0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_ext
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n145.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 17:46:53 CST 2018
68.11/68.32	% done 6991 iterations in 68.124s
68.11/68.32	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
68.11/68.32	% SZS output start Refutation
68.11/68.33	tff(cTHM251F_pme, conjecture,
68.11/68.33	  (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
68.11/68.33	     ((![Xq1:((a * a) > $o)]:
68.11/68.33	         (((![Xx0:a,Xy0:a,Xz:a]:
68.11/68.33	              ((Xq1(Xy0,Xz) & Xq1(Xx0,Xy0)) => Xq1(Xx0,Xz))) & 
68.11/68.33	           (![Xs:a,Xt:a]: ((S(Xs,Xt) | R(Xs,Xt)) => Xq1(Xs,Xt)))) =>
68.11/68.33	          Xq1(Xx,Xy))) =>
68.11/68.33	      (![Xp1:((a * a) > $o)]:
68.11/68.33	         (((![Xx0:a,Xy0:a,Xz:a]:
68.11/68.33	              ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz))) & 
68.11/68.33	           (![Xss:a,Xtt:a]:
68.11/68.33	              (((![Xq3:((a * a) > $o)]:
68.11/68.33	                   (((![Xx0:a,Xy0:a,Xz:a]:
68.11/68.33	                        ((Xq3(Xy0,Xz) & Xq3(Xx0,Xy0)) => Xq3(Xx0,Xz))) & 
68.11/68.33	                     (![Xssss:a,Xtttt:a]:
68.11/68.33	                        (S(Xssss,Xtttt) => Xq3(Xssss,Xtttt)))) =>
68.11/68.33	                    Xq3(Xss,Xtt))) | 
68.11/68.33	                (![Xq2:((a * a) > $o)]:
68.11/68.33	                   (((![Xx0:a,Xy0:a,Xz:a]:
68.11/68.33	                        ((Xq2(Xy0,Xz) & Xq2(Xx0,Xy0)) => Xq2(Xx0,Xz))) & 
68.11/68.33	                     (![Xsss:a,Xttt:a]: (R(Xsss,Xttt) => Xq2(Xsss,Xttt)))) =>
68.11/68.33	                    Xq2(Xss,Xtt)))) =>
68.11/68.33	               Xp1(Xss,Xtt)))) =>
68.11/68.33	          Xp1(Xx,Xy)))))).
68.11/68.33	tff(zf_stmt_0, negated_conjecture,
68.11/68.33	  (~
68.11/68.33	    (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
68.11/68.33	       ((![Xq1:((a * a) > $o)]:
68.11/68.33	           (((![Xx0:a,Xy0:a,Xz:a]:
68.11/68.33	                ((Xq1(Xy0,Xz) & Xq1(Xx0,Xy0)) => Xq1(Xx0,Xz))) & 
68.11/68.33	             (![Xs:a,Xt:a]: ((S(Xs,Xt) | R(Xs,Xt)) => Xq1(Xs,Xt)))) =>
68.11/68.33	            Xq1(Xx,Xy))) =>
68.11/68.33	        (![Xp1:((a * a) > $o)]:
68.11/68.33	           (((![Xx0:a,Xy0:a,Xz:a]:
68.11/68.33	                ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz))) & 
68.11/68.33	             (![Xss:a,Xtt:a]:
68.11/68.33	                (((![Xq3:((a * a) > $o)]:
68.11/68.33	                     (((![Xx0:a,Xy0:a,Xz:a]:
68.11/68.33	                          ((Xq3(Xy0,Xz) & Xq3(Xx0,Xy0)) => Xq3(Xx0,Xz))) & 
68.11/68.33	                       (![Xssss:a,Xtttt:a]:
68.11/68.33	                          (S(Xssss,Xtttt) => Xq3(Xssss,Xtttt)))) =>
68.11/68.33	                      Xq3(Xss,Xtt))) | 
68.11/68.33	                  (![Xq2:((a * a) > $o)]:
68.11/68.33	                     (((![Xx0:a,Xy0:a,Xz:a]:
68.11/68.33	                          ((Xq2(Xy0,Xz) & Xq2(Xx0,Xy0)) => Xq2(Xx0,Xz))) & 
68.11/68.33	                       (![Xsss:a,Xttt:a]: (R(Xsss,Xttt) => Xq2(Xsss,Xttt)))) =>
68.11/68.33	                      Xq2(Xss,Xtt)))) =>
68.11/68.33	                 Xp1(Xss,Xtt)))) =>
68.11/68.33	            Xp1(Xx,Xy))))))).
68.11/68.33	tff('0', plain,
68.11/68.33	    ![X0 : (a * a) > $o]:
68.11/68.33	      (X0(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | sk_S(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X0(sk_Xy0(X0), sk_Xz(X0))),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('1', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X2 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | sk_S(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X2(sk_Xy0(X1), sk_Xz(X1))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['0'])).
68.11/68.33	tff('2', plain,
68.11/68.33	    ![X1 : a, X2 : a, X6 : a, X7 : a]:
68.11/68.33	      (sk_Xp1(X1, X2) | sk_Xq3(X2, X1, X6, X7) | ~ sk_S(X6, X7)),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('3', plain,
68.11/68.33	    ![X1 : a, X2 : a]: (sk_Xp1(X1, X2) | ~ sk_Xq3(X2, X1, X1, X2)),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('4', plain,
68.11/68.33	    ![X0 : a, X1 : a]:
68.11/68.33	      (~ $true | ~ sk_S(X1, X0) | sk_Xp1(X1, X0) | sk_Xp1(X1, X0)),
68.11/68.33	    inference('sup-', [status(thm)], ['2', '3'])).
68.11/68.33	tff('5', plain, ![X0 : a, X1 : a]: (sk_Xp1(X1, X0) | ~ sk_S(X1, X0)),
68.11/68.33	    inference('simplify', [status(thm)], ['4'])).
68.11/68.33	tff('6', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X1(sk_Xy0(X0), sk_Xz(X0))
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X0 != X2
68.11/68.33	       | X1 != X2
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
68.11/68.33	    inference('sup-', [status(thm)], ['1', '5'])).
68.11/68.33	tff('7', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X2
68.11/68.33	       | X0 != X2
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1(sk_Xy0(X0), sk_Xz(X0))),
68.11/68.33	    inference('simplify', [status(thm)], ['6'])).
68.11/68.33	tff('8', plain,
68.11/68.33	    ![X1 : a, X2 : a, X11 : a, X12 : a]:
68.11/68.33	      (sk_Xp1(X1, X2) | sk_Xq2(X2, X1, X11, X12) | ~ sk_R(X11, X12)),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('9', plain,
68.11/68.33	    ![X1 : a, X2 : a]: (sk_Xp1(X1, X2) | ~ sk_Xq2(X2, X1, X1, X2)),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('10', plain,
68.11/68.33	    ![X0 : a, X1 : a]:
68.11/68.33	      (~ $true | ~ sk_R(X1, X0) | sk_Xp1(X1, X0) | sk_Xp1(X1, X0)),
68.11/68.33	    inference('sup-', [status(thm)], ['8', '9'])).
68.11/68.33	tff('11', plain, ![X0 : a, X1 : a]: (sk_Xp1(X1, X0) | ~ sk_R(X1, X0)),
68.11/68.33	    inference('simplify', [status(thm)], ['10'])).
68.11/68.33	tff('12', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X1(sk_Xy0(X0), sk_Xz(X0))
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X0 != X2
68.11/68.33	       | X1 != X2
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
68.11/68.33	    inference('clc', [status(thm)], ['7', '11'])).
68.11/68.33	tff('13', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | X1(sk_Xy0(X0), sk_Xz(X0))),
68.11/68.33	    inference('eq_res', [status(thm)], ['12'])).
68.11/68.33	tff('14', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X2 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X1(sk_Xy0(X0), sk_Xz(X0))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['13'])).
68.11/68.33	tff('15', plain,
68.11/68.33	    ![X0 : (a * a) > $o]:
68.11/68.33	      (X0(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | sk_S(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X0(sk_Xx0(X0), sk_Xy0(X0))),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('16', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X2 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | sk_S(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X2(sk_Xx0(X1), sk_Xy0(X1))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['15'])).
68.11/68.33	tff('17', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X1(sk_Xx0(X0), sk_Xy0(X0))
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X0 != X2
68.11/68.33	       | X1 != X2
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
68.11/68.33	    inference('sup-', [status(thm)], ['16', '5'])).
68.11/68.33	tff('18', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X2
68.11/68.33	       | X0 != X2
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1(sk_Xx0(X0), sk_Xy0(X0))),
68.11/68.33	    inference('simplify', [status(thm)], ['17'])).
68.11/68.33	tff('19', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X1(sk_Xx0(X0), sk_Xy0(X0))
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X0 != X2
68.11/68.33	       | X1 != X2
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
68.11/68.33	    inference('clc', [status(thm)], ['18', '11'])).
68.11/68.33	tff('20', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | X1(sk_Xx0(X0), sk_Xy0(X0))),
68.11/68.33	    inference('eq_res', [status(thm)], ['19'])).
68.11/68.33	tff('21', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X2 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X1(sk_Xx0(X0), sk_Xy0(X0))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['20'])).
68.11/68.33	tff('22', plain,
68.11/68.33	    ![X13 : a, X14 : a, X15 : a]:
68.11/68.33	      (~ sk_Xp1(X13, X14) | ~ sk_Xp1(X14, X15) | sk_Xp1(X13, X15)),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('23', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X0
68.11/68.33	       | sk_Xp1(sk_Xx0(X0), X1)
68.11/68.33	       | ~ sk_Xp1(sk_Xy0(X0), X1)),
68.11/68.33	    inference('sup-', [status(thm)], ['21', '22'])).
68.11/68.33	tff('24', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
68.11/68.33	      (~ sk_Xp1(sk_Xy0(X0), X1)
68.11/68.33	       | sk_Xp1(sk_Xx0(X0), X1)
68.11/68.33	       | X2 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)),
68.11/68.33	    inference('simplify', [status(thm)], ['23'])).
68.11/68.33	tff('25', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1(sk_Xx, sk_Xy)
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | sk_Xp1(sk_Xx0(X0), sk_Xz(X0))),
68.11/68.33	    inference('sup-', [status(thm)], ['14', '24'])).
68.11/68.33	tff('26', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | X1(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)),
68.11/68.33	    inference('simplify', [status(thm)], ['25'])).
68.11/68.33	tff('27', plain,
68.11/68.33	    ![X0 : (a * a) > $o]:
68.11/68.33	      (X0(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | sk_S(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | ~ X0(sk_Xx0(X0), sk_Xz(X0))),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('28', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X2 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | sk_S(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | ~ X2(sk_Xx0(X1), sk_Xz(X1))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['27'])).
68.11/68.33	tff('29', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | ~ X1(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X0 != X2
68.11/68.33	       | X1 != X2
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
68.11/68.33	    inference('sup-', [status(thm)], ['28', '5'])).
68.11/68.33	tff('30', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X2
68.11/68.33	       | X0 != X2
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | sk_R(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | ~ X1(sk_Xx0(X0), sk_Xz(X0))),
68.11/68.33	    inference('simplify', [status(thm)], ['29'])).
68.11/68.33	tff('31', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ X1(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X0 != X2
68.11/68.33	       | X1 != X2
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
68.11/68.33	    inference('clc', [status(thm)], ['30', '11'])).
68.11/68.33	tff('32', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | ~ X1(sk_Xx0(X0), sk_Xz(X0))),
68.11/68.33	    inference('eq_res', [status(thm)], ['31'])).
68.11/68.33	tff('33', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X2 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | ~ X1(sk_Xx0(X0), sk_Xz(X0))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['32'])).
68.11/68.33	tff('34', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X2(sk_Xx, sk_Xy)
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1(sk_Xx, sk_Xy)
68.11/68.33	       | X1 != X0),
68.11/68.33	    inference('clc', [status(thm)], ['26', '33'])).
68.11/68.33	tff('35', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X0 != X1
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | X0 != X1
68.11/68.33	       | sk_Xp1(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | sk_Xp1 != X1),
68.11/68.33	    inference('eq_fact', [status(thm)], ['34'])).
68.11/68.33	tff('36', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1 != X1
68.11/68.33	       | sk_Xp1(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | X0 != X1),
68.11/68.33	    inference('simplify', [status(thm)], ['35'])).
68.11/68.33	tff('37', plain,
68.11/68.33	    ![X0 : (a * a) > $o]:
68.11/68.33	      (X0(sk_Xx, sk_Xy)
68.11/68.33	       | ~ X0(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X0(sk_Xy0(X0), sk_Xz(X0))),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('38', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X0
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | ~ X1(sk_Xs(X2), sk_Xt(X2))
68.11/68.33	       | X3(sk_Xy0(X2), sk_Xz(X2))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['37'])).
68.11/68.33	tff('39', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X0(sk_Xy0(X1), sk_Xz(X1))
68.11/68.33	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0),
68.11/68.33	    inference('eq_res', [status(thm)], ['38'])).
68.11/68.33	tff('40', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X0
68.11/68.33	       | X0(sk_Xy0(X1), sk_Xz(X1))
68.11/68.33	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X3(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['39'])).
68.11/68.33	tff('41', plain, ~ sk_Xp1(sk_Xx, sk_Xy),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('42', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X0 != X1
68.11/68.33	       | X2 != X1
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1(sk_Xy0(X0), sk_Xz(X0))
68.11/68.33	       | sk_Xp1 != X1),
68.11/68.33	    inference('sup-', [status(thm)], ['40', '41'])).
68.11/68.33	tff('43', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1 != X1
68.11/68.33	       | X1(sk_Xy0(X0), sk_Xz(X0))
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X1
68.11/68.33	       | X0 != X1),
68.11/68.33	    inference('simplify', [status(thm)], ['42'])).
68.11/68.33	tff('44', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X1
68.11/68.33	       | sk_Xp1 != X1
68.11/68.33	       | X3(sk_Xy0(X0), sk_Xz(X0))
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X1
68.11/68.33	       | X0 != X1),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['43'])).
68.11/68.33	tff('45', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X0 != X1
68.11/68.33	       | ~ X0(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X2(sk_Xy0(X1), sk_Xz(X1))
68.11/68.33	       | sk_Xp1 != X1
68.11/68.33	       | X2 != X1),
68.11/68.33	    inference('eq_res', [status(thm)], ['44'])).
68.11/68.33	tff('46', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X2 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X1(sk_Xy0(X0), sk_Xz(X0))
68.11/68.33	       | sk_Xp1 != X0),
68.11/68.33	    inference('sup-', [status(thm)], ['36', '45'])).
68.11/68.33	tff('47', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X1(sk_Xy0(X0), sk_Xz(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0),
68.11/68.33	    inference('simplify', [status(thm)], ['46'])).
68.11/68.33	tff('48', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | X1(sk_Xy0(X0), sk_Xz(X0))),
68.11/68.33	    inference('sup-', [status(thm)], ['47', '41'])).
68.11/68.33	tff('49', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (X1(sk_Xy0(X0), sk_Xz(X0)) | X1 != X0 | sk_Xp1 != X0),
68.11/68.33	    inference('simplify', [status(thm)], ['48'])).
68.11/68.33	tff('50', plain,
68.11/68.33	    ![X0 : (a * a) > $o]:
68.11/68.33	      (X0(sk_Xx, sk_Xy)
68.11/68.33	       | ~ X0(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X0(sk_Xx0(X0), sk_Xy0(X0))),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('51', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X0
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | ~ X1(sk_Xs(X2), sk_Xt(X2))
68.11/68.33	       | X3(sk_Xx0(X2), sk_Xy0(X2))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['50'])).
68.11/68.33	tff('52', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X0(sk_Xx0(X1), sk_Xy0(X1))
68.11/68.33	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0),
68.11/68.33	    inference('eq_res', [status(thm)], ['51'])).
68.11/68.33	tff('53', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X0
68.11/68.33	       | X0(sk_Xx0(X1), sk_Xy0(X1))
68.11/68.33	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X3(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['52'])).
68.11/68.33	tff('54', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X0 != X1
68.11/68.33	       | X2 != X1
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1(sk_Xx0(X0), sk_Xy0(X0))
68.11/68.33	       | sk_Xp1 != X1),
68.11/68.33	    inference('sup-', [status(thm)], ['53', '41'])).
68.11/68.33	tff('55', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1 != X1
68.11/68.33	       | X1(sk_Xx0(X0), sk_Xy0(X0))
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X1
68.11/68.33	       | X0 != X1),
68.11/68.33	    inference('simplify', [status(thm)], ['54'])).
68.11/68.33	tff('56', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X1
68.11/68.33	       | sk_Xp1 != X1
68.11/68.33	       | X3(sk_Xx0(X0), sk_Xy0(X0))
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X1
68.11/68.33	       | X0 != X1),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['55'])).
68.11/68.33	tff('57', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X0 != X1
68.11/68.33	       | ~ X0(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X2(sk_Xx0(X1), sk_Xy0(X1))
68.11/68.33	       | sk_Xp1 != X1
68.11/68.33	       | X2 != X1),
68.11/68.33	    inference('eq_res', [status(thm)], ['56'])).
68.11/68.33	tff('58', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X0
68.11/68.33	       | sk_Xp1(sk_Xx0(X0), X1)
68.11/68.33	       | ~ sk_Xp1(sk_Xy0(X0), X1)),
68.11/68.33	    inference('sup-', [status(thm)], ['57', '22'])).
68.11/68.33	tff('59', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
68.11/68.33	      (~ sk_Xp1(sk_Xy0(X0), X1)
68.11/68.33	       | sk_Xp1(sk_Xx0(X0), X1)
68.11/68.33	       | X2 != X0
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | sk_Xp1 != X0),
68.11/68.33	    inference('simplify', [status(thm)], ['58'])).
68.11/68.33	tff('60', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | sk_Xp1(sk_Xx0(X0), sk_Xz(X0))),
68.11/68.33	    inference('sup-', [status(thm)], ['49', '59'])).
68.11/68.33	tff('61', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | sk_Xp1 != X0),
68.11/68.33	    inference('simplify', [status(thm)], ['60'])).
68.11/68.33	tff('62', plain,
68.11/68.33	    ![X0 : (a * a) > $o]:
68.11/68.33	      (X0(sk_Xx, sk_Xy)
68.11/68.33	       | ~ X0(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | ~ X0(sk_Xx0(X0), sk_Xz(X0))),
68.11/68.33	    inference('cnf', [status(esa)], [zf_stmt_0])).
68.11/68.33	tff('63', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X0
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | ~ X1(sk_Xs(X2), sk_Xt(X2))
68.11/68.33	       | ~ X3(sk_Xx0(X2), sk_Xz(X2))),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['62'])).
68.11/68.33	tff('64', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ X0(sk_Xx0(X1), sk_Xz(X1))
68.11/68.33	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X0(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0),
68.11/68.33	    inference('eq_res', [status(thm)], ['63'])).
68.11/68.33	tff('65', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X0
68.11/68.33	       | ~ X0(sk_Xx0(X1), sk_Xz(X1))
68.11/68.33	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | X3(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0
68.11/68.33	       | X1 != X0),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['64'])).
68.11/68.33	tff('66', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X0 != X1
68.11/68.33	       | X2 != X1
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | ~ X1(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | sk_Xp1 != X1),
68.11/68.33	    inference('sup-', [status(thm)], ['65', '41'])).
68.11/68.33	tff('67', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1 != X1
68.11/68.33	       | ~ X1(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X1
68.11/68.33	       | X0 != X1),
68.11/68.33	    inference('simplify', [status(thm)], ['66'])).
68.11/68.33	tff('68', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
68.11/68.33	      X3 : (a * a) > $o]:
68.11/68.33	      (X3 != X1
68.11/68.33	       | sk_Xp1 != X1
68.11/68.33	       | ~ X3(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X2 != X1
68.11/68.33	       | X0 != X1),
68.11/68.33	    inference('ho.purify_applied_variable', [status(thm)], ['67'])).
68.11/68.33	tff('69', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (X0 != X1
68.11/68.33	       | ~ X0(sk_Xs(X1), sk_Xt(X1))
68.11/68.33	       | ~ X2(sk_Xx0(X1), sk_Xz(X1))
68.11/68.33	       | sk_Xp1 != X1
68.11/68.33	       | X2 != X1),
68.11/68.33	    inference('eq_res', [status(thm)], ['68'])).
68.11/68.33	tff('70', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X2 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | ~ X1(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | sk_Xp1 != X0),
68.11/68.33	    inference('sup-', [status(thm)], ['36', '69'])).
68.11/68.33	tff('71', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
68.11/68.33	      (~ X1(sk_Xx0(X0), sk_Xz(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X2(sk_Xx, sk_Xy)
68.11/68.33	       | X2 != X0),
68.11/68.33	    inference('simplify', [status(thm)], ['70'])).
68.11/68.33	tff('72', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | X1 != X0
68.11/68.33	       | ~ X1(sk_Xx0(X0), sk_Xz(X0))),
68.11/68.33	    inference('sup-', [status(thm)], ['71', '41'])).
68.11/68.33	tff('73', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (~ X1(sk_Xx0(X0), sk_Xz(X0)) | X1 != X0 | sk_Xp1 != X0),
68.11/68.33	    inference('simplify', [status(thm)], ['72'])).
68.11/68.33	tff('74', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
68.11/68.33	       | X1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1 != X0),
68.11/68.33	    inference('sup-', [status(thm)], ['61', '73'])).
68.11/68.33	tff('75', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (X1 != X0 | ~ X1(sk_Xs(X0), sk_Xt(X0)) | sk_Xp1 != X0),
68.11/68.33	    inference('simplify', [status(thm)], ['74'])).
68.11/68.33	tff('76', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (~ $true
68.11/68.33	       | X1 != X0
68.11/68.33	       | X1(sk_Xx, sk_Xy)
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1 != X0
68.11/68.33	       | sk_Xp1 != X0),
68.11/68.33	    inference('sup-', [status(thm)], ['36', '75'])).
68.11/68.33	tff('77', plain,
68.11/68.33	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
68.11/68.33	      (sk_Xp1 != X0 | X1(sk_Xx, sk_Xy) | X1 != X0),
68.11/68.33	    inference('simplify', [status(thm)], ['76'])).
68.11/68.33	tff('78', plain,
68.11/68.33	    ![X0 : (a * a) > $o]: (~ $true | sk_Xp1 != X0 | sk_Xp1 != X0),
68.11/68.33	    inference('sup-', [status(thm)], ['77', '41'])).
68.11/68.33	tff('79', plain, ![X0 : (a * a) > $o]: sk_Xp1 != X0,
68.11/68.33	    inference('simplify', [status(thm)], ['78'])).
68.11/68.33	tff('80', plain, $false, inference('eq_res', [status(thm)], ['79'])).
68.11/68.33	
68.11/68.33	% SZS output end Refutation
68.11/68.34	EOF
