0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : purification_int
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-avatar \
0.00/0.01	  --ho \
0.00/0.01	  --force-ho \
0.00/0.01	  --no-ho-elim-pred-var \
0.00/0.01	  --ho-general-ext-pos \
0.00/0.01	  --no-ho-unif \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --ho-purify int \
0.00/0.01	  --ho-no-ext-pos \
0.00/0.01	  --ho-no-ext-neg \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n100.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 17:51:09 CST 2018
31.77/32.03	% done 4102 iterations in 31.818s
31.77/32.03	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
31.77/32.03	% SZS output start Refutation
31.77/32.03	tff(cTHM252A_pme, conjecture,
31.77/32.03	  (![P:((a * a) > $o > $o),R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
31.77/32.03	     ((![Xp:((a * a) > $o)]:
31.77/32.03	         ((P(Xp) & 
31.77/32.03	           (![Xx0:a,Xy0:a]:
31.77/32.03	              (((![Xp0:((a * a) > $o)]:
31.77/32.03	                   ((P(Xp0) & (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp0(Xx1,Xy1)))) =>
31.77/32.03	                    Xp0(Xx0,Xy0))) | 
31.77/32.03	                (![Xp0:((a * a) > $o)]:
31.77/32.03	                   ((P(Xp0) & (![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp0(Xx1,Xy1)))) =>
31.77/32.03	                    Xp0(Xx0,Xy0)))) =>
31.77/32.03	               Xp(Xx0,Xy0)))) =>
31.77/32.03	          Xp(Xx,Xy))) =>
31.77/32.03	      (![Xp:((a * a) > $o)]:
31.77/32.03	         ((P(Xp) & 
31.77/32.03	           (![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp(Xx0,Xy0)))) =>
31.77/32.03	          Xp(Xx,Xy)))))).
31.77/32.03	tff(zf_stmt_0, negated_conjecture,
31.77/32.03	  (~
31.77/32.03	    (![P:((a * a) > $o > $o),R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]:
31.77/32.03	       ((![Xp:((a * a) > $o)]:
31.77/32.03	           ((P(Xp) & 
31.77/32.03	             (![Xx0:a,Xy0:a]:
31.77/32.03	                (((![Xp0:((a * a) > $o)]:
31.77/32.03	                     ((P(Xp0) & 
31.77/32.03	                       (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp0(Xx1,Xy1)))) =>
31.77/32.03	                      Xp0(Xx0,Xy0))) | 
31.77/32.03	                  (![Xp0:((a * a) > $o)]:
31.77/32.03	                     ((P(Xp0) & 
31.77/32.03	                       (![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp0(Xx1,Xy1)))) =>
31.77/32.03	                      Xp0(Xx0,Xy0)))) =>
31.77/32.03	                 Xp(Xx0,Xy0)))) =>
31.77/32.03	            Xp(Xx,Xy))) =>
31.77/32.03	        (![Xp:((a * a) > $o)]:
31.77/32.03	           ((P(Xp) & 
31.77/32.03	             (![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp(Xx0,Xy0)))) =>
31.77/32.03	            Xp(Xx,Xy))))))).
31.77/32.03	tff('0', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.03	      (X0(sk_Xx, sk_Xy)
31.77/32.03	       | X1(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.03	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | X2(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ sk_P(X0)),
31.77/32.03	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.03	tff('1', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
31.77/32.03	      (X5 != X2
31.77/32.03	       | X4 != X1
31.77/32.03	       | X3 != X0
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | X1(sk_Xx0(X3), sk_Xy0(X3))
31.77/32.03	       | sk_R(sk_Xx11(X4), sk_Xy11(X4))
31.77/32.03	       | ~ sk_P(X4)
31.77/32.03	       | X2(sk_Xx0(X3), sk_Xy0(X3))
31.77/32.03	       | sk_S(sk_Xx1(X5), sk_Xy1(X5))
31.77/32.03	       | ~ sk_P(X5)
31.77/32.03	       | ~ sk_P(X3)),
31.77/32.03	    inference('ho.purify_applied_variable', [status(thm)], ['0'])).
31.77/32.03	tff('2', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | X4(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X4
31.77/32.03	       | X3 != X0
31.77/32.03	       | X2 != X0),
31.77/32.03	    inference('eq_fact', [status(thm)], ['1'])).
31.77/32.03	tff('3', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (X2 != X0
31.77/32.03	       | X3 != X0
31.77/32.03	       | X1 != X4
31.77/32.03	       | X4(sk_Xx, sk_Xy)
31.77/32.03	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ sk_P(X1)),
31.77/32.03	    inference('simplify', [status(thm)], ['2'])).
31.77/32.03	tff('4', plain,
31.77/32.03	    ![X0 : (a * a) > $o]:
31.77/32.03	      (X0(sk_Xx, sk_Xy) | ~ X0(sk_Xx0(X0), sk_Xy0(X0)) | ~ sk_P(X0)),
31.77/32.03	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.03	tff('5', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.03	      (X1 != X0
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | ~ X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.03	       | ~ sk_P(X1)),
31.77/32.03	    inference('ho.purify_applied_variable', [status(thm)], ['4'])).
31.77/32.03	tff('6', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | X4(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X4
31.77/32.03	       | X3 != X0
31.77/32.03	       | X2 != X0
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X0),
31.77/32.03	    inference('sup-', [status(thm)], ['3', '5'])).
31.77/32.03	tff('7', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (X1 != X0
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | X2 != X0
31.77/32.03	       | X3 != X0
31.77/32.03	       | X1 != X4
31.77/32.03	       | X4(sk_Xx, sk_Xy)
31.77/32.03	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ sk_P(X1)),
31.77/32.03	    inference('simplify', [status(thm)], ['6'])).
31.77/32.03	tff('8', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X0
31.77/32.03	       | X3 != X0
31.77/32.03	       | X2 != X0
31.77/32.03	       | X1 != X0),
31.77/32.03	    inference('eq_fact', [status(thm)], ['7'])).
31.77/32.03	tff('9', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (X2 != X0
31.77/32.03	       | X3 != X0
31.77/32.03	       | X1 != X0
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ sk_P(X1)),
31.77/32.03	    inference('simplify', [status(thm)], ['8'])).
31.77/32.03	tff('10', plain, ![X3 : a, X4 : a]: (sk_Xp(X3, X4) | ~ sk_R(X3, X4)),
31.77/32.03	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.03	tff('11', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | X3(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X3
31.77/32.03	       | X0 != X3
31.77/32.03	       | X2 != X3
31.77/32.03	       | sk_Xp(sk_Xx11(X0), sk_Xy11(X0))),
31.77/32.03	    inference('sup-', [status(thm)], ['9', '10'])).
31.77/32.03	tff('12', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (sk_Xp(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.03	       | X2 != X3
31.77/32.03	       | X0 != X3
31.77/32.03	       | X1 != X3
31.77/32.03	       | X3(sk_Xx, sk_Xy)
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ sk_P(X1)),
31.77/32.03	    inference('simplify', [status(thm)], ['11'])).
31.77/32.03	tff('13', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.03	      (~ sk_P(X0)
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | X1(sk_Xx, sk_Xy)
31.77/32.03	       | X0 != X1
31.77/32.03	       | X2 != X1
31.77/32.03	       | sk_Xp(sk_Xx11(X2), sk_Xy11(X2))),
31.77/32.03	    inference('eq_res', [status(thm)], ['12'])).
31.77/32.03	tff('14', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (X3 != X1
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | X3(sk_Xx, sk_Xy)
31.77/32.03	       | X0 != X1
31.77/32.03	       | X2 != X1
31.77/32.03	       | sk_Xp(sk_Xx11(X2), sk_Xy11(X2))),
31.77/32.03	    inference('ho.purify_applied_variable', [status(thm)], ['13'])).
31.77/32.03	tff('15', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.03	      (sk_Xp(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.03	       | X0 != X1
31.77/32.03	       | X2(sk_Xx, sk_Xy)
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | X2 != X1),
31.77/32.03	    inference('eq_res', [status(thm)], ['14'])).
31.77/32.03	tff('16', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.03	      (X2 != X1
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | X2(sk_Xx, sk_Xy)
31.77/32.03	       | X0 != X1
31.77/32.03	       | sk_Xp(sk_Xx11(X0), sk_Xy11(X0))),
31.77/32.03	    inference('simplify', [status(thm)], ['15'])).
31.77/32.03	tff('17', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.03	      (sk_Xp(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.03	       | X1(sk_Xx, sk_Xy)
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | sk_S(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | X1 != X0),
31.77/32.03	    inference('eq_res', [status(thm)], ['16'])).
31.77/32.03	tff('18', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.03	      (X1 != X0
31.77/32.03	       | sk_S(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | X1(sk_Xx, sk_Xy)
31.77/32.03	       | sk_Xp(sk_Xx11(X0), sk_Xy11(X0))),
31.77/32.03	    inference('simplify', [status(thm)], ['17'])).
31.77/32.03	tff('19', plain, ![X3 : a, X4 : a]: (sk_Xp(X3, X4) | ~ sk_S(X3, X4)),
31.77/32.03	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.03	tff('20', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | sk_Xp(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.03	       | X1(sk_Xx, sk_Xy)
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | X1 != X0
31.77/32.03	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))),
31.77/32.03	    inference('sup-', [status(thm)], ['18', '19'])).
31.77/32.03	tff('21', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.03	      (sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.03	       | X1 != X0
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | X1(sk_Xx, sk_Xy)
31.77/32.03	       | sk_Xp(sk_Xx11(X0), sk_Xy11(X0))),
31.77/32.03	    inference('simplify', [status(thm)], ['20'])).
31.77/32.03	tff('22', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.03	      (X0(sk_Xx, sk_Xy)
31.77/32.03	       | X1(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.03	       | ~ X1(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | X2(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ sk_P(X0)),
31.77/32.03	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.03	tff('23', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
31.77/32.03	      (X5 != X2
31.77/32.03	       | X4 != X1
31.77/32.03	       | X3 != X0
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | X1(sk_Xx0(X3), sk_Xy0(X3))
31.77/32.03	       | ~ X1(sk_Xx11(X4), sk_Xy11(X4))
31.77/32.03	       | ~ sk_P(X4)
31.77/32.03	       | X2(sk_Xx0(X3), sk_Xy0(X3))
31.77/32.03	       | sk_S(sk_Xx1(X5), sk_Xy1(X5))
31.77/32.03	       | ~ sk_P(X5)
31.77/32.03	       | ~ sk_P(X3)),
31.77/32.03	    inference('ho.purify_applied_variable', [status(thm)], ['22'])).
31.77/32.03	tff('24', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | X4(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X4
31.77/32.03	       | X3 != X0
31.77/32.03	       | X2 != X0),
31.77/32.03	    inference('eq_fact', [status(thm)], ['23'])).
31.77/32.03	tff('25', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (X2 != X0
31.77/32.03	       | X3 != X0
31.77/32.03	       | X1 != X4
31.77/32.03	       | X4(sk_Xx, sk_Xy)
31.77/32.03	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.03	       | sk_S(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ sk_P(X1)),
31.77/32.03	    inference('simplify', [status(thm)], ['24'])).
31.77/32.03	tff('26', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (~ sk_P(X0)
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.03	       | X1(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ X1(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.03	       | X3(sk_Xx, sk_Xy)
31.77/32.03	       | X0 != X3
31.77/32.03	       | X2 != X1),
31.77/32.03	    inference('eq_res', [status(thm)], ['25'])).
31.77/32.03	tff('27', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
31.77/32.03	      (X5 != X1
31.77/32.03	       | X4 != X1
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | sk_S(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.03	       | X4(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.03	       | ~ sk_P(X2)
31.77/32.03	       | ~ X5(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.03	       | X3(sk_Xx, sk_Xy)
31.77/32.03	       | X0 != X3
31.77/32.03	       | X2 != X1),
31.77/32.03	    inference('ho.purify_applied_variable', [status(thm)], ['26'])).
31.77/32.03	tff('28', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (X0 != X1
31.77/32.03	       | X1(sk_Xx, sk_Xy)
31.77/32.03	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | X4(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.03	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | X4 != X3
31.77/32.03	       | X2 != X3),
31.77/32.03	    inference('eq_res', [status(thm)], ['27'])).
31.77/32.03	tff('29', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (X2 != X3
31.77/32.03	       | X4 != X3
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
31.77/32.03	       | X4(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | X1(sk_Xx, sk_Xy)
31.77/32.03	       | X0 != X1),
31.77/32.03	    inference('simplify', [status(thm)], ['28'])).
31.77/32.03	tff('30', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | X1 != X2
31.77/32.03	       | X2(sk_Xx, sk_Xy)
31.77/32.03	       | ~ X3(sk_Xx11(X4), sk_Xy11(X4))
31.77/32.03	       | ~ sk_P(X4)
31.77/32.03	       | sk_S(sk_Xx1(X4), sk_Xy1(X4))
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | X0 != X4
31.77/32.03	       | X3 != X4
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X0),
31.77/32.03	    inference('sup-', [status(thm)], ['29', '5'])).
31.77/32.03	tff('31', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.03	      (X1 != X0
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | X3 != X4
31.77/32.03	       | X0 != X4
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | sk_S(sk_Xx1(X4), sk_Xy1(X4))
31.77/32.03	       | ~ sk_P(X4)
31.77/32.03	       | ~ X3(sk_Xx11(X4), sk_Xy11(X4))
31.77/32.03	       | X2(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X2),
31.77/32.03	    inference('simplify', [status(thm)], ['30'])).
31.77/32.03	tff('32', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | X1 != X0
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | X0 != X3
31.77/32.03	       | X2 != X3
31.77/32.03	       | X1 != X0),
31.77/32.03	    inference('eq_fact', [status(thm)], ['31'])).
31.77/32.03	tff('33', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (X2 != X3
31.77/32.03	       | X0 != X3
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | sk_S(sk_Xx1(X3), sk_Xy1(X3))
31.77/32.03	       | ~ sk_P(X3)
31.77/32.03	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.03	       | X0(sk_Xx, sk_Xy)
31.77/32.03	       | X1 != X0),
31.77/32.03	    inference('simplify', [status(thm)], ['32'])).
31.77/32.03	tff('34', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.03	      (~ $true
31.77/32.03	       | X1 != X2
31.77/32.03	       | X2(sk_Xx, sk_Xy)
31.77/32.03	       | ~ X3(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.03	       | ~ sk_P(X0)
31.77/32.03	       | ~ sk_P(X1)
31.77/32.03	       | X2 != X0
31.77/32.03	       | X3 != X0
31.77/32.03	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))),
31.77/32.03	    inference('sup-', [status(thm)], ['33', '19'])).
31.77/32.03	tff('35', plain,
31.77/32.03	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.03	      X3 : (a * a) > $o]:
31.77/32.04	      (sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | X3 != X0
31.77/32.04	       | X2 != X0
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ X3(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X2),
31.77/32.04	    inference('simplify', [status(thm)], ['34'])).
31.77/32.04	tff('36', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0 != X1
31.77/32.04	       | X1(sk_Xx, sk_Xy)
31.77/32.04	       | ~ X2(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X2 != X1
31.77/32.04	       | sk_Xp(sk_Xx1(X1), sk_Xy1(X1))),
31.77/32.04	    inference('eq_res', [status(thm)], ['35'])).
31.77/32.04	tff('37', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X1
31.77/32.04	       | X0 != X1
31.77/32.04	       | X1(sk_Xx, sk_Xy)
31.77/32.04	       | ~ X2(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X2 != X1
31.77/32.04	       | sk_Xp(sk_Xx1(X3), sk_Xy1(X3))),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['36'])).
31.77/32.04	tff('38', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X2 != X0),
31.77/32.04	    inference('eq_res', [status(thm)], ['37'])).
31.77/32.04	tff('39', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X0
31.77/32.04	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X2 != X0),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['38'])).
31.77/32.04	tff('40', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0(sk_Xx, sk_Xy)
31.77/32.04	       | ~ X1(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | X1 != X2
31.77/32.04	       | sk_Xp(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.04	       | X0 != X2),
31.77/32.04	    inference('eq_res', [status(thm)], ['39'])).
31.77/32.04	tff('41', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0 != X2
31.77/32.04	       | sk_Xp(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.04	       | X1 != X2
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ X1(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | X0(sk_Xx, sk_Xy)),
31.77/32.04	    inference('simplify', [status(thm)], ['40'])).
31.77/32.04	tff('42', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.04	      (X0(sk_Xx, sk_Xy)
31.77/32.04	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X1 != X0
31.77/32.04	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))),
31.77/32.04	    inference('eq_res', [status(thm)], ['41'])).
31.77/32.04	tff('43', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X2 != X0
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | ~ X1(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | X1 != X0
31.77/32.04	       | sk_Xp(sk_Xx1(X2), sk_Xy1(X2))),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['42'])).
31.77/32.04	tff('44', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.04	      (sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ X1(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.04	       | X1(sk_Xx, sk_Xy)
31.77/32.04	       | X0 != X1),
31.77/32.04	    inference('eq_res', [status(thm)], ['43'])).
31.77/32.04	tff('45', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | X1(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X1 != X0
31.77/32.04	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | sk_Xp(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))),
31.77/32.04	    inference('sup-', [status(thm)], ['21', '44'])).
31.77/32.04	tff('46', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.04	      (sk_Xp(sk_Xx, sk_Xy)
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X1(sk_Xx, sk_Xy)),
31.77/32.04	    inference('simplify', [status(thm)], ['45'])).
31.77/32.04	tff('47', plain, ~ sk_Xp(sk_Xx, sk_Xy),
31.77/32.04	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.04	tff('48', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.04	      (X1(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X1 != X0
31.77/32.04	       | sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('clc', [status(thm)], ['46', '47'])).
31.77/32.04	tff('49', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0(sk_Xx, sk_Xy)
31.77/32.04	       | X1(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.04	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | X2(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.04	       | ~ X2(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_P(X0)),
31.77/32.04	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.04	tff('50', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
31.77/32.04	      (X5 != X2
31.77/32.04	       | X4 != X1
31.77/32.04	       | X3 != X0
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X1(sk_Xx0(X3), sk_Xy0(X3))
31.77/32.04	       | sk_R(sk_Xx11(X4), sk_Xy11(X4))
31.77/32.04	       | ~ sk_P(X4)
31.77/32.04	       | X2(sk_Xx0(X3), sk_Xy0(X3))
31.77/32.04	       | ~ X2(sk_Xx1(X5), sk_Xy1(X5))
31.77/32.04	       | ~ sk_P(X5)
31.77/32.04	       | ~ sk_P(X3)),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['49'])).
31.77/32.04	tff('51', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.04	       | X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | X4(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X4
31.77/32.04	       | X3 != X0
31.77/32.04	       | X2 != X0),
31.77/32.04	    inference('eq_fact', [status(thm)], ['50'])).
31.77/32.04	tff('52', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.04	      (X2 != X0
31.77/32.04	       | X3 != X0
31.77/32.04	       | X1 != X4
31.77/32.04	       | X4(sk_Xx, sk_Xy)
31.77/32.04	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.04	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_P(X1)),
31.77/32.04	    inference('simplify', [status(thm)], ['51'])).
31.77/32.04	tff('53', plain,
31.77/32.04	    ![X0 : (a * a) > $o]:
31.77/32.04	      (~ $true | ~ sk_P(X0) | ~ sk_Xp(sk_Xx0(X0), sk_Xy0(X0)) | X0 != sk_Xp),
31.77/32.04	    inference('sup-', [status(thm)], ['5', '47'])).
31.77/32.04	tff('54', plain,
31.77/32.04	    ![X0 : (a * a) > $o]:
31.77/32.04	      (X0 != sk_Xp | ~ sk_Xp(sk_Xx0(X0), sk_Xy0(X0)) | ~ sk_P(X0)),
31.77/32.04	    inference('simplify', [status(thm)], ['53'])).
31.77/32.04	tff('55', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X0 != X3
31.77/32.04	       | X2 != sk_Xp
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('sup-', [status(thm)], ['52', '54'])).
31.77/32.04	tff('56', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X0 != sk_Xp
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X2 != sk_Xp
31.77/32.04	       | X0 != X3
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_P(X0)),
31.77/32.04	    inference('simplify', [status(thm)], ['55'])).
31.77/32.04	tff('57', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (~ sk_P(sk_Xp)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X2
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('eq_res', [status(thm)], ['56'])).
31.77/32.04	tff('58', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X2
31.77/32.04	       | ~ sk_P(sk_Xp)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X3
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['57'])).
31.77/32.04	tff('59', plain, sk_P(sk_Xp), inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.04	tff('60', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X2
31.77/32.04	       | ~ $true
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X3
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('demod', [status(thm)], ['58', '59'])).
31.77/32.04	tff('61', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X0 != sk_Xp
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | sk_Xp != X3
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_R(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X3 != X2),
31.77/32.04	    inference('simplify', [status(thm)], ['60'])).
31.77/32.04	tff('62', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | X4 != X0
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X4(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X2
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X3 != sk_Xp
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('sup-', [status(thm)], ['48', '61'])).
31.77/32.04	tff('63', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.04	      (X3 != sk_Xp
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | X1 != X2
31.77/32.04	       | X4(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X4 != X0
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('simplify', [status(thm)], ['62'])).
31.77/32.04	tff('64', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != X1
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X2 != X0
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | sk_Xp != X2
31.77/32.04	       | X3 != sk_Xp),
31.77/32.04	    inference('eq_fact', [status(thm)], ['63'])).
31.77/32.04	tff('65', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != sk_Xp
31.77/32.04	       | sk_Xp != X2
31.77/32.04	       | sk_R(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | X2 != X0
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | X0 != X1
31.77/32.04	       | X1 != sk_Xp),
31.77/32.04	    inference('simplify', [status(thm)], ['64'])).
31.77/32.04	tff('66', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0 != sk_Xp
31.77/32.04	       | ~ sk_P(sk_Xp)
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X2 != sk_Xp),
31.77/32.04	    inference('eq_res', [status(thm)], ['65'])).
31.77/32.04	tff('67', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X0
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | ~ sk_P(sk_Xp)
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X2 != sk_Xp),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['66'])).
31.77/32.04	tff('68', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X0
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | ~ $true
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X2 != sk_Xp),
31.77/32.04	    inference('demod', [status(thm)], ['67', '59'])).
31.77/32.04	tff('69', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X2 != sk_Xp
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | X1 != X0
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | X3 != X0),
31.77/32.04	    inference('simplify', [status(thm)], ['68'])).
31.77/32.04	tff('70', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0 != X1
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | X2 != sk_Xp),
31.77/32.04	    inference('eq_res', [status(thm)], ['69'])).
31.77/32.04	tff('71', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X2 != sk_Xp
31.77/32.04	       | sk_R(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != X1),
31.77/32.04	    inference('simplify', [status(thm)], ['70'])).
31.77/32.04	tff('72', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | X1 != X2
31.77/32.04	       | X2 != sk_Xp
31.77/32.04	       | X1(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | sk_Xp(sk_Xx11(X0), sk_Xy11(X0))),
31.77/32.04	    inference('sup-', [status(thm)], ['71', '10'])).
31.77/32.04	tff('73', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (sk_Xp(sk_Xx11(X0), sk_Xy11(X0))
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X1(sk_Xx, sk_Xy)
31.77/32.04	       | X2 != sk_Xp
31.77/32.04	       | X1 != X2),
31.77/32.04	    inference('simplify', [status(thm)], ['72'])).
31.77/32.04	tff('74', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0(sk_Xx, sk_Xy)
31.77/32.04	       | X1(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.04	       | ~ X1(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | X2(sk_Xx0(X0), sk_Xy0(X0))
31.77/32.04	       | ~ X2(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_P(X0)),
31.77/32.04	    inference('cnf', [status(esa)], [zf_stmt_0])).
31.77/32.04	tff('75', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o, X5 : (a * a) > $o]:
31.77/32.04	      (X5 != X2
31.77/32.04	       | X4 != X1
31.77/32.04	       | X3 != X0
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X1(sk_Xx0(X3), sk_Xy0(X3))
31.77/32.04	       | ~ X1(sk_Xx11(X4), sk_Xy11(X4))
31.77/32.04	       | ~ sk_P(X4)
31.77/32.04	       | X2(sk_Xx0(X3), sk_Xy0(X3))
31.77/32.04	       | ~ X2(sk_Xx1(X5), sk_Xy1(X5))
31.77/32.04	       | ~ sk_P(X5)
31.77/32.04	       | ~ sk_P(X3)),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['74'])).
31.77/32.04	tff('76', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.04	       | X4(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X4
31.77/32.04	       | X3 != X0
31.77/32.04	       | X2 != X0),
31.77/32.04	    inference('eq_fact', [status(thm)], ['75'])).
31.77/32.04	tff('77', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.04	      (X2 != X0
31.77/32.04	       | X3 != X0
31.77/32.04	       | X1 != X4
31.77/32.04	       | X4(sk_Xx, sk_Xy)
31.77/32.04	       | X0(sk_Xx0(X1), sk_Xy0(X1))
31.77/32.04	       | ~ X0(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | ~ X0(sk_Xx1(X2), sk_Xy1(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_P(X1)),
31.77/32.04	    inference('simplify', [status(thm)], ['76'])).
31.77/32.04	tff('78', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X0 != X3
31.77/32.04	       | X2 != sk_Xp
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('sup-', [status(thm)], ['77', '54'])).
31.77/32.04	tff('79', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X0 != sk_Xp
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X2 != sk_Xp
31.77/32.04	       | X0 != X3
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X1), sk_Xy1(X1))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_P(X0)),
31.77/32.04	    inference('simplify', [status(thm)], ['78'])).
31.77/32.04	tff('80', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (~ sk_P(sk_Xp)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X2
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('eq_res', [status(thm)], ['79'])).
31.77/32.04	tff('81', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X2
31.77/32.04	       | ~ sk_P(sk_Xp)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X3
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['80'])).
31.77/32.04	tff('82', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X2
31.77/32.04	       | ~ $true
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X3
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('demod', [status(thm)], ['81', '59'])).
31.77/32.04	tff('83', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X0 != sk_Xp
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | sk_Xp != X3
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X1), sk_Xy11(X1))
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | ~ sk_Xp(sk_Xx1(X0), sk_Xy1(X0))
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X3 != X2),
31.77/32.04	    inference('simplify', [status(thm)], ['82'])).
31.77/32.04	tff('84', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | X4 != X0
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X4(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X2
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X3 != sk_Xp
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('sup-', [status(thm)], ['48', '83'])).
31.77/32.04	tff('85', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o, X4 : (a * a) > $o]:
31.77/32.04	      (X3 != sk_Xp
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X2(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | X1 != X2
31.77/32.04	       | X4(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_P(X0)
31.77/32.04	       | X4 != X0
31.77/32.04	       | X0 != sk_Xp),
31.77/32.04	    inference('simplify', [status(thm)], ['84'])).
31.77/32.04	tff('86', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (~ $true
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != X1
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X2 != X0
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | sk_Xp != X2
31.77/32.04	       | X3 != sk_Xp),
31.77/32.04	    inference('eq_fact', [status(thm)], ['85'])).
31.77/32.04	tff('87', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != sk_Xp
31.77/32.04	       | sk_Xp != X2
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X3), sk_Xy11(X3))
31.77/32.04	       | ~ sk_P(X3)
31.77/32.04	       | X2 != X0
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | ~ sk_P(X1)
31.77/32.04	       | X0 != X1
31.77/32.04	       | X1 != sk_Xp),
31.77/32.04	    inference('simplify', [status(thm)], ['86'])).
31.77/32.04	tff('88', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0 != sk_Xp
31.77/32.04	       | ~ sk_P(sk_Xp)
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X2 != sk_Xp),
31.77/32.04	    inference('eq_res', [status(thm)], ['87'])).
31.77/32.04	tff('89', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X0
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | ~ sk_P(sk_Xp)
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X2 != sk_Xp),
31.77/32.04	    inference('ho.purify_applied_variable', [status(thm)], ['88'])).
31.77/32.04	tff('90', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X3 != X0
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | ~ $true
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != X0
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | X2 != sk_Xp),
31.77/32.04	    inference('demod', [status(thm)], ['89', '59'])).
31.77/32.04	tff('91', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
31.77/32.04	      X3 : (a * a) > $o]:
31.77/32.04	      (X2 != sk_Xp
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | X1 != X0
31.77/32.04	       | X3(sk_Xx, sk_Xy)
31.77/32.04	       | X0 != sk_Xp
31.77/32.04	       | X3 != X0),
31.77/32.04	    inference('simplify', [status(thm)], ['90'])).
31.77/32.04	tff('92', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X0 != X1
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | sk_Xp != X1
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | X2 != sk_Xp),
31.77/32.04	    inference('eq_res', [status(thm)], ['91'])).
31.77/32.04	tff('93', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X2 != sk_Xp
31.77/32.04	       | ~ sk_Xp(sk_Xx11(X2), sk_Xy11(X2))
31.77/32.04	       | ~ sk_P(X2)
31.77/32.04	       | X0(sk_Xx, sk_Xy)
31.77/32.04	       | X1 != sk_Xp
31.77/32.04	       | X0 != X1),
31.77/32.04	    inference('simplify', [status(thm)], ['92'])).
31.77/32.04	tff('94', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
31.77/32.04	      (X1 != X2 | X2 != sk_Xp | X1(sk_Xx, sk_Xy) | ~ sk_P(X0) | X0 != sk_Xp),
31.77/32.04	    inference('clc', [status(thm)], ['73', '93'])).
31.77/32.04	tff('95', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.04	      (~ $true | X0 != sk_Xp | ~ sk_P(X0) | X1 != sk_Xp | sk_Xp != X1),
31.77/32.04	    inference('sup-', [status(thm)], ['94', '47'])).
31.77/32.04	tff('96', plain,
31.77/32.04	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
31.77/32.04	      (X1 != sk_Xp | ~ sk_P(X0) | X0 != sk_Xp),
31.77/32.04	    inference('simplify', [status(thm)], ['95'])).
31.77/32.04	tff('97', plain, ![X0 : (a * a) > $o]: (X0 != sk_Xp | ~ sk_P(X0)),
31.77/32.04	    inference('condensation', [status(thm)], ['96'])).
31.77/32.04	tff('98', plain, ~ sk_P(sk_Xp), inference('eq_res', [status(thm)], ['97'])).
31.77/32.04	tff('99', plain, ~ $true, inference('demod', [status(thm)], ['98', '59'])).
31.77/32.04	tff('100', plain, $false, inference('simplify', [status(thm)], ['99'])).
31.77/32.04	
31.77/32.04	% SZS output end Refutation
31.77/32.04	EOF
