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    : supatvars_int
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --sup-at-vars \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n149.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
0.98/1.17	% done 3981 iterations in 0.968s
0.98/1.17	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
0.98/1.17	% SZS output start Refutation
0.98/1.18	tff(cTHM261_pme, conjecture,
0.98/1.18	  (![P:(a > $o > $o)]:
0.98/1.18	     (((![Xx:a]:
0.98/1.18	          (?[Xp:(a > $o)]:
0.98/1.18	             ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
0.98/1.18	              P(Xp)))) & 
0.98/1.18	       (![Xp:(a > $o)]: (P(Xp) => (?[Xz:a]: Xp(Xz))))) =>
0.98/1.18	      ((![Xx:a,Xy:a,Xz:a]:
0.98/1.18	          (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
0.98/1.18	            (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
0.98/1.18	           (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
0.98/1.18	       (![Xx:a,Xy:a]:
0.98/1.18	          ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
0.98/1.18	           (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
0.98/1.18	       (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S)))))))).
0.98/1.18	tff(zf_stmt_0, negated_conjecture,
0.98/1.18	  (~
0.98/1.18	    (![P:(a > $o > $o)]:
0.98/1.18	       (((![Xx:a]:
0.98/1.18	            (?[Xp:(a > $o)]:
0.98/1.18	               ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
0.98/1.18	                P(Xp)))) & 
0.98/1.18	         (![Xp:(a > $o)]: (P(Xp) => (?[Xz:a]: Xp(Xz))))) =>
0.98/1.18	        ((![Xx:a,Xy:a,Xz:a]:
0.98/1.18	            (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
0.98/1.18	              (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
0.98/1.18	             (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
0.98/1.18	         (![Xx:a,Xy:a]:
0.98/1.18	            ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
0.98/1.18	             (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
0.98/1.18	         (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S))))))))).
0.98/1.18	tff('0', plain, ![X0 : a]: sk_Xp(X0, X0),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('1', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S1(sk_Xz)
0.98/1.18	       | sk_S2(sk_Xy1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('2', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['1'])).
0.98/1.18	tff('3', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '2'])).
0.98/1.18	tff('4', plain, ![X0 : a]: sk_P(sk_Xp(X0)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('5', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['3', '4'])).
0.98/1.18	tff('6', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['5'])).
0.98/1.18	tff('7', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('8', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['7'])).
0.98/1.18	tff('9', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '8'])).
0.98/1.18	tff('10', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['9', '4'])).
0.98/1.18	tff('11', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['10'])).
0.98/1.18	tff('12', plain,
0.98/1.18	    ![X0 : a, X1 : a > $o]: (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ X1(X0)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('13', plain,
0.98/1.18	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['11', '12'])).
0.98/1.18	tff('14', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('simplify', [status(thm)], ['13'])).
0.98/1.18	tff('15', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('16', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['15'])).
0.98/1.18	tff('17', plain,
0.98/1.18	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '16'])).
0.98/1.18	tff('18', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['17', '4'])).
0.98/1.18	tff('19', plain, (sk_S2(sk_Xy1) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['18'])).
0.98/1.18	tff('20', plain,
0.98/1.18	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
0.98/1.18	    inference('sup-', [status(thm)], ['19', '12'])).
0.98/1.18	tff('21', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['20'])).
0.98/1.18	tff('22', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('23', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['22'])).
0.98/1.18	tff('24', plain,
0.98/1.18	    (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '23'])).
0.98/1.18	tff('25', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['24', '4'])).
0.98/1.18	tff('26', plain, (sk_P(sk_S2) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['25'])).
0.98/1.18	tff('27', plain, (sk_P(sk_S) | sk_S2 = sk_Xp(sk_Xy1)),
0.98/1.18	    inference('clc', [status(thm)], ['21', '26'])).
0.98/1.18	tff('28', plain, ![X2 : a > $o]: (X2(sk_Xz1(X2)) | ~ sk_P(X2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('29', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true | ~ sk_P(X0) | ~ sk_P(X0) | X0 = sk_Xp(sk_Xz1(X0))),
0.98/1.18	    inference('sup-', [status(thm)], ['28', '12'])).
0.98/1.18	tff('30', plain, ![X0 : a > $o]: (X0 = sk_Xp(sk_Xz1(X0)) | ~ sk_P(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['29'])).
0.98/1.18	tff('31', plain,
0.98/1.18	    ![X0 : a > $o, X1 : a]: (X0(X1) = sk_Xp(sk_Xz1(X0), X1) | ~ sk_P(X0)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['30'])).
0.98/1.18	tff('32', plain,
0.98/1.18	    ![X0 : a > $o, X1 : a]:
0.98/1.18	      (~ X0(X1)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xz1(X0)))
0.98/1.18	       | sk_Xp(sk_Xz1(X0)) = sk_Xp(X1)),
0.98/1.18	    inference('sup-', [status(thm)], ['31', '12'])).
0.98/1.18	tff('33', plain,
0.98/1.18	    ![X0 : a > $o, X1 : a]:
0.98/1.18	      (~ X0(X1) | ~ sk_P(X0) | ~ $true | sk_Xp(sk_Xz1(X0)) = sk_Xp(X1)),
0.98/1.18	    inference('demod', [status(thm)], ['32', '4'])).
0.98/1.18	tff('34', plain,
0.98/1.18	    ![X0 : a > $o, X1 : a]:
0.98/1.18	      (sk_Xp(sk_Xz1(X0)) = sk_Xp(X1) | ~ sk_P(X0) | ~ X0(X1)),
0.98/1.18	    inference('simplify', [status(thm)], ['33'])).
0.98/1.18	tff('35', plain,
0.98/1.18	    ![X0 : a]:
0.98/1.18	      (~ $true | ~ sk_P(sk_Xp(X0)) | sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0)),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '34'])).
0.98/1.18	tff('36', plain,
0.98/1.18	    ![X0 : a]: (~ $true | ~ $true | sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0)),
0.98/1.18	    inference('demod', [status(thm)], ['35', '4'])).
0.98/1.18	tff('37', plain, ![X0 : a]: sk_Xp(sk_Xz1(sk_Xp(X0))) = sk_Xp(X0),
0.98/1.18	    inference('simplify', [status(thm)], ['36'])).
0.98/1.18	tff('38', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0) | ~ sk_P(sk_Xp(sk_Xz1(X0)))),
0.98/1.18	    inference('sup+', [status(thm)], ['31', '28'])).
0.98/1.18	tff('39', plain,
0.98/1.18	    ![X0 : a > $o]: (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['38', '4'])).
0.98/1.18	tff('40', plain,
0.98/1.18	    ![X0 : a > $o]: (~ sk_P(X0) | X0(sk_Xz1(sk_Xp(sk_Xz1(X0))))),
0.98/1.18	    inference('simplify', [status(thm)], ['39'])).
0.98/1.18	tff('41', plain,
0.98/1.18	    ![X0 : a]: (sk_Xp(X0, sk_Xz1(sk_Xp(X0))) | ~ sk_P(sk_Xp(X0))),
0.98/1.18	    inference('sup+', [status(thm)], ['37', '40'])).
0.98/1.18	tff('42', plain, ![X0 : a]: (sk_Xp(X0, sk_Xz1(sk_Xp(X0))) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['41', '4'])).
0.98/1.18	tff('43', plain, ![X0 : a]: sk_Xp(X0, sk_Xz1(sk_Xp(X0))),
0.98/1.18	    inference('simplify', [status(thm)], ['42'])).
0.98/1.18	tff('44', plain, (sk_Xp(sk_Xy1, sk_Xz1(sk_S2)) | sk_P(sk_S)),
0.98/1.18	    inference('sup+', [status(thm)], ['27', '43'])).
0.98/1.18	tff('45', plain,
0.98/1.18	    (~ $true
0.98/1.18	     | sk_P(sk_S)
0.98/1.18	     | ~ sk_P(sk_Xp(sk_Xy1))
0.98/1.18	     | sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S2))),
0.98/1.18	    inference('sup-', [status(thm)], ['44', '12'])).
0.98/1.18	tff('46', plain,
0.98/1.18	    (~ $true | sk_P(sk_S) | ~ $true | sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S2))),
0.98/1.18	    inference('demod', [status(thm)], ['45', '4'])).
0.98/1.18	tff('47', plain, (sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S2)) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['46'])).
0.98/1.18	tff('48', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('49', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['48'])).
0.98/1.18	tff('50', plain,
0.98/1.18	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '49'])).
0.98/1.18	tff('51', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['50', '4'])).
0.98/1.18	tff('52', plain, (sk_S2(sk_Xx1) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['51'])).
0.98/1.18	tff('53', plain,
0.98/1.18	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['52', '12'])).
0.98/1.18	tff('54', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['53'])).
0.98/1.18	tff('55', plain, (sk_P(sk_S) | sk_S2 = sk_Xp(sk_Xx1)),
0.98/1.18	    inference('clc', [status(thm)], ['54', '26'])).
0.98/1.18	tff('56', plain, (sk_Xp(sk_Xx1, sk_Xz1(sk_S2)) | sk_P(sk_S)),
0.98/1.18	    inference('sup+', [status(thm)], ['55', '43'])).
0.98/1.18	tff('57', plain,
0.98/1.18	    (~ $true
0.98/1.18	     | sk_P(sk_S)
0.98/1.18	     | ~ sk_P(sk_Xp(sk_Xx1))
0.98/1.18	     | sk_Xp(sk_Xx1) = sk_Xp(sk_Xz1(sk_S2))),
0.98/1.18	    inference('sup-', [status(thm)], ['56', '12'])).
0.98/1.18	tff('58', plain,
0.98/1.18	    (~ $true | sk_P(sk_S) | ~ $true | sk_Xp(sk_Xx1) = sk_Xp(sk_Xz1(sk_S2))),
0.98/1.18	    inference('demod', [status(thm)], ['57', '4'])).
0.98/1.18	tff('59', plain, (sk_Xp(sk_Xx1) = sk_Xp(sk_Xz1(sk_S2)) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['58'])).
0.98/1.18	tff('60', plain, (sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1) | sk_P(sk_S) | sk_P(sk_S)),
0.98/1.18	    inference('sup+', [status(thm)], ['47', '59'])).
0.98/1.18	tff('61', plain, (sk_P(sk_S) | sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1)),
0.98/1.18	    inference('simplify', [status(thm)], ['60'])).
0.98/1.18	tff('62', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))))),
0.98/1.18	    inference('sup-', [status(thm)], ['40', '12'])).
0.98/1.18	tff('63', plain,
0.98/1.18	    ![X0 : a > $o]: (X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['62'])).
0.98/1.18	tff('64', plain,
0.98/1.18	    ![X0 : a > $o, X1 : a]:
0.98/1.18	      (X0(X1) = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))), X1) | ~ sk_P(X0)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['63'])).
0.98/1.18	tff('65', plain,
0.98/1.18	    ![X0 : a, X1 : a]:
0.98/1.18	      (sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1) | ~ sk_P(sk_Xp(X0))),
0.98/1.18	    inference('sup+', [status(thm)], ['37', '64'])).
0.98/1.18	tff('66', plain,
0.98/1.18	    ![X0 : a, X1 : a]:
0.98/1.18	      (sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['65', '4'])).
0.98/1.18	tff('67', plain,
0.98/1.18	    ![X0 : a, X1 : a]: sk_Xp(X0, X1) = sk_Xp(sk_Xz1(sk_Xp(X0)), X1),
0.98/1.18	    inference('simplify', [status(thm)], ['66'])).
0.98/1.18	tff('68', plain,
0.98/1.18	    ![X0 : a]:
0.98/1.18	      (sk_Xp(sk_Xy1, X0) = sk_Xp(sk_Xz1(sk_Xp(sk_Xx1)), X0) | sk_P(sk_S)),
0.98/1.18	    inference('sup+', [status(thm)], ['61', '67'])).
0.98/1.18	tff('69', plain,
0.98/1.18	    ![X0 : a]: (sk_Xp(sk_Xy1, X0) = sk_Xp(sk_Xx1, X0) | sk_P(sk_S)),
0.98/1.18	    inference('demod', [status(thm)], ['68', '67'])).
0.98/1.18	tff('70', plain, (sk_Xp(sk_Xx1, sk_Xy1) | sk_P(sk_S)),
0.98/1.18	    inference('sup+', [status(thm)], ['69', '0'])).
0.98/1.18	tff('71', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (sk_P(sk_S)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('72', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['71'])).
0.98/1.18	tff('73', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_P(sk_S)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '72'])).
0.98/1.18	tff('74', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_P(sk_S)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['73', '4'])).
0.98/1.18	tff('75', plain,
0.98/1.18	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S)),
0.98/1.18	    inference('simplify', [status(thm)], ['74'])).
0.98/1.18	tff('76', plain,
0.98/1.18	    (~ $true
0.98/1.18	     | sk_P(sk_S)
0.98/1.18	     | sk_P(sk_S)
0.98/1.18	     | ~ sk_P(sk_Xp(sk_Xx1))
0.98/1.18	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['70', '75'])).
0.98/1.18	tff('77', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S) | ~ $true | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['76', '4', '0'])).
0.98/1.18	tff('78', plain, sk_P(sk_S), inference('simplify', [status(thm)], ['77'])).
0.98/1.18	tff('79', plain, (sk_S = sk_Xp(sk_Xy) | ~ $true | sk_S2(sk_Xy1)),
0.98/1.18	    inference('demod', [status(thm)], ['14', '78'])).
0.98/1.18	tff('80', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['79'])).
0.98/1.18	tff('81', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['80'])).
0.98/1.18	tff('82', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S1(sk_Xy)
0.98/1.18	       | sk_S2(sk_Xy1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('83', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['82'])).
0.98/1.18	tff('84', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '83'])).
0.98/1.18	tff('85', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['84', '4'])).
0.98/1.18	tff('86', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['85'])).
0.98/1.18	tff('87', plain,
0.98/1.18	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['86', '12'])).
0.98/1.18	tff('88', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('simplify', [status(thm)], ['87'])).
0.98/1.18	tff('89', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('90', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['89'])).
0.98/1.18	tff('91', plain,
0.98/1.18	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '90'])).
0.98/1.18	tff('92', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['91', '4'])).
0.98/1.18	tff('93', plain, (sk_S2(sk_Xy1) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['92'])).
0.98/1.18	tff('94', plain, (sk_S2(sk_Xy1) | sk_S1 = sk_Xp(sk_Xy)),
0.98/1.18	    inference('clc', [status(thm)], ['88', '93'])).
0.98/1.18	tff('95', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['94'])).
0.98/1.18	tff('96', plain,
0.98/1.18	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('sup+', [status(thm)], ['81', '95'])).
0.98/1.18	tff('97', plain, ![X0 : a]: (sk_S2(sk_Xy1) | sk_S1(X0) = sk_S(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['96'])).
0.98/1.18	tff('98', plain, ($true = sk_S(sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('sup+', [status(thm)], ['6', '97'])).
0.98/1.18	tff('99', plain, (sk_S2(sk_Xy1) | $true = sk_S(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['98'])).
0.98/1.18	tff('100', plain,
0.98/1.18	    ![X3 : a > $o, X5 : a > $o]:
0.98/1.18	      (~ sk_P(X5)
0.98/1.18	       | ~ X5(sk_Xx)
0.98/1.18	       | ~ X5(sk_Xz)
0.98/1.18	       | sk_S2(sk_Xy1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('101', plain,
0.98/1.18	    ![X3 : a > $o, X5 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | sk_S2(sk_Xy1)
0.98/1.18	       | ~ X5(sk_Xz)
0.98/1.18	       | ~ X5(sk_Xx)
0.98/1.18	       | ~ sk_P(X5)),
0.98/1.18	    inference('simplify', [status(thm)], ['100'])).
0.98/1.18	tff('102', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | sk_S2(sk_Xy1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '101'])).
0.98/1.18	tff('103', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | sk_S2(sk_Xy1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['102', '4'])).
0.98/1.18	tff('104', plain,
0.98/1.18	    ![X0 : a > $o]: (sk_S2(sk_Xy1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['103'])).
0.98/1.18	tff('105', plain,
0.98/1.18	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('sup-', [status(thm)], ['99', '104'])).
0.98/1.18	tff('106', plain,
0.98/1.18	    (~ $true | sk_S2(sk_Xy1) | ~ $true | ~ sk_S(sk_Xx) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('demod', [status(thm)], ['105', '78'])).
0.98/1.18	tff('107', plain, (~ sk_S(sk_Xx) | sk_S2(sk_Xy1)),
0.98/1.18	    inference('simplify', [status(thm)], ['106'])).
0.98/1.18	tff('108', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('109', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['108'])).
0.98/1.18	tff('110', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '109'])).
0.98/1.18	tff('111', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['110', '4'])).
0.98/1.18	tff('112', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['111'])).
0.98/1.18	tff('113', plain, sk_S2(sk_Xy1),
0.98/1.18	    inference('clc', [status(thm)], ['107', '112'])).
0.98/1.18	tff('114', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
0.98/1.18	    inference('sup-', [status(thm)], ['113', '12'])).
0.98/1.18	tff('115', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2)),
0.98/1.18	    inference('simplify', [status(thm)], ['114'])).
0.98/1.18	tff('116', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | ~ sk_P(sk_S2)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['115'])).
0.98/1.18	tff('117', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (sk_S1(sk_Xz)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('118', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['117'])).
0.98/1.18	tff('119', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_S1(sk_Xz)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '118'])).
0.98/1.18	tff('120', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_S1(sk_Xz)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['119', '4'])).
0.98/1.18	tff('121', plain,
0.98/1.18	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['120'])).
0.98/1.18	tff('122', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xz) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '121'])).
0.98/1.18	tff('123', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xz) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('demod', [status(thm)], ['122', '4'])).
0.98/1.18	tff('124', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['123'])).
0.98/1.18	tff('125', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S1(sk_Xz)),
0.98/1.18	    inference('sup-', [status(thm)], ['116', '124'])).
0.98/1.18	tff('126', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S1(sk_Xz)
0.98/1.18	       | sk_S2(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('127', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['126'])).
0.98/1.18	tff('128', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '127'])).
0.98/1.18	tff('129', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['128', '4'])).
0.98/1.18	tff('130', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['129'])).
0.98/1.18	tff('131', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('132', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['131'])).
0.98/1.18	tff('133', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '132'])).
0.98/1.18	tff('134', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['133', '4'])).
0.98/1.18	tff('135', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['134'])).
0.98/1.18	tff('136', plain,
0.98/1.18	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['135', '12'])).
0.98/1.18	tff('137', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('simplify', [status(thm)], ['136'])).
0.98/1.18	tff('138', plain, (sk_S = sk_Xp(sk_Xy) | ~ $true | sk_S2(sk_Xx1)),
0.98/1.18	    inference('demod', [status(thm)], ['137', '78'])).
0.98/1.18	tff('139', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['138'])).
0.98/1.18	tff('140', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['139'])).
0.98/1.18	tff('141', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S1(sk_Xy)
0.98/1.18	       | sk_S2(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('142', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['141'])).
0.98/1.18	tff('143', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '142'])).
0.98/1.18	tff('144', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['143', '4'])).
0.98/1.18	tff('145', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['144'])).
0.98/1.18	tff('146', plain,
0.98/1.18	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['145', '12'])).
0.98/1.18	tff('147', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('simplify', [status(thm)], ['146'])).
0.98/1.18	tff('148', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('149', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['148'])).
0.98/1.18	tff('150', plain,
0.98/1.18	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '149'])).
0.98/1.18	tff('151', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['150', '4'])).
0.98/1.18	tff('152', plain, (sk_S2(sk_Xx1) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['151'])).
0.98/1.18	tff('153', plain, (sk_S2(sk_Xx1) | sk_S1 = sk_Xp(sk_Xy)),
0.98/1.18	    inference('clc', [status(thm)], ['147', '152'])).
0.98/1.18	tff('154', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['153'])).
0.98/1.18	tff('155', plain,
0.98/1.18	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('sup+', [status(thm)], ['140', '154'])).
0.98/1.18	tff('156', plain, ![X0 : a]: (sk_S2(sk_Xx1) | sk_S1(X0) = sk_S(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['155'])).
0.98/1.18	tff('157', plain, ($true = sk_S(sk_Xz) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('sup+', [status(thm)], ['130', '156'])).
0.98/1.18	tff('158', plain, (sk_S2(sk_Xx1) | $true = sk_S(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['157'])).
0.98/1.18	tff('159', plain,
0.98/1.18	    ![X3 : a > $o, X5 : a > $o]:
0.98/1.18	      (~ sk_P(X5)
0.98/1.18	       | ~ X5(sk_Xx)
0.98/1.18	       | ~ X5(sk_Xz)
0.98/1.18	       | sk_S2(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('160', plain,
0.98/1.18	    ![X3 : a > $o, X5 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | sk_S2(sk_Xx1)
0.98/1.18	       | ~ X5(sk_Xz)
0.98/1.18	       | ~ X5(sk_Xx)
0.98/1.18	       | ~ sk_P(X5)),
0.98/1.18	    inference('simplify', [status(thm)], ['159'])).
0.98/1.18	tff('161', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | sk_S2(sk_Xx1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '160'])).
0.98/1.18	tff('162', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | sk_S2(sk_Xx1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['161', '4'])).
0.98/1.18	tff('163', plain,
0.98/1.18	    ![X0 : a > $o]: (sk_S2(sk_Xx1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['162'])).
0.98/1.18	tff('164', plain,
0.98/1.18	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['158', '163'])).
0.98/1.18	tff('165', plain,
0.98/1.18	    (~ $true | sk_S2(sk_Xx1) | ~ $true | ~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('demod', [status(thm)], ['164', '78'])).
0.98/1.18	tff('166', plain, (~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
0.98/1.18	    inference('simplify', [status(thm)], ['165'])).
0.98/1.18	tff('167', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('168', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['167'])).
0.98/1.18	tff('169', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '168'])).
0.98/1.18	tff('170', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['169', '4'])).
0.98/1.18	tff('171', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['170'])).
0.98/1.18	tff('172', plain, sk_S2(sk_Xx1),
0.98/1.18	    inference('clc', [status(thm)], ['166', '171'])).
0.98/1.18	tff('173', plain, (~ $true | ~ sk_P(sk_S2) | sk_S1(sk_Xz)),
0.98/1.18	    inference('demod', [status(thm)], ['125', '172'])).
0.98/1.18	tff('174', plain, (sk_S1(sk_Xz) | ~ sk_P(sk_S2)),
0.98/1.18	    inference('simplify', [status(thm)], ['173'])).
0.98/1.18	tff('175', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('176', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['175'])).
0.98/1.18	tff('177', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '176'])).
0.98/1.18	tff('178', plain, (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['177', '4'])).
0.98/1.18	tff('179', plain, (sk_P(sk_S2) | sk_S1(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['178'])).
0.98/1.18	tff('180', plain, sk_S1(sk_Xz),
0.98/1.18	    inference('clc', [status(thm)], ['174', '179'])).
0.98/1.18	tff('181', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (sk_S1(sk_Xy)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('182', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['181'])).
0.98/1.18	tff('183', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_S1(sk_Xy)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '182'])).
0.98/1.18	tff('184', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_S1(sk_Xy)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['183', '4'])).
0.98/1.18	tff('185', plain,
0.98/1.18	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['184'])).
0.98/1.18	tff('186', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xy) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '185'])).
0.98/1.18	tff('187', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xy) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('demod', [status(thm)], ['186', '4'])).
0.98/1.18	tff('188', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['187'])).
0.98/1.18	tff('189', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S1(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['116', '188'])).
0.98/1.18	tff('190', plain, (~ $true | ~ sk_P(sk_S2) | sk_S1(sk_Xy)),
0.98/1.18	    inference('demod', [status(thm)], ['189', '172'])).
0.98/1.18	tff('191', plain, (sk_S1(sk_Xy) | ~ sk_P(sk_S2)),
0.98/1.18	    inference('simplify', [status(thm)], ['190'])).
0.98/1.18	tff('192', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('193', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['192'])).
0.98/1.18	tff('194', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '193'])).
0.98/1.18	tff('195', plain, (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['194', '4'])).
0.98/1.18	tff('196', plain, (sk_P(sk_S2) | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['195'])).
0.98/1.18	tff('197', plain,
0.98/1.18	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['196', '12'])).
0.98/1.18	tff('198', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_P(sk_S2)),
0.98/1.18	    inference('simplify', [status(thm)], ['197'])).
0.98/1.18	tff('199', plain, (sk_S = sk_Xp(sk_Xy) | ~ $true | sk_P(sk_S2)),
0.98/1.18	    inference('demod', [status(thm)], ['198', '78'])).
0.98/1.18	tff('200', plain, (sk_P(sk_S2) | sk_S = sk_Xp(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['199'])).
0.98/1.18	tff('201', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_P(sk_S2)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['200'])).
0.98/1.18	tff('202', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('203', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['202'])).
0.98/1.18	tff('204', plain,
0.98/1.18	    (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '203'])).
0.98/1.18	tff('205', plain, (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['204', '4'])).
0.98/1.18	tff('206', plain, (sk_P(sk_S2) | sk_S1(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['205'])).
0.98/1.18	tff('207', plain,
0.98/1.18	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['206', '12'])).
0.98/1.18	tff('208', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_P(sk_S2)),
0.98/1.18	    inference('simplify', [status(thm)], ['207'])).
0.98/1.18	tff('209', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('210', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['209'])).
0.98/1.18	tff('211', plain,
0.98/1.18	    (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '210'])).
0.98/1.18	tff('212', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['211', '4'])).
0.98/1.18	tff('213', plain, (sk_P(sk_S2) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['212'])).
0.98/1.18	tff('214', plain, (sk_P(sk_S2) | sk_S1 = sk_Xp(sk_Xy)),
0.98/1.18	    inference('clc', [status(thm)], ['208', '213'])).
0.98/1.18	tff('215', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_P(sk_S2)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['214'])).
0.98/1.18	tff('216', plain,
0.98/1.18	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_P(sk_S2) | sk_P(sk_S2)),
0.98/1.18	    inference('sup+', [status(thm)], ['201', '215'])).
0.98/1.18	tff('217', plain, ![X0 : a]: (sk_P(sk_S2) | sk_S1(X0) = sk_S(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['216'])).
0.98/1.18	tff('218', plain, ($true = sk_S(sk_Xz) | sk_P(sk_S2) | sk_P(sk_S2)),
0.98/1.18	    inference('sup+', [status(thm)], ['179', '217'])).
0.98/1.18	tff('219', plain, (sk_P(sk_S2) | $true = sk_S(sk_Xz)),
0.98/1.18	    inference('simplify', [status(thm)], ['218'])).
0.98/1.18	tff('220', plain,
0.98/1.18	    ![X3 : a > $o, X5 : a > $o]:
0.98/1.18	      (~ sk_P(X5)
0.98/1.18	       | ~ X5(sk_Xx)
0.98/1.18	       | ~ X5(sk_Xz)
0.98/1.18	       | sk_P(sk_S2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('221', plain,
0.98/1.18	    ![X3 : a > $o, X5 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | sk_P(sk_S2)
0.98/1.18	       | ~ X5(sk_Xz)
0.98/1.18	       | ~ X5(sk_Xx)
0.98/1.18	       | ~ sk_P(X5)),
0.98/1.18	    inference('simplify', [status(thm)], ['220'])).
0.98/1.18	tff('222', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | sk_P(sk_S2)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '221'])).
0.98/1.18	tff('223', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | sk_P(sk_S2)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['222', '4'])).
0.98/1.18	tff('224', plain,
0.98/1.18	    ![X0 : a > $o]: (sk_P(sk_S2) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['223'])).
0.98/1.18	tff('225', plain,
0.98/1.18	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_P(sk_S2)),
0.98/1.18	    inference('sup-', [status(thm)], ['219', '224'])).
0.98/1.18	tff('226', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (sk_S(sk_Xx)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('227', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['226'])).
0.98/1.18	tff('228', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_S(sk_Xx)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '227'])).
0.98/1.18	tff('229', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_S(sk_Xx)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['228', '4'])).
0.98/1.18	tff('230', plain,
0.98/1.18	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['229'])).
0.98/1.18	tff('231', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xx) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '230'])).
0.98/1.18	tff('232', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xx) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('demod', [status(thm)], ['231', '4'])).
0.98/1.18	tff('233', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['232'])).
0.98/1.18	tff('234', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xx)),
0.98/1.18	    inference('sup-', [status(thm)], ['116', '233'])).
0.98/1.18	tff('235', plain, (~ $true | ~ sk_P(sk_S2) | sk_S(sk_Xx)),
0.98/1.18	    inference('demod', [status(thm)], ['234', '172'])).
0.98/1.18	tff('236', plain, (sk_S(sk_Xx) | ~ sk_P(sk_S2)),
0.98/1.18	    inference('simplify', [status(thm)], ['235'])).
0.98/1.18	tff('237', plain,
0.98/1.18	    ![X3 : a > $o]:
0.98/1.18	      (sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('238', plain,
0.98/1.18	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['237'])).
0.98/1.18	tff('239', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '238'])).
0.98/1.18	tff('240', plain, (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['239', '4'])).
0.98/1.18	tff('241', plain, (sk_P(sk_S2) | sk_S(sk_Xx)),
0.98/1.18	    inference('simplify', [status(thm)], ['240'])).
0.98/1.18	tff('242', plain, sk_S(sk_Xx),
0.98/1.18	    inference('clc', [status(thm)], ['236', '241'])).
0.98/1.18	tff('243', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
0.98/1.18	    inference('sup-', [status(thm)], ['242', '12'])).
0.98/1.18	tff('244', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xx)),
0.98/1.18	    inference('demod', [status(thm)], ['243', '78'])).
0.98/1.18	tff('245', plain, sk_S = sk_Xp(sk_Xx),
0.98/1.18	    inference('simplify', [status(thm)], ['244'])).
0.98/1.18	tff('246', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xx, X1),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['245'])).
0.98/1.18	tff('247', plain, sk_S(sk_Xx) = $true,
0.98/1.18	    inference('sup+', [status(thm)], ['0', '246'])).
0.98/1.18	tff('248', plain, (~ $true | sk_P(sk_S2) | ~ $true | ~ $true | sk_P(sk_S2)),
0.98/1.18	    inference('demod', [status(thm)], ['225', '78', '247'])).
0.98/1.18	tff('249', plain, sk_P(sk_S2), inference('simplify', [status(thm)], ['248'])).
0.98/1.18	tff('250', plain, (sk_S1(sk_Xy) | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['191', '249'])).
0.98/1.18	tff('251', plain, sk_S1(sk_Xy), inference('simplify', [status(thm)], ['250'])).
0.98/1.18	tff('252', plain, (~ $true | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['251', '12'])).
0.98/1.18	tff('253', plain,
0.98/1.18	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
0.98/1.18	    inference('sup-', [status(thm)], ['93', '12'])).
0.98/1.18	tff('254', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['253'])).
0.98/1.18	tff('255', plain, (sk_P(sk_S1) | sk_S2 = sk_Xp(sk_Xy1)),
0.98/1.18	    inference('clc', [status(thm)], ['254', '213'])).
0.98/1.18	tff('256', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | sk_P(sk_S1)),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['255'])).
0.98/1.18	tff('257', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (sk_P(sk_S1)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('258', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['257'])).
0.98/1.18	tff('259', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_P(sk_S1)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '258'])).
0.98/1.18	tff('260', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_P(sk_S1)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['259', '4'])).
0.98/1.18	tff('261', plain,
0.98/1.18	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['260'])).
0.98/1.18	tff('262', plain,
0.98/1.18	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '261'])).
0.98/1.18	tff('263', plain,
0.98/1.18	    (~ $true | sk_P(sk_S1) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('demod', [status(thm)], ['262', '4'])).
0.98/1.18	tff('264', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_P(sk_S1)),
0.98/1.18	    inference('simplify', [status(thm)], ['263'])).
0.98/1.18	tff('265', plain, (~ sk_S2(sk_Xx1) | sk_P(sk_S1) | sk_P(sk_S1)),
0.98/1.18	    inference('sup-', [status(thm)], ['256', '264'])).
0.98/1.18	tff('266', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S1)),
0.98/1.18	    inference('demod', [status(thm)], ['265', '172'])).
0.98/1.18	tff('267', plain, sk_P(sk_S1), inference('simplify', [status(thm)], ['266'])).
0.98/1.18	tff('268', plain, (~ $true | ~ $true | sk_S1 = sk_Xp(sk_Xy)),
0.98/1.18	    inference('demod', [status(thm)], ['252', '267'])).
0.98/1.18	tff('269', plain, sk_S1 = sk_Xp(sk_Xy),
0.98/1.18	    inference('simplify', [status(thm)], ['268'])).
0.98/1.18	tff('270', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (sk_S(sk_Xy)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('271', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['270'])).
0.98/1.18	tff('272', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_S(sk_Xy)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '271'])).
0.98/1.18	tff('273', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | sk_S(sk_Xy)
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xy1)
0.98/1.18	       | ~ X0(sk_Xx1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['272', '4'])).
0.98/1.18	tff('274', plain,
0.98/1.18	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['273'])).
0.98/1.18	tff('275', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xy) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '274'])).
0.98/1.18	tff('276', plain,
0.98/1.18	    (~ $true | sk_S(sk_Xy) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.98/1.18	    inference('demod', [status(thm)], ['275', '4'])).
0.98/1.18	tff('277', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S(sk_Xy)),
0.98/1.18	    inference('simplify', [status(thm)], ['276'])).
0.98/1.18	tff('278', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['116', '277'])).
0.98/1.18	tff('279', plain, (~ $true | ~ sk_P(sk_S2) | sk_S(sk_Xy)),
0.98/1.18	    inference('demod', [status(thm)], ['278', '172'])).
0.98/1.18	tff('280', plain, (sk_S(sk_Xy) | ~ sk_P(sk_S2)),
0.98/1.18	    inference('simplify', [status(thm)], ['279'])).
0.98/1.18	tff('281', plain, sk_S(sk_Xy),
0.98/1.18	    inference('clc', [status(thm)], ['280', '196'])).
0.98/1.18	tff('282', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.98/1.18	    inference('sup-', [status(thm)], ['281', '12'])).
0.98/1.18	tff('283', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xy)),
0.98/1.18	    inference('demod', [status(thm)], ['282', '78'])).
0.98/1.18	tff('284', plain, sk_S = sk_Xp(sk_Xy),
0.98/1.18	    inference('simplify', [status(thm)], ['283'])).
0.98/1.18	tff('285', plain, sk_S = sk_S1,
0.98/1.18	    inference('sup+', [status(thm)], ['269', '284'])).
0.98/1.18	tff('286', plain, ![X1 : a]: sk_S(X1) = sk_S1(X1),
0.98/1.18	    inference('ho_complete_eq', [status(thm)], ['285'])).
0.98/1.18	tff('287', plain, sk_S(sk_Xz),
0.98/1.18	    inference('demod', [status(thm)], ['180', '286'])).
0.98/1.18	tff('288', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
0.98/1.18	      (~ sk_P(X5)
0.98/1.18	       | ~ X5(sk_Xx)
0.98/1.18	       | ~ X5(sk_Xz)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X3(sk_Xx2)
0.98/1.18	       | ~ X3(sk_Xx2)),
0.98/1.18	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.98/1.18	tff('289', plain,
0.98/1.18	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
0.98/1.18	      (~ X3(sk_Xx2)
0.98/1.18	       | ~ sk_P(X3)
0.98/1.18	       | ~ X4(sk_Xx1)
0.98/1.18	       | ~ X4(sk_Xy1)
0.98/1.18	       | ~ sk_P(X4)
0.98/1.18	       | ~ X5(sk_Xz)
0.98/1.18	       | ~ X5(sk_Xx)
0.98/1.18	       | ~ sk_P(X5)),
0.98/1.18	    inference('simplify', [status(thm)], ['288'])).
0.98/1.18	tff('290', plain,
0.98/1.18	    ![X0 : a > $o, X1 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | ~ sk_P(X1)
0.98/1.18	       | ~ X1(sk_Xy1)
0.98/1.18	       | ~ X1(sk_Xx1)
0.98/1.18	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.98/1.18	    inference('sup-', [status(thm)], ['0', '289'])).
0.98/1.18	tff('291', plain,
0.98/1.18	    ![X0 : a > $o, X1 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | ~ sk_P(X1)
0.98/1.18	       | ~ X1(sk_Xy1)
0.98/1.18	       | ~ X1(sk_Xx1)
0.98/1.18	       | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['290', '4'])).
0.98/1.18	tff('292', plain,
0.98/1.18	    ![X0 : a > $o, X1 : a > $o]:
0.98/1.18	      (~ X1(sk_Xx1)
0.98/1.18	       | ~ X1(sk_Xy1)
0.98/1.18	       | ~ sk_P(X1)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ sk_P(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['291'])).
0.98/1.18	tff('293', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true
0.98/1.18	       | ~ sk_P(X0)
0.98/1.18	       | ~ X0(sk_Xx)
0.98/1.18	       | ~ X0(sk_Xz)
0.98/1.18	       | ~ sk_P(sk_S2)
0.98/1.18	       | ~ sk_S2(sk_Xx1)),
0.98/1.18	    inference('sup-', [status(thm)], ['113', '292'])).
0.98/1.18	tff('294', plain,
0.98/1.18	    ![X0 : a > $o]:
0.98/1.18	      (~ $true | ~ sk_P(X0) | ~ X0(sk_Xx) | ~ X0(sk_Xz) | ~ $true | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['293', '249', '172'])).
0.98/1.18	tff('295', plain, ![X0 : a > $o]: (~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.98/1.18	    inference('simplify', [status(thm)], ['294'])).
0.98/1.18	tff('296', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx)),
0.98/1.18	    inference('sup-', [status(thm)], ['287', '295'])).
0.98/1.18	tff('297', plain, (~ $true | ~ $true | ~ $true),
0.98/1.18	    inference('demod', [status(thm)], ['296', '78', '247'])).
0.98/1.18	tff('298', plain, $false, inference('simplify', [status(thm)], ['297'])).
0.98/1.18	
0.98/1.18	% SZS output end Refutation
0.98/1.18	EOF
