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   : n148.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 17:29:53 CST 2018
0.00/0.34	% done 608 iterations in 0.136s
0.00/0.34	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
0.00/0.34	% SZS output start Refutation
0.00/0.34	tff(cTHM261_B_pme, conjecture,
0.00/0.34	  (![P:(a > $o > $o)]:
0.00/0.34	     ((![Xx:a]:
0.00/0.34	         (?[Xp:(a > $o)]:
0.00/0.34	            ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
0.00/0.34	             P(Xp)))) =>
0.00/0.34	      ((![Xx:a,Xy:a,Xz:a]:
0.00/0.34	          (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
0.00/0.34	            (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
0.00/0.34	           (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
0.00/0.34	       (![Xx:a,Xy:a]:
0.00/0.34	          ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
0.00/0.34	           (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
0.00/0.34	       (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S)))))))).
0.00/0.34	tff(zf_stmt_0, negated_conjecture,
0.00/0.34	  (~
0.00/0.34	    (![P:(a > $o > $o)]:
0.00/0.34	       ((![Xx:a]:
0.00/0.34	           (?[Xp:(a > $o)]:
0.00/0.34	              ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
0.00/0.34	               P(Xp)))) =>
0.00/0.34	        ((![Xx:a,Xy:a,Xz:a]:
0.00/0.34	            (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
0.00/0.34	              (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
0.00/0.34	             (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
0.00/0.34	         (![Xx:a,Xy:a]:
0.00/0.34	            ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
0.00/0.34	             (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
0.00/0.34	         (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S))))))))).
0.00/0.34	tff('0', plain, ![X0 : a]: sk_Xp(X0, X0),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('1', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S1(sk_Xz)
0.00/0.34	       | sk_S2(sk_Xy1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('2', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['1'])).
0.00/0.34	tff('3', plain,
0.00/0.34	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '2'])).
0.00/0.34	tff('4', plain, ![X0 : a]: sk_P(sk_Xp(X0)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('5', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['3', '4'])).
0.00/0.34	tff('6', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['5'])).
0.00/0.34	tff('7', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('8', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['7'])).
0.00/0.34	tff('9', plain,
0.00/0.34	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '8'])).
0.00/0.34	tff('10', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['9', '4'])).
0.00/0.34	tff('11', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['10'])).
0.00/0.34	tff('12', plain,
0.00/0.34	    ![X0 : a, X1 : a > $o]: (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ X1(X0)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('13', plain,
0.00/0.34	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.00/0.34	    inference('sup-', [status(thm)], ['11', '12'])).
0.00/0.34	tff('14', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('15', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['14'])).
0.00/0.34	tff('16', plain,
0.00/0.34	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '15'])).
0.00/0.34	tff('17', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['16', '4'])).
0.00/0.34	tff('18', plain, (sk_S2(sk_Xy1) | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['17'])).
0.00/0.34	tff('19', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (sk_P(sk_S)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('20', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['19'])).
0.00/0.34	tff('21', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_P(sk_S)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '20'])).
0.00/0.34	tff('22', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_P(sk_S)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['21', '4'])).
0.00/0.34	tff('23', plain,
0.00/0.34	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['22'])).
0.00/0.34	tff('24', plain,
0.00/0.34	    (~ $true | sk_P(sk_S) | sk_P(sk_S) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
0.00/0.34	    inference('sup-', [status(thm)], ['18', '23'])).
0.00/0.34	tff('25', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['24'])).
0.00/0.34	tff('26', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('27', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['26'])).
0.00/0.34	tff('28', plain,
0.00/0.34	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '27'])).
0.00/0.34	tff('29', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['28', '4'])).
0.00/0.34	tff('30', plain, (sk_S2(sk_Xx1) | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['29'])).
0.00/0.34	tff('31', plain, (sk_P(sk_S) | ~ sk_P(sk_S2)),
0.00/0.34	    inference('clc', [status(thm)], ['25', '30'])).
0.00/0.34	tff('32', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('33', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['32'])).
0.00/0.34	tff('34', plain,
0.00/0.34	    (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '33'])).
0.00/0.34	tff('35', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['34', '4'])).
0.00/0.34	tff('36', plain, (sk_P(sk_S2) | sk_P(sk_S)),
0.00/0.34	    inference('simplify', [status(thm)], ['35'])).
0.00/0.34	tff('37', plain, sk_P(sk_S), inference('clc', [status(thm)], ['31', '36'])).
0.00/0.34	tff('38', plain, (~ $true | sk_S2(sk_Xy1) | ~ $true | sk_S = sk_Xp(sk_Xy)),
0.00/0.34	    inference('demod', [status(thm)], ['13', '37'])).
0.00/0.34	tff('39', plain, (sk_S = sk_Xp(sk_Xy) | sk_S2(sk_Xy1)),
0.00/0.34	    inference('simplify', [status(thm)], ['38'])).
0.00/0.34	tff('40', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xy1)),
0.00/0.34	    inference('ho_complete_eq', [status(thm)], ['39'])).
0.00/0.34	tff('41', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S1(sk_Xy)
0.00/0.34	       | sk_S2(sk_Xy1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('42', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['41'])).
0.00/0.34	tff('43', plain,
0.00/0.34	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '42'])).
0.00/0.34	tff('44', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['43', '4'])).
0.00/0.34	tff('45', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['44'])).
0.00/0.34	tff('46', plain,
0.00/0.34	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.00/0.34	    inference('sup-', [status(thm)], ['45', '12'])).
0.00/0.34	tff('47', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
0.00/0.34	    inference('simplify', [status(thm)], ['46'])).
0.00/0.34	tff('48', plain,
0.00/0.34	    ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xy1) | ~ sk_P(sk_S1)),
0.00/0.34	    inference('ho_complete_eq', [status(thm)], ['47'])).
0.00/0.34	tff('49', plain,
0.00/0.34	    ![X0 : a]:
0.00/0.34	      (sk_S1(X0) = sk_S(X0) | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
0.00/0.34	    inference('sup+', [status(thm)], ['40', '48'])).
0.00/0.34	tff('50', plain,
0.00/0.34	    ![X0 : a]: (~ sk_P(sk_S1) | sk_S2(sk_Xy1) | sk_S1(X0) = sk_S(X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['49'])).
0.00/0.34	tff('51', plain,
0.00/0.34	    ($true = sk_S(sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1) | ~ sk_P(sk_S1)),
0.00/0.34	    inference('sup+', [status(thm)], ['6', '50'])).
0.00/0.34	tff('52', plain, (~ sk_P(sk_S1) | sk_S2(sk_Xy1) | $true = sk_S(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['51'])).
0.00/0.34	tff('53', plain,
0.00/0.34	    ![X2 : a > $o, X4 : a > $o]:
0.00/0.34	      (~ sk_P(X4)
0.00/0.34	       | ~ X4(sk_Xx)
0.00/0.34	       | ~ X4(sk_Xz)
0.00/0.34	       | sk_S2(sk_Xy1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('54', plain,
0.00/0.34	    ![X2 : a > $o, X4 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | sk_S2(sk_Xy1)
0.00/0.34	       | ~ X4(sk_Xz)
0.00/0.34	       | ~ X4(sk_Xx)
0.00/0.34	       | ~ sk_P(X4)),
0.00/0.34	    inference('simplify', [status(thm)], ['53'])).
0.00/0.34	tff('55', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | sk_S2(sk_Xy1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '54'])).
0.00/0.34	tff('56', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | sk_S2(sk_Xy1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['55', '4'])).
0.00/0.34	tff('57', plain,
0.00/0.34	    ![X0 : a > $o]: (sk_S2(sk_Xy1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['56'])).
0.00/0.34	tff('58', plain,
0.00/0.34	    (~ $true
0.00/0.34	     | sk_S2(sk_Xy1)
0.00/0.34	     | ~ sk_P(sk_S1)
0.00/0.34	     | ~ sk_P(sk_S)
0.00/0.34	     | ~ sk_S(sk_Xx)
0.00/0.34	     | sk_S2(sk_Xy1)),
0.00/0.34	    inference('sup-', [status(thm)], ['52', '57'])).
0.00/0.34	tff('59', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('60', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['59'])).
0.00/0.34	tff('61', plain,
0.00/0.34	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '60'])).
0.00/0.34	tff('62', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['61', '4'])).
0.00/0.34	tff('63', plain, (sk_S2(sk_Xy1) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['62'])).
0.00/0.34	tff('64', plain,
0.00/0.34	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
0.00/0.34	    inference('sup-', [status(thm)], ['63', '12'])).
0.00/0.34	tff('65', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['64'])).
0.00/0.34	tff('66', plain,
0.00/0.34	    ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | sk_P(sk_S1) | ~ sk_P(sk_S2)),
0.00/0.34	    inference('ho_complete_eq', [status(thm)], ['65'])).
0.00/0.34	tff('67', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('68', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['67'])).
0.00/0.34	tff('69', plain,
0.00/0.34	    (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '68'])).
0.00/0.34	tff('70', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['69', '4'])).
0.00/0.34	tff('71', plain, (sk_P(sk_S2) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['70'])).
0.00/0.34	tff('72', plain, ![X1 : a]: (sk_P(sk_S1) | sk_S2(X1) = sk_Xp(sk_Xy1, X1)),
0.00/0.34	    inference('clc', [status(thm)], ['66', '71'])).
0.00/0.34	tff('73', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (sk_P(sk_S1)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('74', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['73'])).
0.00/0.34	tff('75', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_P(sk_S1)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '74'])).
0.00/0.34	tff('76', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_P(sk_S1)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['75', '4'])).
0.00/0.34	tff('77', plain,
0.00/0.34	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['76'])).
0.00/0.34	tff('78', plain,
0.00/0.34	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '77'])).
0.00/0.34	tff('79', plain, (~ $true | sk_P(sk_S1) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
0.00/0.34	    inference('demod', [status(thm)], ['78', '4'])).
0.00/0.34	tff('80', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['79'])).
0.00/0.34	tff('81', plain, (~ sk_S2(sk_Xx1) | sk_P(sk_S1) | sk_P(sk_S1)),
0.00/0.34	    inference('sup-', [status(thm)], ['72', '80'])).
0.00/0.34	tff('82', plain, (sk_P(sk_S1) | ~ sk_S2(sk_Xx1)),
0.00/0.34	    inference('simplify', [status(thm)], ['81'])).
0.00/0.34	tff('83', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('84', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['83'])).
0.00/0.34	tff('85', plain,
0.00/0.34	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '84'])).
0.00/0.34	tff('86', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['85', '4'])).
0.00/0.34	tff('87', plain, (sk_S2(sk_Xx1) | sk_P(sk_S1)),
0.00/0.34	    inference('simplify', [status(thm)], ['86'])).
0.00/0.34	tff('88', plain, sk_P(sk_S1), inference('clc', [status(thm)], ['82', '87'])).
0.00/0.34	tff('89', plain,
0.00/0.34	    (~ $true
0.00/0.34	     | sk_S2(sk_Xy1)
0.00/0.34	     | ~ $true
0.00/0.34	     | ~ $true
0.00/0.34	     | ~ sk_S(sk_Xx)
0.00/0.34	     | sk_S2(sk_Xy1)),
0.00/0.34	    inference('demod', [status(thm)], ['58', '88', '37'])).
0.00/0.34	tff('90', plain, (~ sk_S(sk_Xx) | sk_S2(sk_Xy1)),
0.00/0.34	    inference('simplify', [status(thm)], ['89'])).
0.00/0.34	tff('91', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('92', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['91'])).
0.00/0.34	tff('93', plain,
0.00/0.34	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '92'])).
0.00/0.34	tff('94', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['93', '4'])).
0.00/0.34	tff('95', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['94'])).
0.00/0.34	tff('96', plain, sk_S2(sk_Xy1), inference('clc', [status(thm)], ['90', '95'])).
0.00/0.34	tff('97', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (sk_S1(sk_Xz)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('98', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['97'])).
0.00/0.34	tff('99', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_S1(sk_Xz)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '98'])).
0.00/0.34	tff('100', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_S1(sk_Xz)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['99', '4'])).
0.00/0.34	tff('101', plain,
0.00/0.34	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['100'])).
0.00/0.34	tff('102', plain, (~ $true | sk_S1(sk_Xz) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
0.00/0.34	    inference('sup-', [status(thm)], ['96', '101'])).
0.00/0.34	tff('103', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['102'])).
0.00/0.34	tff('104', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S1(sk_Xz)
0.00/0.34	       | sk_S2(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('105', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['104'])).
0.00/0.34	tff('106', plain,
0.00/0.34	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '105'])).
0.00/0.34	tff('107', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['106', '4'])).
0.00/0.34	tff('108', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['107'])).
0.00/0.34	tff('109', plain, (sk_S1(sk_Xz) | ~ sk_P(sk_S2)),
0.00/0.34	    inference('clc', [status(thm)], ['103', '108'])).
0.00/0.34	tff('110', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('111', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['110'])).
0.00/0.34	tff('112', plain,
0.00/0.34	    (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '111'])).
0.00/0.34	tff('113', plain, (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['112', '4'])).
0.00/0.34	tff('114', plain, (sk_P(sk_S2) | sk_S1(sk_Xz)),
0.00/0.34	    inference('simplify', [status(thm)], ['113'])).
0.00/0.34	tff('115', plain, sk_S1(sk_Xz),
0.00/0.34	    inference('clc', [status(thm)], ['109', '114'])).
0.00/0.34	tff('116', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (sk_S1(sk_Xy)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('117', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['116'])).
0.00/0.34	tff('118', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_S1(sk_Xy)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '117'])).
0.00/0.34	tff('119', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_S1(sk_Xy)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['118', '4'])).
0.00/0.34	tff('120', plain,
0.00/0.34	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['119'])).
0.00/0.34	tff('121', plain, (~ $true | sk_S1(sk_Xy) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
0.00/0.34	    inference('sup-', [status(thm)], ['96', '120'])).
0.00/0.34	tff('122', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['121'])).
0.00/0.34	tff('123', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S1(sk_Xy)
0.00/0.34	       | sk_S2(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('124', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['123'])).
0.00/0.34	tff('125', plain,
0.00/0.34	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '124'])).
0.00/0.34	tff('126', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['125', '4'])).
0.00/0.34	tff('127', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['126'])).
0.00/0.34	tff('128', plain, (sk_S1(sk_Xy) | ~ sk_P(sk_S2)),
0.00/0.34	    inference('clc', [status(thm)], ['122', '127'])).
0.00/0.34	tff('129', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('130', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['129'])).
0.00/0.34	tff('131', plain,
0.00/0.34	    (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '130'])).
0.00/0.34	tff('132', plain, (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['131', '4'])).
0.00/0.34	tff('133', plain, (sk_P(sk_S2) | sk_S1(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['132'])).
0.00/0.34	tff('134', plain, sk_S1(sk_Xy),
0.00/0.34	    inference('clc', [status(thm)], ['128', '133'])).
0.00/0.34	tff('135', plain, (~ $true | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
0.00/0.34	    inference('sup-', [status(thm)], ['134', '12'])).
0.00/0.34	tff('136', plain, (~ $true | ~ $true | sk_S1 = sk_Xp(sk_Xy)),
0.00/0.34	    inference('demod', [status(thm)], ['135', '88'])).
0.00/0.34	tff('137', plain, sk_S1 = sk_Xp(sk_Xy),
0.00/0.34	    inference('simplify', [status(thm)], ['136'])).
0.00/0.34	tff('138', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (sk_S(sk_Xy)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('139', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['138'])).
0.00/0.34	tff('140', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_S(sk_Xy)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '139'])).
0.00/0.34	tff('141', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_S(sk_Xy)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['140', '4'])).
0.00/0.34	tff('142', plain,
0.00/0.34	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['141'])).
0.00/0.34	tff('143', plain, (~ $true | sk_S(sk_Xy) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
0.00/0.34	    inference('sup-', [status(thm)], ['96', '142'])).
0.00/0.34	tff('144', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['143'])).
0.00/0.34	tff('145', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('146', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['145'])).
0.00/0.34	tff('147', plain,
0.00/0.34	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '146'])).
0.00/0.34	tff('148', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['147', '4'])).
0.00/0.34	tff('149', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['148'])).
0.00/0.34	tff('150', plain, (sk_S(sk_Xy) | ~ sk_P(sk_S2)),
0.00/0.34	    inference('clc', [status(thm)], ['144', '149'])).
0.00/0.34	tff('151', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('152', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['151'])).
0.00/0.34	tff('153', plain,
0.00/0.34	    (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '152'])).
0.00/0.34	tff('154', plain, (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['153', '4'])).
0.00/0.34	tff('155', plain, (sk_P(sk_S2) | sk_S(sk_Xy)),
0.00/0.34	    inference('simplify', [status(thm)], ['154'])).
0.00/0.34	tff('156', plain, sk_S(sk_Xy),
0.00/0.34	    inference('clc', [status(thm)], ['150', '155'])).
0.00/0.34	tff('157', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
0.00/0.34	    inference('sup-', [status(thm)], ['156', '12'])).
0.00/0.34	tff('158', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xy)),
0.00/0.34	    inference('demod', [status(thm)], ['157', '37'])).
0.00/0.34	tff('159', plain, sk_S = sk_Xp(sk_Xy),
0.00/0.34	    inference('simplify', [status(thm)], ['158'])).
0.00/0.34	tff('160', plain, sk_S = sk_S1,
0.00/0.34	    inference('sup+', [status(thm)], ['137', '159'])).
0.00/0.34	tff('161', plain, ![X1 : a]: sk_S(X1) = sk_S1(X1),
0.00/0.34	    inference('ho_complete_eq', [status(thm)], ['160'])).
0.00/0.34	tff('162', plain, sk_S(sk_Xz),
0.00/0.34	    inference('demod', [status(thm)], ['115', '161'])).
0.00/0.34	tff('163', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o, X4 : a > $o]:
0.00/0.34	      (~ sk_P(X4)
0.00/0.34	       | ~ X4(sk_Xx)
0.00/0.34	       | ~ X4(sk_Xz)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('164', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o, X4 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | ~ X4(sk_Xz)
0.00/0.34	       | ~ X4(sk_Xx)
0.00/0.34	       | ~ sk_P(X4)),
0.00/0.34	    inference('simplify', [status(thm)], ['163'])).
0.00/0.34	tff('165', plain,
0.00/0.34	    ![X0 : a > $o, X1 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | ~ sk_P(X1)
0.00/0.34	       | ~ X1(sk_Xy1)
0.00/0.34	       | ~ X1(sk_Xx1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '164'])).
0.00/0.34	tff('166', plain,
0.00/0.34	    ![X0 : a > $o, X1 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | ~ sk_P(X1)
0.00/0.34	       | ~ X1(sk_Xy1)
0.00/0.34	       | ~ X1(sk_Xx1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['165', '4'])).
0.00/0.34	tff('167', plain,
0.00/0.34	    ![X0 : a > $o, X1 : a > $o]:
0.00/0.34	      (~ X1(sk_Xx1)
0.00/0.34	       | ~ X1(sk_Xy1)
0.00/0.34	       | ~ sk_P(X1)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ sk_P(X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['166'])).
0.00/0.34	tff('168', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | ~ sk_P(sk_S2)
0.00/0.34	       | ~ sk_S2(sk_Xx1)),
0.00/0.34	    inference('sup-', [status(thm)], ['96', '167'])).
0.00/0.34	tff('169', plain,
0.00/0.34	    ![X2 : a > $o, X4 : a > $o]:
0.00/0.34	      (~ sk_P(X4)
0.00/0.34	       | ~ X4(sk_Xx)
0.00/0.34	       | ~ X4(sk_Xz)
0.00/0.34	       | sk_P(sk_S2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('170', plain,
0.00/0.34	    ![X2 : a > $o, X4 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | sk_P(sk_S2)
0.00/0.34	       | ~ X4(sk_Xz)
0.00/0.34	       | ~ X4(sk_Xx)
0.00/0.34	       | ~ sk_P(X4)),
0.00/0.34	    inference('simplify', [status(thm)], ['169'])).
0.00/0.34	tff('171', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | sk_P(sk_S2)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '170'])).
0.00/0.34	tff('172', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | sk_P(sk_S2)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['171', '4'])).
0.00/0.34	tff('173', plain,
0.00/0.34	    ![X0 : a > $o]: (sk_P(sk_S2) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['172'])).
0.00/0.34	tff('174', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_P(sk_S2)),
0.00/0.34	    inference('sup-', [status(thm)], ['162', '173'])).
0.00/0.34	tff('175', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (sk_S(sk_Xx)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('176', plain,
0.00/0.34	    ![X2 : a > $o, X3 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X3(sk_Xx1)
0.00/0.34	       | ~ X3(sk_Xy1)
0.00/0.34	       | ~ sk_P(X3)
0.00/0.34	       | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['175'])).
0.00/0.34	tff('177', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_S(sk_Xx)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '176'])).
0.00/0.34	tff('178', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | sk_S(sk_Xx)
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xy1)
0.00/0.34	       | ~ X0(sk_Xx1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['177', '4'])).
0.00/0.34	tff('179', plain,
0.00/0.34	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['178'])).
0.00/0.34	tff('180', plain, (~ $true | sk_S(sk_Xx) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
0.00/0.34	    inference('sup-', [status(thm)], ['96', '179'])).
0.00/0.34	tff('181', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['180'])).
0.00/0.34	tff('182', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('183', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['182'])).
0.00/0.34	tff('184', plain,
0.00/0.34	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '183'])).
0.00/0.34	tff('185', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['184', '4'])).
0.00/0.34	tff('186', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['185'])).
0.00/0.34	tff('187', plain, (sk_S(sk_Xx) | ~ sk_P(sk_S2)),
0.00/0.34	    inference('clc', [status(thm)], ['181', '186'])).
0.00/0.34	tff('188', plain,
0.00/0.34	    ![X2 : a > $o]:
0.00/0.34	      (sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('189', plain,
0.00/0.34	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['188'])).
0.00/0.34	tff('190', plain,
0.00/0.34	    (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '189'])).
0.00/0.34	tff('191', plain, (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['190', '4'])).
0.00/0.34	tff('192', plain, (sk_P(sk_S2) | sk_S(sk_Xx)),
0.00/0.34	    inference('simplify', [status(thm)], ['191'])).
0.00/0.34	tff('193', plain, sk_S(sk_Xx),
0.00/0.34	    inference('clc', [status(thm)], ['187', '192'])).
0.00/0.34	tff('194', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
0.00/0.34	    inference('sup-', [status(thm)], ['193', '12'])).
0.00/0.34	tff('195', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xx)),
0.00/0.34	    inference('demod', [status(thm)], ['194', '37'])).
0.00/0.34	tff('196', plain, sk_S = sk_Xp(sk_Xx),
0.00/0.34	    inference('simplify', [status(thm)], ['195'])).
0.00/0.34	tff('197', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xx, X1),
0.00/0.34	    inference('ho_complete_eq', [status(thm)], ['196'])).
0.00/0.34	tff('198', plain, sk_S(sk_Xx) = $true,
0.00/0.34	    inference('sup+', [status(thm)], ['0', '197'])).
0.00/0.34	tff('199', plain, (~ $true | ~ $true | ~ $true | sk_P(sk_S2)),
0.00/0.34	    inference('demod', [status(thm)], ['174', '37', '198'])).
0.00/0.34	tff('200', plain, sk_P(sk_S2), inference('simplify', [status(thm)], ['199'])).
0.00/0.34	tff('201', plain,
0.00/0.34	    ![X2 : a > $o, X4 : a > $o]:
0.00/0.34	      (~ sk_P(X4)
0.00/0.34	       | ~ X4(sk_Xx)
0.00/0.34	       | ~ X4(sk_Xz)
0.00/0.34	       | sk_S2(sk_Xx1)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | ~ X2(sk_Xx2)
0.00/0.34	       | ~ X2(sk_Xx2)),
0.00/0.34	    inference('cnf', [status(esa)], [zf_stmt_0])).
0.00/0.34	tff('202', plain,
0.00/0.34	    ![X2 : a > $o, X4 : a > $o]:
0.00/0.34	      (~ X2(sk_Xx2)
0.00/0.34	       | ~ sk_P(X2)
0.00/0.34	       | sk_S2(sk_Xx1)
0.00/0.34	       | ~ X4(sk_Xz)
0.00/0.34	       | ~ X4(sk_Xx)
0.00/0.34	       | ~ sk_P(X4)),
0.00/0.34	    inference('simplify', [status(thm)], ['201'])).
0.00/0.34	tff('203', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | sk_S2(sk_Xx1)
0.00/0.34	       | ~ sk_P(sk_Xp(sk_Xx2))),
0.00/0.34	    inference('sup-', [status(thm)], ['0', '202'])).
0.00/0.34	tff('204', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true
0.00/0.34	       | ~ sk_P(X0)
0.00/0.34	       | ~ X0(sk_Xx)
0.00/0.34	       | ~ X0(sk_Xz)
0.00/0.34	       | sk_S2(sk_Xx1)
0.00/0.34	       | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['203', '4'])).
0.00/0.34	tff('205', plain,
0.00/0.34	    ![X0 : a > $o]: (sk_S2(sk_Xx1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['204'])).
0.00/0.34	tff('206', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
0.00/0.34	    inference('sup-', [status(thm)], ['162', '205'])).
0.00/0.34	tff('207', plain, (~ $true | ~ $true | ~ $true | sk_S2(sk_Xx1)),
0.00/0.34	    inference('demod', [status(thm)], ['206', '37', '198'])).
0.00/0.34	tff('208', plain, sk_S2(sk_Xx1),
0.00/0.34	    inference('simplify', [status(thm)], ['207'])).
0.00/0.34	tff('209', plain,
0.00/0.34	    ![X0 : a > $o]:
0.00/0.34	      (~ $true | ~ sk_P(X0) | ~ X0(sk_Xx) | ~ X0(sk_Xz) | ~ $true | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['168', '200', '208'])).
0.00/0.34	tff('210', plain, ![X0 : a > $o]: (~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
0.00/0.34	    inference('simplify', [status(thm)], ['209'])).
0.00/0.34	tff('211', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx)),
0.00/0.34	    inference('sup-', [status(thm)], ['162', '210'])).
0.00/0.34	tff('212', plain, (~ $true | ~ $true | ~ $true),
0.00/0.34	    inference('demod', [status(thm)], ['211', '37', '198'])).
0.00/0.34	tff('213', plain, $false, inference('simplify', [status(thm)], ['212'])).
0.00/0.34	
0.00/0.34	% SZS output end Refutation
0.00/0.34	EOF
