0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : supatvars_ext
0.00/0.00	% Ordering    : rpo6
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --sup-at-vars \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n132.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
2.36/2.57	% done 3603 iterations in 2.365s
2.36/2.57	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
2.36/2.57	% SZS output start Refutation
2.36/2.57	tff(cTHM261_B_pme, conjecture,
2.36/2.57	  (![P:(a > $o > $o)]:
2.36/2.57	     ((![Xx:a]:
2.36/2.57	         (?[Xp:(a > $o)]:
2.36/2.57	            ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
2.36/2.57	             P(Xp)))) =>
2.36/2.57	      ((![Xx:a,Xy:a,Xz:a]:
2.36/2.57	          (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
2.36/2.57	            (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
2.36/2.57	           (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
2.36/2.57	       (![Xx:a,Xy:a]:
2.36/2.57	          ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
2.36/2.57	           (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
2.36/2.57	       (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S)))))))).
2.36/2.57	tff(zf_stmt_0, negated_conjecture,
2.36/2.57	  (~
2.36/2.57	    (![P:(a > $o > $o)]:
2.36/2.57	       ((![Xx:a]:
2.36/2.57	           (?[Xp:(a > $o)]:
2.36/2.57	              ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
2.36/2.57	               P(Xp)))) =>
2.36/2.57	        ((![Xx:a,Xy:a,Xz:a]:
2.36/2.57	            (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
2.36/2.57	              (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
2.36/2.57	             (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
2.36/2.57	         (![Xx:a,Xy:a]:
2.36/2.57	            ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
2.36/2.57	             (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
2.36/2.57	         (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S))))))))).
2.36/2.57	tff('0', plain, ![X0 : a]: sk_Xp(X0, X0),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('1', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('2', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['1'])).
2.36/2.57	tff('3', plain,
2.36/2.57	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '2'])).
2.36/2.57	tff('4', plain, ![X0 : a]: sk_P(sk_Xp(X0)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('5', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['3', '4'])).
2.36/2.57	tff('6', plain, (sk_S2(sk_Xy1) | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['5'])).
2.36/2.57	tff('7', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('8', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['7'])).
2.36/2.57	tff('9', plain,
2.36/2.57	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '8'])).
2.36/2.57	tff('10', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['9', '4'])).
2.36/2.57	tff('11', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['10'])).
2.36/2.57	tff('12', plain,
2.36/2.57	    ![X0 : a, X1 : a > $o]: (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ X1(X0)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('13', plain,
2.36/2.57	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
2.36/2.57	    inference('sup-', [status(thm)], ['11', '12'])).
2.36/2.57	tff('14', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('simplify', [status(thm)], ['13'])).
2.36/2.57	tff('15', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('16', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['15'])).
2.36/2.57	tff('17', plain,
2.36/2.57	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '16'])).
2.36/2.57	tff('18', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['17', '4'])).
2.36/2.57	tff('19', plain, (sk_S2(sk_Xy1) | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['18'])).
2.36/2.57	tff('20', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
2.36/2.57	    inference('clc', [status(thm)], ['14', '19'])).
2.36/2.57	tff('21', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S1(sk_Xy)
2.36/2.57	       | sk_S2(sk_Xy1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('22', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['21'])).
2.36/2.57	tff('23', plain,
2.36/2.57	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '22'])).
2.36/2.57	tff('24', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['23', '4'])).
2.36/2.57	tff('25', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['24'])).
2.36/2.57	tff('26', plain,
2.36/2.57	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
2.36/2.57	    inference('sup-', [status(thm)], ['25', '12'])).
2.36/2.57	tff('27', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('simplify', [status(thm)], ['26'])).
2.36/2.57	tff('28', plain,
2.36/2.57	    (sk_S1 = sk_S | sk_S2(sk_Xy1) | sk_S2(sk_Xy1) | ~ sk_P(sk_S1)),
2.36/2.57	    inference('sup+', [status(thm)], ['20', '27'])).
2.36/2.57	tff('29', plain, (~ sk_P(sk_S1) | sk_S2(sk_Xy1) | sk_S1 = sk_S),
2.36/2.57	    inference('simplify', [status(thm)], ['28'])).
2.36/2.57	tff('30', plain, (~ $true | sk_S2(sk_Xy1) | sk_S1 = sk_S | sk_S2(sk_Xy1)),
2.36/2.57	    inference('sup-', [status(thm)], ['6', '29'])).
2.36/2.57	tff('31', plain, (sk_S1 = sk_S | sk_S2(sk_Xy1)),
2.36/2.57	    inference('simplify', [status(thm)], ['30'])).
2.36/2.57	tff('32', plain, ![X1 : a]: (sk_S1(X1) = sk_S(X1) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['31'])).
2.36/2.57	tff('33', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S1(sk_Xz)
2.36/2.57	       | sk_S2(sk_Xy1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('34', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['33'])).
2.36/2.57	tff('35', plain,
2.36/2.57	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '34'])).
2.36/2.57	tff('36', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['35', '4'])).
2.36/2.57	tff('37', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['36'])).
2.36/2.57	tff('38', plain, (sk_S(sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('sup+', [status(thm)], ['32', '37'])).
2.36/2.57	tff('39', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['38'])).
2.36/2.57	tff('40', plain,
2.36/2.57	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xz)),
2.36/2.57	    inference('sup-', [status(thm)], ['39', '12'])).
2.36/2.57	tff('41', plain, (sk_S = sk_Xp(sk_Xz) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('simplify', [status(thm)], ['40'])).
2.36/2.57	tff('42', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xz)),
2.36/2.57	    inference('clc', [status(thm)], ['41', '19'])).
2.36/2.57	tff('43', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xz, X1) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['42'])).
2.36/2.57	tff('44', plain,
2.36/2.57	    ![X2 : a > $o, X4 : a > $o]:
2.36/2.57	      (~ sk_P(X4)
2.36/2.57	       | ~ X4(sk_Xx)
2.36/2.57	       | ~ X4(sk_Xz)
2.36/2.57	       | sk_S2(sk_Xy1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('45', plain,
2.36/2.57	    ![X2 : a > $o, X4 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | sk_S2(sk_Xy1)
2.36/2.57	       | ~ X4(sk_Xz)
2.36/2.57	       | ~ X4(sk_Xx)
2.36/2.57	       | ~ sk_P(X4)),
2.36/2.57	    inference('simplify', [status(thm)], ['44'])).
2.36/2.57	tff('46', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | sk_S2(sk_Xy1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '45'])).
2.36/2.57	tff('47', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | sk_S2(sk_Xy1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['46', '4'])).
2.36/2.57	tff('48', plain,
2.36/2.57	    ![X0 : a > $o]: (sk_S2(sk_Xy1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
2.36/2.57	    inference('simplify', [status(thm)], ['47'])).
2.36/2.57	tff('49', plain,
2.36/2.57	    (~ $true | ~ sk_P(sk_Xp(sk_Xz)) | ~ sk_Xp(sk_Xz, sk_Xx) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '48'])).
2.36/2.57	tff('50', plain, (~ $true | ~ $true | ~ sk_Xp(sk_Xz, sk_Xx) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('demod', [status(thm)], ['49', '4'])).
2.36/2.57	tff('51', plain, (sk_S2(sk_Xy1) | ~ sk_Xp(sk_Xz, sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['50'])).
2.36/2.57	tff('52', plain, (~ sk_S(sk_Xx) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
2.36/2.57	    inference('sup-', [status(thm)], ['43', '51'])).
2.36/2.57	tff('53', plain, (sk_S2(sk_Xy1) | ~ sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['52'])).
2.36/2.57	tff('54', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('55', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['54'])).
2.36/2.57	tff('56', plain,
2.36/2.57	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '55'])).
2.36/2.57	tff('57', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['56', '4'])).
2.36/2.57	tff('58', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['57'])).
2.36/2.57	tff('59', plain, sk_S2(sk_Xy1), inference('clc', [status(thm)], ['53', '58'])).
2.36/2.57	tff('60', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (sk_S1(sk_Xy)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('61', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['60'])).
2.36/2.57	tff('62', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_S1(sk_Xy)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '61'])).
2.36/2.57	tff('63', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_S1(sk_Xy)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['62', '4'])).
2.36/2.57	tff('64', plain,
2.36/2.57	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['63'])).
2.36/2.57	tff('65', plain, (~ $true | sk_S1(sk_Xy) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['59', '64'])).
2.36/2.57	tff('66', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['65'])).
2.36/2.57	tff('67', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S1(sk_Xy)
2.36/2.57	       | sk_S2(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('68', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['67'])).
2.36/2.57	tff('69', plain,
2.36/2.57	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '68'])).
2.36/2.57	tff('70', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['69', '4'])).
2.36/2.57	tff('71', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['70'])).
2.36/2.57	tff('72', plain, (sk_S1(sk_Xy) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('clc', [status(thm)], ['66', '71'])).
2.36/2.57	tff('73', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('74', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['73'])).
2.36/2.57	tff('75', plain,
2.36/2.57	    (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '74'])).
2.36/2.57	tff('76', plain, (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['75', '4'])).
2.36/2.57	tff('77', plain, (sk_P(sk_S2) | sk_S1(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['76'])).
2.36/2.57	tff('78', plain, sk_S1(sk_Xy), inference('clc', [status(thm)], ['72', '77'])).
2.36/2.57	tff('79', plain, (~ $true | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
2.36/2.57	    inference('sup-', [status(thm)], ['78', '12'])).
2.36/2.57	tff('80', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['79'])).
2.36/2.57	tff('81', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xy, X1) | ~ sk_P(sk_S1)),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['80'])).
2.36/2.57	tff('82', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (sk_S(sk_Xy)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('83', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['82'])).
2.36/2.57	tff('84', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_S(sk_Xy)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '83'])).
2.36/2.57	tff('85', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_S(sk_Xy)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['84', '4'])).
2.36/2.57	tff('86', plain,
2.36/2.57	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['85'])).
2.36/2.57	tff('87', plain, (~ $true | sk_S(sk_Xy) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['59', '86'])).
2.36/2.57	tff('88', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['87'])).
2.36/2.57	tff('89', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('90', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['89'])).
2.36/2.57	tff('91', plain,
2.36/2.57	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '90'])).
2.36/2.57	tff('92', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['91', '4'])).
2.36/2.57	tff('93', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['92'])).
2.36/2.57	tff('94', plain, (sk_S(sk_Xy) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('clc', [status(thm)], ['88', '93'])).
2.36/2.57	tff('95', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('96', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['95'])).
2.36/2.57	tff('97', plain,
2.36/2.57	    (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '96'])).
2.36/2.57	tff('98', plain, (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['97', '4'])).
2.36/2.57	tff('99', plain, (sk_P(sk_S2) | sk_S(sk_Xy)),
2.36/2.57	    inference('simplify', [status(thm)], ['98'])).
2.36/2.57	tff('100', plain, sk_S(sk_Xy), inference('clc', [status(thm)], ['94', '99'])).
2.36/2.57	tff('101', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
2.36/2.57	    inference('sup-', [status(thm)], ['100', '12'])).
2.36/2.57	tff('102', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (sk_P(sk_S)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('103', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['102'])).
2.36/2.57	tff('104', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_P(sk_S)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '103'])).
2.36/2.57	tff('105', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_P(sk_S)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['104', '4'])).
2.36/2.57	tff('106', plain,
2.36/2.57	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['105'])).
2.36/2.57	tff('107', plain, (~ $true | sk_P(sk_S) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['59', '106'])).
2.36/2.57	tff('108', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['107'])).
2.36/2.57	tff('109', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('110', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['109'])).
2.36/2.57	tff('111', plain,
2.36/2.57	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '110'])).
2.36/2.57	tff('112', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['111', '4'])).
2.36/2.57	tff('113', plain, (sk_S2(sk_Xx1) | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['112'])).
2.36/2.57	tff('114', plain, (sk_P(sk_S) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('clc', [status(thm)], ['108', '113'])).
2.36/2.57	tff('115', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('116', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['115'])).
2.36/2.57	tff('117', plain,
2.36/2.57	    (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '116'])).
2.36/2.57	tff('118', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['117', '4'])).
2.36/2.57	tff('119', plain, (sk_P(sk_S2) | sk_P(sk_S)),
2.36/2.57	    inference('simplify', [status(thm)], ['118'])).
2.36/2.57	tff('120', plain, sk_P(sk_S), inference('clc', [status(thm)], ['114', '119'])).
2.36/2.57	tff('121', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xy)),
2.36/2.57	    inference('demod', [status(thm)], ['101', '120'])).
2.36/2.57	tff('122', plain, sk_S = sk_Xp(sk_Xy),
2.36/2.57	    inference('simplify', [status(thm)], ['121'])).
2.36/2.57	tff('123', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xy, X1),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['122'])).
2.36/2.57	tff('124', plain, ![X0 : a]: (sk_S(X0) = sk_S1(X0) | ~ sk_P(sk_S1)),
2.36/2.57	    inference('sup+', [status(thm)], ['81', '123'])).
2.36/2.57	tff('125', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (sk_S1(sk_Xz)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('126', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['125'])).
2.36/2.57	tff('127', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_S1(sk_Xz)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '126'])).
2.36/2.57	tff('128', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_S1(sk_Xz)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['127', '4'])).
2.36/2.57	tff('129', plain,
2.36/2.57	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['128'])).
2.36/2.57	tff('130', plain, (~ $true | sk_S1(sk_Xz) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['59', '129'])).
2.36/2.57	tff('131', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['130'])).
2.36/2.57	tff('132', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S1(sk_Xz)
2.36/2.57	       | sk_S2(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('133', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['132'])).
2.36/2.57	tff('134', plain,
2.36/2.57	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '133'])).
2.36/2.57	tff('135', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['134', '4'])).
2.36/2.57	tff('136', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['135'])).
2.36/2.57	tff('137', plain, (sk_S1(sk_Xz) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('clc', [status(thm)], ['131', '136'])).
2.36/2.57	tff('138', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('139', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['138'])).
2.36/2.57	tff('140', plain,
2.36/2.57	    (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '139'])).
2.36/2.57	tff('141', plain, (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['140', '4'])).
2.36/2.57	tff('142', plain, (sk_P(sk_S2) | sk_S1(sk_Xz)),
2.36/2.57	    inference('simplify', [status(thm)], ['141'])).
2.36/2.57	tff('143', plain, sk_S1(sk_Xz),
2.36/2.57	    inference('clc', [status(thm)], ['137', '142'])).
2.36/2.57	tff('144', plain, (sk_S(sk_Xz) | ~ sk_P(sk_S1)),
2.36/2.57	    inference('sup+', [status(thm)], ['124', '143'])).
2.36/2.57	tff('145', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (sk_P(sk_S1)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('146', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['145'])).
2.36/2.57	tff('147', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_P(sk_S1)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '146'])).
2.36/2.57	tff('148', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_P(sk_S1)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['147', '4'])).
2.36/2.57	tff('149', plain,
2.36/2.57	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['148'])).
2.36/2.57	tff('150', plain, (~ $true | sk_P(sk_S1) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['59', '149'])).
2.36/2.57	tff('151', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['150'])).
2.36/2.57	tff('152', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('153', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['152'])).
2.36/2.57	tff('154', plain,
2.36/2.57	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '153'])).
2.36/2.57	tff('155', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['154', '4'])).
2.36/2.57	tff('156', plain, (sk_S2(sk_Xx1) | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['155'])).
2.36/2.57	tff('157', plain, (sk_P(sk_S1) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('clc', [status(thm)], ['151', '156'])).
2.36/2.57	tff('158', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('159', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['158'])).
2.36/2.57	tff('160', plain,
2.36/2.57	    (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '159'])).
2.36/2.57	tff('161', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['160', '4'])).
2.36/2.57	tff('162', plain, (sk_P(sk_S2) | sk_P(sk_S1)),
2.36/2.57	    inference('simplify', [status(thm)], ['161'])).
2.36/2.57	tff('163', plain, sk_P(sk_S1),
2.36/2.57	    inference('clc', [status(thm)], ['157', '162'])).
2.36/2.57	tff('164', plain, (sk_S = sk_S1 | ~ sk_P(sk_S1)),
2.36/2.57	    inference('sup+', [status(thm)], ['80', '122'])).
2.36/2.57	tff('165', plain, (~ $true | sk_S = sk_S1),
2.36/2.57	    inference('sup-', [status(thm)], ['163', '164'])).
2.36/2.57	tff('166', plain, sk_S = sk_S1, inference('simplify', [status(thm)], ['165'])).
2.36/2.57	tff('167', plain, (sk_S(sk_Xz) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['144', '166', '120'])).
2.36/2.57	tff('168', plain, sk_S(sk_Xz), inference('simplify', [status(thm)], ['167'])).
2.36/2.57	tff('169', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o, X4 : a > $o]:
2.36/2.57	      (~ sk_P(X4)
2.36/2.57	       | ~ X4(sk_Xx)
2.36/2.57	       | ~ X4(sk_Xz)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('170', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o, X4 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | ~ X4(sk_Xz)
2.36/2.57	       | ~ X4(sk_Xx)
2.36/2.57	       | ~ sk_P(X4)),
2.36/2.57	    inference('simplify', [status(thm)], ['169'])).
2.36/2.57	tff('171', plain,
2.36/2.57	    ![X0 : a > $o, X1 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | ~ sk_P(X1)
2.36/2.57	       | ~ X1(sk_Xy1)
2.36/2.57	       | ~ X1(sk_Xx1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '170'])).
2.36/2.57	tff('172', plain,
2.36/2.57	    ![X0 : a > $o, X1 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | ~ sk_P(X1)
2.36/2.57	       | ~ X1(sk_Xy1)
2.36/2.57	       | ~ X1(sk_Xx1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['171', '4'])).
2.36/2.57	tff('173', plain,
2.36/2.57	    ![X0 : a > $o, X1 : a > $o]:
2.36/2.57	      (~ X1(sk_Xx1)
2.36/2.57	       | ~ X1(sk_Xy1)
2.36/2.57	       | ~ sk_P(X1)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ sk_P(X0)),
2.36/2.57	    inference('simplify', [status(thm)], ['172'])).
2.36/2.57	tff('174', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | ~ sk_P(sk_S2)
2.36/2.57	       | ~ sk_S2(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['59', '173'])).
2.36/2.57	tff('175', plain,
2.36/2.57	    ![X2 : a > $o, X4 : a > $o]:
2.36/2.57	      (~ sk_P(X4)
2.36/2.57	       | ~ X4(sk_Xx)
2.36/2.57	       | ~ X4(sk_Xz)
2.36/2.57	       | sk_P(sk_S2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('176', plain,
2.36/2.57	    ![X2 : a > $o, X4 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | sk_P(sk_S2)
2.36/2.57	       | ~ X4(sk_Xz)
2.36/2.57	       | ~ X4(sk_Xx)
2.36/2.57	       | ~ sk_P(X4)),
2.36/2.57	    inference('simplify', [status(thm)], ['175'])).
2.36/2.57	tff('177', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | sk_P(sk_S2)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '176'])).
2.36/2.57	tff('178', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | sk_P(sk_S2)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['177', '4'])).
2.36/2.57	tff('179', plain,
2.36/2.57	    ![X0 : a > $o]: (sk_P(sk_S2) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
2.36/2.57	    inference('simplify', [status(thm)], ['178'])).
2.36/2.57	tff('180', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_P(sk_S2)),
2.36/2.57	    inference('sup-', [status(thm)], ['168', '179'])).
2.36/2.57	tff('181', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (sk_S(sk_Xx)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('182', plain,
2.36/2.57	    ![X2 : a > $o, X3 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X3(sk_Xx1)
2.36/2.57	       | ~ X3(sk_Xy1)
2.36/2.57	       | ~ sk_P(X3)
2.36/2.57	       | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['181'])).
2.36/2.57	tff('183', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_S(sk_Xx)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '182'])).
2.36/2.57	tff('184', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | sk_S(sk_Xx)
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xy1)
2.36/2.57	       | ~ X0(sk_Xx1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['183', '4'])).
2.36/2.57	tff('185', plain,
2.36/2.57	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['184'])).
2.36/2.57	tff('186', plain, (~ $true | sk_S(sk_Xx) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['59', '185'])).
2.36/2.57	tff('187', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['186'])).
2.36/2.57	tff('188', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('189', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['188'])).
2.36/2.57	tff('190', plain,
2.36/2.57	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '189'])).
2.36/2.57	tff('191', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['190', '4'])).
2.36/2.57	tff('192', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['191'])).
2.36/2.57	tff('193', plain, (sk_S(sk_Xx) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('clc', [status(thm)], ['187', '192'])).
2.36/2.57	tff('194', plain,
2.36/2.57	    ![X2 : a > $o]:
2.36/2.57	      (sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('195', plain,
2.36/2.57	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['194'])).
2.36/2.57	tff('196', plain,
2.36/2.57	    (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '195'])).
2.36/2.57	tff('197', plain, (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['196', '4'])).
2.36/2.57	tff('198', plain, (sk_P(sk_S2) | sk_S(sk_Xx)),
2.36/2.57	    inference('simplify', [status(thm)], ['197'])).
2.36/2.57	tff('199', plain, sk_S(sk_Xx),
2.36/2.57	    inference('clc', [status(thm)], ['193', '198'])).
2.36/2.57	tff('200', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
2.36/2.57	    inference('sup-', [status(thm)], ['199', '12'])).
2.36/2.57	tff('201', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xx)),
2.36/2.57	    inference('demod', [status(thm)], ['200', '120'])).
2.36/2.57	tff('202', plain, sk_S = sk_Xp(sk_Xx),
2.36/2.57	    inference('simplify', [status(thm)], ['201'])).
2.36/2.57	tff('203', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xx, X1),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['202'])).
2.36/2.57	tff('204', plain, sk_S(sk_Xx) = $true,
2.36/2.57	    inference('sup+', [status(thm)], ['0', '203'])).
2.36/2.57	tff('205', plain, (~ $true | ~ $true | ~ $true | sk_P(sk_S2)),
2.36/2.57	    inference('demod', [status(thm)], ['180', '120', '204'])).
2.36/2.57	tff('206', plain, sk_P(sk_S2), inference('simplify', [status(thm)], ['205'])).
2.36/2.57	tff('207', plain,
2.36/2.57	    ![X2 : a > $o, X4 : a > $o]:
2.36/2.57	      (~ sk_P(X4)
2.36/2.57	       | ~ X4(sk_Xx)
2.36/2.57	       | ~ X4(sk_Xz)
2.36/2.57	       | sk_S2(sk_Xx1)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | ~ X2(sk_Xx2)
2.36/2.57	       | ~ X2(sk_Xx2)),
2.36/2.57	    inference('cnf', [status(esa)], [zf_stmt_0])).
2.36/2.57	tff('208', plain,
2.36/2.57	    ![X2 : a > $o, X4 : a > $o]:
2.36/2.57	      (~ X2(sk_Xx2)
2.36/2.57	       | ~ sk_P(X2)
2.36/2.57	       | sk_S2(sk_Xx1)
2.36/2.57	       | ~ X4(sk_Xz)
2.36/2.57	       | ~ X4(sk_Xx)
2.36/2.57	       | ~ sk_P(X4)),
2.36/2.57	    inference('simplify', [status(thm)], ['207'])).
2.36/2.57	tff('209', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | sk_S2(sk_Xx1)
2.36/2.57	       | ~ sk_P(sk_Xp(sk_Xx2))),
2.36/2.57	    inference('sup-', [status(thm)], ['0', '208'])).
2.36/2.57	tff('210', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true
2.36/2.57	       | ~ sk_P(X0)
2.36/2.57	       | ~ X0(sk_Xx)
2.36/2.57	       | ~ X0(sk_Xz)
2.36/2.57	       | sk_S2(sk_Xx1)
2.36/2.57	       | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['209', '4'])).
2.36/2.57	tff('211', plain,
2.36/2.57	    ![X0 : a > $o]: (sk_S2(sk_Xx1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
2.36/2.57	    inference('simplify', [status(thm)], ['210'])).
2.36/2.57	tff('212', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['168', '211'])).
2.36/2.57	tff('213', plain, (~ $true | ~ $true | ~ $true | sk_S2(sk_Xx1)),
2.36/2.57	    inference('demod', [status(thm)], ['212', '120', '204'])).
2.36/2.57	tff('214', plain, sk_S2(sk_Xx1),
2.36/2.57	    inference('simplify', [status(thm)], ['213'])).
2.36/2.57	tff('215', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
2.36/2.57	    inference('sup-', [status(thm)], ['214', '12'])).
2.36/2.57	tff('216', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('simplify', [status(thm)], ['215'])).
2.36/2.57	tff('217', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xx1, X1) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['216'])).
2.36/2.57	tff('218', plain, (sk_S2(sk_Xx1) = $true | ~ sk_P(sk_S2)),
2.36/2.57	    inference('sup+', [status(thm)], ['0', '217'])).
2.36/2.57	tff('219', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
2.36/2.57	    inference('sup-', [status(thm)], ['59', '12'])).
2.36/2.57	tff('220', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('simplify', [status(thm)], ['219'])).
2.36/2.57	tff('221', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | ~ sk_P(sk_S2)),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['220'])).
2.36/2.57	tff('222', plain,
2.36/2.57	    ![X0 : $tType, X1 : $tType, X2 : X0 > X1, X3 : X0 > X1]:
2.36/2.57	      (X2 = X3 | X2(zf_ext_diff(X2, X3)) != X3(zf_ext_diff(X2, X3))),
2.36/2.57	    trivial([status(thm)])).
2.36/2.57	tff('223', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_Xp(sk_Xy1, zf_ext_diff(sk_S2, X0))
2.36/2.57	        != X0(zf_ext_diff(sk_Xp(sk_Xy1), X0))
2.36/2.57	       | ~ sk_P(sk_S2)
2.36/2.57	       | sk_Xp(sk_Xy1) = X0),
2.36/2.57	    inference('sup-', [status(thm)], ['220', '222'])).
2.36/2.57	tff('224', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_Xp(sk_Xy1, zf_ext_diff(sk_S2, X0))
2.36/2.57	        != X0(zf_ext_diff(sk_Xp(sk_Xy1), X0))
2.36/2.57	       | ~ $true
2.36/2.57	       | sk_Xp(sk_Xy1) = X0),
2.36/2.57	    inference('demod', [status(thm)], ['223', '206'])).
2.36/2.57	tff('225', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_Xp(sk_Xy1) = X0
2.36/2.57	       | sk_Xp(sk_Xy1, zf_ext_diff(sk_S2, X0))
2.36/2.57	          != X0(zf_ext_diff(sk_Xp(sk_Xy1), X0))),
2.36/2.57	    inference('simplify', [status(thm)], ['224'])).
2.36/2.57	tff('226', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_S2(zf_ext_diff(sk_S2, X0)) != X0(zf_ext_diff(sk_Xp(sk_Xy1), X0))
2.36/2.57	       | ~ sk_P(sk_S2)
2.36/2.57	       | sk_Xp(sk_Xy1) = X0),
2.36/2.57	    inference('sup-', [status(thm)], ['221', '225'])).
2.36/2.57	tff('227', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_S2(zf_ext_diff(sk_S2, X0)) != X0(zf_ext_diff(sk_Xp(sk_Xy1), X0))
2.36/2.57	       | ~ $true
2.36/2.57	       | sk_Xp(sk_Xy1) = X0),
2.36/2.57	    inference('demod', [status(thm)], ['226', '206'])).
2.36/2.57	tff('228', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_Xp(sk_Xy1) = X0
2.36/2.57	       | sk_S2(zf_ext_diff(sk_S2, X0)) != X0(zf_ext_diff(sk_Xp(sk_Xy1), X0))),
2.36/2.57	    inference('simplify', [status(thm)], ['227'])).
2.36/2.57	tff('229', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_S2(zf_ext_diff(sk_S2, X0)) != X0(zf_ext_diff(sk_S2, X0))
2.36/2.57	       | ~ sk_P(sk_S2)
2.36/2.57	       | sk_Xp(sk_Xy1) = X0),
2.36/2.57	    inference('sup-', [status(thm)], ['220', '228'])).
2.36/2.57	tff('230', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_S2(zf_ext_diff(sk_S2, X0)) != X0(zf_ext_diff(sk_S2, X0))
2.36/2.57	       | ~ $true
2.36/2.57	       | sk_Xp(sk_Xy1) = X0),
2.36/2.57	    inference('demod', [status(thm)], ['229', '206'])).
2.36/2.57	tff('231', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (sk_Xp(sk_Xy1) = X0
2.36/2.57	       | sk_S2(zf_ext_diff(sk_S2, X0)) != X0(zf_ext_diff(sk_S2, X0))),
2.36/2.57	    inference('simplify', [status(thm)], ['230'])).
2.36/2.57	tff('232', plain,
2.36/2.57	    ![X0 : a > $o, X1 : a]:
2.36/2.57	      (sk_Xp(sk_Xy1, X1) = X0(X1)
2.36/2.57	       | sk_S2(zf_ext_diff(sk_S2, X0)) != X0(zf_ext_diff(sk_S2, X0))),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['231'])).
2.36/2.57	tff('233', plain, sk_Xp(sk_Xy1) = sk_S2,
2.36/2.57	    inference('eq_res', [status(thm)], ['231'])).
2.36/2.57	tff('234', plain, ![X1 : a]: sk_Xp(sk_Xy1, X1) = sk_S2(X1),
2.36/2.57	    inference('ho_complete_eq', [status(thm)], ['233'])).
2.36/2.57	tff('235', plain,
2.36/2.57	    ![X0 : a > $o, X1 : a]:
2.36/2.57	      (sk_S2(X1) = X0(X1)
2.36/2.57	       | sk_S2(zf_ext_diff(sk_S2, X0)) != X0(zf_ext_diff(sk_S2, X0))),
2.36/2.57	    inference('demod', [status(thm)], ['232', '234'])).
2.36/2.57	tff('236', plain,
2.36/2.57	    (sk_S2(sk_Xx1) = $true
2.36/2.57	     | ~ sk_P(sk_S2)
2.36/2.57	     | sk_S2(zf_ext_diff(sk_S2, sk_S2)) != sk_S2(zf_ext_diff(sk_S2, sk_S2))),
2.36/2.57	    inference('sup+', [status(thm)], ['218', '235'])).
2.36/2.57	tff('237', plain,
2.36/2.57	    (sk_S2(sk_Xx1) = $true
2.36/2.57	     | ~ $true
2.36/2.57	     | sk_S2(zf_ext_diff(sk_S2, sk_S2)) != sk_S2(zf_ext_diff(sk_S2, sk_S2))),
2.36/2.57	    inference('demod', [status(thm)], ['236', '206'])).
2.36/2.57	tff('238', plain, sk_S2(sk_Xx1) = $true,
2.36/2.57	    inference('simplify', [status(thm)], ['237'])).
2.36/2.57	tff('239', plain,
2.36/2.57	    ![X0 : a > $o]:
2.36/2.57	      (~ $true | ~ sk_P(X0) | ~ X0(sk_Xx) | ~ X0(sk_Xz) | ~ $true | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['174', '206', '238'])).
2.36/2.57	tff('240', plain, ![X0 : a > $o]: (~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
2.36/2.57	    inference('simplify', [status(thm)], ['239'])).
2.36/2.57	tff('241', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx)),
2.36/2.57	    inference('sup-', [status(thm)], ['168', '240'])).
2.36/2.57	tff('242', plain, (~ $true | ~ $true | ~ $true),
2.36/2.57	    inference('demod', [status(thm)], ['241', '120', '204'])).
2.36/2.57	tff('243', plain, $false, inference('simplify', [status(thm)], ['242'])).
2.36/2.57	
2.36/2.57	% SZS output end Refutation
2.36/2.57	EOF
