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    : 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   : n173.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
51.11/51.37	% done 5727 iterations in 51.170s
51.11/51.37	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
51.11/51.37	% SZS output start Refutation
51.11/51.37	tff(cTHM251F_pme, conjecture,
51.11/51.37	  (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
51.11/51.37	     ((![Xq1:((a * a) > $o)]:
51.11/51.37	         (((![Xx0:a,Xy0:a,Xz:a]:
51.11/51.37	              ((Xq1(Xy0,Xz) & Xq1(Xx0,Xy0)) => Xq1(Xx0,Xz))) & 
51.11/51.37	           (![Xs:a,Xt:a]: ((S(Xs,Xt) | R(Xs,Xt)) => Xq1(Xs,Xt)))) =>
51.11/51.37	          Xq1(Xx,Xy))) =>
51.11/51.37	      (![Xp1:((a * a) > $o)]:
51.11/51.37	         (((![Xx0:a,Xy0:a,Xz:a]:
51.11/51.37	              ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz))) & 
51.11/51.37	           (![Xss:a,Xtt:a]:
51.11/51.37	              (((![Xq3:((a * a) > $o)]:
51.11/51.37	                   (((![Xx0:a,Xy0:a,Xz:a]:
51.11/51.37	                        ((Xq3(Xy0,Xz) & Xq3(Xx0,Xy0)) => Xq3(Xx0,Xz))) & 
51.11/51.37	                     (![Xssss:a,Xtttt:a]:
51.11/51.37	                        (S(Xssss,Xtttt) => Xq3(Xssss,Xtttt)))) =>
51.11/51.37	                    Xq3(Xss,Xtt))) | 
51.11/51.37	                (![Xq2:((a * a) > $o)]:
51.11/51.37	                   (((![Xx0:a,Xy0:a,Xz:a]:
51.11/51.37	                        ((Xq2(Xy0,Xz) & Xq2(Xx0,Xy0)) => Xq2(Xx0,Xz))) & 
51.11/51.37	                     (![Xsss:a,Xttt:a]: (R(Xsss,Xttt) => Xq2(Xsss,Xttt)))) =>
51.11/51.37	                    Xq2(Xss,Xtt)))) =>
51.11/51.37	               Xp1(Xss,Xtt)))) =>
51.11/51.37	          Xp1(Xx,Xy)))))).
51.11/51.37	tff(zf_stmt_0, negated_conjecture,
51.11/51.37	  (~
51.11/51.37	    (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
51.11/51.37	       ((![Xq1:((a * a) > $o)]:
51.11/51.37	           (((![Xx0:a,Xy0:a,Xz:a]:
51.11/51.37	                ((Xq1(Xy0,Xz) & Xq1(Xx0,Xy0)) => Xq1(Xx0,Xz))) & 
51.11/51.37	             (![Xs:a,Xt:a]: ((S(Xs,Xt) | R(Xs,Xt)) => Xq1(Xs,Xt)))) =>
51.11/51.37	            Xq1(Xx,Xy))) =>
51.11/51.37	        (![Xp1:((a * a) > $o)]:
51.11/51.37	           (((![Xx0:a,Xy0:a,Xz:a]:
51.11/51.37	                ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz))) & 
51.11/51.37	             (![Xss:a,Xtt:a]:
51.11/51.37	                (((![Xq3:((a * a) > $o)]:
51.11/51.37	                     (((![Xx0:a,Xy0:a,Xz:a]:
51.11/51.37	                          ((Xq3(Xy0,Xz) & Xq3(Xx0,Xy0)) => Xq3(Xx0,Xz))) & 
51.11/51.37	                       (![Xssss:a,Xtttt:a]:
51.11/51.37	                          (S(Xssss,Xtttt) => Xq3(Xssss,Xtttt)))) =>
51.11/51.37	                      Xq3(Xss,Xtt))) | 
51.11/51.37	                  (![Xq2:((a * a) > $o)]:
51.11/51.37	                     (((![Xx0:a,Xy0:a,Xz:a]:
51.11/51.37	                          ((Xq2(Xy0,Xz) & Xq2(Xx0,Xy0)) => Xq2(Xx0,Xz))) & 
51.11/51.37	                       (![Xsss:a,Xttt:a]: (R(Xsss,Xttt) => Xq2(Xsss,Xttt)))) =>
51.11/51.37	                      Xq2(Xss,Xtt)))) =>
51.11/51.37	                 Xp1(Xss,Xtt)))) =>
51.11/51.37	            Xp1(Xx,Xy))))))).
51.11/51.37	tff('0', plain,
51.11/51.37	    ![X0 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X0(sk_Xy0(X0), sk_Xz(X0))),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('1', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X2 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X2(sk_Xy0(X1), sk_Xz(X1))),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['0'])).
51.11/51.37	tff('2', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xy0(X1), sk_Xz(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('eq_res', [status(thm)], ['1'])).
51.11/51.37	tff('3', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X2 != X1
51.11/51.37	       | X0(sk_Xy0(X1), sk_Xz(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['2'])).
51.11/51.37	tff('4', plain,
51.11/51.37	    ![X0 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X0(sk_Xx0(X0), sk_Xy0(X0))),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('5', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X2 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X2(sk_Xx0(X1), sk_Xy0(X1))),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['4'])).
51.11/51.37	tff('6', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xx0(X1), sk_Xy0(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('eq_res', [status(thm)], ['5'])).
51.11/51.37	tff('7', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X2 != X1
51.11/51.37	       | X0(sk_Xx0(X1), sk_Xy0(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['6'])).
51.11/51.37	tff('8', plain,
51.11/51.37	    ![X13 : a, X14 : a, X15 : a]:
51.11/51.37	      (~ sk_Xp1(X13, X14) | ~ sk_Xp1(X14, X15) | sk_Xp1(X13, X15)),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('9', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2 != X0
51.11/51.37	       | sk_Xp1(sk_Xx0(X0), X1)
51.11/51.37	       | ~ sk_Xp1(sk_Xy0(X0), X1)),
51.11/51.37	    inference('sup-', [status(thm)], ['7', '8'])).
51.11/51.37	tff('10', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
51.11/51.37	      (~ sk_Xp1(sk_Xy0(X0), X1)
51.11/51.37	       | sk_Xp1(sk_Xx0(X0), X1)
51.11/51.37	       | X2 != X0
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['9'])).
51.11/51.37	tff('11', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2 != X0
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X1 != X0
51.11/51.37	       | sk_Xp1(sk_Xx0(X0), sk_Xz(X0))),
51.11/51.37	    inference('sup-', [status(thm)], ['3', '10'])).
51.11/51.37	tff('12', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (sk_Xp1(sk_Xx0(X0), sk_Xz(X0))
51.11/51.37	       | X1 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X0
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['11'])).
51.11/51.37	tff('13', plain,
51.11/51.37	    ![X0 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | ~ X0(sk_Xx0(X0), sk_Xz(X0))),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('14', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X2 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | ~ X2(sk_Xx0(X1), sk_Xz(X1))),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['13'])).
51.11/51.37	tff('15', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (~ X0(sk_Xx0(X1), sk_Xz(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('eq_res', [status(thm)], ['14'])).
51.11/51.37	tff('16', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X2 != X1
51.11/51.37	       | ~ X0(sk_Xx0(X1), sk_Xz(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['15'])).
51.11/51.37	tff('17', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (sk_Xp1 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_S(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0),
51.11/51.37	    inference('clc', [status(thm)], ['12', '16'])).
51.11/51.37	tff('18', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | X0 != X1
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | X0 != X1
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_Xp1 != X1),
51.11/51.37	    inference('eq_fact', [status(thm)], ['17'])).
51.11/51.37	tff('19', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (sk_Xp1 != X1
51.11/51.37	       | sk_R(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | sk_S(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('simplify', [status(thm)], ['18'])).
51.11/51.37	tff('20', plain,
51.11/51.37	    ![X1 : a, X2 : a, X6 : a, X7 : a]:
51.11/51.37	      (sk_Xp1(X1, X2) | sk_Xq3(X2, X1, X6, X7) | ~ sk_S(X6, X7)),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('21', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : a, X2 : a, X3 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | X3 != X0
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_Xq3(X2, X1, sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1(X1, X2)),
51.11/51.37	    inference('sup-', [status(thm)], ['19', '20'])).
51.11/51.37	tff('22', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : a, X2 : a, X3 : (a * a) > $o]:
51.11/51.37	      (sk_Xp1(X1, X2)
51.11/51.37	       | sk_Xq3(X2, X1, sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_R(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | X3 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['21'])).
51.11/51.37	tff('23', plain,
51.11/51.37	    ![X1 : a, X2 : a, X11 : a, X12 : a]:
51.11/51.37	      (sk_Xp1(X1, X2) | sk_Xq2(X2, X1, X11, X12) | ~ sk_R(X11, X12)),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('24', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : a, X2 : a, X3 : (a * a) > $o, X4 : a, X5 : a]:
51.11/51.37	      (~ $true
51.11/51.37	       | X3 != X0
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_Xq3(X5, X4, sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1(X4, X5)
51.11/51.37	       | sk_Xq2(X2, X1, sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1(X1, X2)),
51.11/51.37	    inference('sup-', [status(thm)], ['22', '23'])).
51.11/51.37	tff('25', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : a, X2 : a, X3 : (a * a) > $o, X4 : a, X5 : a]:
51.11/51.37	      (sk_Xp1(X1, X2)
51.11/51.37	       | sk_Xq2(X2, X1, sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1(X4, X5)
51.11/51.37	       | sk_Xq3(X5, X4, sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | X3 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['24'])).
51.11/51.37	tff('26', plain,
51.11/51.37	    ![X1 : a, X2 : a]: (sk_Xp1(X1, X2) | ~ sk_Xq3(X2, X1, X1, X2)),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('27', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : a, X3 : a]:
51.11/51.37	      (~ $true
51.11/51.37	       | X1 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xq2(X3, X2, sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1(X2, X3)
51.11/51.37	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
51.11/51.37	    inference('sup-', [status(thm)], ['25', '26'])).
51.11/51.37	tff('28', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : a, X3 : a]:
51.11/51.37	      (sk_Xp1(X2, X3)
51.11/51.37	       | sk_Xq2(X3, X2, sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['27'])).
51.11/51.37	tff('29', plain,
51.11/51.37	    ![X1 : a, X2 : a]: (sk_Xp1(X1, X2) | ~ sk_Xq2(X2, X1, X1, X2)),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('30', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | X1 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
51.11/51.37	    inference('sup-', [status(thm)], ['28', '29'])).
51.11/51.37	tff('31', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (sk_Xp1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['30'])).
51.11/51.37	tff('32', plain, ~ sk_Xp1(sk_Xx, sk_Xy),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('33', plain,
51.11/51.37	    ![X0 : (a * a) > $o]:
51.11/51.37	      (~ $true | sk_Xp1 != X0 | sk_Xp1 != X0 | sk_Xp1(sk_Xs(X0), sk_Xt(X0))),
51.11/51.37	    inference('sup-', [status(thm)], ['31', '32'])).
51.11/51.37	tff('34', plain,
51.11/51.37	    ![X0 : (a * a) > $o]: (sk_Xp1(sk_Xs(X0), sk_Xt(X0)) | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['33'])).
51.11/51.37	tff('35', plain,
51.11/51.37	    ![X0 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X0(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X0(sk_Xy0(X0), sk_Xz(X0))),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('36', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (X3 != X0
51.11/51.37	       | X2 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X1(sk_Xs(X2), sk_Xt(X2))
51.11/51.37	       | X3(sk_Xy0(X2), sk_Xz(X2))),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['35'])).
51.11/51.37	tff('37', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xy0(X1), sk_Xz(X1))
51.11/51.37	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X1
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('eq_res', [status(thm)], ['36'])).
51.11/51.37	tff('38', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (X3 != X1
51.11/51.37	       | X0(sk_Xy0(X1), sk_Xz(X1))
51.11/51.37	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X1
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['37'])).
51.11/51.37	tff('39', plain,
51.11/51.37	    ![X0 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X0(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X0(sk_Xx0(X0), sk_Xy0(X0))),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('40', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (X3 != X0
51.11/51.37	       | X2 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X1(sk_Xs(X2), sk_Xt(X2))
51.11/51.37	       | X3(sk_Xx0(X2), sk_Xy0(X2))),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['39'])).
51.11/51.37	tff('41', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xx0(X1), sk_Xy0(X1))
51.11/51.37	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X1
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('eq_res', [status(thm)], ['40'])).
51.11/51.37	tff('42', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (X3 != X1
51.11/51.37	       | X0(sk_Xx0(X1), sk_Xy0(X1))
51.11/51.37	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X1
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['41'])).
51.11/51.37	tff('43', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o, X3 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X2 != X0
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X3 != X0
51.11/51.37	       | sk_Xp1(sk_Xx0(X0), X1)
51.11/51.37	       | ~ sk_Xp1(sk_Xy0(X0), X1)),
51.11/51.37	    inference('sup-', [status(thm)], ['42', '8'])).
51.11/51.37	tff('44', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o, X3 : (a * a) > $o]:
51.11/51.37	      (~ sk_Xp1(sk_Xy0(X0), X1)
51.11/51.37	       | sk_Xp1(sk_Xx0(X0), X1)
51.11/51.37	       | X3 != X0
51.11/51.37	       | ~ X2(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X0
51.11/51.37	       | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['43'])).
51.11/51.37	tff('45', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X3 != X0
51.11/51.37	       | X4(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X3(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X4 != X0
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2 != X0
51.11/51.37	       | sk_Xp1(sk_Xx0(X0), sk_Xz(X0))),
51.11/51.37	    inference('sup-', [status(thm)], ['38', '44'])).
51.11/51.37	tff('46', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
51.11/51.37	      (sk_Xp1(sk_Xx0(X0), sk_Xz(X0))
51.11/51.37	       | X2 != X0
51.11/51.37	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0
51.11/51.37	       | X4 != X0
51.11/51.37	       | ~ X3(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X4(sk_Xx, sk_Xy)
51.11/51.37	       | X3 != X0
51.11/51.37	       | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['45'])).
51.11/51.37	tff('47', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X1
51.11/51.37	       | X2 != X1
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X0 != X1
51.11/51.37	       | X3 != X1
51.11/51.37	       | ~ X3(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X0 != X1
51.11/51.37	       | sk_Xp1(sk_Xx0(X1), sk_Xz(X1))),
51.11/51.37	    inference('eq_fact', [status(thm)], ['46'])).
51.11/51.37	tff('48', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (sk_Xp1(sk_Xx0(X1), sk_Xz(X1))
51.11/51.37	       | ~ X3(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X3 != X1
51.11/51.37	       | X0 != X1
51.11/51.37	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X1
51.11/51.37	       | sk_Xp1 != X1),
51.11/51.37	    inference('simplify', [status(thm)], ['47'])).
51.11/51.37	tff('49', plain,
51.11/51.37	    ![X0 : (a * a) > $o]:
51.11/51.37	      (X0(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X0(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | ~ X0(sk_Xx0(X0), sk_Xz(X0))),
51.11/51.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
51.11/51.37	tff('50', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (X3 != X0
51.11/51.37	       | X2 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X0(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X1(sk_Xs(X2), sk_Xt(X2))
51.11/51.37	       | ~ X3(sk_Xx0(X2), sk_Xz(X2))),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['49'])).
51.11/51.37	tff('51', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (~ X0(sk_Xx0(X1), sk_Xz(X1))
51.11/51.37	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X1
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('eq_res', [status(thm)], ['50'])).
51.11/51.37	tff('52', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (X3 != X1
51.11/51.37	       | ~ X0(sk_Xx0(X1), sk_Xz(X1))
51.11/51.37	       | ~ X2(sk_Xs(X1), sk_Xt(X1))
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X1
51.11/51.37	       | X0 != X1),
51.11/51.37	    inference('ho.purify_applied_variable', [status(thm)], ['51'])).
51.11/51.37	tff('53', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X3 != X0
51.11/51.37	       | X4(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X3(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X4 != X0
51.11/51.37	       | X5 != X0
51.11/51.37	       | ~ X5(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2 != X0),
51.11/51.37	    inference('sup-', [status(thm)], ['48', '52'])).
51.11/51.37	tff('54', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
51.11/51.37	      (X2 != X0
51.11/51.37	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0
51.11/51.37	       | ~ X5(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X5 != X0
51.11/51.37	       | X4 != X0
51.11/51.37	       | ~ X3(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X4(sk_Xx, sk_Xy)
51.11/51.37	       | X3 != X0
51.11/51.37	       | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['53'])).
51.11/51.37	tff('55', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2 != X0
51.11/51.37	       | X3 != X0
51.11/51.37	       | ~ X3(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X4(sk_Xx, sk_Xy)
51.11/51.37	       | X4 != X0),
51.11/51.37	    inference('sup-', [status(thm)], ['34', '54'])).
51.11/51.37	tff('56', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
51.11/51.37	      (X4 != X0
51.11/51.37	       | X4(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X3(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X3 != X0
51.11/51.37	       | X2 != X0
51.11/51.37	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0
51.11/51.37	       | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['55'])).
51.11/51.37	tff('57', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X1 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2 != X0
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | X3 != X0),
51.11/51.37	    inference('sup-', [status(thm)], ['34', '56'])).
51.11/51.37	tff('58', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
51.11/51.37	      X3 : (a * a) > $o]:
51.11/51.37	      (X3 != X0
51.11/51.37	       | X3(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X0
51.11/51.37	       | ~ X1(sk_Xs(X0), sk_Xt(X0))
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0
51.11/51.37	       | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['57'])).
51.11/51.37	tff('59', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (~ $true
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | sk_Xp1 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X2 != X0),
51.11/51.37	    inference('sup-', [status(thm)], ['34', '58'])).
51.11/51.37	tff('60', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
51.11/51.37	      (X2 != X0
51.11/51.37	       | X2(sk_Xx, sk_Xy)
51.11/51.37	       | X1 != X0
51.11/51.37	       | X1(sk_Xx, sk_Xy)
51.11/51.37	       | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['59'])).
51.11/51.37	tff('61', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (~ $true | sk_Xp1 != X0 | X1(sk_Xx, sk_Xy) | X1 != X0 | sk_Xp1 != X0),
51.11/51.37	    inference('sup-', [status(thm)], ['60', '32'])).
51.11/51.37	tff('62', plain,
51.11/51.37	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
51.11/51.37	      (X1 != X0 | X1(sk_Xx, sk_Xy) | sk_Xp1 != X0),
51.11/51.37	    inference('simplify', [status(thm)], ['61'])).
51.11/51.37	tff('63', plain,
51.11/51.37	    ![X0 : (a * a) > $o]: (~ $true | sk_Xp1 != X0 | sk_Xp1 != X0),
51.11/51.37	    inference('sup-', [status(thm)], ['62', '32'])).
51.11/51.37	tff('64', plain, ![X0 : (a * a) > $o]: sk_Xp1 != X0,
51.11/51.37	    inference('simplify', [status(thm)], ['63'])).
51.11/51.37	tff('65', plain, $false, inference('eq_res', [status(thm)], ['64'])).
51.11/51.37	
51.11/51.37	% SZS output end Refutation
51.11/51.38	EOF
