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_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   : n029.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 17:56:38 CST 2018
1.94/2.12	% done 929 iterations in 1.920s
1.94/2.12	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
1.94/2.12	% SZS output start Refutation
1.94/2.13	tff(cTHM251B_pme, conjecture,
1.94/2.13	  (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
1.94/2.13	     ((![Xq:(a > $o)]:
1.94/2.13	         (((![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv))) & 
1.94/2.13	           (![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw)))) =>
1.94/2.13	          Xq(Xy))) =>
1.94/2.13	      (![Xq:(a > $o)]:
1.94/2.13	         (((![Xu:a,Xv:a]:
1.94/2.13	              ((((![Xq0:(a > $o)]:
1.94/2.13	                    (((![Xu0:a,Xv0:a]: ((S(Xu0,Xv0) & Xq0(Xu0)) => Xq0(Xv0))) & 
1.94/2.13	                      (![Xw:a]: (S(Xu,Xw) => Xq0(Xw)))) =>
1.94/2.13	                     Xq0(Xv))) | 
1.94/2.13	                 (![Xq0:(a > $o)]:
1.94/2.13	                    (((![Xu0:a,Xv0:a]: ((R(Xu0,Xv0) & Xq0(Xu0)) => Xq0(Xv0))) & 
1.94/2.13	                      (![Xw:a]: (R(Xu,Xw) => Xq0(Xw)))) =>
1.94/2.13	                     Xq0(Xv)))) & 
1.94/2.13	                Xq(Xu)) =>
1.94/2.13	               Xq(Xv))) & 
1.94/2.13	           (![Xw:a]:
1.94/2.13	              (((![Xq0:(a > $o)]:
1.94/2.13	                   (((![Xu:a,Xv:a]: ((S(Xu,Xv) & Xq0(Xu)) => Xq0(Xv))) & 
1.94/2.13	                     (![Xw0:a]: (S(Xx,Xw0) => Xq0(Xw0)))) =>
1.94/2.13	                    Xq0(Xw))) | 
1.94/2.13	                (![Xq0:(a > $o)]:
1.94/2.13	                   (((![Xu:a,Xv:a]: ((R(Xu,Xv) & Xq0(Xu)) => Xq0(Xv))) & 
1.94/2.13	                     (![Xw0:a]: (R(Xx,Xw0) => Xq0(Xw0)))) =>
1.94/2.13	                    Xq0(Xw)))) =>
1.94/2.13	               Xq(Xw)))) =>
1.94/2.13	          Xq(Xy)))))).
1.94/2.13	tff(zf_stmt_0, negated_conjecture,
1.94/2.13	  (~
1.94/2.13	    (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
1.94/2.13	       ((![Xq:(a > $o)]:
1.94/2.13	           (((![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv))) & 
1.94/2.13	             (![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw)))) =>
1.94/2.13	            Xq(Xy))) =>
1.94/2.13	        (![Xq:(a > $o)]:
1.94/2.13	           (((![Xu:a,Xv:a]:
1.94/2.13	                ((((![Xq0:(a > $o)]:
1.94/2.13	                      (((![Xu0:a,Xv0:a]:
1.94/2.13	                           ((S(Xu0,Xv0) & Xq0(Xu0)) => Xq0(Xv0))) & 
1.94/2.13	                        (![Xw:a]: (S(Xu,Xw) => Xq0(Xw)))) =>
1.94/2.13	                       Xq0(Xv))) | 
1.94/2.13	                   (![Xq0:(a > $o)]:
1.94/2.13	                      (((![Xu0:a,Xv0:a]:
1.94/2.13	                           ((R(Xu0,Xv0) & Xq0(Xu0)) => Xq0(Xv0))) & 
1.94/2.13	                        (![Xw:a]: (R(Xu,Xw) => Xq0(Xw)))) =>
1.94/2.13	                       Xq0(Xv)))) & 
1.94/2.13	                  Xq(Xu)) =>
1.94/2.13	                 Xq(Xv))) & 
1.94/2.13	             (![Xw:a]:
1.94/2.13	                (((![Xq0:(a > $o)]:
1.94/2.13	                     (((![Xu:a,Xv:a]: ((S(Xu,Xv) & Xq0(Xu)) => Xq0(Xv))) & 
1.94/2.13	                       (![Xw0:a]: (S(Xx,Xw0) => Xq0(Xw0)))) =>
1.94/2.13	                      Xq0(Xw))) | 
1.94/2.13	                  (![Xq0:(a > $o)]:
1.94/2.13	                     (((![Xu:a,Xv:a]: ((R(Xu,Xv) & Xq0(Xu)) => Xq0(Xv))) & 
1.94/2.13	                       (![Xw0:a]: (R(Xx,Xw0) => Xq0(Xw0)))) =>
1.94/2.13	                      Xq0(Xw)))) =>
1.94/2.13	                 Xq(Xw)))) =>
1.94/2.13	            Xq(Xy))))))).
1.94/2.13	tff('0', plain,
1.94/2.13	    ![X0 : a > $o]:
1.94/2.13	      (X0(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_S(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X0(sk_Xu(X0))),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('1', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X1 != X0
1.94/2.13	       | X0(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X1))
1.94/2.13	       | sk_S(sk_Xx, sk_Xw(X1))
1.94/2.13	       | X0(sk_Xu(X1))),
1.94/2.13	    inference('ho.purify_applied_variable', [status(thm)], ['0'])).
1.94/2.13	tff('2', plain,
1.94/2.13	    ![X1 : a, X4 : a]: (sk_Xq(X1) | sk_Xq0(X1, X4) | ~ sk_S(sk_Xx, X4)),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('3', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | X2(sk_Xu(X0))
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | X0 != X2
1.94/2.13	       | sk_Xq0(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(X1)),
1.94/2.13	    inference('sup-', [status(thm)], ['1', '2'])).
1.94/2.13	tff('4', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (sk_Xq(X1)
1.94/2.13	       | sk_Xq0(X1, sk_Xw(X0))
1.94/2.13	       | X0 != X2
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X2(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['3'])).
1.94/2.13	tff('5', plain, ![X1 : a]: (sk_Xq(X1) | ~ sk_Xq0(X1, X1)),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('6', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | X1(sk_Xu(X0))
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['4', '5'])).
1.94/2.13	tff('7', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (sk_Xq(sk_Xw(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X1(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['6'])).
1.94/2.13	tff('8', plain,
1.94/2.13	    ![X1 : a, X7 : a]: (sk_Xq(X1) | sk_Xq01(X1, X7) | ~ sk_R(sk_Xx, X7)),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('9', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | X2(sk_Xu(X0))
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | X0 != X2
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq01(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(X1)),
1.94/2.13	    inference('sup-', [status(thm)], ['7', '8'])).
1.94/2.13	tff('10', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (sk_Xq(X1)
1.94/2.13	       | sk_Xq01(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | X0 != X2
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | X2(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['9'])).
1.94/2.13	tff('11', plain, ![X1 : a]: (sk_Xq(X1) | ~ sk_Xq01(X1, X1)),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('12', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | X1(sk_Xu(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['10', '11'])).
1.94/2.13	tff('13', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (sk_Xq(sk_Xw(X0)) | X0 != X1 | X1(sk_Xy) | X1(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['12'])).
1.94/2.13	tff('14', plain,
1.94/2.13	    ![X0 : a > $o]:
1.94/2.13	      (X0(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_S(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_S(sk_Xu(X0), sk_Xv(X0))
1.94/2.13	       | sk_R(sk_Xu(X0), sk_Xv(X0))),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('15', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X1 != X0
1.94/2.13	       | X0(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X1))
1.94/2.13	       | sk_S(sk_Xx, sk_Xw(X1))
1.94/2.13	       | sk_S(sk_Xu(X1), sk_Xv(X1))
1.94/2.13	       | sk_R(sk_Xu(X1), sk_Xv(X1))),
1.94/2.13	    inference('ho.purify_applied_variable', [status(thm)], ['14'])).
1.94/2.13	tff('16', plain,
1.94/2.13	    ![X8 : a, X9 : a, X13 : a]:
1.94/2.13	      (~ sk_Xq(X8) | ~ sk_S(X8, X13) | sk_Xq02(X9, X8, X13) | sk_Xq(X9)),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('17', plain,
1.94/2.13	    ![X8 : a, X9 : a]: (~ sk_Xq(X8) | ~ sk_Xq02(X9, X8, X9) | sk_Xq(X9)),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('18', plain,
1.94/2.13	    ![X0 : a, X1 : a]:
1.94/2.13	      (~ $true
1.94/2.13	       | sk_Xq(X0)
1.94/2.13	       | ~ sk_S(X1, X0)
1.94/2.13	       | ~ sk_Xq(X1)
1.94/2.13	       | sk_Xq(X0)
1.94/2.13	       | ~ sk_Xq(X1)),
1.94/2.13	    inference('sup-', [status(thm)], ['16', '17'])).
1.94/2.13	tff('19', plain,
1.94/2.13	    ![X0 : a, X1 : a]: (~ sk_Xq(X1) | ~ sk_S(X1, X0) | sk_Xq(X0)),
1.94/2.13	    inference('simplify', [status(thm)], ['18'])).
1.94/2.13	tff('20', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | sk_R(sk_Xu(X0), sk_Xv(X0))
1.94/2.13	       | sk_S(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['15', '19'])).
1.94/2.13	tff('21', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_S(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_R(sk_Xu(X0), sk_Xv(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['20'])).
1.94/2.13	tff('22', plain,
1.94/2.13	    ![X8 : a, X9 : a, X10 : a]:
1.94/2.13	      (~ sk_Xq(X8) | ~ sk_R(X8, X10) | sk_Xq03(X9, X8, X10) | sk_Xq(X9)),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('23', plain,
1.94/2.13	    ![X8 : a, X9 : a]: (~ sk_Xq(X8) | ~ sk_Xq03(X9, X8, X9) | sk_Xq(X9)),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('24', plain,
1.94/2.13	    ![X0 : a, X1 : a]:
1.94/2.13	      (~ $true
1.94/2.13	       | sk_Xq(X0)
1.94/2.13	       | ~ sk_R(X1, X0)
1.94/2.13	       | ~ sk_Xq(X1)
1.94/2.13	       | sk_Xq(X0)
1.94/2.13	       | ~ sk_Xq(X1)),
1.94/2.13	    inference('sup-', [status(thm)], ['22', '23'])).
1.94/2.13	tff('25', plain,
1.94/2.13	    ![X0 : a, X1 : a]: (~ sk_Xq(X1) | ~ sk_R(X1, X0) | sk_Xq(X0)),
1.94/2.13	    inference('simplify', [status(thm)], ['24'])).
1.94/2.13	tff('26', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (sk_S(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('clc', [status(thm)], ['21', '25'])).
1.94/2.13	tff('27', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | X0 != X2
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_Xq0(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(X1)),
1.94/2.13	    inference('sup-', [status(thm)], ['26', '2'])).
1.94/2.13	tff('28', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (sk_Xq(X1)
1.94/2.13	       | sk_Xq0(X1, sk_Xw(X0))
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | X0 != X2
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['27'])).
1.94/2.13	tff('29', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['28', '5'])).
1.94/2.13	tff('30', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['29'])).
1.94/2.13	tff('31', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | X0 != X2
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq01(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(X1)),
1.94/2.13	    inference('sup-', [status(thm)], ['30', '8'])).
1.94/2.13	tff('32', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (sk_Xq(X1)
1.94/2.13	       | sk_Xq01(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | X0 != X2
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['31'])).
1.94/2.13	tff('33', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['32', '11'])).
1.94/2.13	tff('34', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (sk_Xq(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['33'])).
1.94/2.13	tff('35', plain,
1.94/2.13	    ![X0 : a > $o]:
1.94/2.13	      (X0(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | sk_S(sk_Xx, sk_Xw(X0))
1.94/2.13	       | ~ X0(sk_Xv(X0))),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('36', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X1 != X0
1.94/2.13	       | X0(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X1))
1.94/2.13	       | sk_S(sk_Xx, sk_Xw(X1))
1.94/2.13	       | ~ X0(sk_Xv(X1))),
1.94/2.13	    inference('ho.purify_applied_variable', [status(thm)], ['35'])).
1.94/2.13	tff('37', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ X2(sk_Xv(X0))
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | X0 != X2
1.94/2.13	       | sk_Xq0(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(X1)),
1.94/2.13	    inference('sup-', [status(thm)], ['36', '2'])).
1.94/2.13	tff('38', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (sk_Xq(X1)
1.94/2.13	       | sk_Xq0(X1, sk_Xw(X0))
1.94/2.13	       | X0 != X2
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | ~ X2(sk_Xv(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['37'])).
1.94/2.13	tff('39', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ X1(sk_Xv(X0))
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['38', '5'])).
1.94/2.13	tff('40', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (sk_Xq(sk_Xw(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | sk_R(sk_Xx, sk_Xw(X0))
1.94/2.13	       | ~ X1(sk_Xv(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['39'])).
1.94/2.13	tff('41', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ X2(sk_Xv(X0))
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | X0 != X2
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq01(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(X1)),
1.94/2.13	    inference('sup-', [status(thm)], ['40', '8'])).
1.94/2.13	tff('42', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a, X2 : a > $o]:
1.94/2.13	      (sk_Xq(X1)
1.94/2.13	       | sk_Xq01(X1, sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | X0 != X2
1.94/2.13	       | X2(sk_Xy)
1.94/2.13	       | ~ X2(sk_Xv(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['41'])).
1.94/2.13	tff('43', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ X1(sk_Xv(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['42', '11'])).
1.94/2.13	tff('44', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (sk_Xq(sk_Xw(X0)) | X0 != X1 | X1(sk_Xy) | ~ X1(sk_Xv(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['43'])).
1.94/2.13	tff('45', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['34', '44'])).
1.94/2.13	tff('46', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['45'])).
1.94/2.13	tff('47', plain, ~ sk_Xq(sk_Xy), inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('48', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | X0 != sk_Xq),
1.94/2.13	    inference('clc', [status(thm)], ['46', '47'])).
1.94/2.13	tff('49', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1),
1.94/2.13	    inference('sup-', [status(thm)], ['13', '48'])).
1.94/2.13	tff('50', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != X1 | X1(sk_Xy) | sk_Xq(sk_Xw(X0)) | X0 != sk_Xq | sk_Xq(sk_Xy)),
1.94/2.13	    inference('simplify', [status(thm)], ['49'])).
1.94/2.13	tff('51', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != sk_Xq | sk_Xq(sk_Xw(X0)) | X1(sk_Xy) | X0 != X1),
1.94/2.13	    inference('clc', [status(thm)], ['50', '47'])).
1.94/2.13	tff('52', plain,
1.94/2.13	    ![X0 : a > $o]: (X0(sk_Xy) | ~ X0(sk_Xw(X0)) | X0(sk_Xu(X0))),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('53', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X1 != X0 | X0(sk_Xy) | ~ X0(sk_Xw(X1)) | X0(sk_Xu(X1))),
1.94/2.13	    inference('ho.purify_applied_variable', [status(thm)], ['52'])).
1.94/2.13	tff('54', plain,
1.94/2.13	    ![X0 : a > $o]:
1.94/2.13	      (X0(sk_Xy)
1.94/2.13	       | ~ X0(sk_Xw(X0))
1.94/2.13	       | sk_S(sk_Xu(X0), sk_Xv(X0))
1.94/2.13	       | sk_R(sk_Xu(X0), sk_Xv(X0))),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('55', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X1 != X0
1.94/2.13	       | X0(sk_Xy)
1.94/2.13	       | ~ X0(sk_Xw(X1))
1.94/2.13	       | sk_S(sk_Xu(X1), sk_Xv(X1))
1.94/2.13	       | sk_R(sk_Xu(X1), sk_Xv(X1))),
1.94/2.13	    inference('ho.purify_applied_variable', [status(thm)], ['54'])).
1.94/2.13	tff('56', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | sk_R(sk_Xu(X0), sk_Xv(X0))
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['55', '19'])).
1.94/2.13	tff('57', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | sk_R(sk_Xu(X0), sk_Xv(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['56'])).
1.94/2.13	tff('58', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ X1(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | sk_Xq(sk_Xv(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('clc', [status(thm)], ['57', '25'])).
1.94/2.13	tff('59', plain,
1.94/2.13	    ![X0 : a > $o]: (X0(sk_Xy) | ~ X0(sk_Xw(X0)) | ~ X0(sk_Xv(X0))),
1.94/2.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.94/2.13	tff('60', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X1 != X0 | X0(sk_Xy) | ~ X0(sk_Xw(X1)) | ~ X0(sk_Xv(X1))),
1.94/2.13	    inference('ho.purify_applied_variable', [status(thm)], ['59'])).
1.94/2.13	tff('61', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq),
1.94/2.13	    inference('sup-', [status(thm)], ['58', '60'])).
1.94/2.13	tff('62', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | ~ sk_Xq(sk_Xw(X0))
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['61'])).
1.94/2.13	tff('63', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | ~ sk_Xq(sk_Xw(X0))
1.94/2.13	       | X0 != sk_Xq),
1.94/2.13	    inference('clc', [status(thm)], ['62', '47'])).
1.94/2.13	tff('64', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | ~ sk_Xq(sk_Xw(X0))
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1),
1.94/2.13	    inference('sup-', [status(thm)], ['53', '63'])).
1.94/2.13	tff('65', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | ~ sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['64'])).
1.94/2.13	tff('66', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ sk_Xq(sk_Xw(X0))
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1),
1.94/2.13	    inference('clc', [status(thm)], ['65', '47'])).
1.94/2.13	tff('67', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | X1(sk_Xu(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | ~ sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['13', '66'])).
1.94/2.13	tff('68', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X1(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['67'])).
1.94/2.13	tff('69', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X1(sk_Xu(X0)) | X1(sk_Xy) | X0 != X1 | X0 != sk_Xq | sk_Xq(sk_Xy)),
1.94/2.13	    inference('clc', [status(thm)], ['68', '13'])).
1.94/2.13	tff('70', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != sk_Xq | X0 != X1 | X1(sk_Xy) | X1(sk_Xu(X0))),
1.94/2.13	    inference('clc', [status(thm)], ['69', '47'])).
1.94/2.13	tff('71', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ X1(sk_Xv(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | ~ sk_Xq(sk_Xw(X0))),
1.94/2.13	    inference('sup-', [status(thm)], ['44', '66'])).
1.94/2.13	tff('72', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ sk_Xq(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | ~ X1(sk_Xv(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['71'])).
1.94/2.13	tff('73', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ X1(sk_Xv(X0)) | X1(sk_Xy) | X0 != X1 | X0 != sk_Xq | sk_Xq(sk_Xy)),
1.94/2.13	    inference('clc', [status(thm)], ['72', '44'])).
1.94/2.13	tff('74', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != sk_Xq | X0 != X1 | X1(sk_Xy) | ~ X1(sk_Xv(X0))),
1.94/2.13	    inference('clc', [status(thm)], ['73', '47'])).
1.94/2.13	tff('75', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | X0 != sk_Xq),
1.94/2.13	    inference('sup-', [status(thm)], ['58', '74'])).
1.94/2.13	tff('76', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1
1.94/2.13	       | ~ sk_Xq(sk_Xu(X0))),
1.94/2.13	    inference('simplify', [status(thm)], ['75'])).
1.94/2.13	tff('77', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ sk_Xq(sk_Xu(X0))
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | X0 != sk_Xq),
1.94/2.13	    inference('clc', [status(thm)], ['76', '47'])).
1.94/2.13	tff('78', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | ~ X1(sk_Xw(X0))
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != X1),
1.94/2.13	    inference('sup-', [status(thm)], ['70', '77'])).
1.94/2.13	tff('79', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != X1 | X1(sk_Xy) | ~ X1(sk_Xw(X0)) | X0 != sk_Xq | sk_Xq(sk_Xy)),
1.94/2.13	    inference('simplify', [status(thm)], ['78'])).
1.94/2.13	tff('80', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (X0 != sk_Xq | ~ X1(sk_Xw(X0)) | X1(sk_Xy) | X0 != X1),
1.94/2.13	    inference('clc', [status(thm)], ['79', '47'])).
1.94/2.13	tff('81', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (~ $true
1.94/2.13	       | X0 != X1
1.94/2.13	       | X1(sk_Xy)
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | X0 != sk_Xq
1.94/2.13	       | sk_Xq(sk_Xy)
1.94/2.13	       | X0 != sk_Xq),
1.94/2.13	    inference('sup-', [status(thm)], ['51', '80'])).
1.94/2.13	tff('82', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]:
1.94/2.13	      (sk_Xq(sk_Xy) | X0 != sk_Xq | X1(sk_Xy) | X0 != X1),
1.94/2.13	    inference('simplify', [status(thm)], ['81'])).
1.94/2.13	tff('83', plain,
1.94/2.13	    ![X0 : a > $o, X1 : a > $o]: (X0 != X1 | X1(sk_Xy) | X0 != sk_Xq),
1.94/2.13	    inference('clc', [status(thm)], ['82', '47'])).
1.94/2.13	tff('84', plain, ![X0 : a > $o]: (~ $true | X0 != sk_Xq | X0 != sk_Xq),
1.94/2.13	    inference('sup-', [status(thm)], ['83', '47'])).
1.94/2.13	tff('85', plain, ![X0 : a > $o]: X0 != sk_Xq,
1.94/2.13	    inference('simplify', [status(thm)], ['84'])).
1.94/2.13	tff('86', plain, $false, inference('eq_res', [status(thm)], ['85'])).
1.94/2.13	
1.94/2.13	% SZS output end Refutation
1.94/2.13	EOF
