sk_Xv1(X3))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('82', plain,
133.70/133.91	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o, X6 : a > $o]:
133.70/133.91	      (X6 != X3
133.70/133.91	       | X5 != X3
133.70/133.91	       | X4 != X3
133.70/133.91	       | X3(sk_Xz)
133.70/133.91	       | ~ X4(sk_Xw1(X5))
133.70/133.91	       | ~ X6(sk_Xv1(X5))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['81'])).
133.70/133.91	tff('83', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ X0(sk_Xv1(X1)) | ~ X2(sk_Xw1(X1)) | X1(sk_Xz) | X2 != X1 | X0 != X1),
133.70/133.91	    inference('eq_res', [status(thm)], ['82'])).
133.70/133.91	tff('84', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (X3 != X1
133.70/133.91	       | ~ X0(sk_Xv1(X1))
133.70/133.91	       | ~ X2(sk_Xw1(X1))
133.70/133.91	       | X3(sk_Xz)
133.70/133.91	       | X2 != X1
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['83'])).
133.70/133.91	tff('85', plain, ~ sk_Xq(sk_Xz), inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('86', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X0 != X1
133.70/133.91	       | X2 != X1
133.70/133.91	       | ~ X2(sk_Xw1(X1))
133.70/133.91	       | ~ X0(sk_Xv1(X1))
133.70/133.91	       | sk_Xq != X1),
133.70/133.91	    inference('sup-', [status(thm)], ['84', '85'])).
133.70/133.91	tff('87', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (sk_Xq != X1
133.70/133.91	       | ~ X0(sk_Xv1(X1))
133.70/133.91	       | ~ X2(sk_Xw1(X1))
133.70/133.91	       | X2 != X1
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('simplify', [status(thm)], ['86'])).
133.70/133.91	tff('88', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X2 != X0
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | ~ sk_Xq(sk_Xy)
133.70/133.91	       | X1 != X0
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | ~ X1(sk_Xv1(X0))
133.70/133.91	       | sk_Xq != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['74', '87'])).
133.70/133.91	tff('89', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ X1(sk_Xv1(X0))
133.70/133.91	       | X1 != X0
133.70/133.91	       | ~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X2 != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['88'])).
133.70/133.91	tff('90', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | sk_Xq != X3
133.70/133.91	       | sk_Xq != X3
133.70/133.91	       | X0 != X1
133.70/133.91	       | X0(sk_Xz)
133.70/133.91	       | sk_Xq != X1
133.70/133.91	       | X2 != X1
133.70/133.91	       | ~ X2(sk_Xv1(X1))),
133.70/133.91	    inference('sup-', [status(thm)], ['51', '89'])).
133.70/133.91	tff('91', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (~ X2(sk_Xv1(X1))
133.70/133.91	       | X2 != X1
133.70/133.91	       | sk_Xq != X1
133.70/133.91	       | X0(sk_Xz)
133.70/133.91	       | X0 != X1
133.70/133.91	       | sk_Xq != X3),
133.70/133.91	    inference('simplify', [status(thm)], ['90'])).
133.70/133.91	tff('92', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | sk_Xq != X1
133.70/133.91	       | sk_Xq != X1
133.70/133.91	       | X2 != X1
133.70/133.91	       | ~ X2(sk_Xv1(X1))),
133.70/133.91	    inference('sup-', [status(thm)], ['91', '85'])).
133.70/133.91	tff('93', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ X2(sk_Xv1(X1)) | X2 != X1 | sk_Xq != X1 | sk_Xq != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['92'])).
133.70/133.91	tff('94', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]: (~ X0(sk_Xv1(X1)) | X0 != X1 | sk_Xq != X1),
133.70/133.91	    inference('condensation', [status(thm)], ['93'])).
133.70/133.91	tff('95', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X1 != X0
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | ~ X1(sk_Xw1(X0))
133.70/133.91	       | X2 != X0
133.70/133.91	       | ~ sk_Xq(sk_Xu1(X0))
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | sk_Xq != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['80', '94'])).
133.70/133.91	tff('96', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (sk_Xq != X0
133.70/133.91	       | ~ sk_Xq(sk_Xu1(X0))
133.70/133.91	       | X2 != X0
133.70/133.91	       | ~ X1(sk_Xw1(X0))
133.70/133.91	       | X2(sk_Xz)
133.70/133.91	       | X1 != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['95'])).
133.70/133.91	tff('97', plain,
133.70/133.91	    ![X3 : a > $o]: (X3(sk_Xz) | ~ X3(sk_Xw1(X3)) | X3(sk_Xu1(X3))),
133.70/133.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
133.70/133.91	tff('98', plain,
133.70/133.91	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o, X6 : a > $o]:
133.70/133.91	      (X6 != X3
133.70/133.91	       | X5 != X3
133.70/133.91	       | X4 != X3
133.70/133.91	       | X3(sk_Xz)
133.70/133.91	       | ~ X4(sk_Xw1(X5))
133.70/133.91	       | X6(sk_Xu1(X5))),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['97'])).
133.70/133.91	tff('99', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X0(sk_Xu1(X1)) | ~ X2(sk_Xw1(X1)) | X1(sk_Xz) | X2 != X1 | X0 != X1),
133.70/133.91	    inference('eq_res', [status(thm)], ['98'])).
133.70/133.91	tff('100', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o, X3 : a > $o]:
133.70/133.91	      (X3 != X1
133.70/133.91	       | X0(sk_Xu1(X1))
133.70/133.91	       | ~ X2(sk_Xw1(X1))
133.70/133.91	       | X3(sk_Xz)
133.70/133.91	       | X2 != X1
133.70/133.91	       | X0 != X1),
133.70/133.91	    inference('ho.purify_applied_variable', [status(thm)], ['99'])).
133.70/133.91	tff('101', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (X1 != X0 | X2(sk_Xz) | ~ X1(sk_Xw1(X0)) | X2 != X0 | sk_Xq != X0),
133.70/133.91	    inference('clc', [status(thm)], ['96', '100'])).
133.70/133.91	tff('102', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true | sk_Xq != X0 | sk_Xq != X0 | ~ X1(sk_Xw1(X0)) | X1 != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['101', '85'])).
133.70/133.91	tff('103', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]: (X1 != X0 | ~ X1(sk_Xw1(X0)) | sk_Xq != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['102'])).
133.70/133.91	tff('104', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | X1 != X0
133.70/133.91	       | X1(sk_Xz)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | ~ sk_Xq(sk_Xy)
133.70/133.91	       | sk_Xq != X0
133.70/133.91	       | sk_Xq != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['74', '103'])).
133.70/133.91	tff('105', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]:
133.70/133.91	      (~ sk_Xq(sk_Xy) | sk_Xq != X0 | X1(sk_Xz) | X1 != X0),
133.70/133.91	    inference('simplify', [status(thm)], ['104'])).
133.70/133.91	tff('106', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (~ $true
133.70/133.91	       | sk_Xq != X2
133.70/133.91	       | sk_Xq != X2
133.70/133.91	       | X0 != X1
133.70/133.91	       | X0(sk_Xz)
133.70/133.91	       | sk_Xq != X1),
133.70/133.91	    inference('sup-', [status(thm)], ['51', '105'])).
133.70/133.91	tff('107', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o, X2 : a > $o]:
133.70/133.91	      (sk_Xq != X1 | X0(sk_Xz) | X0 != X1 | sk_Xq != X2),
133.70/133.91	    inference('simplify', [status(thm)], ['106'])).
133.70/133.91	tff('108', plain,
133.70/133.91	    ![X0 : a > $o, X1 : a > $o]: (sk_Xq != X0 | X1(sk_Xz) | X1 != X0),
133.70/133.91	    inference('condensation', [status(thm)], ['107'])).
133.70/133.91	tff('109', plain, ![X0 : a > $o]: (~ $true | sk_Xq != X0 | sk_Xq != X0),
133.70/133.91	    inference('sup-', [status(thm)], ['108', '85'])).
133.70/133.91	tff('110', plain, ![X0 : a > $o]: sk_Xq != X0,
133.70/133.91	    inference('simplify', [status(thm)], ['109'])).
133.70/133.91	tff('111', plain, $false, inference('eq_res', [status(thm)], ['110'])).
133.70/133.91	
133.70/133.91	% SZS output end Refutation
133.70/133.92	EOF
