0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : supatvars_ext
0.00/0.00	% Ordering    : rpo6
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	  --sup-at-vars \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n095.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 17:30:08 CST 2018
2.16/2.38	% done 4169 iterations in 2.177s
2.16/2.38	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
2.16/2.38	% SZS output start Refutation
2.16/2.38	tff(cTHM261_pme, conjecture,
2.16/2.38	  (![P:(a > $o > $o)]:
2.16/2.38	     (((![Xx:a]:
2.16/2.38	          (?[Xp:(a > $o)]:
2.16/2.38	             ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
2.16/2.38	              P(Xp)))) & 
2.16/2.38	       (![Xp:(a > $o)]: (P(Xp) => (?[Xz:a]: Xp(Xz))))) =>
2.16/2.38	      ((![Xx:a,Xy:a,Xz:a]:
2.16/2.38	          (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
2.16/2.38	            (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
2.16/2.38	           (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
2.16/2.38	       (![Xx:a,Xy:a]:
2.16/2.38	          ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
2.16/2.38	           (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
2.16/2.38	       (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S)))))))).
2.16/2.38	tff(zf_stmt_0, negated_conjecture,
2.16/2.38	  (~
2.16/2.38	    (![P:(a > $o > $o)]:
2.16/2.38	       (((![Xx:a]:
2.16/2.38	            (?[Xp:(a > $o)]:
2.16/2.38	               ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
2.16/2.38	                P(Xp)))) & 
2.16/2.38	         (![Xp:(a > $o)]: (P(Xp) => (?[Xz:a]: Xp(Xz))))) =>
2.16/2.38	        ((![Xx:a,Xy:a,Xz:a]:
2.16/2.38	            (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
2.16/2.38	              (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
2.16/2.38	             (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
2.16/2.38	         (![Xx:a,Xy:a]:
2.16/2.38	            ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
2.16/2.38	             (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
2.16/2.38	         (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S))))))))).
2.16/2.38	tff('0', plain, ![X0 : a]: sk_Xp(X0, X0),
2.16/2.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.38	tff('1', plain,
2.16/2.38	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.38	      (sk_S1(sk_Xz)
2.16/2.38	       | ~ sk_P(X4)
2.16/2.38	       | ~ X4(sk_Xy1)
2.16/2.38	       | ~ X4(sk_Xx1)
2.16/2.38	       | ~ sk_P(X3)
2.16/2.38	       | ~ X3(sk_Xx2)
2.16/2.38	       | ~ X3(sk_Xx2)),
2.16/2.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.38	tff('2', plain,
2.16/2.38	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.38	      (~ X3(sk_Xx2)
2.16/2.38	       | ~ sk_P(X3)
2.16/2.38	       | ~ X4(sk_Xx1)
2.16/2.38	       | ~ X4(sk_Xy1)
2.16/2.38	       | ~ sk_P(X4)
2.16/2.38	       | sk_S1(sk_Xz)),
2.16/2.38	    inference('simplify', [status(thm)], ['1'])).
2.16/2.38	tff('3', plain,
2.16/2.38	    ![X0 : a > $o]:
2.16/2.38	      (~ $true
2.16/2.38	       | sk_S1(sk_Xz)
2.16/2.38	       | ~ sk_P(X0)
2.16/2.38	       | ~ X0(sk_Xy1)
2.16/2.38	       | ~ X0(sk_Xx1)
2.16/2.38	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.38	    inference('sup-', [status(thm)], ['0', '2'])).
2.16/2.38	tff('4', plain, ![X0 : a]: sk_P(sk_Xp(X0)),
2.16/2.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.38	tff('5', plain,
2.16/2.38	    ![X0 : a > $o]:
2.16/2.38	      (~ $true
2.16/2.38	       | sk_S1(sk_Xz)
2.16/2.38	       | ~ sk_P(X0)
2.16/2.38	       | ~ X0(sk_Xy1)
2.16/2.38	       | ~ X0(sk_Xx1)
2.16/2.38	       | ~ $true),
2.16/2.38	    inference('demod', [status(thm)], ['3', '4'])).
2.16/2.38	tff('6', plain,
2.16/2.38	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xz)),
2.16/2.38	    inference('simplify', [status(thm)], ['5'])).
2.16/2.38	tff('7', plain,
2.16/2.38	    (~ $true | sk_S1(sk_Xz) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.38	    inference('sup-', [status(thm)], ['0', '6'])).
2.16/2.38	tff('8', plain, (~ $true | sk_S1(sk_Xz) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.38	    inference('demod', [status(thm)], ['7', '4'])).
2.16/2.38	tff('9', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S1(sk_Xz)),
2.16/2.38	    inference('simplify', [status(thm)], ['8'])).
2.16/2.38	tff('10', plain,
2.16/2.38	    ![X3 : a > $o]:
2.16/2.38	      (sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.38	tff('11', plain,
2.16/2.38	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S(sk_Xx)),
2.16/2.38	    inference('simplify', [status(thm)], ['10'])).
2.16/2.38	tff('12', plain,
2.16/2.38	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.38	    inference('sup-', [status(thm)], ['0', '11'])).
2.16/2.38	tff('13', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ $true),
2.16/2.38	    inference('demod', [status(thm)], ['12', '4'])).
2.16/2.38	tff('14', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xx)),
2.16/2.38	    inference('simplify', [status(thm)], ['13'])).
2.16/2.38	tff('15', plain,
2.16/2.38	    ![X0 : a, X1 : a > $o]: (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ X1(X0)),
2.16/2.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.38	tff('16', plain,
2.16/2.38	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
2.16/2.38	    inference('sup-', [status(thm)], ['14', '15'])).
2.16/2.38	tff('17', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
2.16/2.38	    inference('simplify', [status(thm)], ['16'])).
2.16/2.38	tff('18', plain,
2.16/2.38	    ![X3 : a > $o]:
2.16/2.38	      (sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.38	tff('19', plain,
2.16/2.38	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_P(sk_S)),
2.16/2.38	    inference('simplify', [status(thm)], ['18'])).
2.16/2.38	tff('20', plain,
2.16/2.38	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.38	    inference('sup-', [status(thm)], ['0', '19'])).
2.16/2.38	tff('21', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ $true),
2.16/2.38	    inference('demod', [status(thm)], ['20', '4'])).
2.16/2.38	tff('22', plain, (sk_S2(sk_Xy1) | sk_P(sk_S)),
2.16/2.38	    inference('simplify', [status(thm)], ['21'])).
2.16/2.38	tff('23', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xx)),
2.16/2.38	    inference('clc', [status(thm)], ['17', '22'])).
2.16/2.38	tff('24', plain, ![X2 : a > $o]: (X2(sk_Xz1(X2)) | ~ sk_P(X2)),
2.16/2.38	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.38	tff('25', plain,
2.16/2.38	    ![X0 : a > $o]:
2.16/2.38	      (~ $true | ~ sk_P(X0) | ~ sk_P(X0) | X0 = sk_Xp(sk_Xz1(X0))),
2.16/2.38	    inference('sup-', [status(thm)], ['24', '15'])).
2.16/2.38	tff('26', plain, ![X0 : a > $o]: (X0 = sk_Xp(sk_Xz1(X0)) | ~ sk_P(X0)),
2.16/2.38	    inference('simplify', [status(thm)], ['25'])).
2.16/2.38	tff('27', plain,
2.16/2.38	    ![X0 : a > $o, X1 : a]: (X0(X1) = sk_Xp(sk_Xz1(X0), X1) | ~ sk_P(X0)),
2.16/2.38	    inference('ho_complete_eq', [status(thm)], ['26'])).
2.16/2.38	tff('28', plain,
2.16/2.38	    ![X0 : a > $o, X1 : a]:
2.16/2.38	      (~ X0(X1)
2.16/2.38	       | ~ sk_P(X0)
2.16/2.38	       | ~ sk_P(sk_Xp(sk_Xz1(X0)))
2.16/2.38	       | sk_Xp(sk_Xz1(X0)) = sk_Xp(X1)),
2.16/2.38	    inference('sup-', [status(thm)], ['27', '15'])).
2.16/2.38	tff('29', plain,
2.16/2.38	    ![X0 : a > $o, X1 : a]:
2.16/2.38	      (~ X0(X1) | ~ sk_P(X0) | ~ $true | sk_Xp(sk_Xz1(X0)) = sk_Xp(X1)),
2.16/2.38	    inference('demod', [status(thm)], ['28', '4'])).
2.16/2.38	tff('30', plain,
2.16/2.38	    ![X0 : a > $o, X1 : a]:
2.16/2.38	      (sk_Xp(sk_Xz1(X0)) = sk_Xp(X1) | ~ sk_P(X0) | ~ X0(X1)),
2.16/2.38	    inference('simplify', [status(thm)], ['29'])).
2.16/2.38	tff('31', plain,
2.16/2.38	    ![X0 : a]:
2.16/2.38	      (~ $true | ~ sk_P(sk_Xp(X0)) | sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0)),
2.16/2.38	    inference('sup-', [status(thm)], ['0', '30'])).
2.16/2.38	tff('32', plain,
2.16/2.38	    ![X0 : a]: (~ $true | ~ $true | sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0)),
2.16/2.38	    inference('demod', [status(thm)], ['31', '4'])).
2.16/2.39	tff('33', plain, ![X0 : a]: sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0),
2.16/2.39	    inference('simplify', [status(thm)], ['32'])).
2.16/2.39	tff('34', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0) | ~ sk_P(sk_Xp(sk_Xz1(X0)))),
2.16/2.39	    inference('sup+', [status(thm)], ['27', '24'])).
2.16/2.39	tff('35', plain,
2.16/2.39	    ![X0 : a > $o]: (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['34', '4'])).
2.16/2.39	tff('36', plain,
2.16/2.39	    ![X0 : a > $o]: (~ sk_P(X0) | X0(sk_Xz1(sk_Xp(sk_Xz1(X0))))),
2.16/2.39	    inference('simplify', [status(thm)], ['35'])).
2.16/2.39	tff('37', plain,
2.16/2.39	    ![X0 : a]: (sk_Xp(X0, sk_Xz1(sk_Xp(X0))) | ~ sk_P(sk_Xp(X0))),
2.16/2.39	    inference('sup+', [status(thm)], ['33', '36'])).
2.16/2.39	tff('38', plain, ![X0 : a]: (sk_Xp(X0, sk_Xz1(sk_Xp(X0))) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['37', '4'])).
2.16/2.39	tff('39', plain, ![X0 : a]: sk_Xp(X0, sk_Xz1(sk_Xp(X0))),
2.16/2.39	    inference('simplify', [status(thm)], ['38'])).
2.16/2.39	tff('40', plain, (sk_Xp(sk_Xx, sk_Xz1(sk_S)) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['23', '39'])).
2.16/2.39	tff('41', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_S2(sk_Xy1)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xx))
2.16/2.39	     | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('sup-', [status(thm)], ['40', '15'])).
2.16/2.39	tff('42', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('demod', [status(thm)], ['41', '4'])).
2.16/2.39	tff('43', plain, (sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S)) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('simplify', [status(thm)], ['42'])).
2.16/2.39	tff('44', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('45', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['44'])).
2.16/2.39	tff('46', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '45'])).
2.16/2.39	tff('47', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['46', '4'])).
2.16/2.39	tff('48', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['47'])).
2.16/2.39	tff('49', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
2.16/2.39	    inference('sup-', [status(thm)], ['48', '15'])).
2.16/2.39	tff('50', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('simplify', [status(thm)], ['49'])).
2.16/2.39	tff('51', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
2.16/2.39	    inference('clc', [status(thm)], ['50', '22'])).
2.16/2.39	tff('52', plain, (sk_Xp(sk_Xy, sk_Xz1(sk_S)) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['51', '39'])).
2.16/2.39	tff('53', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_S2(sk_Xy1)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xy))
2.16/2.39	     | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('sup-', [status(thm)], ['52', '15'])).
2.16/2.39	tff('54', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('demod', [status(thm)], ['53', '4'])).
2.16/2.39	tff('55', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S)) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('simplify', [status(thm)], ['54'])).
2.16/2.39	tff('56', plain,
2.16/2.39	    (sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['43', '55'])).
2.16/2.39	tff('57', plain, (sk_S2(sk_Xy1) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['56'])).
2.16/2.39	tff('58', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))))),
2.16/2.39	    inference('sup-', [status(thm)], ['36', '15'])).
2.16/2.39	tff('59', plain,
2.16/2.39	    ![X0 : a > $o]: (X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['58'])).
2.16/2.39	tff('60', plain,
2.16/2.39	    ![X0 : a > $o, X1 : a]:
2.16/2.39	      (X0(X1) = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))), X1) | ~ sk_P(X0)),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['59'])).
2.16/2.39	tff('61', plain,
2.16/2.39	    ![X0 : a, X1 : a]:
2.16/2.39	      (sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1) | ~ sk_P(sk_Xp(X0))),
2.16/2.39	    inference('sup+', [status(thm)], ['33', '60'])).
2.16/2.39	tff('62', plain,
2.16/2.39	    ![X0 : a, X1 : a]:
2.16/2.39	      (sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['61', '4'])).
2.16/2.39	tff('63', plain,
2.16/2.39	    ![X0 : a, X1 : a]: sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1),
2.16/2.39	    inference('simplify', [status(thm)], ['62'])).
2.16/2.39	tff('64', plain,
2.16/2.39	    ![X0 : a]:
2.16/2.39	      (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xz1(sk_Xp(sk_Xx)), X0) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['57', '63'])).
2.16/2.39	tff('65', plain,
2.16/2.39	    ![X0 : a]: (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xx, X0) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('demod', [status(thm)], ['64', '63'])).
2.16/2.39	tff('66', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S1(sk_Xz)
2.16/2.39	       | sk_S2(sk_Xy1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('67', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
2.16/2.39	    inference('simplify', [status(thm)], ['66'])).
2.16/2.39	tff('68', plain,
2.16/2.39	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '67'])).
2.16/2.39	tff('69', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['68', '4'])).
2.16/2.39	tff('70', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
2.16/2.39	    inference('simplify', [status(thm)], ['69'])).
2.16/2.39	tff('71', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xz)),
2.16/2.39	    inference('sup-', [status(thm)], ['70', '15'])).
2.16/2.39	tff('72', plain, (sk_S1 = sk_Xp(sk_Xz) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('simplify', [status(thm)], ['71'])).
2.16/2.39	tff('73', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('74', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['73'])).
2.16/2.39	tff('75', plain,
2.16/2.39	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '74'])).
2.16/2.39	tff('76', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['75', '4'])).
2.16/2.39	tff('77', plain, (sk_S2(sk_Xy1) | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['76'])).
2.16/2.39	tff('78', plain, (sk_S2(sk_Xy1) | sk_S1 = sk_Xp(sk_Xz)),
2.16/2.39	    inference('clc', [status(thm)], ['72', '77'])).
2.16/2.39	tff('79', plain, (sk_Xp(sk_Xz, sk_Xz1(sk_S1)) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['78', '39'])).
2.16/2.39	tff('80', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_S2(sk_Xy1)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xz))
2.16/2.39	     | sk_Xp(sk_Xz) = sk_Xp(sk_Xz1(sk_S1))),
2.16/2.39	    inference('sup-', [status(thm)], ['79', '15'])).
2.16/2.39	tff('81', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xz) = sk_Xp(sk_Xz1(sk_S1))),
2.16/2.39	    inference('demod', [status(thm)], ['80', '4'])).
2.16/2.39	tff('82', plain, (sk_Xp(sk_Xz) = sk_Xp(sk_Xz1(sk_S1)) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('simplify', [status(thm)], ['81'])).
2.16/2.39	tff('83', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S1(sk_Xy)
2.16/2.39	       | sk_S2(sk_Xy1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('84', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['83'])).
2.16/2.39	tff('85', plain,
2.16/2.39	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '84'])).
2.16/2.39	tff('86', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['85', '4'])).
2.16/2.39	tff('87', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['86'])).
2.16/2.39	tff('88', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
2.16/2.39	    inference('sup-', [status(thm)], ['87', '15'])).
2.16/2.39	tff('89', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('simplify', [status(thm)], ['88'])).
2.16/2.39	tff('90', plain, (sk_S2(sk_Xy1) | sk_S1 = sk_Xp(sk_Xy)),
2.16/2.39	    inference('clc', [status(thm)], ['89', '77'])).
2.16/2.39	tff('91', plain, (sk_Xp(sk_Xy, sk_Xz1(sk_S1)) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['90', '39'])).
2.16/2.39	tff('92', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_S2(sk_Xy1)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xy))
2.16/2.39	     | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S1))),
2.16/2.39	    inference('sup-', [status(thm)], ['91', '15'])).
2.16/2.39	tff('93', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S1))),
2.16/2.39	    inference('demod', [status(thm)], ['92', '4'])).
2.16/2.39	tff('94', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S1)) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('simplify', [status(thm)], ['93'])).
2.16/2.39	tff('95', plain,
2.16/2.39	    (sk_Xp(sk_Xy) = sk_Xp(sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['82', '94'])).
2.16/2.39	tff('96', plain, (sk_S2(sk_Xy1) | sk_Xp(sk_Xy) = sk_Xp(sk_Xz)),
2.16/2.39	    inference('simplify', [status(thm)], ['95'])).
2.16/2.39	tff('97', plain,
2.16/2.39	    ![X0 : a]:
2.16/2.39	      (sk_Xp(sk_Xz, X0) = sk_Xp(sk_Xz1(sk_Xp(sk_Xy)), X0) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['96', '63'])).
2.16/2.39	tff('98', plain,
2.16/2.39	    ![X0 : a]: (sk_Xp(sk_Xz, X0) = sk_Xp(sk_Xy, X0) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('demod', [status(thm)], ['97', '63'])).
2.16/2.39	tff('99', plain, (sk_Xp(sk_Xy, sk_Xz) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['98', '0'])).
2.16/2.39	tff('100', plain, (sk_Xp(sk_Xx, sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup+', [status(thm)], ['65', '99'])).
2.16/2.39	tff('101', plain, (sk_S2(sk_Xy1) | sk_Xp(sk_Xx, sk_Xz)),
2.16/2.39	    inference('simplify', [status(thm)], ['100'])).
2.16/2.39	tff('102', plain,
2.16/2.39	    ![X3 : a > $o, X5 : a > $o]:
2.16/2.39	      (~ sk_P(X5)
2.16/2.39	       | ~ X5(sk_Xx)
2.16/2.39	       | ~ X5(sk_Xz)
2.16/2.39	       | sk_S2(sk_Xy1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('103', plain,
2.16/2.39	    ![X3 : a > $o, X5 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | sk_S2(sk_Xy1)
2.16/2.39	       | ~ X5(sk_Xz)
2.16/2.39	       | ~ X5(sk_Xx)
2.16/2.39	       | ~ sk_P(X5)),
2.16/2.39	    inference('simplify', [status(thm)], ['102'])).
2.16/2.39	tff('104', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | sk_S2(sk_Xy1)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '103'])).
2.16/2.39	tff('105', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | sk_S2(sk_Xy1)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['104', '4'])).
2.16/2.39	tff('106', plain,
2.16/2.39	    ![X0 : a > $o]: (sk_S2(sk_Xy1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['105'])).
2.16/2.39	tff('107', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_S2(sk_Xy1)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xx))
2.16/2.39	     | ~ sk_Xp(sk_Xx, sk_Xx)
2.16/2.39	     | sk_S2(sk_Xy1)),
2.16/2.39	    inference('sup-', [status(thm)], ['101', '106'])).
2.16/2.39	tff('108', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xy1) | ~ $true | ~ $true | sk_S2(sk_Xy1)),
2.16/2.39	    inference('demod', [status(thm)], ['107', '4', '0'])).
2.16/2.39	tff('109', plain, sk_S2(sk_Xy1),
2.16/2.39	    inference('simplify', [status(thm)], ['108'])).
2.16/2.39	tff('110', plain,
2.16/2.39	    (~ $true | ~ sk_P(sk_S2) | sk_Xp(sk_Xz1(sk_S2)) = sk_Xp(sk_Xy1)),
2.16/2.39	    inference('sup-', [status(thm)], ['109', '30'])).
2.16/2.39	tff('111', plain, (sk_Xp(sk_Xz1(sk_S2)) = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2)),
2.16/2.39	    inference('simplify', [status(thm)], ['110'])).
2.16/2.39	tff('112', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('113', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S1(sk_Xz)),
2.16/2.39	    inference('simplify', [status(thm)], ['112'])).
2.16/2.39	tff('114', plain,
2.16/2.39	    (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '113'])).
2.16/2.39	tff('115', plain, (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['114', '4'])).
2.16/2.39	tff('116', plain, (sk_P(sk_S2) | sk_S1(sk_Xz)),
2.16/2.39	    inference('simplify', [status(thm)], ['115'])).
2.16/2.39	tff('117', plain,
2.16/2.39	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xz)),
2.16/2.39	    inference('sup-', [status(thm)], ['116', '15'])).
2.16/2.39	tff('118', plain, (sk_S1 = sk_Xp(sk_Xz) | ~ sk_P(sk_S1) | sk_P(sk_S2)),
2.16/2.39	    inference('simplify', [status(thm)], ['117'])).
2.16/2.39	tff('119', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('120', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['119'])).
2.16/2.39	tff('121', plain,
2.16/2.39	    (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '120'])).
2.16/2.39	tff('122', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['121', '4'])).
2.16/2.39	tff('123', plain, (sk_P(sk_S2) | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['122'])).
2.16/2.39	tff('124', plain, (sk_P(sk_S2) | sk_S1 = sk_Xp(sk_Xz)),
2.16/2.39	    inference('clc', [status(thm)], ['118', '123'])).
2.16/2.39	tff('125', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xz, X1) | sk_P(sk_S2)),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['124'])).
2.16/2.39	tff('126', plain,
2.16/2.39	    ![X3 : a > $o, X5 : a > $o]:
2.16/2.39	      (~ sk_P(X5)
2.16/2.39	       | ~ X5(sk_Xx)
2.16/2.39	       | ~ X5(sk_Xz)
2.16/2.39	       | sk_P(sk_S2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('127', plain,
2.16/2.39	    ![X3 : a > $o, X5 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | sk_P(sk_S2)
2.16/2.39	       | ~ X5(sk_Xz)
2.16/2.39	       | ~ X5(sk_Xx)
2.16/2.39	       | ~ sk_P(X5)),
2.16/2.39	    inference('simplify', [status(thm)], ['126'])).
2.16/2.39	tff('128', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | sk_P(sk_S2)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '127'])).
2.16/2.39	tff('129', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | sk_P(sk_S2)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['128', '4'])).
2.16/2.39	tff('130', plain,
2.16/2.39	    ![X0 : a > $o]: (sk_P(sk_S2) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['129'])).
2.16/2.39	tff('131', plain,
2.16/2.39	    (~ $true | ~ sk_P(sk_Xp(sk_Xz)) | ~ sk_Xp(sk_Xz, sk_Xx) | sk_P(sk_S2)),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '130'])).
2.16/2.39	tff('132', plain, (~ $true | ~ $true | ~ sk_Xp(sk_Xz, sk_Xx) | sk_P(sk_S2)),
2.16/2.39	    inference('demod', [status(thm)], ['131', '4'])).
2.16/2.39	tff('133', plain, (sk_P(sk_S2) | ~ sk_Xp(sk_Xz, sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['132'])).
2.16/2.39	tff('134', plain, (~ sk_S1(sk_Xx) | sk_P(sk_S2) | sk_P(sk_S2)),
2.16/2.39	    inference('sup-', [status(thm)], ['125', '133'])).
2.16/2.39	tff('135', plain, (sk_P(sk_S2) | ~ sk_S1(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['134'])).
2.16/2.39	tff('136', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('137', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['136'])).
2.16/2.39	tff('138', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '137'])).
2.16/2.39	tff('139', plain, (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['138', '4'])).
2.16/2.39	tff('140', plain, (sk_P(sk_S2) | sk_S(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['139'])).
2.16/2.39	tff('141', plain,
2.16/2.39	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
2.16/2.39	    inference('sup-', [status(thm)], ['140', '15'])).
2.16/2.39	tff('142', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_P(sk_S2)),
2.16/2.39	    inference('simplify', [status(thm)], ['141'])).
2.16/2.39	tff('143', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('144', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_P(sk_S)),
2.16/2.39	    inference('simplify', [status(thm)], ['143'])).
2.16/2.39	tff('145', plain,
2.16/2.39	    (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '144'])).
2.16/2.39	tff('146', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['145', '4'])).
2.16/2.39	tff('147', plain, (sk_P(sk_S2) | sk_P(sk_S)),
2.16/2.39	    inference('simplify', [status(thm)], ['146'])).
2.16/2.39	tff('148', plain, (sk_P(sk_S2) | sk_S = sk_Xp(sk_Xx)),
2.16/2.39	    inference('clc', [status(thm)], ['142', '147'])).
2.16/2.39	tff('149', plain, (sk_Xp(sk_Xx, sk_Xz1(sk_S)) | sk_P(sk_S2)),
2.16/2.39	    inference('sup+', [status(thm)], ['148', '39'])).
2.16/2.39	tff('150', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_P(sk_S2)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xx))
2.16/2.39	     | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('sup-', [status(thm)], ['149', '15'])).
2.16/2.39	tff('151', plain,
2.16/2.39	    (~ $true | sk_P(sk_S2) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('demod', [status(thm)], ['150', '4'])).
2.16/2.39	tff('152', plain, (sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S)) | sk_P(sk_S2)),
2.16/2.39	    inference('simplify', [status(thm)], ['151'])).
2.16/2.39	tff('153', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('154', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['153'])).
2.16/2.39	tff('155', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '154'])).
2.16/2.39	tff('156', plain, (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['155', '4'])).
2.16/2.39	tff('157', plain, (sk_P(sk_S2) | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['156'])).
2.16/2.39	tff('158', plain,
2.16/2.39	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
2.16/2.39	    inference('sup-', [status(thm)], ['157', '15'])).
2.16/2.39	tff('159', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_P(sk_S2)),
2.16/2.39	    inference('simplify', [status(thm)], ['158'])).
2.16/2.39	tff('160', plain, (sk_P(sk_S2) | sk_S = sk_Xp(sk_Xy)),
2.16/2.39	    inference('clc', [status(thm)], ['159', '147'])).
2.16/2.39	tff('161', plain, (sk_Xp(sk_Xy, sk_Xz1(sk_S)) | sk_P(sk_S2)),
2.16/2.39	    inference('sup+', [status(thm)], ['160', '39'])).
2.16/2.39	tff('162', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_P(sk_S2)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xy))
2.16/2.39	     | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('sup-', [status(thm)], ['161', '15'])).
2.16/2.39	tff('163', plain,
2.16/2.39	    (~ $true | sk_P(sk_S2) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('demod', [status(thm)], ['162', '4'])).
2.16/2.39	tff('164', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S)) | sk_P(sk_S2)),
2.16/2.39	    inference('simplify', [status(thm)], ['163'])).
2.16/2.39	tff('165', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_P(sk_S2) | sk_P(sk_S2)),
2.16/2.39	    inference('sup+', [status(thm)], ['152', '164'])).
2.16/2.39	tff('166', plain, (sk_P(sk_S2) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['165'])).
2.16/2.39	tff('167', plain,
2.16/2.39	    ![X0 : a]:
2.16/2.39	      (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xz1(sk_Xp(sk_Xx)), X0) | sk_P(sk_S2)),
2.16/2.39	    inference('sup+', [status(thm)], ['166', '63'])).
2.16/2.39	tff('168', plain,
2.16/2.39	    ![X0 : a]: (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xx, X0) | sk_P(sk_S2)),
2.16/2.39	    inference('demod', [status(thm)], ['167', '63'])).
2.16/2.39	tff('169', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('170', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['169'])).
2.16/2.39	tff('171', plain,
2.16/2.39	    (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '170'])).
2.16/2.39	tff('172', plain, (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['171', '4'])).
2.16/2.39	tff('173', plain, (sk_P(sk_S2) | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['172'])).
2.16/2.39	tff('174', plain,
2.16/2.39	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
2.16/2.39	    inference('sup-', [status(thm)], ['173', '15'])).
2.16/2.39	tff('175', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_P(sk_S2)),
2.16/2.39	    inference('simplify', [status(thm)], ['174'])).
2.16/2.39	tff('176', plain, (sk_P(sk_S2) | sk_S1 = sk_Xp(sk_Xy)),
2.16/2.39	    inference('clc', [status(thm)], ['175', '123'])).
2.16/2.39	tff('177', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_P(sk_S2)),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['176'])).
2.16/2.39	tff('178', plain,
2.16/2.39	    ![X0 : a]: (sk_S1(X0) = sk_Xp(sk_Xx, X0) | sk_P(sk_S2) | sk_P(sk_S2)),
2.16/2.39	    inference('sup+', [status(thm)], ['168', '177'])).
2.16/2.39	tff('179', plain, ![X0 : a]: (sk_P(sk_S2) | sk_S1(X0) = sk_Xp(sk_Xx, X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['178'])).
2.16/2.39	tff('180', plain, (sk_S1(sk_Xx) | sk_P(sk_S2)),
2.16/2.39	    inference('sup+', [status(thm)], ['179', '0'])).
2.16/2.39	tff('181', plain, sk_P(sk_S2),
2.16/2.39	    inference('clc', [status(thm)], ['135', '180'])).
2.16/2.39	tff('182', plain, (sk_Xp(sk_Xz1(sk_S2)) = sk_Xp(sk_Xy1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['111', '181'])).
2.16/2.39	tff('183', plain, sk_Xp(sk_Xz1(sk_S2)) = sk_Xp(sk_Xy1),
2.16/2.39	    inference('simplify', [status(thm)], ['182'])).
2.16/2.39	tff('184', plain, (sk_S2(sk_Xz1(sk_Xp(sk_Xy1))) | ~ sk_P(sk_S2)),
2.16/2.39	    inference('sup+', [status(thm)], ['183', '36'])).
2.16/2.39	tff('185', plain, (sk_S2(sk_Xz1(sk_Xp(sk_Xy1))) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['184', '181'])).
2.16/2.39	tff('186', plain, sk_S2(sk_Xz1(sk_Xp(sk_Xy1))),
2.16/2.39	    inference('simplify', [status(thm)], ['185'])).
2.16/2.39	tff('187', plain,
2.16/2.39	    (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xz1(sk_Xp(sk_Xy1)))),
2.16/2.39	    inference('sup-', [status(thm)], ['186', '15'])).
2.16/2.39	tff('188', plain, (~ $true | ~ $true | sk_S2 = sk_Xp(sk_Xy1)),
2.16/2.39	    inference('demod', [status(thm)], ['187', '181', '33'])).
2.16/2.39	tff('189', plain, sk_S2 = sk_Xp(sk_Xy1),
2.16/2.39	    inference('simplify', [status(thm)], ['188'])).
2.16/2.39	tff('190', plain, ![X1 : a]: sk_S2(X1) = sk_Xp(sk_Xy1, X1),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['189'])).
2.16/2.39	tff('191', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S1(sk_Xz)
2.16/2.39	       | sk_S2(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('192', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
2.16/2.39	    inference('simplify', [status(thm)], ['191'])).
2.16/2.39	tff('193', plain,
2.16/2.39	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '192'])).
2.16/2.39	tff('194', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['193', '4'])).
2.16/2.39	tff('195', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
2.16/2.39	    inference('simplify', [status(thm)], ['194'])).
2.16/2.39	tff('196', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xz)),
2.16/2.39	    inference('sup-', [status(thm)], ['195', '15'])).
2.16/2.39	tff('197', plain, (sk_S1 = sk_Xp(sk_Xz) | ~ sk_P(sk_S1) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('simplify', [status(thm)], ['196'])).
2.16/2.39	tff('198', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('199', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['198'])).
2.16/2.39	tff('200', plain,
2.16/2.39	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '199'])).
2.16/2.39	tff('201', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['200', '4'])).
2.16/2.39	tff('202', plain, (sk_S2(sk_Xx1) | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['201'])).
2.16/2.39	tff('203', plain, (sk_S2(sk_Xx1) | sk_S1 = sk_Xp(sk_Xz)),
2.16/2.39	    inference('clc', [status(thm)], ['197', '202'])).
2.16/2.39	tff('204', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xz, X1) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['203'])).
2.16/2.39	tff('205', plain,
2.16/2.39	    ![X3 : a > $o, X5 : a > $o]:
2.16/2.39	      (~ sk_P(X5)
2.16/2.39	       | ~ X5(sk_Xx)
2.16/2.39	       | ~ X5(sk_Xz)
2.16/2.39	       | sk_S2(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('206', plain,
2.16/2.39	    ![X3 : a > $o, X5 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | sk_S2(sk_Xx1)
2.16/2.39	       | ~ X5(sk_Xz)
2.16/2.39	       | ~ X5(sk_Xx)
2.16/2.39	       | ~ sk_P(X5)),
2.16/2.39	    inference('simplify', [status(thm)], ['205'])).
2.16/2.39	tff('207', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | sk_S2(sk_Xx1)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '206'])).
2.16/2.39	tff('208', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | sk_S2(sk_Xx1)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['207', '4'])).
2.16/2.39	tff('209', plain,
2.16/2.39	    ![X0 : a > $o]: (sk_S2(sk_Xx1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['208'])).
2.16/2.39	tff('210', plain,
2.16/2.39	    (~ $true | ~ sk_P(sk_Xp(sk_Xz)) | ~ sk_Xp(sk_Xz, sk_Xx) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '209'])).
2.16/2.39	tff('211', plain,
2.16/2.39	    (~ $true | ~ $true | ~ sk_Xp(sk_Xz, sk_Xx) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('demod', [status(thm)], ['210', '4'])).
2.16/2.39	tff('212', plain, (sk_S2(sk_Xx1) | ~ sk_Xp(sk_Xz, sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['211'])).
2.16/2.39	tff('213', plain, (~ sk_S1(sk_Xx) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('sup-', [status(thm)], ['204', '212'])).
2.16/2.39	tff('214', plain, (sk_S2(sk_Xx1) | ~ sk_S1(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['213'])).
2.16/2.39	tff('215', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('216', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['215'])).
2.16/2.39	tff('217', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '216'])).
2.16/2.39	tff('218', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['217', '4'])).
2.16/2.39	tff('219', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['218'])).
2.16/2.39	tff('220', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
2.16/2.39	    inference('sup-', [status(thm)], ['219', '15'])).
2.16/2.39	tff('221', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('simplify', [status(thm)], ['220'])).
2.16/2.39	tff('222', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('223', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_P(sk_S)),
2.16/2.39	    inference('simplify', [status(thm)], ['222'])).
2.16/2.39	tff('224', plain,
2.16/2.39	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '223'])).
2.16/2.39	tff('225', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['224', '4'])).
2.16/2.39	tff('226', plain, (sk_S2(sk_Xx1) | sk_P(sk_S)),
2.16/2.39	    inference('simplify', [status(thm)], ['225'])).
2.16/2.39	tff('227', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xx)),
2.16/2.39	    inference('clc', [status(thm)], ['221', '226'])).
2.16/2.39	tff('228', plain, (sk_Xp(sk_Xx, sk_Xz1(sk_S)) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('sup+', [status(thm)], ['227', '39'])).
2.16/2.39	tff('229', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_S2(sk_Xx1)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xx))
2.16/2.39	     | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('sup-', [status(thm)], ['228', '15'])).
2.16/2.39	tff('230', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xx1) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('demod', [status(thm)], ['229', '4'])).
2.16/2.39	tff('231', plain, (sk_Xp(sk_Xx) = sk_Xp(sk_Xz1(sk_S)) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('simplify', [status(thm)], ['230'])).
2.16/2.39	tff('232', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('233', plain,
2.16/2.39	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['232'])).
2.16/2.39	tff('234', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '233'])).
2.16/2.39	tff('235', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['234', '4'])).
2.16/2.39	tff('236', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['235'])).
2.16/2.39	tff('237', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
2.16/2.39	    inference('sup-', [status(thm)], ['236', '15'])).
2.16/2.39	tff('238', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('simplify', [status(thm)], ['237'])).
2.16/2.39	tff('239', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xy)),
2.16/2.39	    inference('clc', [status(thm)], ['238', '226'])).
2.16/2.39	tff('240', plain, (sk_Xp(sk_Xy, sk_Xz1(sk_S)) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('sup+', [status(thm)], ['239', '39'])).
2.16/2.39	tff('241', plain,
2.16/2.39	    (~ $true
2.16/2.39	     | sk_S2(sk_Xx1)
2.16/2.39	     | ~ sk_P(sk_Xp(sk_Xy))
2.16/2.39	     | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('sup-', [status(thm)], ['240', '15'])).
2.16/2.39	tff('242', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xx1) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S))),
2.16/2.39	    inference('demod', [status(thm)], ['241', '4'])).
2.16/2.39	tff('243', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xz1(sk_S)) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('simplify', [status(thm)], ['242'])).
2.16/2.39	tff('244', plain,
2.16/2.39	    (sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('sup+', [status(thm)], ['231', '243'])).
2.16/2.39	tff('245', plain, (sk_S2(sk_Xx1) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['244'])).
2.16/2.39	tff('246', plain,
2.16/2.39	    ![X0 : a]:
2.16/2.39	      (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xz1(sk_Xp(sk_Xx)), X0) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('sup+', [status(thm)], ['245', '63'])).
2.16/2.39	tff('247', plain,
2.16/2.39	    ![X0 : a]: (sk_Xp(sk_Xy, X0) = sk_Xp(sk_Xx, X0) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('demod', [status(thm)], ['246', '63'])).
2.16/2.39	tff('248', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (sk_S1(sk_Xy)
2.16/2.39	       | sk_S2(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('249', plain,
2.16/2.39	    ![X3 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['248'])).
2.16/2.39	tff('250', plain,
2.16/2.39	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '249'])).
2.16/2.39	tff('251', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['250', '4'])).
2.16/2.39	tff('252', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['251'])).
2.16/2.39	tff('253', plain,
2.16/2.39	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
2.16/2.39	    inference('sup-', [status(thm)], ['252', '15'])).
2.16/2.39	tff('254', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('simplify', [status(thm)], ['253'])).
2.16/2.39	tff('255', plain, (sk_S2(sk_Xx1) | sk_S1 = sk_Xp(sk_Xy)),
2.16/2.39	    inference('clc', [status(thm)], ['254', '202'])).
2.16/2.39	tff('256', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['255'])).
2.16/2.39	tff('257', plain,
2.16/2.39	    ![X0 : a]: (sk_S1(X0) = sk_Xp(sk_Xx, X0) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('sup+', [status(thm)], ['247', '256'])).
2.16/2.39	tff('258', plain, ![X0 : a]: (sk_S2(sk_Xx1) | sk_S1(X0) = sk_Xp(sk_Xx, X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['257'])).
2.16/2.39	tff('259', plain, (sk_S1(sk_Xx) | sk_S2(sk_Xx1)),
2.16/2.39	    inference('sup+', [status(thm)], ['258', '0'])).
2.16/2.39	tff('260', plain, sk_S2(sk_Xx1),
2.16/2.39	    inference('clc', [status(thm)], ['214', '259'])).
2.16/2.39	tff('261', plain, (~ $true | sk_S1(sk_Xz)),
2.16/2.39	    inference('demod', [status(thm)], ['9', '190', '260'])).
2.16/2.39	tff('262', plain, sk_S1(sk_Xz), inference('simplify', [status(thm)], ['261'])).
2.16/2.39	tff('263', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (sk_S(sk_Xy)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('264', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['263'])).
2.16/2.39	tff('265', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_S(sk_Xy)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '264'])).
2.16/2.39	tff('266', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_S(sk_Xy)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['265', '4'])).
2.16/2.39	tff('267', plain,
2.16/2.39	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['266'])).
2.16/2.39	tff('268', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xy) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '267'])).
2.16/2.39	tff('269', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xy) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('demod', [status(thm)], ['268', '4'])).
2.16/2.39	tff('270', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['269'])).
2.16/2.39	tff('271', plain, (~ $true | sk_S(sk_Xy)),
2.16/2.39	    inference('demod', [status(thm)], ['270', '190', '260'])).
2.16/2.39	tff('272', plain, sk_S(sk_Xy), inference('simplify', [status(thm)], ['271'])).
2.16/2.39	tff('273', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
2.16/2.39	    inference('sup-', [status(thm)], ['272', '15'])).
2.16/2.39	tff('274', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (sk_P(sk_S)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('275', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | sk_P(sk_S)),
2.16/2.39	    inference('simplify', [status(thm)], ['274'])).
2.16/2.39	tff('276', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_P(sk_S)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '275'])).
2.16/2.39	tff('277', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_P(sk_S)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['276', '4'])).
2.16/2.39	tff('278', plain,
2.16/2.39	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S)),
2.16/2.39	    inference('simplify', [status(thm)], ['277'])).
2.16/2.39	tff('279', plain,
2.16/2.39	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '278'])).
2.16/2.39	tff('280', plain, (~ $true | sk_P(sk_S) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('demod', [status(thm)], ['279', '4'])).
2.16/2.39	tff('281', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_P(sk_S)),
2.16/2.39	    inference('simplify', [status(thm)], ['280'])).
2.16/2.39	tff('282', plain, (~ $true | sk_P(sk_S)),
2.16/2.39	    inference('demod', [status(thm)], ['281', '190', '260'])).
2.16/2.39	tff('283', plain, sk_P(sk_S), inference('simplify', [status(thm)], ['282'])).
2.16/2.39	tff('284', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xy)),
2.16/2.39	    inference('demod', [status(thm)], ['273', '283'])).
2.16/2.39	tff('285', plain, sk_S = sk_Xp(sk_Xy),
2.16/2.39	    inference('simplify', [status(thm)], ['284'])).
2.16/2.39	tff('286', plain, (~ $true | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xz)),
2.16/2.39	    inference('sup-', [status(thm)], ['262', '15'])).
2.16/2.39	tff('287', plain, (sk_S1 = sk_Xp(sk_Xz) | ~ sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['286'])).
2.16/2.39	tff('288', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (sk_P(sk_S1)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('289', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['288'])).
2.16/2.39	tff('290', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_P(sk_S1)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '289'])).
2.16/2.39	tff('291', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_P(sk_S1)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['290', '4'])).
2.16/2.39	tff('292', plain,
2.16/2.39	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['291'])).
2.16/2.39	tff('293', plain,
2.16/2.39	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '292'])).
2.16/2.39	tff('294', plain,
2.16/2.39	    (~ $true | sk_P(sk_S1) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('demod', [status(thm)], ['293', '4'])).
2.16/2.39	tff('295', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_P(sk_S1)),
2.16/2.39	    inference('simplify', [status(thm)], ['294'])).
2.16/2.39	tff('296', plain, (~ $true | sk_P(sk_S1)),
2.16/2.39	    inference('demod', [status(thm)], ['295', '190', '260'])).
2.16/2.39	tff('297', plain, sk_P(sk_S1), inference('simplify', [status(thm)], ['296'])).
2.16/2.39	tff('298', plain, (sk_S1 = sk_Xp(sk_Xz) | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['287', '297'])).
2.16/2.39	tff('299', plain, sk_S1 = sk_Xp(sk_Xz),
2.16/2.39	    inference('simplify', [status(thm)], ['298'])).
2.16/2.39	tff('300', plain, ![X1 : a]: sk_S1(X1) = sk_Xp(sk_Xz, X1),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['299'])).
2.16/2.39	tff('301', plain,
2.16/2.39	    ![X0 : a, X1 : a > $o]:
2.16/2.39	      (~ sk_Xp(sk_Xz1(X1), X0) | ~ sk_P(X1) | ~ sk_P(X1) | X1 = sk_Xp(X0)),
2.16/2.39	    inference('sup-', [status(thm)], ['27', '15'])).
2.16/2.39	tff('302', plain,
2.16/2.39	    ![X0 : a, X1 : a > $o]:
2.16/2.39	      (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ sk_Xp(sk_Xz1(X1), X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['301'])).
2.16/2.39	tff('303', plain,
2.16/2.39	    ![X0 : a, X1 : a]:
2.16/2.39	      (~ sk_Xp(X1, X0) | ~ sk_P(sk_Xp(X1)) | sk_Xp(X1) = sk_Xp(X0)),
2.16/2.39	    inference('sup-', [status(thm)], ['63', '302'])).
2.16/2.39	tff('304', plain,
2.16/2.39	    ![X0 : a, X1 : a]: (~ sk_Xp(X1, X0) | ~ $true | sk_Xp(X1) = sk_Xp(X0)),
2.16/2.39	    inference('demod', [status(thm)], ['303', '4'])).
2.16/2.39	tff('305', plain,
2.16/2.39	    ![X0 : a, X1 : a]: (sk_Xp(X1) = sk_Xp(X0) | ~ sk_Xp(X1, X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['304'])).
2.16/2.39	tff('306', plain, ![X0 : a]: (~ sk_S1(X0) | sk_Xp(sk_Xz) = sk_Xp(X0)),
2.16/2.39	    inference('sup-', [status(thm)], ['300', '305'])).
2.16/2.39	tff('307', plain, ![X0 : a]: (~ sk_S1(X0) | sk_S1 = sk_Xp(X0)),
2.16/2.39	    inference('demod', [status(thm)], ['306', '299'])).
2.16/2.39	tff('308', plain, (sk_S1 = sk_S | ~ sk_S1(sk_Xy)),
2.16/2.39	    inference('sup+', [status(thm)], ['285', '307'])).
2.16/2.39	tff('309', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (sk_S1(sk_Xy)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('310', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['309'])).
2.16/2.39	tff('311', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_S1(sk_Xy)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '310'])).
2.16/2.39	tff('312', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_S1(sk_Xy)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['311', '4'])).
2.16/2.39	tff('313', plain,
2.16/2.39	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['312'])).
2.16/2.39	tff('314', plain,
2.16/2.39	    (~ $true | sk_S1(sk_Xy) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '313'])).
2.16/2.39	tff('315', plain,
2.16/2.39	    (~ $true | sk_S1(sk_Xy) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('demod', [status(thm)], ['314', '4'])).
2.16/2.39	tff('316', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S1(sk_Xy)),
2.16/2.39	    inference('simplify', [status(thm)], ['315'])).
2.16/2.39	tff('317', plain, (~ $true | sk_S1(sk_Xy)),
2.16/2.39	    inference('demod', [status(thm)], ['316', '190', '260'])).
2.16/2.39	tff('318', plain, sk_S1(sk_Xy), inference('simplify', [status(thm)], ['317'])).
2.16/2.39	tff('319', plain, (sk_S1 = sk_S | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['308', '318'])).
2.16/2.39	tff('320', plain, sk_S1 = sk_S, inference('simplify', [status(thm)], ['319'])).
2.16/2.39	tff('321', plain, ![X1 : a]: sk_S1(X1) = sk_S(X1),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['320'])).
2.16/2.39	tff('322', plain, sk_S(sk_Xz),
2.16/2.39	    inference('demod', [status(thm)], ['262', '321'])).
2.16/2.39	tff('323', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
2.16/2.39	      (~ sk_P(X5)
2.16/2.39	       | ~ X5(sk_Xx)
2.16/2.39	       | ~ X5(sk_Xz)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('324', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | ~ X5(sk_Xz)
2.16/2.39	       | ~ X5(sk_Xx)
2.16/2.39	       | ~ sk_P(X5)),
2.16/2.39	    inference('simplify', [status(thm)], ['323'])).
2.16/2.39	tff('325', plain,
2.16/2.39	    ![X0 : a > $o, X1 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | ~ sk_P(X1)
2.16/2.39	       | ~ X1(sk_Xy1)
2.16/2.39	       | ~ X1(sk_Xx1)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '324'])).
2.16/2.39	tff('326', plain,
2.16/2.39	    ![X0 : a > $o, X1 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | ~ sk_P(X1)
2.16/2.39	       | ~ X1(sk_Xy1)
2.16/2.39	       | ~ X1(sk_Xx1)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['325', '4'])).
2.16/2.39	tff('327', plain,
2.16/2.39	    ![X0 : a > $o, X1 : a > $o]:
2.16/2.39	      (~ X1(sk_Xx1)
2.16/2.39	       | ~ X1(sk_Xy1)
2.16/2.39	       | ~ sk_P(X1)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ sk_P(X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['326'])).
2.16/2.39	tff('328', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xx)
2.16/2.39	       | ~ X0(sk_Xz)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xy1))
2.16/2.39	       | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '327'])).
2.16/2.39	tff('329', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true | ~ sk_P(X0) | ~ X0(sk_Xx) | ~ X0(sk_Xz) | ~ $true | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['328', '189', '181', '190', '260'])).
2.16/2.39	tff('330', plain, ![X0 : a > $o]: (~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
2.16/2.39	    inference('simplify', [status(thm)], ['329'])).
2.16/2.39	tff('331', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx)),
2.16/2.39	    inference('sup-', [status(thm)], ['322', '330'])).
2.16/2.39	tff('332', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (sk_S(sk_Xx)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X3(sk_Xx2)
2.16/2.39	       | ~ X3(sk_Xx2)),
2.16/2.39	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.16/2.39	tff('333', plain,
2.16/2.39	    ![X3 : a > $o, X4 : a > $o]:
2.16/2.39	      (~ X3(sk_Xx2)
2.16/2.39	       | ~ sk_P(X3)
2.16/2.39	       | ~ X4(sk_Xx1)
2.16/2.39	       | ~ X4(sk_Xy1)
2.16/2.39	       | ~ sk_P(X4)
2.16/2.39	       | sk_S(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['332'])).
2.16/2.39	tff('334', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_S(sk_Xx)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '333'])).
2.16/2.39	tff('335', plain,
2.16/2.39	    ![X0 : a > $o]:
2.16/2.39	      (~ $true
2.16/2.39	       | sk_S(sk_Xx)
2.16/2.39	       | ~ sk_P(X0)
2.16/2.39	       | ~ X0(sk_Xy1)
2.16/2.39	       | ~ X0(sk_Xx1)
2.16/2.39	       | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['334', '4'])).
2.16/2.39	tff('336', plain,
2.16/2.39	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['335'])).
2.16/2.39	tff('337', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xx) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('sup-', [status(thm)], ['0', '336'])).
2.16/2.39	tff('338', plain,
2.16/2.39	    (~ $true | sk_S(sk_Xx) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
2.16/2.39	    inference('demod', [status(thm)], ['337', '4'])).
2.16/2.39	tff('339', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S(sk_Xx)),
2.16/2.39	    inference('simplify', [status(thm)], ['338'])).
2.16/2.39	tff('340', plain, (~ $true | sk_S(sk_Xx)),
2.16/2.39	    inference('demod', [status(thm)], ['339', '190', '260'])).
2.16/2.39	tff('341', plain, sk_S(sk_Xx), inference('simplify', [status(thm)], ['340'])).
2.16/2.39	tff('342', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
2.16/2.39	    inference('sup-', [status(thm)], ['341', '15'])).
2.16/2.39	tff('343', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xx)),
2.16/2.39	    inference('demod', [status(thm)], ['342', '283'])).
2.16/2.39	tff('344', plain, sk_S = sk_Xp(sk_Xx),
2.16/2.39	    inference('simplify', [status(thm)], ['343'])).
2.16/2.39	tff('345', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xx, X1),
2.16/2.39	    inference('ho_complete_eq', [status(thm)], ['344'])).
2.16/2.39	tff('346', plain, sk_S(sk_Xx) = $true,
2.16/2.39	    inference('sup+', [status(thm)], ['0', '345'])).
2.16/2.39	tff('347', plain, (~ $true | ~ $true | ~ $true),
2.16/2.39	    inference('demod', [status(thm)], ['331', '283', '346'])).
2.16/2.39	tff('348', plain, $false, inference('simplify', [status(thm)], ['347'])).
2.16/2.39	
2.16/2.39	% SZS output end Refutation
2.16/2.39	EOF
