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   : n094.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 17:49:39 CST 2018
0.00/0.26	% done 63 iterations in 0.061s
0.00/0.26	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.00/0.26	% SZS output start Refutation
0.00/0.26	tff(cTHM70_pme, conjecture,
0.00/0.26	  (![S:((a * a) > $o > $o),Xx:a,Xy:a,Xz:a]:
0.00/0.26	     (((![Xp:((a * a) > $o)]:
0.00/0.26	          ((S(Xp) & 
0.00/0.26	            (![Xx0:a,Xy0:a,Xz0:a]:
0.00/0.26	               ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0)))) =>
0.00/0.26	           Xp(Xy,Xz))) & 
0.00/0.26	       (![Xp:((a * a) > $o)]:
0.00/0.26	          ((S(Xp) & 
0.00/0.26	            (![Xx0:a,Xy0:a,Xz0:a]:
0.00/0.26	               ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0)))) =>
0.00/0.26	           Xp(Xx,Xy)))) =>
0.00/0.26	      (![Xp:((a * a) > $o)]:
0.00/0.26	         ((S(Xp) & 
0.00/0.26	           (![Xx0:a,Xy0:a,Xz0:a]:
0.00/0.26	              ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0)))) =>
0.00/0.26	          Xp(Xx,Xz)))))).
0.00/0.26	tff(zf_stmt_0, negated_conjecture,
0.00/0.26	  (~
0.00/0.26	    (![S:((a * a) > $o > $o),Xx:a,Xy:a,Xz:a]:
0.00/0.26	       (((![Xp:((a * a) > $o)]:
0.00/0.26	            ((S(Xp) & 
0.00/0.26	              (![Xx0:a,Xy0:a,Xz0:a]:
0.00/0.26	                 ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0)))) =>
0.00/0.26	             Xp(Xy,Xz))) & 
0.00/0.26	         (![Xp:((a * a) > $o)]:
0.00/0.26	            ((S(Xp) & 
0.00/0.26	              (![Xx0:a,Xy0:a,Xz0:a]:
0.00/0.26	                 ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0)))) =>
0.00/0.26	             Xp(Xx,Xy)))) =>
0.00/0.26	        (![Xp:((a * a) > $o)]:
0.00/0.26	           ((S(Xp) & 
0.00/0.26	             (![Xx0:a,Xy0:a,Xz0:a]:
0.00/0.26	                ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0)))) =>
0.00/0.26	            Xp(Xx,Xz))))))).
0.00/0.26	tff('0', plain,
0.00/0.26	    ![X3 : (a * a) > $o]:
0.00/0.26	      (X3(sk_Xy, sk_Xz) | X3(sk_Xy01(X3), sk_Xz01(X3)) | ~ sk_S(X3)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('1', plain,
0.00/0.26	    ![X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
0.00/0.26	      (X5 != X3
0.00/0.26	       | X4 != X3
0.00/0.26	       | X3(sk_Xy, sk_Xz)
0.00/0.26	       | X4(sk_Xy01(X5), sk_Xz01(X5))
0.00/0.26	       | ~ sk_S(X5)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['0'])).
0.00/0.26	tff('2', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ sk_S(X0)
0.00/0.26	       | X1(sk_Xy01(X0), sk_Xz01(X0))
0.00/0.26	       | X0(sk_Xy, sk_Xz)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('eq_res', [status(thm)], ['1'])).
0.00/0.26	tff('3', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X1(sk_Xy01(X0), sk_Xz01(X0))
0.00/0.26	       | X2(sk_Xy, sk_Xz)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['2'])).
0.00/0.26	tff('4', plain,
0.00/0.26	    ![X3 : (a * a) > $o]:
0.00/0.26	      (X3(sk_Xy, sk_Xz) | X3(sk_Xx01(X3), sk_Xy01(X3)) | ~ sk_S(X3)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('5', plain,
0.00/0.26	    ![X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
0.00/0.26	      (X5 != X3
0.00/0.26	       | X4 != X3
0.00/0.26	       | X3(sk_Xy, sk_Xz)
0.00/0.26	       | X4(sk_Xx01(X5), sk_Xy01(X5))
0.00/0.26	       | ~ sk_S(X5)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['4'])).
0.00/0.26	tff('6', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ sk_S(X0)
0.00/0.26	       | X1(sk_Xx01(X0), sk_Xy01(X0))
0.00/0.26	       | X0(sk_Xy, sk_Xz)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('eq_res', [status(thm)], ['5'])).
0.00/0.26	tff('7', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X1(sk_Xx01(X0), sk_Xy01(X0))
0.00/0.26	       | X2(sk_Xy, sk_Xz)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['6'])).
0.00/0.26	tff('8', plain,
0.00/0.26	    ![X0 : a, X1 : a, X2 : a]:
0.00/0.26	      (~ sk_Xp(X0, X1) | ~ sk_Xp(X1, X2) | sk_Xp(X0, X2)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('9', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
0.00/0.26	      (~ $true
0.00/0.26	       | sk_Xp != X0
0.00/0.26	       | X2(sk_Xy, sk_Xz)
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2 != X0
0.00/0.26	       | sk_Xp(sk_Xx01(X0), X1)
0.00/0.26	       | ~ sk_Xp(sk_Xy01(X0), X1)),
0.00/0.26	    inference('sup-', [status(thm)], ['7', '8'])).
0.00/0.26	tff('10', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
0.00/0.26	      (~ sk_Xp(sk_Xy01(X0), X1)
0.00/0.26	       | sk_Xp(sk_Xx01(X0), X1)
0.00/0.26	       | X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2(sk_Xy, sk_Xz)
0.00/0.26	       | sk_Xp != X0),
0.00/0.26	    inference('simplify', [status(thm)], ['9'])).
0.00/0.26	tff('11', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (~ $true
0.00/0.26	       | sk_Xp != X0
0.00/0.26	       | X2(sk_Xy, sk_Xz)
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2 != X0
0.00/0.26	       | sk_Xp != X0
0.00/0.26	       | X1(sk_Xy, sk_Xz)
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X1 != X0
0.00/0.26	       | sk_Xp(sk_Xx01(X0), sk_Xz01(X0))),
0.00/0.26	    inference('sup-', [status(thm)], ['3', '10'])).
0.00/0.26	tff('12', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (sk_Xp(sk_Xx01(X0), sk_Xz01(X0))
0.00/0.26	       | X1 != X0
0.00/0.26	       | X1(sk_Xy, sk_Xz)
0.00/0.26	       | X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2(sk_Xy, sk_Xz)
0.00/0.26	       | sk_Xp != X0),
0.00/0.26	    inference('simplify', [status(thm)], ['11'])).
0.00/0.26	tff('13', plain,
0.00/0.26	    ![X3 : (a * a) > $o]:
0.00/0.26	      (X3(sk_Xy, sk_Xz) | ~ X3(sk_Xx01(X3), sk_Xz01(X3)) | ~ sk_S(X3)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('14', plain,
0.00/0.26	    ![X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
0.00/0.26	      (X5 != X3
0.00/0.26	       | X4 != X3
0.00/0.26	       | X3(sk_Xy, sk_Xz)
0.00/0.26	       | ~ X4(sk_Xx01(X5), sk_Xz01(X5))
0.00/0.26	       | ~ sk_S(X5)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['13'])).
0.00/0.26	tff('15', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ sk_S(X0)
0.00/0.26	       | ~ X1(sk_Xx01(X0), sk_Xz01(X0))
0.00/0.26	       | X0(sk_Xy, sk_Xz)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('eq_res', [status(thm)], ['14'])).
0.00/0.26	tff('16', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | ~ X1(sk_Xx01(X0), sk_Xz01(X0))
0.00/0.26	       | X2(sk_Xy, sk_Xz)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['15'])).
0.00/0.26	tff('17', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (sk_Xp != X0
0.00/0.26	       | X2(sk_Xy, sk_Xz)
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2 != X0
0.00/0.26	       | X1(sk_Xy, sk_Xz)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('clc', [status(thm)], ['12', '16'])).
0.00/0.26	tff('18', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ $true
0.00/0.26	       | X0 != X1
0.00/0.26	       | X0(sk_Xy, sk_Xz)
0.00/0.26	       | X0 != X1
0.00/0.26	       | ~ sk_S(X1)
0.00/0.26	       | sk_Xp != X1),
0.00/0.26	    inference('eq_fact', [status(thm)], ['17'])).
0.00/0.26	tff('19', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (sk_Xp != X1 | ~ sk_S(X1) | X0(sk_Xy, sk_Xz) | X0 != X1),
0.00/0.26	    inference('simplify', [status(thm)], ['18'])).
0.00/0.26	tff('20', plain,
0.00/0.26	    ![X0 : (a * a) > $o]: (X0 != sk_Xp | X0(sk_Xy, sk_Xz) | ~ sk_S(sk_Xp)),
0.00/0.26	    inference('eq_res', [status(thm)], ['19'])).
0.00/0.26	tff('21', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (X1 != X0 | X0 != sk_Xp | X1(sk_Xy, sk_Xz) | ~ sk_S(sk_Xp)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['20'])).
0.00/0.26	tff('22', plain, sk_S(sk_Xp), inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('23', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (X1 != X0 | X0 != sk_Xp | X1(sk_Xy, sk_Xz) | ~ $true),
0.00/0.26	    inference('demod', [status(thm)], ['21', '22'])).
0.00/0.26	tff('24', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (X1(sk_Xy, sk_Xz) | X0 != sk_Xp | X1 != X0),
0.00/0.26	    inference('simplify', [status(thm)], ['23'])).
0.00/0.26	tff('25', plain,
0.00/0.26	    ![X4 : (a * a) > $o]:
0.00/0.26	      (X4(sk_Xx, sk_Xy) | X4(sk_Xy0(X4), sk_Xz0(X4)) | ~ sk_S(X4)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('26', plain,
0.00/0.26	    ![X4 : (a * a) > $o, X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.00/0.26	      (X6 != X4
0.00/0.26	       | X5 != X4
0.00/0.26	       | X4(sk_Xx, sk_Xy)
0.00/0.26	       | X5(sk_Xy0(X6), sk_Xz0(X6))
0.00/0.26	       | ~ sk_S(X6)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['25'])).
0.00/0.26	tff('27', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ sk_S(X0) | X1(sk_Xy0(X0), sk_Xz0(X0)) | X0(sk_Xx, sk_Xy) | X1 != X0),
0.00/0.26	    inference('eq_res', [status(thm)], ['26'])).
0.00/0.26	tff('28', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X1(sk_Xy0(X0), sk_Xz0(X0))
0.00/0.26	       | X2(sk_Xx, sk_Xy)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['27'])).
0.00/0.26	tff('29', plain,
0.00/0.26	    ![X4 : (a * a) > $o]:
0.00/0.26	      (X4(sk_Xx, sk_Xy) | X4(sk_Xx0(X4), sk_Xy0(X4)) | ~ sk_S(X4)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('30', plain,
0.00/0.26	    ![X4 : (a * a) > $o, X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.00/0.26	      (X6 != X4
0.00/0.26	       | X5 != X4
0.00/0.26	       | X4(sk_Xx, sk_Xy)
0.00/0.26	       | X5(sk_Xx0(X6), sk_Xy0(X6))
0.00/0.26	       | ~ sk_S(X6)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['29'])).
0.00/0.26	tff('31', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ sk_S(X0) | X1(sk_Xx0(X0), sk_Xy0(X0)) | X0(sk_Xx, sk_Xy) | X1 != X0),
0.00/0.26	    inference('eq_res', [status(thm)], ['30'])).
0.00/0.26	tff('32', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X1(sk_Xx0(X0), sk_Xy0(X0))
0.00/0.26	       | X2(sk_Xx, sk_Xy)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['31'])).
0.00/0.26	tff('33', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
0.00/0.26	      (~ $true
0.00/0.26	       | sk_Xp != X0
0.00/0.26	       | X2(sk_Xx, sk_Xy)
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2 != X0
0.00/0.26	       | sk_Xp(sk_Xx0(X0), X1)
0.00/0.26	       | ~ sk_Xp(sk_Xy0(X0), X1)),
0.00/0.26	    inference('sup-', [status(thm)], ['32', '8'])).
0.00/0.26	tff('34', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
0.00/0.26	      (~ sk_Xp(sk_Xy0(X0), X1)
0.00/0.26	       | sk_Xp(sk_Xx0(X0), X1)
0.00/0.26	       | X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2(sk_Xx, sk_Xy)
0.00/0.26	       | sk_Xp != X0),
0.00/0.26	    inference('simplify', [status(thm)], ['33'])).
0.00/0.26	tff('35', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (~ $true
0.00/0.26	       | sk_Xp != X0
0.00/0.26	       | X2(sk_Xx, sk_Xy)
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2 != X0
0.00/0.26	       | sk_Xp != X0
0.00/0.26	       | X1(sk_Xx, sk_Xy)
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X1 != X0
0.00/0.26	       | sk_Xp(sk_Xx0(X0), sk_Xz0(X0))),
0.00/0.26	    inference('sup-', [status(thm)], ['28', '34'])).
0.00/0.26	tff('36', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (sk_Xp(sk_Xx0(X0), sk_Xz0(X0))
0.00/0.26	       | X1 != X0
0.00/0.26	       | X1(sk_Xx, sk_Xy)
0.00/0.26	       | X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2(sk_Xx, sk_Xy)
0.00/0.26	       | sk_Xp != X0),
0.00/0.26	    inference('simplify', [status(thm)], ['35'])).
0.00/0.26	tff('37', plain,
0.00/0.26	    ![X4 : (a * a) > $o]:
0.00/0.26	      (X4(sk_Xx, sk_Xy) | ~ X4(sk_Xx0(X4), sk_Xz0(X4)) | ~ sk_S(X4)),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('38', plain,
0.00/0.26	    ![X4 : (a * a) > $o, X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.00/0.26	      (X6 != X4
0.00/0.26	       | X5 != X4
0.00/0.26	       | X4(sk_Xx, sk_Xy)
0.00/0.26	       | ~ X5(sk_Xx0(X6), sk_Xz0(X6))
0.00/0.26	       | ~ sk_S(X6)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['37'])).
0.00/0.26	tff('39', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ sk_S(X0)
0.00/0.26	       | ~ X1(sk_Xx0(X0), sk_Xz0(X0))
0.00/0.26	       | X0(sk_Xx, sk_Xy)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('eq_res', [status(thm)], ['38'])).
0.00/0.26	tff('40', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (X2 != X0
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | ~ X1(sk_Xx0(X0), sk_Xz0(X0))
0.00/0.26	       | X2(sk_Xx, sk_Xy)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['39'])).
0.00/0.26	tff('41', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
0.00/0.26	      (sk_Xp != X0
0.00/0.26	       | X2(sk_Xx, sk_Xy)
0.00/0.26	       | ~ sk_S(X0)
0.00/0.26	       | X2 != X0
0.00/0.26	       | X1(sk_Xx, sk_Xy)
0.00/0.26	       | X1 != X0),
0.00/0.26	    inference('clc', [status(thm)], ['36', '40'])).
0.00/0.26	tff('42', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ $true
0.00/0.26	       | X0 != X1
0.00/0.26	       | X0(sk_Xx, sk_Xy)
0.00/0.26	       | X0 != X1
0.00/0.26	       | ~ sk_S(X1)
0.00/0.26	       | sk_Xp != X1),
0.00/0.26	    inference('eq_fact', [status(thm)], ['41'])).
0.00/0.26	tff('43', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (sk_Xp != X1 | ~ sk_S(X1) | X0(sk_Xx, sk_Xy) | X0 != X1),
0.00/0.26	    inference('simplify', [status(thm)], ['42'])).
0.00/0.26	tff('44', plain,
0.00/0.26	    ![X0 : (a * a) > $o]: (X0 != sk_Xp | X0(sk_Xx, sk_Xy) | ~ sk_S(sk_Xp)),
0.00/0.26	    inference('eq_res', [status(thm)], ['43'])).
0.00/0.26	tff('45', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (X1 != X0 | X0 != sk_Xp | X1(sk_Xx, sk_Xy) | ~ sk_S(sk_Xp)),
0.00/0.26	    inference('ho.purify_applied_variable', [status(thm)], ['44'])).
0.00/0.26	tff('46', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (X1 != X0 | X0 != sk_Xp | X1(sk_Xx, sk_Xy) | ~ $true),
0.00/0.26	    inference('demod', [status(thm)], ['45', '22'])).
0.00/0.26	tff('47', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (X1(sk_Xx, sk_Xy) | X0 != sk_Xp | X1 != X0),
0.00/0.26	    inference('simplify', [status(thm)], ['46'])).
0.00/0.26	tff('48', plain,
0.00/0.26	    ![X0 : a, X1 : (a * a) > $o]:
0.00/0.26	      (~ $true
0.00/0.26	       | sk_Xp != X1
0.00/0.26	       | X1 != sk_Xp
0.00/0.26	       | sk_Xp(sk_Xx, X0)
0.00/0.26	       | ~ sk_Xp(sk_Xy, X0)),
0.00/0.26	    inference('sup-', [status(thm)], ['47', '8'])).
0.00/0.26	tff('49', plain,
0.00/0.26	    ![X0 : a, X1 : (a * a) > $o]:
0.00/0.26	      (~ sk_Xp(sk_Xy, X0) | sk_Xp(sk_Xx, X0) | sk_Xp != X1),
0.00/0.26	    inference('simplify', [status(thm)], ['48'])).
0.00/0.26	tff('50', plain, ~ sk_Xp(sk_Xx, sk_Xz),
0.00/0.26	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.26	tff('51', plain,
0.00/0.26	    ![X0 : (a * a) > $o]: (~ $true | sk_Xp != X0 | ~ sk_Xp(sk_Xy, sk_Xz)),
0.00/0.26	    inference('sup-', [status(thm)], ['49', '50'])).
0.00/0.26	tff('52', plain, ![X0 : (a * a) > $o]: (~ sk_Xp(sk_Xy, sk_Xz) | sk_Xp != X0),
0.00/0.26	    inference('simplify', [status(thm)], ['51'])).
0.00/0.26	tff('53', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
0.00/0.26	      (~ $true | sk_Xp != X1 | X1 != sk_Xp | sk_Xp != X0),
0.00/0.26	    inference('sup-', [status(thm)], ['24', '52'])).
0.00/0.26	tff('54', plain,
0.00/0.26	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]: (sk_Xp != X0 | sk_Xp != X1),
0.00/0.26	    inference('simplify', [status(thm)], ['53'])).
0.00/0.26	tff('55', plain, ![X0 : (a * a) > $o]: sk_Xp != X0,
0.00/0.26	    inference('condensation', [status(thm)], ['54'])).
0.00/0.26	tff('56', plain, $false, inference('eq_res', [status(thm)], ['55'])).
0.00/0.26	
0.00/0.26	% SZS output end Refutation
0.00/0.26	EOF
