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    : 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	  --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   : n118.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
0.00/0.20	% DateTime   : Fri Feb  2 17:30:08 CST 2018
0.90/1.13	% done 2513 iterations in 0.924s
0.90/1.13	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
0.90/1.13	% SZS output start Refutation
0.90/1.13	tff(cTHM261_pme, conjecture,
0.90/1.13	  (![P:(a > $o > $o)]:
0.90/1.13	     (((![Xx:a]:
0.90/1.13	          (?[Xp:(a > $o)]:
0.90/1.13	             ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
0.90/1.13	              P(Xp)))) & 
0.90/1.13	       (![Xp:(a > $o)]: (P(Xp) => (?[Xz:a]: Xp(Xz))))) =>
0.90/1.13	      ((![Xx:a,Xy:a,Xz:a]:
0.90/1.13	          (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
0.90/1.13	            (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
0.90/1.13	           (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
0.90/1.13	       (![Xx:a,Xy:a]:
0.90/1.13	          ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
0.90/1.13	           (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
0.90/1.13	       (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S)))))))).
0.90/1.13	tff(zf_stmt_0, negated_conjecture,
0.90/1.13	  (~
0.90/1.13	    (![P:(a > $o > $o)]:
0.90/1.13	       (((![Xx:a]:
0.90/1.13	            (?[Xp:(a > $o)]:
0.90/1.13	               ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
0.90/1.13	                P(Xp)))) & 
0.90/1.13	         (![Xp:(a > $o)]: (P(Xp) => (?[Xz:a]: Xp(Xz))))) =>
0.90/1.13	        ((![Xx:a,Xy:a,Xz:a]:
0.90/1.13	            (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
0.90/1.13	              (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
0.90/1.13	             (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
0.90/1.13	         (![Xx:a,Xy:a]:
0.90/1.13	            ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
0.90/1.13	             (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
0.90/1.13	         (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S))))))))).
0.90/1.13	tff('0', plain, ![X0 : a]: sk_Xp(X0, X0),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('1', plain,
0.90/1.13	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.13	      (sk_S1(sk_Xz)
0.90/1.13	       | ~ sk_P(X4)
0.90/1.13	       | ~ X4(sk_Xy1)
0.90/1.13	       | ~ X4(sk_Xx1)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | ~ X3(sk_Xx2)
0.90/1.13	       | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('2', plain,
0.90/1.13	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.13	      (~ X3(sk_Xx2)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | ~ X4(sk_Xx1)
0.90/1.13	       | ~ X4(sk_Xy1)
0.90/1.13	       | ~ sk_P(X4)
0.90/1.13	       | sk_S1(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['1'])).
0.90/1.13	tff('3', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | sk_S1(sk_Xz)
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ X0(sk_Xy1)
0.90/1.13	       | ~ X0(sk_Xx1)
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '2'])).
0.90/1.13	tff('4', plain, ![X0 : a]: sk_P(sk_Xp(X0)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('5', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | sk_S1(sk_Xz)
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ X0(sk_Xy1)
0.90/1.13	       | ~ X0(sk_Xx1)
0.90/1.13	       | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['3', '4'])).
0.90/1.13	tff('6', plain,
0.90/1.13	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['5'])).
0.90/1.13	tff('7', plain,
0.90/1.13	    (~ $true | sk_S1(sk_Xz) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '6'])).
0.90/1.13	tff('8', plain, (~ $true | sk_S1(sk_Xz) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.13	    inference('demod', [status(thm)], ['7', '4'])).
0.90/1.13	tff('9', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S1(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['8'])).
0.90/1.13	tff('10', plain, ![X2 : a > $o]: (X2(sk_Xz1(X2)) | ~ sk_P(X2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('11', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_S1(sk_Xz)
0.90/1.13	       | sk_S2(sk_Xy1)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | ~ X3(sk_Xx2)
0.90/1.13	       | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('12', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['11'])).
0.90/1.13	tff('13', plain,
0.90/1.13	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '12'])).
0.90/1.13	tff('14', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['13', '4'])).
0.90/1.13	tff('15', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['14'])).
0.90/1.13	tff('16', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('17', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S(sk_Xy)),
0.90/1.13	    inference('simplify', [status(thm)], ['16'])).
0.90/1.13	tff('18', plain,
0.90/1.13	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '17'])).
0.90/1.13	tff('19', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['18', '4'])).
0.90/1.13	tff('20', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xy)),
0.90/1.13	    inference('simplify', [status(thm)], ['19'])).
0.90/1.13	tff('21', plain,
0.90/1.13	    ![X0 : a, X1 : a > $o]: (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ X1(X0)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('22', plain,
0.90/1.13	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.90/1.13	    inference('sup-', [status(thm)], ['20', '21'])).
0.90/1.13	tff('23', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('simplify', [status(thm)], ['22'])).
0.90/1.13	tff('24', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('25', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['24'])).
0.90/1.13	tff('26', plain,
0.90/1.13	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '25'])).
0.90/1.13	tff('27', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['26', '4'])).
0.90/1.13	tff('28', plain, (sk_S2(sk_Xy1) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['27'])).
0.90/1.13	tff('29', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
0.90/1.13	    inference('clc', [status(thm)], ['23', '28'])).
0.90/1.13	tff('30', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('ho_complete_eq', [status(thm)], ['29'])).
0.90/1.13	tff('31', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_S1(sk_Xy)
0.90/1.13	       | sk_S2(sk_Xy1)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | ~ X3(sk_Xx2)
0.90/1.13	       | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('32', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
0.90/1.13	    inference('simplify', [status(thm)], ['31'])).
0.90/1.13	tff('33', plain,
0.90/1.13	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '32'])).
0.90/1.13	tff('34', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['33', '4'])).
0.90/1.13	tff('35', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
0.90/1.13	    inference('simplify', [status(thm)], ['34'])).
0.90/1.13	tff('36', plain,
0.90/1.13	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.90/1.13	    inference('sup-', [status(thm)], ['35', '21'])).
0.90/1.13	tff('37', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('simplify', [status(thm)], ['36'])).
0.90/1.13	tff('38', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('39', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_P(sk_S1)),
0.90/1.13	    inference('simplify', [status(thm)], ['38'])).
0.90/1.13	tff('40', plain,
0.90/1.13	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '39'])).
0.90/1.13	tff('41', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['40', '4'])).
0.90/1.13	tff('42', plain, (sk_S2(sk_Xy1) | sk_P(sk_S1)),
0.90/1.13	    inference('simplify', [status(thm)], ['41'])).
0.90/1.13	tff('43', plain, (sk_S2(sk_Xy1) | sk_S1 = sk_Xp(sk_Xy)),
0.90/1.13	    inference('clc', [status(thm)], ['37', '42'])).
0.90/1.13	tff('44', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('ho_complete_eq', [status(thm)], ['43'])).
0.90/1.13	tff('45', plain,
0.90/1.13	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('sup+', [status(thm)], ['30', '44'])).
0.90/1.13	tff('46', plain, ![X0 : a]: (sk_S2(sk_Xy1) | sk_S1(X0) = sk_S(X0)),
0.90/1.13	    inference('simplify', [status(thm)], ['45'])).
0.90/1.13	tff('47', plain, ($true = sk_S(sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('sup+', [status(thm)], ['15', '46'])).
0.90/1.13	tff('48', plain, (sk_S2(sk_Xy1) | $true = sk_S(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['47'])).
0.90/1.13	tff('49', plain,
0.90/1.13	    ![X3 : a > $o, X5 : a > $o]:
0.90/1.13	      (~ sk_P(X5)
0.90/1.13	       | ~ X5(sk_Xx)
0.90/1.13	       | ~ X5(sk_Xz)
0.90/1.13	       | sk_S2(sk_Xy1)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | ~ X3(sk_Xx2)
0.90/1.13	       | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('50', plain,
0.90/1.13	    ![X3 : a > $o, X5 : a > $o]:
0.90/1.13	      (~ X3(sk_Xx2)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | sk_S2(sk_Xy1)
0.90/1.13	       | ~ X5(sk_Xz)
0.90/1.13	       | ~ X5(sk_Xx)
0.90/1.13	       | ~ sk_P(X5)),
0.90/1.13	    inference('simplify', [status(thm)], ['49'])).
0.90/1.13	tff('51', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ X0(sk_Xx)
0.90/1.13	       | ~ X0(sk_Xz)
0.90/1.13	       | sk_S2(sk_Xy1)
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '50'])).
0.90/1.13	tff('52', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ X0(sk_Xx)
0.90/1.13	       | ~ X0(sk_Xz)
0.90/1.13	       | sk_S2(sk_Xy1)
0.90/1.13	       | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['51', '4'])).
0.90/1.13	tff('53', plain,
0.90/1.13	    ![X0 : a > $o]: (sk_S2(sk_Xy1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.90/1.13	    inference('simplify', [status(thm)], ['52'])).
0.90/1.13	tff('54', plain,
0.90/1.13	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('sup-', [status(thm)], ['48', '53'])).
0.90/1.13	tff('55', plain,
0.90/1.13	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
0.90/1.13	    inference('sup-', [status(thm)], ['28', '21'])).
0.90/1.13	tff('56', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['55'])).
0.90/1.13	tff('57', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('58', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['57'])).
0.90/1.13	tff('59', plain,
0.90/1.13	    (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '58'])).
0.90/1.13	tff('60', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['59', '4'])).
0.90/1.13	tff('61', plain, (sk_P(sk_S2) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['60'])).
0.90/1.13	tff('62', plain, (sk_P(sk_S) | sk_S2 = sk_Xp(sk_Xy1)),
0.90/1.13	    inference('clc', [status(thm)], ['56', '61'])).
0.90/1.13	tff('63', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | sk_P(sk_S)),
0.90/1.13	    inference('ho_complete_eq', [status(thm)], ['62'])).
0.90/1.13	tff('64', plain,
0.90/1.13	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.13	      (sk_P(sk_S)
0.90/1.13	       | ~ sk_P(X4)
0.90/1.13	       | ~ X4(sk_Xy1)
0.90/1.13	       | ~ X4(sk_Xx1)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | ~ X3(sk_Xx2)
0.90/1.13	       | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('65', plain,
0.90/1.13	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.13	      (~ X3(sk_Xx2)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | ~ X4(sk_Xx1)
0.90/1.13	       | ~ X4(sk_Xy1)
0.90/1.13	       | ~ sk_P(X4)
0.90/1.13	       | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['64'])).
0.90/1.13	tff('66', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | sk_P(sk_S)
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ X0(sk_Xy1)
0.90/1.13	       | ~ X0(sk_Xx1)
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '65'])).
0.90/1.13	tff('67', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | sk_P(sk_S)
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ X0(sk_Xy1)
0.90/1.13	       | ~ X0(sk_Xx1)
0.90/1.13	       | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['66', '4'])).
0.90/1.13	tff('68', plain,
0.90/1.13	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['67'])).
0.90/1.13	tff('69', plain,
0.90/1.13	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '68'])).
0.90/1.13	tff('70', plain, (~ $true | sk_P(sk_S) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.13	    inference('demod', [status(thm)], ['69', '4'])).
0.90/1.13	tff('71', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['70'])).
0.90/1.13	tff('72', plain, (~ sk_S2(sk_Xx1) | sk_P(sk_S) | sk_P(sk_S)),
0.90/1.13	    inference('sup-', [status(thm)], ['63', '71'])).
0.90/1.13	tff('73', plain, (sk_P(sk_S) | ~ sk_S2(sk_Xx1)),
0.90/1.13	    inference('simplify', [status(thm)], ['72'])).
0.90/1.13	tff('74', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('75', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['74'])).
0.90/1.13	tff('76', plain,
0.90/1.13	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '75'])).
0.90/1.13	tff('77', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['76', '4'])).
0.90/1.13	tff('78', plain, (sk_S2(sk_Xx1) | sk_P(sk_S)),
0.90/1.13	    inference('simplify', [status(thm)], ['77'])).
0.90/1.13	tff('79', plain, sk_P(sk_S), inference('clc', [status(thm)], ['73', '78'])).
0.90/1.13	tff('80', plain,
0.90/1.13	    (~ $true | sk_S2(sk_Xy1) | ~ $true | ~ sk_S(sk_Xx) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('demod', [status(thm)], ['54', '79'])).
0.90/1.13	tff('81', plain, (~ sk_S(sk_Xx) | sk_S2(sk_Xy1)),
0.90/1.13	    inference('simplify', [status(thm)], ['80'])).
0.90/1.13	tff('82', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('83', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xy1) | sk_S(sk_Xx)),
0.90/1.13	    inference('simplify', [status(thm)], ['82'])).
0.90/1.13	tff('84', plain,
0.90/1.13	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '83'])).
0.90/1.13	tff('85', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['84', '4'])).
0.90/1.13	tff('86', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xx)),
0.90/1.13	    inference('simplify', [status(thm)], ['85'])).
0.90/1.13	tff('87', plain, sk_S2(sk_Xy1), inference('clc', [status(thm)], ['81', '86'])).
0.90/1.13	tff('88', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
0.90/1.13	    inference('sup-', [status(thm)], ['87', '21'])).
0.90/1.13	tff('89', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2)),
0.90/1.13	    inference('simplify', [status(thm)], ['88'])).
0.90/1.13	tff('90', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | ~ sk_P(sk_S2)),
0.90/1.13	    inference('ho_complete_eq', [status(thm)], ['89'])).
0.90/1.13	tff('91', plain,
0.90/1.13	    (sk_S2(sk_Xz1(sk_Xp(sk_Xy1))) = $true
0.90/1.13	     | ~ sk_P(sk_Xp(sk_Xy1))
0.90/1.13	     | ~ sk_P(sk_S2)),
0.90/1.13	    inference('sup+', [status(thm)], ['10', '90'])).
0.90/1.13	tff('92', plain,
0.90/1.13	    (sk_S2(sk_Xz1(sk_Xp(sk_Xy1))) = $true | ~ $true | ~ sk_P(sk_S2)),
0.90/1.13	    inference('demod', [status(thm)], ['91', '4'])).
0.90/1.13	tff('93', plain, (~ sk_P(sk_S2) | sk_S2(sk_Xz1(sk_Xp(sk_Xy1))) = $true),
0.90/1.13	    inference('simplify', [status(thm)], ['92'])).
0.90/1.13	tff('94', plain,
0.90/1.13	    (~ $true
0.90/1.13	     | ~ sk_P(sk_S2)
0.90/1.13	     | ~ sk_P(sk_S2)
0.90/1.13	     | sk_S2 = sk_Xp(sk_Xz1(sk_Xp(sk_Xy1)))),
0.90/1.13	    inference('sup-', [status(thm)], ['93', '21'])).
0.90/1.13	tff('95', plain, (sk_S2 = sk_Xp(sk_Xz1(sk_Xp(sk_Xy1))) | ~ sk_P(sk_S2)),
0.90/1.13	    inference('simplify', [status(thm)], ['94'])).
0.90/1.13	tff('96', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true | ~ sk_P(X0) | ~ sk_P(X0) | X0 = sk_Xp(sk_Xz1(X0))),
0.90/1.13	    inference('sup-', [status(thm)], ['10', '21'])).
0.90/1.13	tff('97', plain, ![X0 : a > $o]: (X0 = sk_Xp(sk_Xz1(X0)) | ~ sk_P(X0)),
0.90/1.13	    inference('simplify', [status(thm)], ['96'])).
0.90/1.13	tff('98', plain,
0.90/1.13	    ![X0 : a > $o, X1 : a]: (X0(X1) = sk_Xp(sk_Xz1(X0), X1) | ~ sk_P(X0)),
0.90/1.13	    inference('ho_complete_eq', [status(thm)], ['97'])).
0.90/1.13	tff('99', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) = $true
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xz1(X0)))
0.90/1.13	       | ~ sk_P(X0)),
0.90/1.13	    inference('sup+', [status(thm)], ['10', '98'])).
0.90/1.13	tff('100', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) = $true | ~ $true | ~ sk_P(X0)),
0.90/1.13	    inference('demod', [status(thm)], ['99', '4'])).
0.90/1.13	tff('101', plain,
0.90/1.13	    ![X0 : a > $o]: (~ sk_P(X0) | X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) = $true),
0.90/1.13	    inference('simplify', [status(thm)], ['100'])).
0.90/1.13	tff('102', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))))),
0.90/1.13	    inference('sup-', [status(thm)], ['101', '21'])).
0.90/1.13	tff('103', plain,
0.90/1.13	    ![X0 : a > $o]: (X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0)),
0.90/1.13	    inference('simplify', [status(thm)], ['102'])).
0.90/1.13	tff('104', plain,
0.90/1.13	    (sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S2))
0.90/1.13	     | ~ sk_P(sk_S2)
0.90/1.13	     | ~ sk_P(sk_Xp(sk_Xy1))),
0.90/1.13	    inference('sup+', [status(thm)], ['95', '103'])).
0.90/1.13	tff('105', plain,
0.90/1.13	    (sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S2)) | ~ sk_P(sk_S2) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['104', '4'])).
0.90/1.13	tff('106', plain, (~ sk_P(sk_S2) | sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S2))),
0.90/1.13	    inference('simplify', [status(thm)], ['105'])).
0.90/1.13	tff('107', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('108', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S1(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['107'])).
0.90/1.13	tff('109', plain,
0.90/1.13	    (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '108'])).
0.90/1.13	tff('110', plain, (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['109', '4'])).
0.90/1.13	tff('111', plain, (sk_P(sk_S2) | sk_S1(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['110'])).
0.90/1.13	tff('112', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('113', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S(sk_Xy)),
0.90/1.13	    inference('simplify', [status(thm)], ['112'])).
0.90/1.13	tff('114', plain,
0.90/1.13	    (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '113'])).
0.90/1.13	tff('115', plain, (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['114', '4'])).
0.90/1.13	tff('116', plain, (sk_P(sk_S2) | sk_S(sk_Xy)),
0.90/1.13	    inference('simplify', [status(thm)], ['115'])).
0.90/1.13	tff('117', plain,
0.90/1.13	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.90/1.13	    inference('sup-', [status(thm)], ['116', '21'])).
0.90/1.13	tff('118', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_P(sk_S2)),
0.90/1.13	    inference('simplify', [status(thm)], ['117'])).
0.90/1.13	tff('119', plain, (sk_P(sk_S2) | sk_S = sk_Xp(sk_Xy)),
0.90/1.13	    inference('clc', [status(thm)], ['118', '61'])).
0.90/1.13	tff('120', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_P(sk_S2)),
0.90/1.13	    inference('ho_complete_eq', [status(thm)], ['119'])).
0.90/1.13	tff('121', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('122', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S1(sk_Xy)),
0.90/1.13	    inference('simplify', [status(thm)], ['121'])).
0.90/1.13	tff('123', plain,
0.90/1.13	    (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '122'])).
0.90/1.13	tff('124', plain, (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['123', '4'])).
0.90/1.13	tff('125', plain, (sk_P(sk_S2) | sk_S1(sk_Xy)),
0.90/1.13	    inference('simplify', [status(thm)], ['124'])).
0.90/1.13	tff('126', plain,
0.90/1.13	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.90/1.13	    inference('sup-', [status(thm)], ['125', '21'])).
0.90/1.13	tff('127', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_P(sk_S2)),
0.90/1.13	    inference('simplify', [status(thm)], ['126'])).
0.90/1.13	tff('128', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('129', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_P(sk_S1)),
0.90/1.13	    inference('simplify', [status(thm)], ['128'])).
0.90/1.13	tff('130', plain,
0.90/1.13	    (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '129'])).
0.90/1.13	tff('131', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['130', '4'])).
0.90/1.13	tff('132', plain, (sk_P(sk_S2) | sk_P(sk_S1)),
0.90/1.13	    inference('simplify', [status(thm)], ['131'])).
0.90/1.13	tff('133', plain, (sk_P(sk_S2) | sk_S1 = sk_Xp(sk_Xy)),
0.90/1.13	    inference('clc', [status(thm)], ['127', '132'])).
0.90/1.13	tff('134', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_P(sk_S2)),
0.90/1.13	    inference('ho_complete_eq', [status(thm)], ['133'])).
0.90/1.13	tff('135', plain,
0.90/1.13	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_P(sk_S2) | sk_P(sk_S2)),
0.90/1.13	    inference('sup+', [status(thm)], ['120', '134'])).
0.90/1.13	tff('136', plain, ![X0 : a]: (sk_P(sk_S2) | sk_S1(X0) = sk_S(X0)),
0.90/1.13	    inference('simplify', [status(thm)], ['135'])).
0.90/1.13	tff('137', plain, ($true = sk_S(sk_Xz) | sk_P(sk_S2) | sk_P(sk_S2)),
0.90/1.13	    inference('sup+', [status(thm)], ['111', '136'])).
0.90/1.13	tff('138', plain, (sk_P(sk_S2) | $true = sk_S(sk_Xz)),
0.90/1.13	    inference('simplify', [status(thm)], ['137'])).
0.90/1.13	tff('139', plain,
0.90/1.13	    ![X3 : a > $o, X5 : a > $o]:
0.90/1.13	      (~ sk_P(X5)
0.90/1.13	       | ~ X5(sk_Xx)
0.90/1.13	       | ~ X5(sk_Xz)
0.90/1.13	       | sk_P(sk_S2)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | ~ X3(sk_Xx2)
0.90/1.13	       | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('140', plain,
0.90/1.13	    ![X3 : a > $o, X5 : a > $o]:
0.90/1.13	      (~ X3(sk_Xx2)
0.90/1.13	       | ~ sk_P(X3)
0.90/1.13	       | sk_P(sk_S2)
0.90/1.13	       | ~ X5(sk_Xz)
0.90/1.13	       | ~ X5(sk_Xx)
0.90/1.13	       | ~ sk_P(X5)),
0.90/1.13	    inference('simplify', [status(thm)], ['139'])).
0.90/1.13	tff('141', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ X0(sk_Xx)
0.90/1.13	       | ~ X0(sk_Xz)
0.90/1.13	       | sk_P(sk_S2)
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '140'])).
0.90/1.13	tff('142', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ X0(sk_Xx)
0.90/1.13	       | ~ X0(sk_Xz)
0.90/1.13	       | sk_P(sk_S2)
0.90/1.13	       | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['141', '4'])).
0.90/1.13	tff('143', plain,
0.90/1.13	    ![X0 : a > $o]: (sk_P(sk_S2) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.90/1.13	    inference('simplify', [status(thm)], ['142'])).
0.90/1.13	tff('144', plain,
0.90/1.13	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_P(sk_S2)),
0.90/1.13	    inference('sup-', [status(thm)], ['138', '143'])).
0.90/1.13	tff('145', plain,
0.90/1.13	    (~ $true | sk_P(sk_S2) | ~ $true | ~ sk_S(sk_Xx) | sk_P(sk_S2)),
0.90/1.13	    inference('demod', [status(thm)], ['144', '79'])).
0.90/1.13	tff('146', plain, (~ sk_S(sk_Xx) | sk_P(sk_S2)),
0.90/1.13	    inference('simplify', [status(thm)], ['145'])).
0.90/1.13	tff('147', plain,
0.90/1.13	    ![X3 : a > $o]:
0.90/1.13	      (sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.13	tff('148', plain,
0.90/1.13	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_P(sk_S2) | sk_S(sk_Xx)),
0.90/1.13	    inference('simplify', [status(thm)], ['147'])).
0.90/1.13	tff('149', plain,
0.90/1.13	    (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.13	    inference('sup-', [status(thm)], ['0', '148'])).
0.90/1.13	tff('150', plain, (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['149', '4'])).
0.90/1.13	tff('151', plain, (sk_P(sk_S2) | sk_S(sk_Xx)),
0.90/1.13	    inference('simplify', [status(thm)], ['150'])).
0.90/1.13	tff('152', plain, sk_P(sk_S2),
0.90/1.13	    inference('clc', [status(thm)], ['146', '151'])).
0.90/1.13	tff('153', plain, (~ $true | sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S2))),
0.90/1.13	    inference('demod', [status(thm)], ['106', '152'])).
0.90/1.13	tff('154', plain, sk_Xp(sk_Xy1) = sk_Xp(sk_Xz1(sk_S2)),
0.90/1.13	    inference('simplify', [status(thm)], ['153'])).
0.90/1.13	tff('155', plain,
0.90/1.13	    ![X0 : a > $o, X1 : a]:
0.90/1.13	      (X0(X1) = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))), X1) | ~ sk_P(X0)),
0.90/1.13	    inference('ho_complete_eq', [status(thm)], ['103'])).
0.90/1.13	tff('156', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (X0(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))))) = $true
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xz1(X0)))
0.90/1.13	       | ~ sk_P(X0)),
0.90/1.13	    inference('sup+', [status(thm)], ['101', '98'])).
0.90/1.13	tff('157', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (X0(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))))) = $true
0.90/1.13	       | ~ $true
0.90/1.13	       | ~ sk_P(X0)),
0.90/1.13	    inference('demod', [status(thm)], ['156', '4'])).
0.90/1.13	tff('158', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ sk_P(X0) | X0(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))))) = $true),
0.90/1.13	    inference('simplify', [status(thm)], ['157'])).
0.90/1.13	tff('159', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ $true
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))))))),
0.90/1.13	    inference('sup-', [status(thm)], ['158', '21'])).
0.90/1.13	tff('160', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (X0 = sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))))) | ~ sk_P(X0)),
0.90/1.13	    inference('simplify', [status(thm)], ['159'])).
0.90/1.13	tff('161', plain,
0.90/1.13	    ![X0 : a > $o]: (X0(sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0)),
0.90/1.13	    inference('sup+', [status(thm)], ['155', '0'])).
0.90/1.13	tff('162', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))), sk_Xz1(X0))
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))))),
0.90/1.13	    inference('sup+', [status(thm)], ['160', '161'])).
0.90/1.13	tff('163', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))), sk_Xz1(X0)) | ~ sk_P(X0) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['162', '4'])).
0.90/1.13	tff('164', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ sk_P(X0) | sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))), sk_Xz1(X0))),
0.90/1.13	    inference('simplify', [status(thm)], ['163'])).
0.90/1.13	tff('165', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (sk_Xp(sk_Xz1(X0), sk_Xz1(sk_Xp(sk_Xz1(X0))))
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xz1(X0)))),
0.90/1.13	    inference('sup+', [status(thm)], ['103', '164'])).
0.90/1.13	tff('166', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (sk_Xp(sk_Xz1(X0), sk_Xz1(sk_Xp(sk_Xz1(X0)))) | ~ sk_P(X0) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['165', '4'])).
0.90/1.13	tff('167', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ sk_P(X0) | sk_Xp(sk_Xz1(X0), sk_Xz1(sk_Xp(sk_Xz1(X0))))),
0.90/1.13	    inference('simplify', [status(thm)], ['166'])).
0.90/1.13	tff('168', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (X0(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))))))
0.90/1.13	       | ~ sk_P(X0)
0.90/1.13	       | ~ sk_P(sk_Xp(sk_Xz1(X0)))),
0.90/1.13	    inference('sup+', [status(thm)], ['155', '167'])).
0.90/1.13	tff('169', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (X0(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0)))))) | ~ sk_P(X0) | ~ $true),
0.90/1.13	    inference('demod', [status(thm)], ['168', '4'])).
0.90/1.13	tff('170', plain,
0.90/1.13	    ![X0 : a > $o]:
0.90/1.13	      (~ sk_P(X0) | X0(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xz1(X0))))))),
0.90/1.13	    inference('simplify', [status(thm)], ['169'])).
0.90/1.13	tff('171', plain,
0.90/1.13	    (sk_S2(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xy1)))))
0.90/1.13	     | ~ sk_P(sk_S2)
0.90/1.13	     | ~ sk_P(sk_S2)),
0.90/1.13	    inference('sup+', [status(thm)], ['106', '170'])).
0.90/1.13	tff('172', plain,
0.90/1.13	    (~ sk_P(sk_S2) | sk_S2(sk_Xz1(sk_Xp(sk_Xz1(sk_Xp(sk_Xy1)))))),
0.90/1.13	    inference('simplify', [status(thm)], ['171'])).
0.90/1.13	tff('173', plain,
0.90/1.13	    (sk_S2(sk_Xz1(sk_Xp(sk_Xz1(sk_S2)))) | ~ sk_P(sk_S2) | ~ sk_P(sk_S2)),
0.90/1.13	    inference('sup+', [status(thm)], ['89', '172'])).
0.90/1.13	tff('174', plain, (~ sk_P(sk_S2) | sk_S2(sk_Xz1(sk_Xp(sk_Xz1(sk_S2))))),
0.90/1.14	    inference('simplify', [status(thm)], ['173'])).
0.90/1.14	tff('175', plain, (~ $true | sk_S2(sk_Xz1(sk_Xp(sk_Xz1(sk_S2))))),
0.90/1.14	    inference('demod', [status(thm)], ['174', '152'])).
0.90/1.14	tff('176', plain, sk_S2(sk_Xz1(sk_Xp(sk_Xz1(sk_S2)))),
0.90/1.14	    inference('simplify', [status(thm)], ['175'])).
0.90/1.14	tff('177', plain, (sk_S2(sk_Xz1(sk_S2)) | ~ sk_P(sk_S2)),
0.90/1.14	    inference('sup+', [status(thm)], ['97', '176'])).
0.90/1.14	tff('178', plain, (sk_S2(sk_Xz1(sk_S2)) | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['177', '152'])).
0.90/1.14	tff('179', plain, sk_S2(sk_Xz1(sk_S2)),
0.90/1.14	    inference('simplify', [status(thm)], ['178'])).
0.90/1.14	tff('180', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xz1(sk_S2))),
0.90/1.14	    inference('sup-', [status(thm)], ['179', '21'])).
0.90/1.14	tff('181', plain, (~ $true | ~ $true | sk_S2 = sk_Xp(sk_Xz1(sk_S2))),
0.90/1.14	    inference('demod', [status(thm)], ['180', '152'])).
0.90/1.14	tff('182', plain, sk_S2 = sk_Xp(sk_Xz1(sk_S2)),
0.90/1.14	    inference('simplify', [status(thm)], ['181'])).
0.90/1.14	tff('183', plain, sk_S2 = sk_Xp(sk_Xy1),
0.90/1.14	    inference('sup+', [status(thm)], ['154', '182'])).
0.90/1.14	tff('184', plain, ![X1 : a]: sk_S2(X1) = sk_Xp(sk_Xy1, X1),
0.90/1.14	    inference('ho_complete_eq', [status(thm)], ['183'])).
0.90/1.14	tff('185', plain,
0.90/1.14	    ![X3 : a > $o]:
0.90/1.14	      (sk_S1(sk_Xz)
0.90/1.14	       | sk_S2(sk_Xx1)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X3(sk_Xx2)
0.90/1.14	       | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('186', plain,
0.90/1.14	    ![X3 : a > $o]:
0.90/1.14	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
0.90/1.14	    inference('simplify', [status(thm)], ['185'])).
0.90/1.14	tff('187', plain,
0.90/1.14	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '186'])).
0.90/1.14	tff('188', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['187', '4'])).
0.90/1.14	tff('189', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
0.90/1.14	    inference('simplify', [status(thm)], ['188'])).
0.90/1.14	tff('190', plain,
0.90/1.14	    ![X3 : a > $o]:
0.90/1.14	      (sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('191', plain,
0.90/1.14	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['190'])).
0.90/1.14	tff('192', plain,
0.90/1.14	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '191'])).
0.90/1.14	tff('193', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['192', '4'])).
0.90/1.14	tff('194', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['193'])).
0.90/1.14	tff('195', plain,
0.90/1.14	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.90/1.14	    inference('sup-', [status(thm)], ['194', '21'])).
0.90/1.14	tff('196', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('simplify', [status(thm)], ['195'])).
0.90/1.14	tff('197', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xy)),
0.90/1.14	    inference('clc', [status(thm)], ['196', '78'])).
0.90/1.14	tff('198', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('ho_complete_eq', [status(thm)], ['197'])).
0.90/1.14	tff('199', plain,
0.90/1.14	    ![X3 : a > $o]:
0.90/1.14	      (sk_S1(sk_Xy)
0.90/1.14	       | sk_S2(sk_Xx1)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X3(sk_Xx2)
0.90/1.14	       | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('200', plain,
0.90/1.14	    ![X3 : a > $o]:
0.90/1.14	      (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['199'])).
0.90/1.14	tff('201', plain,
0.90/1.14	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '200'])).
0.90/1.14	tff('202', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['201', '4'])).
0.90/1.14	tff('203', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['202'])).
0.90/1.14	tff('204', plain,
0.90/1.14	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.90/1.14	    inference('sup-', [status(thm)], ['203', '21'])).
0.90/1.14	tff('205', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('simplify', [status(thm)], ['204'])).
0.90/1.14	tff('206', plain,
0.90/1.14	    ![X3 : a > $o]:
0.90/1.14	      (sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('207', plain,
0.90/1.14	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_P(sk_S1)),
0.90/1.14	    inference('simplify', [status(thm)], ['206'])).
0.90/1.14	tff('208', plain,
0.90/1.14	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '207'])).
0.90/1.14	tff('209', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['208', '4'])).
0.90/1.14	tff('210', plain, (sk_S2(sk_Xx1) | sk_P(sk_S1)),
0.90/1.14	    inference('simplify', [status(thm)], ['209'])).
0.90/1.14	tff('211', plain, (sk_S2(sk_Xx1) | sk_S1 = sk_Xp(sk_Xy)),
0.90/1.14	    inference('clc', [status(thm)], ['205', '210'])).
0.90/1.14	tff('212', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('ho_complete_eq', [status(thm)], ['211'])).
0.90/1.14	tff('213', plain,
0.90/1.14	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('sup+', [status(thm)], ['198', '212'])).
0.90/1.14	tff('214', plain, ![X0 : a]: (sk_S2(sk_Xx1) | sk_S1(X0) = sk_S(X0)),
0.90/1.14	    inference('simplify', [status(thm)], ['213'])).
0.90/1.14	tff('215', plain, ($true = sk_S(sk_Xz) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('sup+', [status(thm)], ['189', '214'])).
0.90/1.14	tff('216', plain, (sk_S2(sk_Xx1) | $true = sk_S(sk_Xz)),
0.90/1.14	    inference('simplify', [status(thm)], ['215'])).
0.90/1.14	tff('217', plain,
0.90/1.14	    ![X3 : a > $o, X5 : a > $o]:
0.90/1.14	      (~ sk_P(X5)
0.90/1.14	       | ~ X5(sk_Xx)
0.90/1.14	       | ~ X5(sk_Xz)
0.90/1.14	       | sk_S2(sk_Xx1)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X3(sk_Xx2)
0.90/1.14	       | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('218', plain,
0.90/1.14	    ![X3 : a > $o, X5 : a > $o]:
0.90/1.14	      (~ X3(sk_Xx2)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | sk_S2(sk_Xx1)
0.90/1.14	       | ~ X5(sk_Xz)
0.90/1.14	       | ~ X5(sk_Xx)
0.90/1.14	       | ~ sk_P(X5)),
0.90/1.14	    inference('simplify', [status(thm)], ['217'])).
0.90/1.14	tff('219', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xx)
0.90/1.14	       | ~ X0(sk_Xz)
0.90/1.14	       | sk_S2(sk_Xx1)
0.90/1.14	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '218'])).
0.90/1.14	tff('220', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xx)
0.90/1.14	       | ~ X0(sk_Xz)
0.90/1.14	       | sk_S2(sk_Xx1)
0.90/1.14	       | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['219', '4'])).
0.90/1.14	tff('221', plain,
0.90/1.14	    ![X0 : a > $o]: (sk_S2(sk_Xx1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.90/1.14	    inference('simplify', [status(thm)], ['220'])).
0.90/1.14	tff('222', plain,
0.90/1.14	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('sup-', [status(thm)], ['216', '221'])).
0.90/1.14	tff('223', plain,
0.90/1.14	    (~ $true | sk_S2(sk_Xx1) | ~ $true | ~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('demod', [status(thm)], ['222', '79'])).
0.90/1.14	tff('224', plain, (~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
0.90/1.14	    inference('simplify', [status(thm)], ['223'])).
0.90/1.14	tff('225', plain,
0.90/1.14	    ![X3 : a > $o]:
0.90/1.14	      (sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(X3) | ~ X3(sk_Xx2) | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('226', plain,
0.90/1.14	    ![X3 : a > $o]: (~ X3(sk_Xx2) | ~ sk_P(X3) | sk_S2(sk_Xx1) | sk_S(sk_Xx)),
0.90/1.14	    inference('simplify', [status(thm)], ['225'])).
0.90/1.14	tff('227', plain,
0.90/1.14	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '226'])).
0.90/1.14	tff('228', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['227', '4'])).
0.90/1.14	tff('229', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xx)),
0.90/1.14	    inference('simplify', [status(thm)], ['228'])).
0.90/1.14	tff('230', plain, sk_S2(sk_Xx1),
0.90/1.14	    inference('clc', [status(thm)], ['224', '229'])).
0.90/1.14	tff('231', plain, (~ $true | sk_S1(sk_Xz)),
0.90/1.14	    inference('demod', [status(thm)], ['9', '184', '230'])).
0.90/1.14	tff('232', plain, sk_S1(sk_Xz), inference('simplify', [status(thm)], ['231'])).
0.90/1.14	tff('233', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.14	      (sk_S1(sk_Xy)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X3(sk_Xx2)
0.90/1.14	       | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('234', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.14	      (~ X3(sk_Xx2)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | sk_S1(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['233'])).
0.90/1.14	tff('235', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | sk_S1(sk_Xy)
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xy1)
0.90/1.14	       | ~ X0(sk_Xx1)
0.90/1.14	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '234'])).
0.90/1.14	tff('236', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | sk_S1(sk_Xy)
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xy1)
0.90/1.14	       | ~ X0(sk_Xx1)
0.90/1.14	       | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['235', '4'])).
0.90/1.14	tff('237', plain,
0.90/1.14	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['236'])).
0.90/1.14	tff('238', plain,
0.90/1.14	    (~ $true | sk_S1(sk_Xy) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '237'])).
0.90/1.14	tff('239', plain,
0.90/1.14	    (~ $true | sk_S1(sk_Xy) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.14	    inference('demod', [status(thm)], ['238', '4'])).
0.90/1.14	tff('240', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S1(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['239'])).
0.90/1.14	tff('241', plain, (~ $true | sk_S1(sk_Xy)),
0.90/1.14	    inference('demod', [status(thm)], ['240', '184', '230'])).
0.90/1.14	tff('242', plain, sk_S1(sk_Xy), inference('simplify', [status(thm)], ['241'])).
0.90/1.14	tff('243', plain, (~ $true | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.90/1.14	    inference('sup-', [status(thm)], ['242', '21'])).
0.90/1.14	tff('244', plain,
0.90/1.14	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
0.90/1.14	    inference('sup-', [status(thm)], ['42', '21'])).
0.90/1.14	tff('245', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_P(sk_S1)),
0.90/1.14	    inference('simplify', [status(thm)], ['244'])).
0.90/1.14	tff('246', plain, (sk_P(sk_S1) | sk_S2 = sk_Xp(sk_Xy1)),
0.90/1.14	    inference('clc', [status(thm)], ['245', '132'])).
0.90/1.14	tff('247', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | sk_P(sk_S1)),
0.90/1.14	    inference('ho_complete_eq', [status(thm)], ['246'])).
0.90/1.14	tff('248', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.14	      (sk_P(sk_S1)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X3(sk_Xx2)
0.90/1.14	       | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('249', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.14	      (~ X3(sk_Xx2)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | sk_P(sk_S1)),
0.90/1.14	    inference('simplify', [status(thm)], ['248'])).
0.90/1.14	tff('250', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | sk_P(sk_S1)
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xy1)
0.90/1.14	       | ~ X0(sk_Xx1)
0.90/1.14	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '249'])).
0.90/1.14	tff('251', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | sk_P(sk_S1)
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xy1)
0.90/1.14	       | ~ X0(sk_Xx1)
0.90/1.14	       | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['250', '4'])).
0.90/1.14	tff('252', plain,
0.90/1.14	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S1)),
0.90/1.14	    inference('simplify', [status(thm)], ['251'])).
0.90/1.14	tff('253', plain,
0.90/1.14	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '252'])).
0.90/1.14	tff('254', plain,
0.90/1.14	    (~ $true | sk_P(sk_S1) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.14	    inference('demod', [status(thm)], ['253', '4'])).
0.90/1.14	tff('255', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_P(sk_S1)),
0.90/1.14	    inference('simplify', [status(thm)], ['254'])).
0.90/1.14	tff('256', plain, (~ sk_S2(sk_Xx1) | sk_P(sk_S1) | sk_P(sk_S1)),
0.90/1.14	    inference('sup-', [status(thm)], ['247', '255'])).
0.90/1.14	tff('257', plain, (sk_P(sk_S1) | ~ sk_S2(sk_Xx1)),
0.90/1.14	    inference('simplify', [status(thm)], ['256'])).
0.90/1.14	tff('258', plain, sk_P(sk_S1),
0.90/1.14	    inference('clc', [status(thm)], ['257', '210'])).
0.90/1.14	tff('259', plain, (~ $true | ~ $true | sk_S1 = sk_Xp(sk_Xy)),
0.90/1.14	    inference('demod', [status(thm)], ['243', '258'])).
0.90/1.14	tff('260', plain, sk_S1 = sk_Xp(sk_Xy),
0.90/1.14	    inference('simplify', [status(thm)], ['259'])).
0.90/1.14	tff('261', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.14	      (sk_S(sk_Xy)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X3(sk_Xx2)
0.90/1.14	       | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('262', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.14	      (~ X3(sk_Xx2)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | sk_S(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['261'])).
0.90/1.14	tff('263', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | sk_S(sk_Xy)
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xy1)
0.90/1.14	       | ~ X0(sk_Xx1)
0.90/1.14	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '262'])).
0.90/1.14	tff('264', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | sk_S(sk_Xy)
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xy1)
0.90/1.14	       | ~ X0(sk_Xx1)
0.90/1.14	       | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['263', '4'])).
0.90/1.14	tff('265', plain,
0.90/1.14	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['264'])).
0.90/1.14	tff('266', plain,
0.90/1.14	    (~ $true | sk_S(sk_Xy) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '265'])).
0.90/1.14	tff('267', plain,
0.90/1.14	    (~ $true | sk_S(sk_Xy) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.14	    inference('demod', [status(thm)], ['266', '4'])).
0.90/1.14	tff('268', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S(sk_Xy)),
0.90/1.14	    inference('simplify', [status(thm)], ['267'])).
0.90/1.14	tff('269', plain, (~ $true | sk_S(sk_Xy)),
0.90/1.14	    inference('demod', [status(thm)], ['268', '184', '230'])).
0.90/1.14	tff('270', plain, sk_S(sk_Xy), inference('simplify', [status(thm)], ['269'])).
0.90/1.14	tff('271', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.90/1.14	    inference('sup-', [status(thm)], ['270', '21'])).
0.90/1.14	tff('272', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xy)),
0.90/1.14	    inference('demod', [status(thm)], ['271', '79'])).
0.90/1.14	tff('273', plain, sk_S = sk_Xp(sk_Xy),
0.90/1.14	    inference('simplify', [status(thm)], ['272'])).
0.90/1.14	tff('274', plain, sk_S = sk_S1,
0.90/1.14	    inference('sup+', [status(thm)], ['260', '273'])).
0.90/1.14	tff('275', plain, ![X1 : a]: sk_S(X1) = sk_S1(X1),
0.90/1.14	    inference('ho_complete_eq', [status(thm)], ['274'])).
0.90/1.14	tff('276', plain, sk_S(sk_Xz),
0.90/1.14	    inference('demod', [status(thm)], ['232', '275'])).
0.90/1.14	tff('277', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
0.90/1.14	      (~ sk_P(X5)
0.90/1.14	       | ~ X5(sk_Xx)
0.90/1.14	       | ~ X5(sk_Xz)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X3(sk_Xx2)
0.90/1.14	       | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('278', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o, X5 : a > $o]:
0.90/1.14	      (~ X3(sk_Xx2)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | ~ X5(sk_Xz)
0.90/1.14	       | ~ X5(sk_Xx)
0.90/1.14	       | ~ sk_P(X5)),
0.90/1.14	    inference('simplify', [status(thm)], ['277'])).
0.90/1.14	tff('279', plain,
0.90/1.14	    ![X0 : a > $o, X1 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xx)
0.90/1.14	       | ~ X0(sk_Xz)
0.90/1.14	       | ~ sk_P(X1)
0.90/1.14	       | ~ X1(sk_Xy1)
0.90/1.14	       | ~ X1(sk_Xx1)
0.90/1.14	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '278'])).
0.90/1.14	tff('280', plain,
0.90/1.14	    ![X0 : a > $o, X1 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xx)
0.90/1.14	       | ~ X0(sk_Xz)
0.90/1.14	       | ~ sk_P(X1)
0.90/1.14	       | ~ X1(sk_Xy1)
0.90/1.14	       | ~ X1(sk_Xx1)
0.90/1.14	       | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['279', '4'])).
0.90/1.14	tff('281', plain,
0.90/1.14	    ![X0 : a > $o, X1 : a > $o]:
0.90/1.14	      (~ X1(sk_Xx1)
0.90/1.14	       | ~ X1(sk_Xy1)
0.90/1.14	       | ~ sk_P(X1)
0.90/1.14	       | ~ X0(sk_Xz)
0.90/1.14	       | ~ X0(sk_Xx)
0.90/1.14	       | ~ sk_P(X0)),
0.90/1.14	    inference('simplify', [status(thm)], ['280'])).
0.90/1.14	tff('282', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xx)
0.90/1.14	       | ~ X0(sk_Xz)
0.90/1.14	       | ~ sk_P(sk_S2)
0.90/1.14	       | ~ sk_S2(sk_Xx1)),
0.90/1.14	    inference('sup-', [status(thm)], ['87', '281'])).
0.90/1.14	tff('283', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true | ~ sk_P(X0) | ~ X0(sk_Xx) | ~ X0(sk_Xz) | ~ $true | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['282', '152', '230'])).
0.90/1.14	tff('284', plain, ![X0 : a > $o]: (~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.90/1.14	    inference('simplify', [status(thm)], ['283'])).
0.90/1.14	tff('285', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx)),
0.90/1.14	    inference('sup-', [status(thm)], ['276', '284'])).
0.90/1.14	tff('286', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.14	      (sk_S(sk_Xx)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X3(sk_Xx2)
0.90/1.14	       | ~ X3(sk_Xx2)),
0.90/1.14	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.90/1.14	tff('287', plain,
0.90/1.14	    ![X3 : a > $o, X4 : a > $o]:
0.90/1.14	      (~ X3(sk_Xx2)
0.90/1.14	       | ~ sk_P(X3)
0.90/1.14	       | ~ X4(sk_Xx1)
0.90/1.14	       | ~ X4(sk_Xy1)
0.90/1.14	       | ~ sk_P(X4)
0.90/1.14	       | sk_S(sk_Xx)),
0.90/1.14	    inference('simplify', [status(thm)], ['286'])).
0.90/1.14	tff('288', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | sk_S(sk_Xx)
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xy1)
0.90/1.14	       | ~ X0(sk_Xx1)
0.90/1.14	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '287'])).
0.90/1.14	tff('289', plain,
0.90/1.14	    ![X0 : a > $o]:
0.90/1.14	      (~ $true
0.90/1.14	       | sk_S(sk_Xx)
0.90/1.14	       | ~ sk_P(X0)
0.90/1.14	       | ~ X0(sk_Xy1)
0.90/1.14	       | ~ X0(sk_Xx1)
0.90/1.14	       | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['288', '4'])).
0.90/1.14	tff('290', plain,
0.90/1.14	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xx)),
0.90/1.14	    inference('simplify', [status(thm)], ['289'])).
0.90/1.14	tff('291', plain,
0.90/1.14	    (~ $true | sk_S(sk_Xx) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.14	    inference('sup-', [status(thm)], ['0', '290'])).
0.90/1.14	tff('292', plain,
0.90/1.14	    (~ $true | sk_S(sk_Xx) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.90/1.14	    inference('demod', [status(thm)], ['291', '4'])).
0.90/1.14	tff('293', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S(sk_Xx)),
0.90/1.14	    inference('simplify', [status(thm)], ['292'])).
0.90/1.14	tff('294', plain, (~ $true | sk_S(sk_Xx)),
0.90/1.14	    inference('demod', [status(thm)], ['293', '184', '230'])).
0.90/1.14	tff('295', plain, sk_S(sk_Xx), inference('simplify', [status(thm)], ['294'])).
0.90/1.14	tff('296', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
0.90/1.14	    inference('sup-', [status(thm)], ['295', '21'])).
0.90/1.14	tff('297', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xx)),
0.90/1.14	    inference('demod', [status(thm)], ['296', '79'])).
0.90/1.14	tff('298', plain, sk_S = sk_Xp(sk_Xx),
0.90/1.14	    inference('simplify', [status(thm)], ['297'])).
0.90/1.14	tff('299', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xx, X1),
0.90/1.14	    inference('ho_complete_eq', [status(thm)], ['298'])).
0.90/1.14	tff('300', plain, sk_S(sk_Xx) = $true,
0.90/1.14	    inference('sup+', [status(thm)], ['0', '299'])).
0.90/1.14	tff('301', plain, (~ $true | ~ $true | ~ $true),
0.90/1.14	    inference('demod', [status(thm)], ['285', '79', '300'])).
0.90/1.14	tff('302', plain, $false, inference('simplify', [status(thm)], ['301'])).
0.90/1.14	
0.90/1.14	% SZS output end Refutation
0.90/1.14	EOF
