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_ext
0.00/0.00	% Ordering    : kbo
0.00/0.00	% 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 ext \
0.00/0.01	  --ho-ext-axiom \
0.00/0.01	  --restrict-hidden-sup-at-vars \
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   : n030.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 17:49:39 CST 2018
6.01/6.19	% done 1230 iterations in 5.984s
6.01/6.19	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
6.01/6.19	% SZS output start Refutation
6.01/6.19	tff(cTHM136_pme, conjecture,
6.01/6.19	  (![Xr:((a * a) > $o),Xx:a,Xy:a,Xz:a]:
6.01/6.19	     (((![Xp:((a * a) > $o)]:
6.01/6.19	          (((![Xx0:a,Xy0:a,Xz0:a]:
6.01/6.19	               ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
6.01/6.19	            (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
6.01/6.19	           Xp(Xy,Xz))) & 
6.01/6.19	       (![Xp:((a * a) > $o)]:
6.01/6.19	          (((![Xx0:a,Xy0:a,Xz0:a]:
6.01/6.19	               ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
6.01/6.19	            (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
6.01/6.19	           Xp(Xx,Xy)))) =>
6.01/6.19	      (![Xp:((a * a) > $o)]:
6.01/6.19	         (((![Xx0:a,Xy0:a,Xz0:a]:
6.01/6.19	              ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
6.01/6.19	           (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
6.01/6.19	          Xp(Xx,Xz)))))).
6.01/6.19	tff(zf_stmt_0, negated_conjecture,
6.01/6.19	  (~
6.01/6.19	    (![Xr:((a * a) > $o),Xx:a,Xy:a,Xz:a]:
6.01/6.19	       (((![Xp:((a * a) > $o)]:
6.01/6.19	            (((![Xx0:a,Xy0:a,Xz0:a]:
6.01/6.19	                 ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
6.01/6.19	              (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
6.01/6.19	             Xp(Xy,Xz))) & 
6.01/6.20	         (![Xp:((a * a) > $o)]:
6.01/6.20	            (((![Xx0:a,Xy0:a,Xz0:a]:
6.01/6.20	                 ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
6.01/6.20	              (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
6.01/6.20	             Xp(Xx,Xy)))) =>
6.01/6.20	        (![Xp:((a * a) > $o)]:
6.01/6.20	           (((![Xx0:a,Xy0:a,Xz0:a]:
6.01/6.20	                ((Xp(Xy0,Xz0) & Xp(Xx0,Xy0)) => Xp(Xx0,Xz0))) & 
6.01/6.20	             (![Xx0:a,Xy0:a]: (Xr(Xx0,Xy0) => Xp(Xx0,Xy0)))) =>
6.01/6.20	            Xp(Xx,Xz))))))).
6.01/6.20	tff('0', plain, ![X3 : a, X4 : a]: (sk_Xp(X3, X4) | ~ sk_Xr(X3, X4)),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('1', plain,
6.01/6.20	    ![X5 : (a * a) > $o]:
6.01/6.20	      (X5(sk_Xy, sk_Xz)
6.01/6.20	       | ~ X5(sk_Xx02(X5), sk_Xy02(X5))
6.01/6.20	       | X5(sk_Xy03(X5), sk_Xz01(X5))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('2', plain,
6.01/6.20	    ![X5 : (a * a) > $o, X6 : (a * a) > $o, X7 : (a * a) > $o, 
6.01/6.20	      X8 : (a * a) > $o]:
6.01/6.20	      (X8 != X5
6.01/6.20	       | X7 != X5
6.01/6.20	       | X6 != X5
6.01/6.20	       | X5(sk_Xy, sk_Xz)
6.01/6.20	       | ~ X6(sk_Xx02(X7), sk_Xy02(X7))
6.01/6.20	       | X8(sk_Xy03(X7), sk_Xz01(X7))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['1'])).
6.01/6.20	tff('3', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X0(sk_Xy03(X1), sk_Xz01(X1))
6.01/6.20	       | ~ X2(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['2'])).
6.01/6.20	tff('4', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
6.01/6.20	      X3 : (a * a) > $o]:
6.01/6.20	      (X3 != X1
6.01/6.20	       | X0(sk_Xy03(X1), sk_Xz01(X1))
6.01/6.20	       | ~ X2(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X3(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['3'])).
6.01/6.20	tff('5', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | ~ sk_Xr(sk_Xx02(X0), sk_Xy02(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X1(sk_Xy03(X0), sk_Xz01(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['0', '4'])).
6.01/6.20	tff('6', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X0
6.01/6.20	       | X1(sk_Xy03(X0), sk_Xz01(X0))
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xr(sk_Xx02(X0), sk_Xy02(X0))),
6.01/6.20	    inference('simplify', [status(thm)], ['5'])).
6.01/6.20	tff('7', plain,
6.01/6.20	    ![X5 : (a * a) > $o]:
6.01/6.20	      (X5(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xr(sk_Xx02(X5), sk_Xy02(X5))
6.01/6.20	       | X5(sk_Xy03(X5), sk_Xz01(X5))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('8', plain,
6.01/6.20	    ![X5 : (a * a) > $o, X6 : (a * a) > $o, X7 : (a * a) > $o]:
6.01/6.20	      (X7 != X5
6.01/6.20	       | X6 != X5
6.01/6.20	       | X5(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xr(sk_Xx02(X6), sk_Xy02(X6))
6.01/6.20	       | X7(sk_Xy03(X6), sk_Xz01(X6))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['7'])).
6.01/6.20	tff('9', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (X0(sk_Xy03(X1), sk_Xz01(X1))
6.01/6.20	       | sk_Xr(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['8'])).
6.01/6.20	tff('10', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X1
6.01/6.20	       | X0(sk_Xy03(X1), sk_Xz01(X1))
6.01/6.20	       | sk_Xr(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['9'])).
6.01/6.20	tff('11', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X1(sk_Xy03(X0), sk_Xz01(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('clc', [status(thm)], ['6', '10'])).
6.01/6.20	tff('12', plain,
6.01/6.20	    ![X5 : (a * a) > $o]:
6.01/6.20	      (X5(sk_Xy, sk_Xz)
6.01/6.20	       | ~ X5(sk_Xx02(X5), sk_Xy02(X5))
6.01/6.20	       | X5(sk_Xx03(X5), sk_Xy03(X5))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('13', plain,
6.01/6.20	    ![X5 : (a * a) > $o, X6 : (a * a) > $o, X7 : (a * a) > $o, 
6.01/6.20	      X8 : (a * a) > $o]:
6.01/6.20	      (X8 != X5
6.01/6.20	       | X7 != X5
6.01/6.20	       | X6 != X5
6.01/6.20	       | X5(sk_Xy, sk_Xz)
6.01/6.20	       | ~ X6(sk_Xx02(X7), sk_Xy02(X7))
6.01/6.20	       | X8(sk_Xx03(X7), sk_Xy03(X7))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['12'])).
6.01/6.20	tff('14', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X0(sk_Xx03(X1), sk_Xy03(X1))
6.01/6.20	       | ~ X2(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['13'])).
6.01/6.20	tff('15', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
6.01/6.20	      X3 : (a * a) > $o]:
6.01/6.20	      (X3 != X1
6.01/6.20	       | X0(sk_Xx03(X1), sk_Xy03(X1))
6.01/6.20	       | ~ X2(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X3(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['14'])).
6.01/6.20	tff('16', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | ~ sk_Xr(sk_Xx02(X0), sk_Xy02(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X1(sk_Xx03(X0), sk_Xy03(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['0', '15'])).
6.01/6.20	tff('17', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X0
6.01/6.20	       | X1(sk_Xx03(X0), sk_Xy03(X0))
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xr(sk_Xx02(X0), sk_Xy02(X0))),
6.01/6.20	    inference('simplify', [status(thm)], ['16'])).
6.01/6.20	tff('18', plain,
6.01/6.20	    ![X5 : (a * a) > $o]:
6.01/6.20	      (X5(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xr(sk_Xx02(X5), sk_Xy02(X5))
6.01/6.20	       | X5(sk_Xx03(X5), sk_Xy03(X5))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('19', plain,
6.01/6.20	    ![X5 : (a * a) > $o, X6 : (a * a) > $o, X7 : (a * a) > $o]:
6.01/6.20	      (X7 != X5
6.01/6.20	       | X6 != X5
6.01/6.20	       | X5(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xr(sk_Xx02(X6), sk_Xy02(X6))
6.01/6.20	       | X7(sk_Xx03(X6), sk_Xy03(X6))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['18'])).
6.01/6.20	tff('20', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (X0(sk_Xx03(X1), sk_Xy03(X1))
6.01/6.20	       | sk_Xr(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['19'])).
6.01/6.20	tff('21', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X1
6.01/6.20	       | X0(sk_Xx03(X1), sk_Xy03(X1))
6.01/6.20	       | sk_Xr(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['20'])).
6.01/6.20	tff('22', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X1(sk_Xx03(X0), sk_Xy03(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('clc', [status(thm)], ['17', '21'])).
6.01/6.20	tff('23', plain,
6.01/6.20	    ![X0 : a, X1 : a, X2 : a]:
6.01/6.20	      (~ sk_Xp(X0, X1) | ~ sk_Xp(X1, X2) | sk_Xp(X0, X2)),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('24', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | X2 != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp(sk_Xx03(X0), X1)
6.01/6.20	       | ~ sk_Xp(sk_Xy03(X0), X1)),
6.01/6.20	    inference('sup-', [status(thm)], ['22', '23'])).
6.01/6.20	tff('25', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
6.01/6.20	      (~ sk_Xp(sk_Xy03(X0), X1)
6.01/6.20	       | sk_Xp(sk_Xx03(X0), X1)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['24'])).
6.01/6.20	tff('26', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | X2 != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1 != X0
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp(sk_Xx03(X0), sk_Xz01(X0))),
6.01/6.20	    inference('sup-', [status(thm)], ['11', '25'])).
6.01/6.20	tff('27', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (sk_Xp(sk_Xx03(X0), sk_Xz01(X0))
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['26'])).
6.01/6.20	tff('28', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | X0 != X1
6.01/6.20	       | X0(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X1
6.01/6.20	       | X0 != X1
6.01/6.20	       | sk_Xp(sk_Xx03(X1), sk_Xz01(X1))),
6.01/6.20	    inference('eq_fact', [status(thm)], ['27'])).
6.01/6.20	tff('29', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (sk_Xp(sk_Xx03(X1), sk_Xz01(X1))
6.01/6.20	       | sk_Xp != X1
6.01/6.20	       | X0(sk_Xy, sk_Xz)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('simplify', [status(thm)], ['28'])).
6.01/6.20	tff('30', plain,
6.01/6.20	    ![X5 : (a * a) > $o]:
6.01/6.20	      (X5(sk_Xy, sk_Xz)
6.01/6.20	       | ~ X5(sk_Xx02(X5), sk_Xy02(X5))
6.01/6.20	       | ~ X5(sk_Xx03(X5), sk_Xz01(X5))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('31', plain,
6.01/6.20	    ![X5 : (a * a) > $o, X6 : (a * a) > $o, X7 : (a * a) > $o, 
6.01/6.20	      X8 : (a * a) > $o]:
6.01/6.20	      (X8 != X5
6.01/6.20	       | X7 != X5
6.01/6.20	       | X6 != X5
6.01/6.20	       | X5(sk_Xy, sk_Xz)
6.01/6.20	       | ~ X6(sk_Xx02(X7), sk_Xy02(X7))
6.01/6.20	       | ~ X8(sk_Xx03(X7), sk_Xz01(X7))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['30'])).
6.01/6.20	tff('32', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ X0(sk_Xx03(X1), sk_Xz01(X1))
6.01/6.20	       | ~ X2(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['31'])).
6.01/6.20	tff('33', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
6.01/6.20	      X3 : (a * a) > $o]:
6.01/6.20	      (X3 != X1
6.01/6.20	       | ~ X0(sk_Xx03(X1), sk_Xz01(X1))
6.01/6.20	       | ~ X2(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X3(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['32'])).
6.01/6.20	tff('34', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | ~ sk_Xr(sk_Xx02(X0), sk_Xy02(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | ~ X1(sk_Xx03(X0), sk_Xz01(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['0', '33'])).
6.01/6.20	tff('35', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X0
6.01/6.20	       | ~ X1(sk_Xx03(X0), sk_Xz01(X0))
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xr(sk_Xx02(X0), sk_Xy02(X0))),
6.01/6.20	    inference('simplify', [status(thm)], ['34'])).
6.01/6.20	tff('36', plain,
6.01/6.20	    ![X5 : (a * a) > $o]:
6.01/6.20	      (X5(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xr(sk_Xx02(X5), sk_Xy02(X5))
6.01/6.20	       | ~ X5(sk_Xx03(X5), sk_Xz01(X5))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('37', plain,
6.01/6.20	    ![X5 : (a * a) > $o, X6 : (a * a) > $o, X7 : (a * a) > $o]:
6.01/6.20	      (X7 != X5
6.01/6.20	       | X6 != X5
6.01/6.20	       | X5(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xr(sk_Xx02(X6), sk_Xy02(X6))
6.01/6.20	       | ~ X7(sk_Xx03(X6), sk_Xz01(X6))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['36'])).
6.01/6.20	tff('38', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ X0(sk_Xx03(X1), sk_Xz01(X1))
6.01/6.20	       | sk_Xr(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['37'])).
6.01/6.20	tff('39', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X1
6.01/6.20	       | ~ X0(sk_Xx03(X1), sk_Xz01(X1))
6.01/6.20	       | sk_Xr(sk_Xx02(X1), sk_Xy02(X1))
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['38'])).
6.01/6.20	tff('40', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | ~ X1(sk_Xx03(X0), sk_Xz01(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('clc', [status(thm)], ['35', '39'])).
6.01/6.20	tff('41', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | X2 != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1 != X0
6.01/6.20	       | X1(sk_Xy, sk_Xz)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['29', '40'])).
6.01/6.20	tff('42', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1(sk_Xy, sk_Xz)
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xy, sk_Xz)
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['41'])).
6.01/6.20	tff('43', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ $true | X0 != X1 | X0(sk_Xy, sk_Xz) | sk_Xp != X1 | X0 != X1),
6.01/6.20	    inference('eq_fact', [status(thm)], ['42'])).
6.01/6.20	tff('44', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (sk_Xp != X1 | X0(sk_Xy, sk_Xz) | X0 != X1),
6.01/6.20	    inference('simplify', [status(thm)], ['43'])).
6.01/6.20	tff('45', plain,
6.01/6.20	    ![X6 : (a * a) > $o]:
6.01/6.20	      (X6(sk_Xx, sk_Xy)
6.01/6.20	       | ~ X6(sk_Xx0(X6), sk_Xy0(X6))
6.01/6.20	       | X6(sk_Xy01(X6), sk_Xz0(X6))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('46', plain,
6.01/6.20	    ![X6 : (a * a) > $o, X7 : (a * a) > $o, X8 : (a * a) > $o, 
6.01/6.20	      X9 : (a * a) > $o]:
6.01/6.20	      (X9 != X6
6.01/6.20	       | X8 != X6
6.01/6.20	       | X7 != X6
6.01/6.20	       | X6(sk_Xx, sk_Xy)
6.01/6.20	       | ~ X7(sk_Xx0(X8), sk_Xy0(X8))
6.01/6.20	       | X9(sk_Xy01(X8), sk_Xz0(X8))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['45'])).
6.01/6.20	tff('47', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X0(sk_Xy01(X1), sk_Xz0(X1))
6.01/6.20	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['46'])).
6.01/6.20	tff('48', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
6.01/6.20	      X3 : (a * a) > $o]:
6.01/6.20	      (X3 != X1
6.01/6.20	       | X0(sk_Xy01(X1), sk_Xz0(X1))
6.01/6.20	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X3(sk_Xx, sk_Xy)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['47'])).
6.01/6.20	tff('49', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | X1(sk_Xy01(X0), sk_Xz0(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['0', '48'])).
6.01/6.20	tff('50', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X0
6.01/6.20	       | X1(sk_Xy01(X0), sk_Xz0(X0))
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
6.01/6.20	    inference('simplify', [status(thm)], ['49'])).
6.01/6.20	tff('51', plain,
6.01/6.20	    ![X6 : (a * a) > $o]:
6.01/6.20	      (X6(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X6), sk_Xy0(X6))
6.01/6.20	       | X6(sk_Xy01(X6), sk_Xz0(X6))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('52', plain,
6.01/6.20	    ![X6 : (a * a) > $o, X7 : (a * a) > $o, X8 : (a * a) > $o]:
6.01/6.20	      (X8 != X6
6.01/6.20	       | X7 != X6
6.01/6.20	       | X6(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X7), sk_Xy0(X7))
6.01/6.20	       | X8(sk_Xy01(X7), sk_Xz0(X7))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['51'])).
6.01/6.20	tff('53', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (X0(sk_Xy01(X1), sk_Xz0(X1))
6.01/6.20	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['52'])).
6.01/6.20	tff('54', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X1
6.01/6.20	       | X0(sk_Xy01(X1), sk_Xz0(X1))
6.01/6.20	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['53'])).
6.01/6.20	tff('55', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | X1(sk_Xy01(X0), sk_Xz0(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('clc', [status(thm)], ['50', '54'])).
6.01/6.20	tff('56', plain,
6.01/6.20	    ![X0 : a, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X1
6.01/6.20	       | X2(sk_Xy01(X1), sk_Xz0(X1))
6.01/6.20	       | sk_Xp != X1
6.01/6.20	       | X2 != X1
6.01/6.20	       | sk_Xp(sk_Xx, X0)
6.01/6.20	       | ~ sk_Xp(sk_Xy, X0)),
6.01/6.20	    inference('sup-', [status(thm)], ['55', '23'])).
6.01/6.20	tff('57', plain,
6.01/6.20	    ![X0 : a, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ sk_Xp(sk_Xy, X0)
6.01/6.20	       | sk_Xp(sk_Xx, X0)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X2(sk_Xy01(X1), sk_Xz0(X1))
6.01/6.20	       | sk_Xp != X1),
6.01/6.20	    inference('simplify', [status(thm)], ['56'])).
6.01/6.20	tff('58', plain, ~ sk_Xp(sk_Xx, sk_Xz),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('59', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1(sk_Xy01(X0), sk_Xz0(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xp(sk_Xy, sk_Xz)),
6.01/6.20	    inference('sup-', [status(thm)], ['57', '58'])).
6.01/6.20	tff('60', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ sk_Xp(sk_Xy, sk_Xz)
6.01/6.20	       | X1 != X0
6.01/6.20	       | X1(sk_Xy01(X0), sk_Xz0(X0))
6.01/6.20	       | sk_Xp != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['59'])).
6.01/6.20	tff('61', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X2
6.01/6.20	       | sk_Xp != X2
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1(sk_Xy01(X0), sk_Xz0(X0))
6.01/6.20	       | X1 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['44', '60'])).
6.01/6.20	tff('62', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0 | X1(sk_Xy01(X0), sk_Xz0(X0)) | sk_Xp != X0 | sk_Xp != X2),
6.01/6.20	    inference('simplify', [status(thm)], ['61'])).
6.01/6.20	tff('63', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (X0 != X1 | X0(sk_Xy01(X1), sk_Xz0(X1)) | sk_Xp != X1),
6.01/6.20	    inference('condensation', [status(thm)], ['62'])).
6.01/6.20	tff('64', plain,
6.01/6.20	    ![X6 : (a * a) > $o]:
6.01/6.20	      (X6(sk_Xx, sk_Xy)
6.01/6.20	       | ~ X6(sk_Xx0(X6), sk_Xy0(X6))
6.01/6.20	       | X6(sk_Xx01(X6), sk_Xy01(X6))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('65', plain,
6.01/6.20	    ![X6 : (a * a) > $o, X7 : (a * a) > $o, X8 : (a * a) > $o, 
6.01/6.20	      X9 : (a * a) > $o]:
6.01/6.20	      (X9 != X6
6.01/6.20	       | X8 != X6
6.01/6.20	       | X7 != X6
6.01/6.20	       | X6(sk_Xx, sk_Xy)
6.01/6.20	       | ~ X7(sk_Xx0(X8), sk_Xy0(X8))
6.01/6.20	       | X9(sk_Xx01(X8), sk_Xy01(X8))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['64'])).
6.01/6.20	tff('66', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X0(sk_Xx01(X1), sk_Xy01(X1))
6.01/6.20	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['65'])).
6.01/6.20	tff('67', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
6.01/6.20	      X3 : (a * a) > $o]:
6.01/6.20	      (X3 != X1
6.01/6.20	       | X0(sk_Xx01(X1), sk_Xy01(X1))
6.01/6.20	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X3(sk_Xx, sk_Xy)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['66'])).
6.01/6.20	tff('68', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | X1(sk_Xx01(X0), sk_Xy01(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['0', '67'])).
6.01/6.20	tff('69', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X0
6.01/6.20	       | X1(sk_Xx01(X0), sk_Xy01(X0))
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
6.01/6.20	    inference('simplify', [status(thm)], ['68'])).
6.01/6.20	tff('70', plain,
6.01/6.20	    ![X6 : (a * a) > $o]:
6.01/6.20	      (X6(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X6), sk_Xy0(X6))
6.01/6.20	       | X6(sk_Xx01(X6), sk_Xy01(X6))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('71', plain,
6.01/6.20	    ![X6 : (a * a) > $o, X7 : (a * a) > $o, X8 : (a * a) > $o]:
6.01/6.20	      (X8 != X6
6.01/6.20	       | X7 != X6
6.01/6.20	       | X6(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X7), sk_Xy0(X7))
6.01/6.20	       | X8(sk_Xx01(X7), sk_Xy01(X7))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['70'])).
6.01/6.20	tff('72', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (X0(sk_Xx01(X1), sk_Xy01(X1))
6.01/6.20	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['71'])).
6.01/6.20	tff('73', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X1
6.01/6.20	       | X0(sk_Xx01(X1), sk_Xy01(X1))
6.01/6.20	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['72'])).
6.01/6.20	tff('74', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
6.01/6.20	       | X2 != X0
6.01/6.20	       | sk_Xp(sk_Xx01(X0), X1)
6.01/6.20	       | ~ sk_Xp(sk_Xy01(X0), X1)),
6.01/6.20	    inference('sup-', [status(thm)], ['73', '23'])).
6.01/6.20	tff('75', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : a, X2 : (a * a) > $o]:
6.01/6.20	      (~ sk_Xp(sk_Xy01(X0), X1)
6.01/6.20	       | sk_Xp(sk_Xx01(X0), X1)
6.01/6.20	       | X2 != X0
6.01/6.20	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xp != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['74'])).
6.01/6.20	tff('76', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp(sk_Xx01(X0), sk_Xz0(X0))),
6.01/6.20	    inference('sup-', [status(thm)], ['63', '75'])).
6.01/6.20	tff('77', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (sk_Xp(sk_Xx01(X0), sk_Xz0(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xp != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['76'])).
6.01/6.20	tff('78', plain,
6.01/6.20	    ![X6 : (a * a) > $o]:
6.01/6.20	      (X6(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X6), sk_Xy0(X6))
6.01/6.20	       | ~ X6(sk_Xx01(X6), sk_Xz0(X6))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('79', plain,
6.01/6.20	    ![X6 : (a * a) > $o, X7 : (a * a) > $o, X8 : (a * a) > $o]:
6.01/6.20	      (X8 != X6
6.01/6.20	       | X7 != X6
6.01/6.20	       | X6(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X7), sk_Xy0(X7))
6.01/6.20	       | ~ X8(sk_Xx01(X7), sk_Xz0(X7))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['78'])).
6.01/6.20	tff('80', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ X0(sk_Xx01(X1), sk_Xz0(X1))
6.01/6.20	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['79'])).
6.01/6.20	tff('81', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X1
6.01/6.20	       | ~ X0(sk_Xx01(X1), sk_Xz0(X1))
6.01/6.20	       | sk_Xr(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['80'])).
6.01/6.20	tff('82', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (sk_Xp != X0
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
6.01/6.20	       | X1 != X0),
6.01/6.20	    inference('clc', [status(thm)], ['77', '81'])).
6.01/6.20	tff('83', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | X1(sk_Xx01(X0), sk_Xy01(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('clc', [status(thm)], ['69', '82'])).
6.01/6.20	tff('84', plain,
6.01/6.20	    ![X0 : a, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X1
6.01/6.20	       | X2(sk_Xx01(X1), sk_Xy01(X1))
6.01/6.20	       | sk_Xp != X1
6.01/6.20	       | X2 != X1
6.01/6.20	       | sk_Xp(sk_Xx, X0)
6.01/6.20	       | ~ sk_Xp(sk_Xy, X0)),
6.01/6.20	    inference('sup-', [status(thm)], ['83', '23'])).
6.01/6.20	tff('85', plain,
6.01/6.20	    ![X0 : a, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ sk_Xp(sk_Xy, X0)
6.01/6.20	       | sk_Xp(sk_Xx, X0)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X2(sk_Xx01(X1), sk_Xy01(X1))
6.01/6.20	       | sk_Xp != X1),
6.01/6.20	    inference('simplify', [status(thm)], ['84'])).
6.01/6.20	tff('86', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1(sk_Xx01(X0), sk_Xy01(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xp(sk_Xy, sk_Xz)),
6.01/6.20	    inference('sup-', [status(thm)], ['85', '58'])).
6.01/6.20	tff('87', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ sk_Xp(sk_Xy, sk_Xz)
6.01/6.20	       | X1 != X0
6.01/6.20	       | X1(sk_Xx01(X0), sk_Xy01(X0))
6.01/6.20	       | sk_Xp != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['86'])).
6.01/6.20	tff('88', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X2
6.01/6.20	       | sk_Xp != X2
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1(sk_Xx01(X0), sk_Xy01(X0))
6.01/6.20	       | X1 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['44', '87'])).
6.01/6.20	tff('89', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0 | X1(sk_Xx01(X0), sk_Xy01(X0)) | sk_Xp != X0 | sk_Xp != X2),
6.01/6.20	    inference('simplify', [status(thm)], ['88'])).
6.01/6.20	tff('90', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (X0 != X1 | X0(sk_Xx01(X1), sk_Xy01(X1)) | sk_Xp != X1),
6.01/6.20	    inference('condensation', [status(thm)], ['89'])).
6.01/6.20	tff('91', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : a]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp(sk_Xx01(X0), X1)
6.01/6.20	       | ~ sk_Xp(sk_Xy01(X0), X1)),
6.01/6.20	    inference('sup-', [status(thm)], ['90', '23'])).
6.01/6.20	tff('92', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : a]:
6.01/6.20	      (~ sk_Xp(sk_Xy01(X0), X1) | sk_Xp(sk_Xx01(X0), X1) | sk_Xp != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['91'])).
6.01/6.20	tff('93', plain,
6.01/6.20	    ![X0 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | sk_Xp(sk_Xx01(X0), sk_Xz0(X0))),
6.01/6.20	    inference('sup-', [status(thm)], ['63', '92'])).
6.01/6.20	tff('94', plain,
6.01/6.20	    ![X0 : (a * a) > $o]: (sk_Xp(sk_Xx01(X0), sk_Xz0(X0)) | sk_Xp != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['93'])).
6.01/6.20	tff('95', plain,
6.01/6.20	    ![X6 : (a * a) > $o]:
6.01/6.20	      (X6(sk_Xx, sk_Xy)
6.01/6.20	       | ~ X6(sk_Xx0(X6), sk_Xy0(X6))
6.01/6.20	       | ~ X6(sk_Xx01(X6), sk_Xz0(X6))),
6.01/6.20	    inference('cnf', [status(esa)], [zf_stmt_0])).
6.01/6.20	tff('96', plain,
6.01/6.20	    ![X6 : (a * a) > $o, X7 : (a * a) > $o, X8 : (a * a) > $o, 
6.01/6.20	      X9 : (a * a) > $o]:
6.01/6.20	      (X9 != X6
6.01/6.20	       | X8 != X6
6.01/6.20	       | X7 != X6
6.01/6.20	       | X6(sk_Xx, sk_Xy)
6.01/6.20	       | ~ X7(sk_Xx0(X8), sk_Xy0(X8))
6.01/6.20	       | ~ X9(sk_Xx01(X8), sk_Xz0(X8))),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['95'])).
6.01/6.20	tff('97', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ X0(sk_Xx01(X1), sk_Xz0(X1))
6.01/6.20	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X1(sk_Xx, sk_Xy)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('eq_res', [status(thm)], ['96'])).
6.01/6.20	tff('98', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o, 
6.01/6.20	      X3 : (a * a) > $o]:
6.01/6.20	      (X3 != X1
6.01/6.20	       | ~ X0(sk_Xx01(X1), sk_Xz0(X1))
6.01/6.20	       | ~ X2(sk_Xx0(X1), sk_Xy0(X1))
6.01/6.20	       | X3(sk_Xx, sk_Xy)
6.01/6.20	       | X2 != X1
6.01/6.20	       | X0 != X1),
6.01/6.20	    inference('ho.purify_applied_variable', [status(thm)], ['97'])).
6.01/6.20	tff('99', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | ~ X1(sk_Xx01(X0), sk_Xz0(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['0', '98'])).
6.01/6.20	tff('100', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X2 != X0
6.01/6.20	       | ~ X1(sk_Xx01(X0), sk_Xz0(X0))
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xr(sk_Xx0(X0), sk_Xy0(X0))),
6.01/6.20	    inference('simplify', [status(thm)], ['99'])).
6.01/6.20	tff('101', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | X2(sk_Xx, sk_Xy)
6.01/6.20	       | ~ X1(sk_Xx01(X0), sk_Xz0(X0))
6.01/6.20	       | X2 != X0),
6.01/6.20	    inference('clc', [status(thm)], ['100', '81'])).
6.01/6.20	tff('102', plain,
6.01/6.20	    ![X0 : a, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X1
6.01/6.20	       | ~ X2(sk_Xx01(X1), sk_Xz0(X1))
6.01/6.20	       | sk_Xp != X1
6.01/6.20	       | X2 != X1
6.01/6.20	       | sk_Xp(sk_Xx, X0)
6.01/6.20	       | ~ sk_Xp(sk_Xy, X0)),
6.01/6.20	    inference('sup-', [status(thm)], ['101', '23'])).
6.01/6.20	tff('103', plain,
6.01/6.20	    ![X0 : a, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ sk_Xp(sk_Xy, X0)
6.01/6.20	       | sk_Xp(sk_Xx, X0)
6.01/6.20	       | X2 != X1
6.01/6.20	       | ~ X2(sk_Xx01(X1), sk_Xz0(X1))
6.01/6.20	       | sk_Xp != X1),
6.01/6.20	    inference('simplify', [status(thm)], ['102'])).
6.01/6.20	tff('104', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | ~ X1(sk_Xx01(X0), sk_Xz0(X0))
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ sk_Xp(sk_Xy, sk_Xz)),
6.01/6.20	    inference('sup-', [status(thm)], ['103', '58'])).
6.01/6.20	tff('105', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (~ sk_Xp(sk_Xy, sk_Xz)
6.01/6.20	       | X1 != X0
6.01/6.20	       | ~ X1(sk_Xx01(X0), sk_Xz0(X0))
6.01/6.20	       | sk_Xp != X0),
6.01/6.20	    inference('simplify', [status(thm)], ['104'])).
6.01/6.20	tff('106', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (~ $true
6.01/6.20	       | sk_Xp != X2
6.01/6.20	       | sk_Xp != X2
6.01/6.20	       | sk_Xp != X0
6.01/6.20	       | ~ X1(sk_Xx01(X0), sk_Xz0(X0))
6.01/6.20	       | X1 != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['44', '105'])).
6.01/6.20	tff('107', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o, X2 : (a * a) > $o]:
6.01/6.20	      (X1 != X0 | ~ X1(sk_Xx01(X0), sk_Xz0(X0)) | sk_Xp != X0 | sk_Xp != X2),
6.01/6.20	    inference('simplify', [status(thm)], ['106'])).
6.01/6.20	tff('108', plain,
6.01/6.20	    ![X0 : (a * a) > $o, X1 : (a * a) > $o]:
6.01/6.20	      (X0 != X1 | ~ X0(sk_Xx01(X1), sk_Xz0(X1)) | sk_Xp != X1),
6.01/6.20	    inference('condensation', [status(thm)], ['107'])).
6.01/6.20	tff('109', plain,
6.01/6.20	    ![X0 : (a * a) > $o]: (~ $true | sk_Xp != X0 | sk_Xp != X0 | sk_Xp != X0),
6.01/6.20	    inference('sup-', [status(thm)], ['94', '108'])).
6.01/6.20	tff('110', plain, ![X0 : (a * a) > $o]: sk_Xp != X0,
6.01/6.20	    inference('simplify', [status(thm)], ['109'])).
6.01/6.20	tff('111', plain, $false, inference('eq_res', [status(thm)], ['110'])).
6.01/6.20	
6.01/6.20	% SZS output end Refutation
6.01/6.20	EOF
