0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_int
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify int \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n177.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:51:08 CST 2018
16.79/17.00	% done 1111 iterations in 16.793s
16.79/17.00	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
16.79/17.00	% SZS output start Refutation
16.79/17.00	tff(cTHM252A_pme, conjecture,
16.79/17.00	  (![P:((a * a) > $o > $o),R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
16.79/17.00	     ((![Xp:((a * a) > $o)]:
16.79/17.00	         ((P(Xp) & 
16.79/17.00	           (![Xx0:a,Xy0:a]:
16.79/17.00	              (((![Xp0:((a * a) > $o)]:
16.79/17.00	                   ((P(Xp0) & (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp0(Xx1,Xy1)))) =>
16.79/17.00	                    Xp0(Xx0,Xy0))) | 
16.79/17.00	                (![Xp0:((a * a) > $o)]:
16.79/17.00	                   ((P(Xp0) & (![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp0(Xx1,Xy1)))) =>
16.79/17.00	                    Xp0(Xx0,Xy0)))) =>
16.79/17.00	               Xp(Xx0,Xy0)))) =>
16.79/17.00	          Xp(Xx,Xy))) =>
16.79/17.00	      (![Xp:((a * a) > $o)]:
16.79/17.00	         ((P(Xp) & 
16.79/17.00	           (![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp(Xx0,Xy0)))) =>
16.79/17.00	          Xp(Xx,Xy)))))).
16.79/17.00	tff(zf_stmt_0, negated_conjecture,
16.79/17.00	  (~
16.79/17.00	    (![P:((a * a) > $o > $o),R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
16.79/17.00	       ((![Xp:((a * a) > $o)]:
16.79/17.00	           ((P(Xp) & 
16.79/17.00	             (![Xx0:a,Xy0:a]:
16.79/17.00	                (((![Xp0:((a * a) > $o)]:
16.79/17.00	                     ((P(Xp0) & 
16.79/17.00	                       (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp0(Xx1,Xy1)))) =>
16.79/17.00	                      Xp0(Xx0,Xy0))) | 
16.79/17.00	                  (![Xp0:((a * a) > $o)]:
16.79/17.00	                     ((P(Xp0) & 
16.79/17.00	                       (![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp0(Xx1,Xy1)))) =>
16.79/17.00	                      Xp0(Xx0,Xy0)))) =>
16.79/17.00	                 Xp(Xx0,Xy0)))) =>
16.79/17.00	            Xp(Xx,Xy))) =>
16.79/17.00	        (![Xp:((a * a) > $o)]:
16.79/17.00	           ((P(Xp) & 
16.79/17.00	             (![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp(Xx0,Xy0)))) =>
16.79/17.00	            Xp(Xx,Xy))))))).
16.79/17.00	tff('0', plain, sk_P(sk_Xp), inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('1', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X2(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X0)),
16.79/17.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('2', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
16.79/17.00	      (X5 != X2
16.79/17.00	       | X4 != X1
16.79/17.00	       | X3 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1(sk_Xx0(X3), sk_Xy0(X3))
16.79/17.00	       | sk_R(sk_Xx11(X4), sk_Xy11(X4))
16.79/17.00	       | ~ sk_P(X4)
16.79/17.00	       | X2(sk_Xx0(X3), sk_Xy0(X3))
16.79/17.00	       | sk_S(sk_Xx1(X5), sk_Xy1(X5))
16.79/17.00	       | ~ sk_P(X5)
16.79/17.00	       | ~ sk_P(X3)),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['1'])).
16.79/17.00	tff('3', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X4
16.79/17.00	       | X3 != X0
16.79/17.00	       | X2 != X0),
16.79/17.00	    inference('eq_fact', [status(thm)], ['2'])).
16.79/17.00	tff('4', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X2 != X0
16.79/17.00	       | X3 != X0
16.79/17.00	       | X1 != X4
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X1)),
16.79/17.00	    inference('simplify', [status(thm)], ['3'])).
16.79/17.00	tff('5', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | X1(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X3(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != X3
16.79/17.00	       | X2 != X1),
16.79/17.00	    inference('eq_res', [status(thm)], ['4'])).
16.79/17.00	tff('6', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X4 != X1
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | X4(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X3(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != X3
16.79/17.00	       | X2 != X1),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['5'])).
16.79/17.00	tff('7', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X0 != X1
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | X3(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X3 != X2),
16.79/17.00	    inference('eq_res', [status(thm)], ['6'])).
16.79/17.00	tff('8', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X3 != X2
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X3(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != X1),
16.79/17.00	    inference('simplify', [status(thm)], ['7'])).
16.79/17.00	tff('9', plain,
16.79/17.00	    ![X0 : (a * a) > $o]:
16.79/17.00	      (X0(sk_Xx, sk_Xy) | ~ X0(sk_Xx0(X0), sk_Xy0(X0)) | ~ sk_P(X0)),
16.79/17.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('10', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (X1 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X1)),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['9'])).
16.79/17.00	tff('11', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X1 != X2
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X0 != X3
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('sup-', [status(thm)], ['8', '10'])).
16.79/17.00	tff('12', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X1 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != X3
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X2),
16.79/17.00	    inference('simplify', [status(thm)], ['11'])).
16.79/17.00	tff('13', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0 != X1
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X0 != X2
16.79/17.00	       | X0(sk_Xx, sk_Xy)),
16.79/17.00	    inference('eq_res', [status(thm)], ['12'])).
16.79/17.00	tff('14', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X3 != X0
16.79/17.00	       | X0 != X1
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X0 != X2
16.79/17.00	       | X3(sk_Xx, sk_Xy)),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['13'])).
16.79/17.00	tff('15', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X2
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X1 != X0
16.79/17.00	       | X0 != X1),
16.79/17.00	    inference('eq_fact', [status(thm)], ['14'])).
16.79/17.00	tff('16', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X1 != X0
16.79/17.00	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X1 != X2
16.79/17.00	       | X0(sk_Xx, sk_Xy)),
16.79/17.00	    inference('simplify', [status(thm)], ['15'])).
16.79/17.00	tff('17', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (X0(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('eq_res', [status(thm)], ['16'])).
16.79/17.00	tff('18', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (X1 != X0
16.79/17.00	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X0(sk_Xx, sk_Xy)),
16.79/17.00	    inference('simplify', [status(thm)], ['17'])).
16.79/17.00	tff('19', plain, ![X3 : a, X4 : a]: (sk_Xp(X3, X4) | ~ sk_S(X3, X4)),
16.79/17.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('20', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | sk_R(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X0 != X1
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))),
16.79/17.00	    inference('sup-', [status(thm)], ['18', '19'])).
16.79/17.00	tff('21', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | X0 != X1
16.79/17.00	       | sk_R(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X1(sk_Xx, sk_Xy)),
16.79/17.00	    inference('simplify', [status(thm)], ['20'])).
16.79/17.00	tff('22', plain, ![X3 : a, X4 : a]: (sk_Xp(X3, X4) | ~ sk_R(X3, X4)),
16.79/17.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('23', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X0 != X1
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | sk_Xp(sk_Xx11(X0), sk_Xy11(X0))),
16.79/17.00	    inference('sup-', [status(thm)], ['21', '22'])).
16.79/17.00	tff('24', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | X0 != X1
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X1(sk_Xx, sk_Xy)),
16.79/17.00	    inference('simplify', [status(thm)], ['23'])).
16.79/17.00	tff('25', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ X1(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X2(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X0)),
16.79/17.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('26', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
16.79/17.00	      (X5 != X2
16.79/17.00	       | X4 != X1
16.79/17.00	       | X3 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1(sk_Xx0(X3), sk_Xy0(X3))
16.79/17.00	       | ~ X1(sk_Xx11(X4), sk_Xy11(X4))
16.79/17.00	       | ~ sk_P(X4)
16.79/17.00	       | X2(sk_Xx0(X3), sk_Xy0(X3))
16.79/17.00	       | sk_S(sk_Xx1(X5), sk_Xy1(X5))
16.79/17.00	       | ~ sk_P(X5)
16.79/17.00	       | ~ sk_P(X3)),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['25'])).
16.79/17.00	tff('27', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X4
16.79/17.00	       | X3 != X0
16.79/17.00	       | X2 != X0),
16.79/17.00	    inference('eq_fact', [status(thm)], ['26'])).
16.79/17.00	tff('28', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X2 != X0
16.79/17.00	       | X3 != X0
16.79/17.00	       | X1 != X4
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X1)),
16.79/17.00	    inference('simplify', [status(thm)], ['27'])).
16.79/17.00	tff('29', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | X1(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X1(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X3(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != X3
16.79/17.00	       | X2 != X1),
16.79/17.00	    inference('eq_res', [status(thm)], ['28'])).
16.79/17.00	tff('30', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
16.79/17.00	      (X5 != X1
16.79/17.00	       | X4 != X1
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | X4(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X5(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X3(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != X3
16.79/17.00	       | X2 != X1),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['29'])).
16.79/17.00	tff('31', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X0 != X1
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X4(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X4 != X3
16.79/17.00	       | X2 != X3),
16.79/17.00	    inference('eq_res', [status(thm)], ['30'])).
16.79/17.00	tff('32', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X2 != X3
16.79/17.00	       | X4 != X3
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
16.79/17.00	       | X4(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != X1),
16.79/17.00	    inference('simplify', [status(thm)], ['31'])).
16.79/17.00	tff('33', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X1 != X2
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X3(sk_Xx11(X4), sk_Xy11(X4))
16.79/17.00	       | ~ sk_P(X4)
16.79/17.00	       | sk_S(sk_Xx1(X4), sk_Xy1(X4))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X0 != X4
16.79/17.00	       | X3 != X4
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('sup-', [status(thm)], ['32', '10'])).
16.79/17.00	tff('34', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X1 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X3 != X4
16.79/17.00	       | X0 != X4
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X4), sk_Xy1(X4))
16.79/17.00	       | ~ sk_P(X4)
16.79/17.00	       | ~ X3(sk_Xx11(X4), sk_Xy11(X4))
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X2),
16.79/17.00	    inference('simplify', [status(thm)], ['33'])).
16.79/17.00	tff('35', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X1 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X0 != X3
16.79/17.00	       | X2 != X3
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('eq_fact', [status(thm)], ['34'])).
16.79/17.00	tff('36', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X2 != X3
16.79/17.00	       | X0 != X3
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('simplify', [status(thm)], ['35'])).
16.79/17.00	tff('37', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X1 != X2
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X3(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X2 != X0
16.79/17.00	       | X3 != X0
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))),
16.79/17.00	    inference('sup-', [status(thm)], ['36', '19'])).
16.79/17.00	tff('38', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | X3 != X0
16.79/17.00	       | X2 != X0
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X3(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X2),
16.79/17.00	    inference('simplify', [status(thm)], ['37'])).
16.79/17.00	tff('39', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0 != X1
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X2(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X2 != X1
16.79/17.00	       | sk_Xp(sk_Xx1(X1), sk_Xy1(X1))),
16.79/17.00	    inference('eq_res', [status(thm)], ['38'])).
16.79/17.00	tff('40', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X3 != X1
16.79/17.00	       | X0 != X1
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X2 != X1
16.79/17.00	       | sk_Xp(sk_Xx1(X3), sk_Xy1(X3))),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['39'])).
16.79/17.00	tff('41', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | X1 != X0
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X2 != X0),
16.79/17.00	    inference('eq_res', [status(thm)], ['40'])).
16.79/17.00	tff('42', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X3 != X0
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | X1 != X0
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X3(sk_Xx, sk_Xy)
16.79/17.00	       | X2 != X0),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['41'])).
16.79/17.00	tff('43', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X1(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | X1 != X2
16.79/17.00	       | sk_Xp(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X0 != X2),
16.79/17.00	    inference('eq_res', [status(thm)], ['42'])).
16.79/17.00	tff('44', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0 != X2
16.79/17.00	       | sk_Xp(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X1 != X2
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X1(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X0(sk_Xx, sk_Xy)),
16.79/17.00	    inference('simplify', [status(thm)], ['43'])).
16.79/17.00	tff('45', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (X0(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X1 != X0
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))),
16.79/17.00	    inference('eq_res', [status(thm)], ['44'])).
16.79/17.00	tff('46', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X2 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X1(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | X1 != X0
16.79/17.00	       | sk_Xp(sk_Xx1(X2), sk_Xy1(X2))),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['45'])).
16.79/17.00	tff('47', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != X1),
16.79/17.00	    inference('eq_res', [status(thm)], ['46'])).
16.79/17.00	tff('48', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X1(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X0 != X1
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | sk_Xp(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))),
16.79/17.00	    inference('sup-', [status(thm)], ['24', '47'])).
16.79/17.00	tff('49', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | X0 != X1
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X1(sk_Xx, sk_Xy)),
16.79/17.00	    inference('simplify', [status(thm)], ['48'])).
16.79/17.00	tff('50', plain, ~ sk_Xp(sk_Xx, sk_Xy),
16.79/17.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('51', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (X1(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X0 != X1
16.79/17.00	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | X0 != sk_Xp),
16.79/17.00	    inference('clc', [status(thm)], ['49', '50'])).
16.79/17.00	tff('52', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X2(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ X2(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X0)),
16.79/17.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('53', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
16.79/17.00	      (X5 != X2
16.79/17.00	       | X4 != X1
16.79/17.00	       | X3 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1(sk_Xx0(X3), sk_Xy0(X3))
16.79/17.00	       | sk_R(sk_Xx11(X4), sk_Xy11(X4))
16.79/17.00	       | ~ sk_P(X4)
16.79/17.00	       | X2(sk_Xx0(X3), sk_Xy0(X3))
16.79/17.00	       | ~ X2(sk_Xx1(X5), sk_Xy1(X5))
16.79/17.00	       | ~ sk_P(X5)
16.79/17.00	       | ~ sk_P(X3)),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['52'])).
16.79/17.00	tff('54', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X4
16.79/17.00	       | X3 != X0
16.79/17.00	       | X2 != X0),
16.79/17.00	    inference('eq_fact', [status(thm)], ['53'])).
16.79/17.00	tff('55', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X2 != X0
16.79/17.00	       | X3 != X0
16.79/17.00	       | X1 != X4
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X1)),
16.79/17.00	    inference('simplify', [status(thm)], ['54'])).
16.79/17.00	tff('56', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X3(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X3(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X4
16.79/17.00	       | X0 != X3
16.79/17.00	       | X2 != X3
16.79/17.00	       | sk_Xp(sk_Xx11(X0), sk_Xy11(X0))),
16.79/17.00	    inference('sup-', [status(thm)], ['55', '22'])).
16.79/17.00	tff('57', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X2 != X3
16.79/17.00	       | X0 != X3
16.79/17.00	       | X1 != X4
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X3(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ X3(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X1)),
16.79/17.00	    inference('simplify', [status(thm)], ['56'])).
16.79/17.00	tff('58', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ X1(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X2(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ X2(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X0)),
16.79/17.00	    inference('cnf', [status(esa)], [zf_stmt_0])).
16.79/17.00	tff('59', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
16.79/17.00	      (X5 != X2
16.79/17.00	       | X4 != X1
16.79/17.00	       | X3 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1(sk_Xx0(X3), sk_Xy0(X3))
16.79/17.00	       | ~ X1(sk_Xx11(X4), sk_Xy11(X4))
16.79/17.00	       | ~ sk_P(X4)
16.79/17.00	       | X2(sk_Xx0(X3), sk_Xy0(X3))
16.79/17.00	       | ~ X2(sk_Xx1(X5), sk_Xy1(X5))
16.79/17.00	       | ~ sk_P(X5)
16.79/17.00	       | ~ sk_P(X3)),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['58'])).
16.79/17.00	tff('60', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X4
16.79/17.00	       | X3 != X0
16.79/17.00	       | X2 != X0),
16.79/17.00	    inference('eq_fact', [status(thm)], ['59'])).
16.79/17.00	tff('61', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X2 != X0
16.79/17.00	       | X3 != X0
16.79/17.00	       | X1 != X4
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X0(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X1)),
16.79/17.00	    inference('simplify', [status(thm)], ['60'])).
16.79/17.00	tff('62', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ X2(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | X2(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X3 != X2
16.79/17.00	       | X1 != X2),
16.79/17.00	    inference('sup-', [status(thm)], ['61', '50'])).
16.79/17.00	tff('63', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X1 != X2
16.79/17.00	       | X3 != X2
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X2(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ X2(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X0)),
16.79/17.00	    inference('simplify', [status(thm)], ['62'])).
16.79/17.00	tff('64', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | X3 != X0
16.79/17.00	       | X2 != X0
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('sup-', [status(thm)], ['63', '10'])).
16.79/17.00	tff('65', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X1 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)
16.79/17.00	       | X2 != X0
16.79/17.00	       | X3 != X0
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X1)),
16.79/17.00	    inference('simplify', [status(thm)], ['64'])).
16.79/17.00	tff('66', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ X0(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X0(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X2 != X0
16.79/17.00	       | X1 != X0
16.79/17.00	       | X0(sk_Xx, sk_Xy)),
16.79/17.00	    inference('eq_res', [status(thm)], ['65'])).
16.79/17.00	tff('67', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
16.79/17.00	      (X5 != X0
16.79/17.00	       | X4 != X0
16.79/17.00	       | X3 != X0
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ X3(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X4(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X2 != X0
16.79/17.00	       | X1 != X0
16.79/17.00	       | X5(sk_Xx, sk_Xy)),
16.79/17.00	    inference('ho.purify_applied_variable', [status(thm)], ['66'])).
16.79/17.00	tff('68', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X0 != X1
16.79/17.00	       | X2 != X1
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | ~ X3(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X4(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X4 != X1
16.79/17.00	       | X3 != X1
16.79/17.00	       | sk_Xp != X1),
16.79/17.00	    inference('sup-', [status(thm)], ['67', '50'])).
16.79/17.00	tff('69', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X3 != X1
16.79/17.00	       | X4 != X1
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X4(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X3(sk_Xx11(X2), sk_Xy11(X2))
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | X2 != X1
16.79/17.00	       | X0 != X1),
16.79/17.00	    inference('simplify', [status(thm)], ['68'])).
16.79/17.00	tff('70', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X0 != X1
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | ~ X2(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ X3(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X3 != X1
16.79/17.00	       | X2 != X1),
16.79/17.00	    inference('eq_res', [status(thm)], ['69'])).
16.79/17.00	tff('71', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X2 != X1
16.79/17.00	       | X3 != X1
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X3(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ X2(sk_Xx11(X1), sk_Xy11(X1))
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | X0 != X1),
16.79/17.00	    inference('simplify', [status(thm)], ['70'])).
16.79/17.00	tff('72', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0 != sk_Xp
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X2(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X2 != X0
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('eq_res', [status(thm)], ['71'])).
16.79/17.00	tff('73', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X1 != X0
16.79/17.00	       | X2 != X0
16.79/17.00	       | ~ X2(sk_Xx1(X0), sk_Xy1(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X0 != sk_Xp),
16.79/17.00	    inference('simplify', [status(thm)], ['72'])).
16.79/17.00	tff('74', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X0 != X2
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | sk_Xp != X0
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('sup-', [status(thm)], ['51', '73'])).
16.79/17.00	tff('75', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X1 != X0
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X0 != X2
16.79/17.00	       | X0 != sk_Xp),
16.79/17.00	    inference('simplify', [status(thm)], ['74'])).
16.79/17.00	tff('76', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
16.79/17.00	       | X1 != X0),
16.79/17.00	    inference('sup-', [status(thm)], ['75', '50'])).
16.79/17.00	tff('77', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (X1 != X0 | ~ X1(sk_Xx11(X0), sk_Xy11(X0)) | ~ sk_P(X0) | X0 != sk_Xp),
16.79/17.00	    inference('simplify', [status(thm)], ['76'])).
16.79/17.00	tff('78', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ X3(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | X3(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | X1 != X4
16.79/17.00	       | X0 != X3
16.79/17.00	       | X2 != X3
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | sk_Xp != X0),
16.79/17.00	    inference('sup-', [status(thm)], ['57', '77'])).
16.79/17.00	tff('79', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
16.79/17.00	      (X0 != sk_Xp
16.79/17.00	       | X2 != X3
16.79/17.00	       | X0 != X3
16.79/17.00	       | X1 != X4
16.79/17.00	       | X4(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X3(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ X3(sk_Xx1(X2), sk_Xy1(X2))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X1)),
16.79/17.00	    inference('simplify', [status(thm)], ['78'])).
16.79/17.00	tff('80', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ X2(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | X2(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X3 != X2
16.79/17.00	       | X1 != X2
16.79/17.00	       | X3 != sk_Xp),
16.79/17.00	    inference('sup-', [status(thm)], ['79', '50'])).
16.79/17.00	tff('81', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X3 != sk_Xp
16.79/17.00	       | X1 != X2
16.79/17.00	       | X3 != X2
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X2(sk_Xx0(X0), sk_Xy0(X0))
16.79/17.00	       | ~ X2(sk_Xx1(X1), sk_Xy1(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X0)),
16.79/17.00	    inference('simplify', [status(thm)], ['80'])).
16.79/17.00	tff('82', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X0 != X3
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X3(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | sk_Xp(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | X2 != sk_Xp
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X2 != sk_Xp),
16.79/17.00	    inference('sup-', [status(thm)], ['51', '81'])).
16.79/17.00	tff('83', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (X2 != sk_Xp
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | sk_Xp(sk_Xx0(X1), sk_Xy0(X1))
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X3(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X0 != X3
16.79/17.00	       | X0 != sk_Xp),
16.79/17.00	    inference('simplify', [status(thm)], ['82'])).
16.79/17.00	tff('84', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | X1 != X2
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X3 != sk_Xp
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | sk_Xp(sk_Xx, sk_Xy)
16.79/17.00	       | X0 != sk_Xp),
16.79/17.00	    inference('sup-', [status(thm)], ['83', '10'])).
16.79/17.00	tff('85', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
16.79/17.00	      X3 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx, sk_Xy)
16.79/17.00	       | X3 != sk_Xp
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | ~ sk_P(X3)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X2(sk_Xx, sk_Xy)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | X1 != X2
16.79/17.00	       | X1 != sk_Xp),
16.79/17.00	    inference('simplify', [status(thm)], ['84'])).
16.79/17.00	tff('86', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | X2 != sk_Xp
16.79/17.00	       | sk_Xp(sk_Xx, sk_Xy)),
16.79/17.00	    inference('sup-', [status(thm)], ['85', '50'])).
16.79/17.00	tff('87', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (sk_Xp(sk_Xx, sk_Xy)
16.79/17.00	       | X2 != sk_Xp
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | X0 != sk_Xp),
16.79/17.00	    inference('simplify', [status(thm)], ['86'])).
16.79/17.00	tff('88', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
16.79/17.00	      (X0 != sk_Xp
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | ~ sk_P(X2)
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | X2 != sk_Xp),
16.79/17.00	    inference('clc', [status(thm)], ['87', '50'])).
16.79/17.00	tff('89', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (~ $true
16.79/17.00	       | X0 != sk_Xp
16.79/17.00	       | X1 != sk_Xp
16.79/17.00	       | ~ sk_P(X0)
16.79/17.00	       | ~ sk_P(X1)
16.79/17.00	       | sk_Xp != sk_Xp),
16.79/17.00	    inference('sup-', [status(thm)], ['0', '88'])).
16.79/17.00	tff('90', plain,
16.79/17.00	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
16.79/17.00	      (~ sk_P(X1) | ~ sk_P(X0) | X1 != sk_Xp | X0 != sk_Xp),
16.79/17.00	    inference('simplify', [status(thm)], ['89'])).
16.79/17.00	tff('91', plain,
16.79/17.00	    ![X0 : (a * a) > $o]:
16.79/17.00	      (~ $true | X0 != sk_Xp | sk_Xp != sk_Xp | ~ sk_P(X0)),
16.79/17.00	    inference('sup-', [status(thm)], ['0', '90'])).
16.79/17.00	tff('92', plain, ![X0 : (a * a) > $o]: (~ sk_P(X0) | X0 != sk_Xp),
16.79/17.00	    inference('simplify', [status(thm)], ['91'])).
16.79/17.00	tff('93', plain, (~ $true | sk_Xp != sk_Xp),
16.79/17.00	    inference('sup-', [status(thm)], ['0', '92'])).
16.79/17.00	tff('94', plain, $false, inference('simplify', [status(thm)], ['93'])).
16.79/17.00	
16.79/17.00	% SZS output end Refutation
16.79/17.01	EOF
