0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_int
0.00/0.00	% Ordering    : 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 int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n067.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:49:39 CST 2018
0.41/0.60	% done 315 iterations in 0.403s
0.41/0.60	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.41/0.60	% SZS output start Refutation
0.41/0.60	tff(cTHM136_pme, conjecture,
0.41/0.60	  (![Xr:((a * a) > $o),Xx:a,Xy:a,Xz:a]:
0.41/0.60	     (((![Xp:((a * a) > $o)]:
0.41/0.60	          (((![Xx0:a,Xy0:a,Xz0:a]:
0.41/0.60	               ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
0.41/0.60	            (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
0.41/0.60	           Xp(Xy,Xz))) & 
0.41/0.60	       (![Xp:((a * a) > $o)]:
0.41/0.60	          (((![Xx0:a,Xy0:a,Xz0:a]:
0.41/0.60	               ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
0.41/0.60	            (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
0.41/0.60	           Xp(Xx,Xy)))) =>
0.41/0.60	      (![Xp:((a * a) > $o)]:
0.41/0.60	         (((![Xx0:a,Xy0:a,Xz0:a]:
0.41/0.60	              ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
0.41/0.60	           (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
0.41/0.60	          Xp(Xx,Xz)))))).
0.41/0.60	tff(zf_stmt_0, negated_conjecture,
0.41/0.60	  (~
0.41/0.60	    (![Xr:((a * a) > $o),Xx:a,Xy:a,Xz:a]:
0.41/0.60	       (((![Xp:((a * a) > $o)]:
0.41/0.60	            (((![Xx0:a,Xy0:a,Xz0:a]:
0.41/0.60	                 ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
0.41/0.60	              (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
0.41/0.60	             Xp(Xy,Xz))) & 
0.41/0.60	         (![Xp:((a * a) > $o)]:
0.41/0.60	            (((![Xx0:a,Xy0:a,Xz0:a]:
0.41/0.60	                 ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
0.41/0.60	              (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
0.41/0.60	             Xp(Xx,Xy)))) =>
0.41/0.60	        (![Xp:((a * a) > $o)]:
0.41/0.60	           (((![Xx0:a,Xy0:a,Xz0:a]:
0.41/0.60	                ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
0.41/0.60	             (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
0.41/0.60	            Xp(Xx,Xz))))))).
0.41/0.60	tff('0', plain, ![X3 : a, X4 : a]: (sk_Xp(X3, X4) | ~ sk_Xr(X3, X4)),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('1', plain,
0.41/0.60	    ![X6 : (a * a) > $o]:
0.41/0.60	      (X6(sk_Xx, sk_Xy)
0.41/0.60	       | ~ X6(sk_Xx0(X6), sk_Xy0(X6))
0.41/0.60	       | X6(sk_Xy01(X6), sk_Xz0(X6))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('2', plain,
0.41/0.60	    ![X6 : (a * a) > $o, X7 : (a * a) > $o]:
0.41/0.60	      (X7 != X6
0.41/0.60	       | X6(sk_Xx, sk_Xy)
0.41/0.60	       | ~ X6(sk_Xx0(X7), sk_Xy0(X7))
0.41/0.60	       | X6(sk_Xy01(X7), sk_Xz0(X7))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['1'])).
0.41/0.60	tff('3', plain,
0.41/0.60	    ![X6 : (a * a) > $o]:
0.41/0.60	      (X6(sk_Xx, sk_Xy)
0.41/0.60	       | ~ X6(sk_Xx0(X6), sk_Xy0(X6))
0.41/0.60	       | X6(sk_Xx01(X6), sk_Xy01(X6))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('4', plain,
0.41/0.60	    ![X6 : (a * a) > $o, X7 : (a * a) > $o]:
0.41/0.60	      (X7 != X6
0.41/0.60	       | X6(sk_Xx, sk_Xy)
0.41/0.60	       | ~ X6(sk_Xx0(X7), sk_Xy0(X7))
0.41/0.60	       | X6(sk_Xx01(X7), sk_Xy01(X7))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['3'])).
0.41/0.60	tff('5', plain,
0.41/0.60	    ![X0 : a, X1 : a, X2 : a]:
0.41/0.60	      (~ sk_Xp(X0, X1) | ~ sk_Xp(X1, X2) | sk_Xp(X0, X2)),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('6', plain,
0.41/0.60	    ![X0 : (a * a) > $o, X1 : a]:
0.41/0.60	      (~ $true
0.41/0.60	       | ~ sk_Xp(sk_Xx0(X0), sk_Xy0(X0))
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx01(X0), X1)
0.41/0.60	       | ~ sk_Xp(sk_Xy01(X0), X1)),
0.41/0.60	    inference('sup-', [status(thm)], ['4', '5'])).
0.41/0.60	tff('7', plain,
0.41/0.60	    ![X0 : (a * a) > $o, X1 : a]:
0.41/0.60	      (~ sk_Xp(sk_Xy01(X0), X1)
0.41/0.60	       | sk_Xp(sk_Xx01(X0), X1)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | ~ sk_Xp(sk_Xx0(X0), sk_Xy0(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['6'])).
0.41/0.60	tff('8', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (~ $true
0.41/0.60	       | ~ sk_Xp(sk_Xx0(X0), sk_Xy0(X0))
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | ~ sk_Xp(sk_Xx0(X0), sk_Xy0(X0))
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx01(X0), sk_Xz0(X0))),
0.41/0.60	    inference('sup-', [status(thm)], ['2', '7'])).
0.41/0.60	tff('9', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (sk_Xp(sk_Xx01(X0), sk_Xz0(X0))
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | ~ sk_Xp(sk_Xx0(X0), sk_Xy0(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['8'])).
0.41/0.60	tff('10', plain,
0.41/0.60	    ![X6 : (a * a) > $o]:
0.41/0.60	      (X6(sk_Xx, sk_Xy)
0.41/0.60	       | ~ X6(sk_Xx0(X6), sk_Xy0(X6))
0.41/0.60	       | ~ X6(sk_Xx01(X6), sk_Xz0(X6))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('11', plain,
0.41/0.60	    ![X6 : (a * a) > $o, X7 : (a * a) > $o]:
0.41/0.60	      (X7 != X6
0.41/0.60	       | X6(sk_Xx, sk_Xy)
0.41/0.60	       | ~ X6(sk_Xx0(X7), sk_Xy0(X7))
0.41/0.60	       | ~ X6(sk_Xx01(X7), sk_Xz0(X7))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['10'])).
0.41/0.60	tff('12', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (~ sk_Xp(sk_Xx0(X0), sk_Xy0(X0)) | sk_Xp(sk_Xx, sk_Xy) | X0 != sk_Xp),
0.41/0.60	    inference('clc', [status(thm)], ['9', '11'])).
0.41/0.60	tff('13', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (~ $true
0.41/0.60	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)),
0.41/0.60	    inference('sup-', [status(thm)], ['0', '12'])).
0.41/0.60	tff('14', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (sk_Xp(sk_Xx, sk_Xy) | X0 != sk_Xp | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['13'])).
0.41/0.60	tff('15', plain,
0.41/0.60	    ![X6 : (a * a) > $o]:
0.41/0.60	      (X6(sk_Xx, sk_Xy)
0.41/0.60	       | sk_Xr(sk_Xx0(X6), sk_Xy0(X6))
0.41/0.60	       | X6(sk_Xy01(X6), sk_Xz0(X6))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('16', plain,
0.41/0.60	    ![X6 : (a * a) > $o, X7 : (a * a) > $o]:
0.41/0.60	      (X7 != X6
0.41/0.60	       | X6(sk_Xx, sk_Xy)
0.41/0.60	       | sk_Xr(sk_Xx0(X7), sk_Xy0(X7))
0.41/0.60	       | X6(sk_Xy01(X7), sk_Xz0(X7))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['15'])).
0.41/0.60	tff('17', plain,
0.41/0.60	    ![X6 : (a * a) > $o]:
0.41/0.60	      (X6(sk_Xx, sk_Xy)
0.41/0.60	       | sk_Xr(sk_Xx0(X6), sk_Xy0(X6))
0.41/0.60	       | X6(sk_Xx01(X6), sk_Xy01(X6))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('18', plain,
0.41/0.60	    ![X6 : (a * a) > $o, X7 : (a * a) > $o]:
0.41/0.60	      (X7 != X6
0.41/0.60	       | X6(sk_Xx, sk_Xy)
0.41/0.60	       | sk_Xr(sk_Xx0(X7), sk_Xy0(X7))
0.41/0.60	       | X6(sk_Xx01(X7), sk_Xy01(X7))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['17'])).
0.41/0.60	tff('19', plain,
0.41/0.60	    ![X0 : (a * a) > $o, X1 : a]:
0.41/0.60	      (~ $true
0.41/0.60	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx01(X0), X1)
0.41/0.60	       | ~ sk_Xp(sk_Xy01(X0), X1)),
0.41/0.60	    inference('sup-', [status(thm)], ['18', '5'])).
0.41/0.60	tff('20', plain,
0.41/0.60	    ![X0 : (a * a) > $o, X1 : a]:
0.41/0.60	      (~ sk_Xp(sk_Xy01(X0), X1)
0.41/0.60	       | sk_Xp(sk_Xx01(X0), X1)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['19'])).
0.41/0.60	tff('21', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (~ $true
0.41/0.60	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx01(X0), sk_Xz0(X0))),
0.41/0.60	    inference('sup-', [status(thm)], ['16', '20'])).
0.41/0.60	tff('22', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (sk_Xp(sk_Xx01(X0), sk_Xz0(X0))
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx, sk_Xy)
0.41/0.60	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['21'])).
0.41/0.60	tff('23', plain,
0.41/0.60	    ![X6 : (a * a) > $o]:
0.41/0.60	      (X6(sk_Xx, sk_Xy)
0.41/0.60	       | sk_Xr(sk_Xx0(X6), sk_Xy0(X6))
0.41/0.60	       | ~ X6(sk_Xx01(X6), sk_Xz0(X6))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('24', plain,
0.41/0.60	    ![X6 : (a * a) > $o, X7 : (a * a) > $o]:
0.41/0.60	      (X7 != X6
0.41/0.60	       | X6(sk_Xx, sk_Xy)
0.41/0.60	       | sk_Xr(sk_Xx0(X7), sk_Xy0(X7))
0.41/0.60	       | ~ X6(sk_Xx01(X7), sk_Xz0(X7))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['23'])).
0.41/0.60	tff('25', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (sk_Xr(sk_Xx0(X0), sk_Xy0(X0)) | sk_Xp(sk_Xx, sk_Xy) | X0 != sk_Xp),
0.41/0.60	    inference('clc', [status(thm)], ['22', '24'])).
0.41/0.60	tff('26', plain, ![X0 : (a * a) > $o]: (X0 != sk_Xp | sk_Xp(sk_Xx, sk_Xy)),
0.41/0.60	    inference('clc', [status(thm)], ['14', '25'])).
0.41/0.60	tff('27', plain, sk_Xp(sk_Xx, sk_Xy),
0.41/0.60	    inference('eq_res', [status(thm)], ['26'])).
0.41/0.60	tff('28', plain,
0.41/0.60	    ![X0 : a]: (~ $true | sk_Xp(sk_Xx, X0) | ~ sk_Xp(sk_Xy, X0)),
0.41/0.60	    inference('sup-', [status(thm)], ['27', '5'])).
0.41/0.60	tff('29', plain, ![X0 : a]: (~ sk_Xp(sk_Xy, X0) | sk_Xp(sk_Xx, X0)),
0.41/0.60	    inference('simplify', [status(thm)], ['28'])).
0.41/0.60	tff('30', plain, ~ sk_Xp(sk_Xx, sk_Xz),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('31', plain, (~ $true | ~ sk_Xp(sk_Xy, sk_Xz)),
0.41/0.60	    inference('sup-', [status(thm)], ['29', '30'])).
0.41/0.60	tff('32', plain,
0.41/0.60	    ![X5 : (a * a) > $o]:
0.41/0.60	      (X5(sk_Xy, sk_Xz)
0.41/0.60	       | ~ X5(sk_Xx02(X5), sk_Xy02(X5))
0.41/0.60	       | X5(sk_Xy03(X5), sk_Xz01(X5))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('33', plain,
0.41/0.60	    ![X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.41/0.60	      (X6 != X5
0.41/0.60	       | X5(sk_Xy, sk_Xz)
0.41/0.60	       | ~ X5(sk_Xx02(X6), sk_Xy02(X6))
0.41/0.60	       | X5(sk_Xy03(X6), sk_Xz01(X6))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['32'])).
0.41/0.60	tff('34', plain,
0.41/0.60	    ![X5 : (a * a) > $o]:
0.41/0.60	      (X5(sk_Xy, sk_Xz)
0.41/0.60	       | ~ X5(sk_Xx02(X5), sk_Xy02(X5))
0.41/0.60	       | X5(sk_Xx03(X5), sk_Xy03(X5))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('35', plain,
0.41/0.60	    ![X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.41/0.60	      (X6 != X5
0.41/0.60	       | X5(sk_Xy, sk_Xz)
0.41/0.60	       | ~ X5(sk_Xx02(X6), sk_Xy02(X6))
0.41/0.60	       | X5(sk_Xx03(X6), sk_Xy03(X6))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['34'])).
0.41/0.60	tff('36', plain,
0.41/0.60	    ![X0 : (a * a) > $o, X1 : a]:
0.41/0.60	      (~ $true
0.41/0.60	       | ~ sk_Xp(sk_Xx02(X0), sk_Xy02(X0))
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx03(X0), X1)
0.41/0.60	       | ~ sk_Xp(sk_Xy03(X0), X1)),
0.41/0.60	    inference('sup-', [status(thm)], ['35', '5'])).
0.41/0.60	tff('37', plain,
0.41/0.60	    ![X0 : (a * a) > $o, X1 : a]:
0.41/0.60	      (~ sk_Xp(sk_Xy03(X0), X1)
0.41/0.60	       | sk_Xp(sk_Xx03(X0), X1)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | ~ sk_Xp(sk_Xx02(X0), sk_Xy02(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['36'])).
0.41/0.60	tff('38', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (~ $true
0.41/0.60	       | ~ sk_Xp(sk_Xx02(X0), sk_Xy02(X0))
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | ~ sk_Xp(sk_Xx02(X0), sk_Xy02(X0))
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx03(X0), sk_Xz01(X0))),
0.41/0.60	    inference('sup-', [status(thm)], ['33', '37'])).
0.41/0.60	tff('39', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (sk_Xp(sk_Xx03(X0), sk_Xz01(X0))
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | ~ sk_Xp(sk_Xx02(X0), sk_Xy02(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['38'])).
0.41/0.60	tff('40', plain,
0.41/0.60	    ![X5 : (a * a) > $o]:
0.41/0.60	      (X5(sk_Xy, sk_Xz)
0.41/0.60	       | ~ X5(sk_Xx02(X5), sk_Xy02(X5))
0.41/0.60	       | ~ X5(sk_Xx03(X5), sk_Xz01(X5))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('41', plain,
0.41/0.60	    ![X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.41/0.60	      (X6 != X5
0.41/0.60	       | X5(sk_Xy, sk_Xz)
0.41/0.60	       | ~ X5(sk_Xx02(X6), sk_Xy02(X6))
0.41/0.60	       | ~ X5(sk_Xx03(X6), sk_Xz01(X6))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['40'])).
0.41/0.60	tff('42', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (~ sk_Xp(sk_Xx02(X0), sk_Xy02(X0)) | sk_Xp(sk_Xy, sk_Xz) | X0 != sk_Xp),
0.41/0.60	    inference('clc', [status(thm)], ['39', '41'])).
0.41/0.60	tff('43', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (~ $true
0.41/0.60	       | ~ sk_Xr(sk_Xx02(X0), sk_Xy02(X0))
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)),
0.41/0.60	    inference('sup-', [status(thm)], ['0', '42'])).
0.41/0.60	tff('44', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (sk_Xp(sk_Xy, sk_Xz) | X0 != sk_Xp | ~ sk_Xr(sk_Xx02(X0), sk_Xy02(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['43'])).
0.41/0.60	tff('45', plain,
0.41/0.60	    ![X5 : (a * a) > $o]:
0.41/0.60	      (X5(sk_Xy, sk_Xz)
0.41/0.60	       | sk_Xr(sk_Xx02(X5), sk_Xy02(X5))
0.41/0.60	       | X5(sk_Xy03(X5), sk_Xz01(X5))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('46', plain,
0.41/0.60	    ![X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.41/0.60	      (X6 != X5
0.41/0.60	       | X5(sk_Xy, sk_Xz)
0.41/0.60	       | sk_Xr(sk_Xx02(X6), sk_Xy02(X6))
0.41/0.60	       | X5(sk_Xy03(X6), sk_Xz01(X6))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['45'])).
0.41/0.60	tff('47', plain,
0.41/0.60	    ![X5 : (a * a) > $o]:
0.41/0.60	      (X5(sk_Xy, sk_Xz)
0.41/0.60	       | sk_Xr(sk_Xx02(X5), sk_Xy02(X5))
0.41/0.60	       | X5(sk_Xx03(X5), sk_Xy03(X5))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('48', plain,
0.41/0.60	    ![X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.41/0.60	      (X6 != X5
0.41/0.60	       | X5(sk_Xy, sk_Xz)
0.41/0.60	       | sk_Xr(sk_Xx02(X6), sk_Xy02(X6))
0.41/0.60	       | X5(sk_Xx03(X6), sk_Xy03(X6))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['47'])).
0.41/0.60	tff('49', plain,
0.41/0.60	    ![X0 : (a * a) > $o, X1 : a]:
0.41/0.60	      (~ $true
0.41/0.60	       | sk_Xr(sk_Xx02(X0), sk_Xy02(X0))
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx03(X0), X1)
0.41/0.60	       | ~ sk_Xp(sk_Xy03(X0), X1)),
0.41/0.60	    inference('sup-', [status(thm)], ['48', '5'])).
0.41/0.60	tff('50', plain,
0.41/0.60	    ![X0 : (a * a) > $o, X1 : a]:
0.41/0.60	      (~ sk_Xp(sk_Xy03(X0), X1)
0.41/0.60	       | sk_Xp(sk_Xx03(X0), X1)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | sk_Xr(sk_Xx02(X0), sk_Xy02(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['49'])).
0.41/0.60	tff('51', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (~ $true
0.41/0.60	       | sk_Xr(sk_Xx02(X0), sk_Xy02(X0))
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xr(sk_Xx02(X0), sk_Xy02(X0))
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xx03(X0), sk_Xz01(X0))),
0.41/0.60	    inference('sup-', [status(thm)], ['46', '50'])).
0.41/0.60	tff('52', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (sk_Xp(sk_Xx03(X0), sk_Xz01(X0))
0.41/0.60	       | X0 != sk_Xp
0.41/0.60	       | sk_Xp(sk_Xy, sk_Xz)
0.41/0.60	       | sk_Xr(sk_Xx02(X0), sk_Xy02(X0))),
0.41/0.60	    inference('simplify', [status(thm)], ['51'])).
0.41/0.60	tff('53', plain,
0.41/0.60	    ![X5 : (a * a) > $o]:
0.41/0.60	      (X5(sk_Xy, sk_Xz)
0.41/0.60	       | sk_Xr(sk_Xx02(X5), sk_Xy02(X5))
0.41/0.60	       | ~ X5(sk_Xx03(X5), sk_Xz01(X5))),
0.41/0.60	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.41/0.60	tff('54', plain,
0.41/0.60	    ![X5 : (a * a) > $o, X6 : (a * a) > $o]:
0.41/0.60	      (X6 != X5
0.41/0.60	       | X5(sk_Xy, sk_Xz)
0.41/0.60	       | sk_Xr(sk_Xx02(X6), sk_Xy02(X6))
0.41/0.60	       | ~ X5(sk_Xx03(X6), sk_Xz01(X6))),
0.41/0.60	    inference('ho.purify_applied_variable', [status(thm)], ['53'])).
0.41/0.60	tff('55', plain,
0.41/0.60	    ![X0 : (a * a) > $o]:
0.41/0.60	      (sk_Xr(sk_Xx02(X0), sk_Xy02(X0)) | sk_Xp(sk_Xy, sk_Xz) | X0 != sk_Xp),
0.41/0.60	    inference('clc', [status(thm)], ['52', '54'])).
0.41/0.60	tff('56', plain, ![X0 : (a * a) > $o]: (X0 != sk_Xp | sk_Xp(sk_Xy, sk_Xz)),
0.41/0.60	    inference('clc', [status(thm)], ['44', '55'])).
0.41/0.60	tff('57', plain, sk_Xp(sk_Xy, sk_Xz),
0.41/0.60	    inference('eq_res', [status(thm)], ['56'])).
0.41/0.60	tff('58', plain, (~ $true | ~ $true),
0.41/0.60	    inference('demod', [status(thm)], ['31', '57'])).
0.41/0.60	tff('59', plain, $false, inference('simplify', [status(thm)], ['58'])).
0.41/0.60	
0.41/0.60	% SZS output end Refutation
0.41/0.60	EOF
