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    : 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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n186.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:39:39 CST 2018
2.12/2.37	% done 522 iterations in 2.173s
2.12/2.37	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
2.12/2.37	% SZS output start Refutation
2.12/2.37	tff(cT146A_pme, conjecture,
2.12/2.37	  (![Xr:(($i * $i) > $o),Xx,Xy]:
2.12/2.37	     ((![Xp:(($i * $i) > $o)]:
2.12/2.37	         (((![Xu,Xv,Xw]: ((Xr(Xv,Xw) & Xp(Xu,Xv)) => Xp(Xu,Xw))) & 
2.12/2.37	           (![Xx0,Xy0]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
2.12/2.37	          Xp(Xx,Xy))) =>
2.12/2.37	      (![Xp:(($i * $i) > $o)]:
2.12/2.37	         (((![Xx0,Xy0,Xz]: ((Xp(Xy0,Xz) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz))) & 
2.12/2.37	           (![Xx0,Xy0]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
2.12/2.37	          Xp(Xx,Xy)))))).
2.12/2.37	tff(zf_stmt_0, negated_conjecture,
2.12/2.37	  (~
2.12/2.37	    (![Xr:(($i * $i) > $o),Xx,Xy]:
2.12/2.37	       ((![Xp:(($i * $i) > $o)]:
2.12/2.37	           (((![Xu,Xv,Xw]: ((Xr(Xv,Xw) & Xp(Xu,Xv)) => Xp(Xu,Xw))) & 
2.12/2.37	             (![Xx0,Xy0]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
2.12/2.37	            Xp(Xx,Xy))) =>
2.12/2.37	        (![Xp:(($i * $i) > $o)]:
2.12/2.37	           (((![Xx0,Xy0,Xz]: ((Xp(Xy0,Xz) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz))) & 
2.12/2.37	             (![Xx0,Xy0]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
2.12/2.37	            Xp(Xx,Xy))))))).
2.12/2.37	tff('0', plain, ![X1, X2]: (sk_Xp(X1, X2) | ~ sk_Xr(X1, X2)),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('1', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]:
2.12/2.37	      (X0(sk_Xx, sk_Xy)
2.12/2.37	       | ~ X0(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | sk_Xr(sk_Xv(X0), sk_Xw(X0))),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('2', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X2 != X0
2.12/2.37	       | X1 != X0
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | ~ X1(sk_Xx0(X2), sk_Xy0(X2))
2.12/2.37	       | sk_Xr(sk_Xv(X2), sk_Xw(X2))),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['1'])).
2.12/2.37	tff('3', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (sk_Xr(sk_Xv(X0), sk_Xw(X0))
2.12/2.37	       | ~ X1(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('eq_res', [status(thm)], ['2'])).
2.12/2.37	tff('4', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X2 != X0
2.12/2.37	       | sk_Xr(sk_Xv(X0), sk_Xw(X0))
2.12/2.37	       | ~ X1(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X2(sk_Xx, sk_Xy)
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['3'])).
2.12/2.37	tff('5', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | X1(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xv(X0), sk_Xw(X0))
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('sup-', [status(thm)], ['0', '4'])).
2.12/2.37	tff('6', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (X1 != X0
2.12/2.37	       | sk_Xr(sk_Xv(X0), sk_Xw(X0))
2.12/2.37	       | X1(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
2.12/2.37	    inference('simplify', [status(thm)], ['5'])).
2.12/2.37	tff('7', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]:
2.12/2.37	      (X0(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | sk_Xr(sk_Xv(X0), sk_Xw(X0))),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('8', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (X1 != X0
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | sk_Xr(sk_Xv(X1), sk_Xw(X1))),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['7'])).
2.12/2.37	tff('9', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (sk_Xp != X0
2.12/2.37	       | X1(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xv(X0), sk_Xw(X0))
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('clc', [status(thm)], ['6', '8'])).
2.12/2.37	tff('10', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]:
2.12/2.37	      (X0(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X0(sk_Xu(X0), sk_Xv(X0))),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('11', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X2 != X0
2.12/2.37	       | X1 != X0
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | X2(sk_Xu(X1), sk_Xv(X1))),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['10'])).
2.12/2.37	tff('12', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (X0(sk_Xu(X1), sk_Xv(X1))
2.12/2.37	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('eq_res', [status(thm)], ['11'])).
2.12/2.37	tff('13', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X2 != X0
2.12/2.37	       | X0(sk_Xu(X1), sk_Xv(X1))
2.12/2.37	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | X2(sk_Xx, sk_Xy)
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['12'])).
2.12/2.37	tff('14', plain,
2.12/2.37	    ![X3, X4, X5]: (~ sk_Xp(X3, X4) | ~ sk_Xp(X4, X5) | sk_Xp(X3, X5)),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('15', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | X0 != sk_Xp
2.12/2.37	       | X2(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X2 != sk_Xp
2.12/2.37	       | sk_Xp(sk_Xu(X0), X1)
2.12/2.37	       | ~ sk_Xp(sk_Xv(X0), X1)),
2.12/2.37	    inference('sup-', [status(thm)], ['13', '14'])).
2.12/2.37	tff('16', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ sk_Xp(sk_Xv(X0), X1)
2.12/2.37	       | sk_Xp(sk_Xu(X0), X1)
2.12/2.37	       | X2 != sk_Xp
2.12/2.37	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X2(sk_Xx, sk_Xy)
2.12/2.37	       | X0 != sk_Xp),
2.12/2.37	    inference('simplify', [status(thm)], ['15'])).
2.12/2.37	tff('17', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1, X2 : ($i * $i) > $o, X3 : ($i * $i) > $o]:
2.12/2.37	      (X3 != X2
2.12/2.37	       | ~ sk_Xp(sk_Xv(X0), X1)
2.12/2.37	       | sk_Xp(sk_Xu(X0), X1)
2.12/2.37	       | X2 != sk_Xp
2.12/2.37	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X3(sk_Xx, sk_Xy)
2.12/2.37	       | X0 != sk_Xp),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['16'])).
2.12/2.37	tff('18', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]:
2.12/2.37	      (X0(sk_Xx, sk_Xy)
2.12/2.37	       | ~ X0(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X0(sk_Xu(X0), sk_Xv(X0))),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('19', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o, 
2.12/2.37	      X3 : ($i * $i) > $o]:
2.12/2.37	      (X3 != X0
2.12/2.37	       | X2 != X0
2.12/2.37	       | X1 != X0
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | ~ X1(sk_Xx0(X2), sk_Xy0(X2))
2.12/2.37	       | X3(sk_Xu(X2), sk_Xv(X2))),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['18'])).
2.12/2.37	tff('20', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X0(sk_Xu(X1), sk_Xv(X1))
2.12/2.37	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | X2 != X0
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('eq_res', [status(thm)], ['19'])).
2.12/2.37	tff('21', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o, 
2.12/2.37	      X3 : ($i * $i) > $o]:
2.12/2.37	      (X3 != X0
2.12/2.37	       | X0(sk_Xu(X1), sk_Xv(X1))
2.12/2.37	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | X3(sk_Xx, sk_Xy)
2.12/2.37	       | X2 != X0
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['20'])).
2.12/2.37	tff('22', plain, ~ sk_Xp(sk_Xx, sk_Xy),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('23', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | X0 != X1
2.12/2.37	       | X2 != X1
2.12/2.37	       | ~ X2(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X1(sk_Xu(X0), sk_Xv(X0))
2.12/2.37	       | sk_Xp != X1),
2.12/2.37	    inference('sup-', [status(thm)], ['21', '22'])).
2.12/2.37	tff('24', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (sk_Xp != X1
2.12/2.37	       | X1(sk_Xu(X0), sk_Xv(X0))
2.12/2.37	       | ~ X2(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X2 != X1
2.12/2.37	       | X0 != X1),
2.12/2.37	    inference('simplify', [status(thm)], ['23'])).
2.12/2.37	tff('25', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o, 
2.12/2.37	      X3 : ($i * $i) > $o]:
2.12/2.37	      (X3 != X1
2.12/2.37	       | sk_Xp != X1
2.12/2.37	       | X3(sk_Xu(X0), sk_Xv(X0))
2.12/2.37	       | ~ X2(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X2 != X1
2.12/2.37	       | X0 != X1),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['24'])).
2.12/2.37	tff('26', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X0 != X1
2.12/2.37	       | sk_Xp != X1
2.12/2.37	       | X2(sk_Xu(X0), sk_Xv(X0))
2.12/2.37	       | sk_Xp != X1
2.12/2.37	       | X2 != X1),
2.12/2.37	    inference('sup-', [status(thm)], ['0', '25'])).
2.12/2.37	tff('27', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X2 != X1
2.12/2.37	       | X2(sk_Xu(X0), sk_Xv(X0))
2.12/2.37	       | sk_Xp != X1
2.12/2.37	       | X0 != X1
2.12/2.37	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
2.12/2.37	    inference('simplify', [status(thm)], ['26'])).
2.12/2.37	tff('28', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | X1(sk_Xu(X0), sk_Xv(X0))
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('eq_res', [status(thm)], ['27'])).
2.12/2.37	tff('29', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1]:
2.12/2.37	      (~ $true
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | sk_Xp(sk_Xu(X0), X1)
2.12/2.37	       | ~ sk_Xp(sk_Xv(X0), X1)),
2.12/2.37	    inference('sup-', [status(thm)], ['28', '14'])).
2.12/2.37	tff('30', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1]:
2.12/2.37	      (~ sk_Xp(sk_Xv(X0), X1)
2.12/2.37	       | sk_Xp(sk_Xu(X0), X1)
2.12/2.37	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | sk_Xp != X0),
2.12/2.37	    inference('simplify', [status(thm)], ['29'])).
2.12/2.37	tff('31', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1, X2 : ($i * $i) > $o, X3 : ($i * $i) > $o]:
2.12/2.37	      (X0 != sk_Xp
2.12/2.37	       | X3(sk_Xx, sk_Xy)
2.12/2.37	       | X2 != sk_Xp
2.12/2.37	       | sk_Xp(sk_Xu(X0), X1)
2.12/2.37	       | ~ sk_Xp(sk_Xv(X0), X1)
2.12/2.37	       | X3 != X2),
2.12/2.37	    inference('clc', [status(thm)], ['17', '30'])).
2.12/2.37	tff('32', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | ~ sk_Xp(sk_Xv(X2), X1)
2.12/2.37	       | sk_Xp(sk_Xu(X2), X1)
2.12/2.37	       | X0 != sk_Xp
2.12/2.37	       | X2 != sk_Xp),
2.12/2.37	    inference('sup-', [status(thm)], ['31', '22'])).
2.12/2.37	tff('33', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1, X2 : ($i * $i) > $o]:
2.12/2.37	      (X2 != sk_Xp
2.12/2.37	       | sk_Xp(sk_Xu(X2), X1)
2.12/2.37	       | ~ sk_Xp(sk_Xv(X2), X1)
2.12/2.37	       | sk_Xp != X0),
2.12/2.37	    inference('simplify', [status(thm)], ['32'])).
2.12/2.37	tff('34', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1]:
2.12/2.37	      (sk_Xp != X0 | sk_Xp(sk_Xu(X0), X1) | ~ sk_Xp(sk_Xv(X0), X1)),
2.12/2.37	    inference('condensation', [status(thm)], ['33'])).
2.12/2.37	tff('35', plain,
2.12/2.37	    ![X0, X1 : ($i * $i) > $o]:
2.12/2.37	      (~ $true | ~ sk_Xr(sk_Xv(X1), X0) | sk_Xp(sk_Xu(X1), X0) | sk_Xp != X1),
2.12/2.37	    inference('sup-', [status(thm)], ['0', '34'])).
2.12/2.37	tff('36', plain,
2.12/2.37	    ![X0, X1 : ($i * $i) > $o]:
2.12/2.37	      (sk_Xp != X1 | sk_Xp(sk_Xu(X1), X0) | ~ sk_Xr(sk_Xv(X1), X0)),
2.12/2.37	    inference('simplify', [status(thm)], ['35'])).
2.12/2.37	tff('37', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]:
2.12/2.37	      (X0(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | ~ X0(sk_Xu(X0), sk_Xw(X0))),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('38', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X2 != X0
2.12/2.37	       | X1 != X0
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | ~ X2(sk_Xu(X1), sk_Xw(X1))),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['37'])).
2.12/2.37	tff('39', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]:
2.12/2.37	      (X0(sk_Xx, sk_Xy)
2.12/2.37	       | ~ X0(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | ~ X0(sk_Xu(X0), sk_Xw(X0))),
2.12/2.37	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.12/2.37	tff('40', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o, 
2.12/2.37	      X3 : ($i * $i) > $o]:
2.12/2.37	      (X3 != X0
2.12/2.37	       | X2 != X0
2.12/2.37	       | X1 != X0
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | ~ X1(sk_Xx0(X2), sk_Xy0(X2))
2.12/2.37	       | ~ X3(sk_Xu(X2), sk_Xw(X2))),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['39'])).
2.12/2.37	tff('41', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ X0(sk_Xu(X1), sk_Xw(X1))
2.12/2.37	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | X0(sk_Xx, sk_Xy)
2.12/2.37	       | X2 != X0
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('eq_res', [status(thm)], ['40'])).
2.12/2.37	tff('42', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o, 
2.12/2.37	      X3 : ($i * $i) > $o]:
2.12/2.37	      (X3 != X0
2.12/2.37	       | ~ X0(sk_Xu(X1), sk_Xw(X1))
2.12/2.37	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | X3(sk_Xx, sk_Xy)
2.12/2.37	       | X2 != X0
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['41'])).
2.12/2.37	tff('43', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | X0 != X1
2.12/2.37	       | X2 != X1
2.12/2.37	       | ~ X2(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | ~ X1(sk_Xu(X0), sk_Xw(X0))
2.12/2.37	       | sk_Xp != X1),
2.12/2.37	    inference('sup-', [status(thm)], ['42', '22'])).
2.12/2.37	tff('44', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (sk_Xp != X1
2.12/2.37	       | ~ X1(sk_Xu(X0), sk_Xw(X0))
2.12/2.37	       | ~ X2(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X2 != X1
2.12/2.37	       | X0 != X1),
2.12/2.37	    inference('simplify', [status(thm)], ['43'])).
2.12/2.37	tff('45', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o, 
2.12/2.37	      X3 : ($i * $i) > $o]:
2.12/2.37	      (X3 != X1
2.12/2.37	       | sk_Xp != X1
2.12/2.37	       | ~ X3(sk_Xu(X0), sk_Xw(X0))
2.12/2.37	       | ~ X2(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X2 != X1
2.12/2.37	       | X0 != X1),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['44'])).
2.12/2.37	tff('46', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X0 != X1
2.12/2.37	       | ~ X0(sk_Xx0(X1), sk_Xy0(X1))
2.12/2.37	       | ~ X2(sk_Xu(X1), sk_Xw(X1))
2.12/2.37	       | sk_Xp != X1
2.12/2.37	       | X2 != X1),
2.12/2.37	    inference('eq_res', [status(thm)], ['45'])).
2.12/2.37	tff('47', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | ~ sk_Xr(sk_Xv(X0), sk_Xw(X0))
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | ~ X1(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('sup-', [status(thm)], ['36', '46'])).
2.12/2.37	tff('48', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (X1 != X0
2.12/2.37	       | ~ X1(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | ~ sk_Xr(sk_Xv(X0), sk_Xw(X0))),
2.12/2.37	    inference('simplify', [status(thm)], ['47'])).
2.12/2.37	tff('49', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | X2 != X0
2.12/2.37	       | X2(sk_Xx, sk_Xy)
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | ~ X1(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('sup-', [status(thm)], ['9', '48'])).
2.12/2.37	tff('50', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X1 != X0
2.12/2.37	       | ~ X1(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | X2(sk_Xx, sk_Xy)
2.12/2.37	       | X2 != X0),
2.12/2.37	    inference('simplify', [status(thm)], ['49'])).
2.12/2.37	tff('51', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | ~ X1(sk_Xx0(X0), sk_Xy0(X0))
2.12/2.37	       | X1 != X0),
2.12/2.37	    inference('sup-', [status(thm)], ['50', '22'])).
2.12/2.37	tff('52', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (X1 != X0 | ~ X1(sk_Xx0(X0), sk_Xy0(X0)) | sk_Xp != X0),
2.12/2.37	    inference('simplify', [status(thm)], ['51'])).
2.12/2.37	tff('53', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]:
2.12/2.37	      (~ $true | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0)) | sk_Xp != X0 | sk_Xp != X0),
2.12/2.37	    inference('sup-', [status(thm)], ['0', '52'])).
2.12/2.37	tff('54', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]: (sk_Xp != X0 | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
2.12/2.37	    inference('simplify', [status(thm)], ['53'])).
2.12/2.37	tff('55', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | ~ X1(sk_Xu(X0), sk_Xw(X0))
2.12/2.37	       | X2(sk_Xx, sk_Xy)
2.12/2.37	       | X0 != X2
2.12/2.37	       | X1 != X2
2.12/2.37	       | sk_Xp != X0),
2.12/2.37	    inference('sup-', [status(thm)], ['38', '54'])).
2.12/2.37	tff('56', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (sk_Xp != X0
2.12/2.37	       | X1 != X2
2.12/2.37	       | X0 != X2
2.12/2.37	       | X2(sk_Xx, sk_Xy)
2.12/2.37	       | ~ X1(sk_Xu(X0), sk_Xw(X0))),
2.12/2.37	    inference('simplify', [status(thm)], ['55'])).
2.12/2.37	tff('57', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | ~ X0(sk_Xu(X1), sk_Xw(X1))
2.12/2.37	       | X1 != sk_Xp
2.12/2.37	       | X0 != sk_Xp
2.12/2.37	       | sk_Xp != X1),
2.12/2.37	    inference('sup-', [status(thm)], ['56', '22'])).
2.12/2.37	tff('58', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (X0 != sk_Xp | X1 != sk_Xp | ~ X0(sk_Xu(X1), sk_Xw(X1))),
2.12/2.37	    inference('simplify', [status(thm)], ['57'])).
2.12/2.37	tff('59', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o, X2 : ($i * $i) > $o]:
2.12/2.37	      (X2 != X0 | X0 != sk_Xp | X1 != sk_Xp | ~ X2(sk_Xu(X1), sk_Xw(X1))),
2.12/2.37	    inference('ho.purify_applied_variable', [status(thm)], ['58'])).
2.12/2.37	tff('60', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (~ $true
2.12/2.37	       | ~ sk_Xr(sk_Xv(X0), sk_Xw(X0))
2.12/2.37	       | sk_Xp != X0
2.12/2.37	       | X0 != sk_Xp
2.12/2.37	       | X1 != sk_Xp
2.12/2.37	       | sk_Xp != X1),
2.12/2.37	    inference('sup-', [status(thm)], ['36', '59'])).
2.12/2.37	tff('61', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (X1 != sk_Xp | sk_Xp != X0 | ~ sk_Xr(sk_Xv(X0), sk_Xw(X0))),
2.12/2.37	    inference('simplify', [status(thm)], ['60'])).
2.12/2.37	tff('62', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]: (~ sk_Xr(sk_Xv(X0), sk_Xw(X0)) | sk_Xp != X0),
2.12/2.37	    inference('condensation', [status(thm)], ['61'])).
2.12/2.37	tff('63', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (~ $true | X1 != X0 | X1(sk_Xx, sk_Xy) | sk_Xp != X0 | sk_Xp != X0),
2.12/2.37	    inference('sup-', [status(thm)], ['9', '62'])).
2.12/2.37	tff('64', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o, X1 : ($i * $i) > $o]:
2.12/2.37	      (sk_Xp != X0 | X1(sk_Xx, sk_Xy) | X1 != X0),
2.12/2.37	    inference('simplify', [status(thm)], ['63'])).
2.12/2.37	tff('65', plain,
2.12/2.37	    ![X0 : ($i * $i) > $o]: (~ $true | sk_Xp != X0 | sk_Xp != X0),
2.12/2.37	    inference('sup-', [status(thm)], ['64', '22'])).
2.12/2.37	tff('66', plain, ![X0 : ($i * $i) > $o]: sk_Xp != X0,
2.12/2.37	    inference('simplify', [status(thm)], ['65'])).
2.12/2.37	tff('67', plain, $false, inference('eq_res', [status(thm)], ['66'])).
2.12/2.37	
2.12/2.37	% SZS output end Refutation
2.12/2.37	EOF
