0.00/0.01	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : supatvars_int
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-avatar \
0.00/0.01	  --ho \
0.00/0.01	  --force-ho \
0.00/0.01	  --no-ho-elim-pred-var \
0.00/0.01	  --ho-general-ext-pos \
0.00/0.01	  --no-ho-unif \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2  \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --sup-at-vars \
0.00/0.01	  --ho-no-ext-pos \
0.00/0.01	  --ho-no-ext-neg \
0.00/0.01	  --ho-prim-enum none \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --dont-select-ho-var-lits \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n146.star.cs.uiowa.edu
0.00/0.20	% Model      : x86_64 x86_64
0.00/0.20	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.20	% Memory     : 32218.625MB
0.00/0.20	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.20	% CPULimit   : 300
0.00/0.20	% DateTime   : Fri Feb  2 17:29:53 CST 2018
1.34/1.54	% done 4566 iterations in 1.338s
1.34/1.54	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
1.34/1.54	% SZS output start Refutation
1.34/1.55	tff(cTHM261_B_pme, conjecture,
1.34/1.55	  (![P:(a > $o > $o)]:
1.34/1.55	     ((![Xx:a]:
1.34/1.55	         (?[Xp:(a > $o)]:
1.34/1.55	            ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
1.34/1.55	             P(Xp)))) =>
1.34/1.55	      ((![Xx:a,Xy:a,Xz:a]:
1.34/1.55	          (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
1.34/1.55	            (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
1.34/1.55	           (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
1.34/1.55	       (![Xx:a,Xy:a]:
1.34/1.55	          ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
1.34/1.55	           (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
1.34/1.55	       (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S)))))))).
1.34/1.55	tff(zf_stmt_0, negated_conjecture,
1.34/1.55	  (~
1.34/1.55	    (![P:(a > $o > $o)]:
1.34/1.55	       ((![Xx:a]:
1.34/1.55	           (?[Xp:(a > $o)]:
1.34/1.55	              ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
1.34/1.55	               P(Xp)))) =>
1.34/1.55	        ((![Xx:a,Xy:a,Xz:a]:
1.34/1.55	            (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
1.34/1.55	              (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
1.34/1.55	             (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
1.34/1.55	         (![Xx:a,Xy:a]:
1.34/1.55	            ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
1.34/1.55	             (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
1.34/1.55	         (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S))))))))).
1.34/1.55	tff('0', plain, ![X0 : a]: sk_Xp(X0, X0),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('1', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S1(sk_Xz)
1.34/1.55	       | sk_S2(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('2', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['1'])).
1.34/1.55	tff('3', plain,
1.34/1.55	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '2'])).
1.34/1.55	tff('4', plain, ![X0 : a]: sk_P(sk_Xp(X0)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('5', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['3', '4'])).
1.34/1.55	tff('6', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['5'])).
1.34/1.55	tff('7', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('8', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['7'])).
1.34/1.55	tff('9', plain,
1.34/1.55	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '8'])).
1.34/1.55	tff('10', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['9', '4'])).
1.34/1.55	tff('11', plain, (sk_S2(sk_Xx1) | sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['10'])).
1.34/1.55	tff('12', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('13', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['12'])).
1.34/1.55	tff('14', plain,
1.34/1.55	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '13'])).
1.34/1.55	tff('15', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['14', '4'])).
1.34/1.55	tff('16', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['15'])).
1.34/1.55	tff('17', plain,
1.34/1.55	    ![X0 : a, X1 : a > $o]: (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ X1(X0)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('18', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.34/1.55	    inference('sup-', [status(thm)], ['16', '17'])).
1.34/1.55	tff('19', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
1.34/1.55	    inference('simplify', [status(thm)], ['18'])).
1.34/1.55	tff('20', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('21', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['20'])).
1.34/1.55	tff('22', plain,
1.34/1.55	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '21'])).
1.34/1.55	tff('23', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['22', '4'])).
1.34/1.55	tff('24', plain, (sk_S2(sk_Xx1) | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['23'])).
1.34/1.55	tff('25', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xy)),
1.34/1.55	    inference('clc', [status(thm)], ['19', '24'])).
1.34/1.55	tff('26', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S1(sk_Xy)
1.34/1.55	       | sk_S2(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('27', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['26'])).
1.34/1.55	tff('28', plain,
1.34/1.55	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '27'])).
1.34/1.55	tff('29', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['28', '4'])).
1.34/1.55	tff('30', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['29'])).
1.34/1.55	tff('31', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.34/1.55	    inference('sup-', [status(thm)], ['30', '17'])).
1.34/1.55	tff('32', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xx1)),
1.34/1.55	    inference('simplify', [status(thm)], ['31'])).
1.34/1.55	tff('33', plain,
1.34/1.55	    (sk_S1 = sk_S | sk_S2(sk_Xx1) | sk_S2(sk_Xx1) | ~ sk_P(sk_S1)),
1.34/1.55	    inference('sup+', [status(thm)], ['25', '32'])).
1.34/1.55	tff('34', plain, (~ sk_P(sk_S1) | sk_S2(sk_Xx1) | sk_S1 = sk_S),
1.34/1.55	    inference('simplify', [status(thm)], ['33'])).
1.34/1.55	tff('35', plain, (~ $true | sk_S2(sk_Xx1) | sk_S1 = sk_S | sk_S2(sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['11', '34'])).
1.34/1.55	tff('36', plain, (sk_S1 = sk_S | sk_S2(sk_Xx1)),
1.34/1.55	    inference('simplify', [status(thm)], ['35'])).
1.34/1.55	tff('37', plain, ![X1 : a]: (sk_S1(X1) = sk_S(X1) | sk_S2(sk_Xx1)),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['36'])).
1.34/1.55	tff('38', plain, ($true = sk_S(sk_Xz) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
1.34/1.55	    inference('sup+', [status(thm)], ['6', '37'])).
1.34/1.55	tff('39', plain, (sk_S2(sk_Xx1) | $true = sk_S(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['38'])).
1.34/1.55	tff('40', plain,
1.34/1.55	    ![X2 : a > $o, X4 : a > $o]:
1.34/1.55	      (~ sk_P(X4)
1.34/1.55	       | ~ X4(sk_Xx)
1.34/1.55	       | ~ X4(sk_Xz)
1.34/1.55	       | sk_S2(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('41', plain,
1.34/1.55	    ![X2 : a > $o, X4 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | sk_S2(sk_Xx1)
1.34/1.55	       | ~ X4(sk_Xz)
1.34/1.55	       | ~ X4(sk_Xx)
1.34/1.55	       | ~ sk_P(X4)),
1.34/1.55	    inference('simplify', [status(thm)], ['40'])).
1.34/1.55	tff('42', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | sk_S2(sk_Xx1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '41'])).
1.34/1.55	tff('43', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | sk_S2(sk_Xx1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['42', '4'])).
1.34/1.55	tff('44', plain,
1.34/1.55	    ![X0 : a > $o]: (sk_S2(sk_Xx1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.34/1.55	    inference('simplify', [status(thm)], ['43'])).
1.34/1.55	tff('45', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['39', '44'])).
1.34/1.55	tff('46', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('47', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['46'])).
1.34/1.55	tff('48', plain,
1.34/1.55	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '47'])).
1.34/1.55	tff('49', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['48', '4'])).
1.34/1.55	tff('50', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['49'])).
1.34/1.55	tff('51', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.34/1.55	    inference('sup-', [status(thm)], ['50', '17'])).
1.34/1.55	tff('52', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('simplify', [status(thm)], ['51'])).
1.34/1.55	tff('53', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('54', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['53'])).
1.34/1.55	tff('55', plain,
1.34/1.55	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '54'])).
1.34/1.55	tff('56', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['55', '4'])).
1.34/1.55	tff('57', plain, (sk_S2(sk_Xy1) | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['56'])).
1.34/1.55	tff('58', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xx)),
1.34/1.55	    inference('clc', [status(thm)], ['52', '57'])).
1.34/1.55	tff('59', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xx, X1) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['58'])).
1.34/1.55	tff('60', plain,
1.34/1.55	    ![X0 : a]:
1.34/1.55	      (~ sk_S(X0)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx))
1.34/1.55	       | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.34/1.55	    inference('sup-', [status(thm)], ['59', '17'])).
1.34/1.55	tff('61', plain,
1.34/1.55	    ![X0 : a]:
1.34/1.55	      (~ sk_S(X0) | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.34/1.55	    inference('demod', [status(thm)], ['60', '4'])).
1.34/1.55	tff('62', plain,
1.34/1.55	    ![X0 : a]: (sk_Xp(sk_Xx) = sk_Xp(X0) | sk_S2(sk_Xy1) | ~ sk_S(X0)),
1.34/1.55	    inference('simplify', [status(thm)], ['61'])).
1.34/1.55	tff('63', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('64', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['63'])).
1.34/1.55	tff('65', plain,
1.34/1.55	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '64'])).
1.34/1.55	tff('66', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['65', '4'])).
1.34/1.55	tff('67', plain, (sk_S2(sk_Xy1) | sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['66'])).
1.34/1.55	tff('68', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('69', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['68'])).
1.34/1.55	tff('70', plain,
1.34/1.55	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '69'])).
1.34/1.55	tff('71', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['70', '4'])).
1.34/1.55	tff('72', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['71'])).
1.34/1.55	tff('73', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.34/1.55	    inference('sup-', [status(thm)], ['72', '17'])).
1.34/1.55	tff('74', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('simplify', [status(thm)], ['73'])).
1.34/1.55	tff('75', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
1.34/1.55	    inference('clc', [status(thm)], ['74', '57'])).
1.34/1.55	tff('76', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S1(sk_Xy)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('77', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['76'])).
1.34/1.55	tff('78', plain,
1.34/1.55	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '77'])).
1.34/1.55	tff('79', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['78', '4'])).
1.34/1.55	tff('80', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['79'])).
1.34/1.55	tff('81', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.34/1.55	    inference('sup-', [status(thm)], ['80', '17'])).
1.34/1.55	tff('82', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('simplify', [status(thm)], ['81'])).
1.34/1.55	tff('83', plain,
1.34/1.55	    (sk_S1 = sk_S | sk_S2(sk_Xy1) | sk_S2(sk_Xy1) | ~ sk_P(sk_S1)),
1.34/1.55	    inference('sup+', [status(thm)], ['75', '82'])).
1.34/1.55	tff('84', plain, (~ sk_P(sk_S1) | sk_S2(sk_Xy1) | sk_S1 = sk_S),
1.34/1.55	    inference('simplify', [status(thm)], ['83'])).
1.34/1.55	tff('85', plain, (~ $true | sk_S2(sk_Xy1) | sk_S1 = sk_S | sk_S2(sk_Xy1)),
1.34/1.55	    inference('sup-', [status(thm)], ['67', '84'])).
1.34/1.55	tff('86', plain, (sk_S1 = sk_S | sk_S2(sk_Xy1)),
1.34/1.55	    inference('simplify', [status(thm)], ['85'])).
1.34/1.55	tff('87', plain, ![X1 : a]: (sk_S1(X1) = sk_S(X1) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['86'])).
1.34/1.55	tff('88', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S1(sk_Xz)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('89', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['88'])).
1.34/1.55	tff('90', plain,
1.34/1.55	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '89'])).
1.34/1.55	tff('91', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['90', '4'])).
1.34/1.55	tff('92', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['91'])).
1.34/1.55	tff('93', plain, (sk_S(sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('sup+', [status(thm)], ['87', '92'])).
1.34/1.55	tff('94', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['93'])).
1.34/1.55	tff('95', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xz)),
1.34/1.55	    inference('sup-', [status(thm)], ['94', '17'])).
1.34/1.55	tff('96', plain, (sk_S = sk_Xp(sk_Xz) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('simplify', [status(thm)], ['95'])).
1.34/1.55	tff('97', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xz)),
1.34/1.55	    inference('clc', [status(thm)], ['96', '57'])).
1.34/1.55	tff('98', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xz, X1) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['97'])).
1.34/1.55	tff('99', plain,
1.34/1.55	    ![X0 : a]:
1.34/1.55	      (~ sk_S(X0)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xz))
1.34/1.55	       | sk_Xp(sk_Xz) = sk_Xp(X0)),
1.34/1.55	    inference('sup-', [status(thm)], ['98', '17'])).
1.34/1.55	tff('100', plain,
1.34/1.55	    ![X0 : a]:
1.34/1.55	      (~ sk_S(X0) | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xz) = sk_Xp(X0)),
1.34/1.55	    inference('demod', [status(thm)], ['99', '4'])).
1.34/1.55	tff('101', plain,
1.34/1.55	    ![X0 : a]: (sk_Xp(sk_Xz) = sk_Xp(X0) | sk_S2(sk_Xy1) | ~ sk_S(X0)),
1.34/1.55	    inference('simplify', [status(thm)], ['100'])).
1.34/1.55	tff('102', plain,
1.34/1.55	    ![X0 : a]:
1.34/1.55	      (sk_Xp(sk_Xz) = sk_Xp(sk_Xx)
1.34/1.55	       | ~ sk_S(X0)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ sk_S(X0)
1.34/1.55	       | sk_S2(sk_Xy1)),
1.34/1.55	    inference('sup+', [status(thm)], ['62', '101'])).
1.34/1.55	tff('103', plain,
1.34/1.55	    ![X0 : a]: (sk_S2(sk_Xy1) | ~ sk_S(X0) | sk_Xp(sk_Xz) = sk_Xp(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['102'])).
1.34/1.55	tff('104', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xy1) | sk_Xp(sk_Xz) = sk_Xp(sk_Xx) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('sup-', [status(thm)], ['50', '103'])).
1.34/1.55	tff('105', plain, (sk_Xp(sk_Xz) = sk_Xp(sk_Xx) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('simplify', [status(thm)], ['104'])).
1.34/1.55	tff('106', plain,
1.34/1.55	    ![X1 : a]: (sk_Xp(sk_Xz, X1) = sk_Xp(sk_Xx, X1) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['105'])).
1.34/1.55	tff('107', plain, (sk_Xp(sk_Xx, sk_Xz) | sk_S2(sk_Xy1)),
1.34/1.55	    inference('sup+', [status(thm)], ['106', '0'])).
1.34/1.55	tff('108', plain,
1.34/1.55	    ![X2 : a > $o, X4 : a > $o]:
1.34/1.55	      (~ sk_P(X4)
1.34/1.55	       | ~ X4(sk_Xx)
1.34/1.55	       | ~ X4(sk_Xz)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('109', plain,
1.34/1.55	    ![X2 : a > $o, X4 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ X4(sk_Xz)
1.34/1.55	       | ~ X4(sk_Xx)
1.34/1.55	       | ~ sk_P(X4)),
1.34/1.55	    inference('simplify', [status(thm)], ['108'])).
1.34/1.55	tff('110', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '109'])).
1.34/1.55	tff('111', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | sk_S2(sk_Xy1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['110', '4'])).
1.34/1.55	tff('112', plain,
1.34/1.55	    ![X0 : a > $o]: (sk_S2(sk_Xy1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.34/1.55	    inference('simplify', [status(thm)], ['111'])).
1.34/1.55	tff('113', plain,
1.34/1.55	    (~ $true
1.34/1.55	     | sk_S2(sk_Xy1)
1.34/1.55	     | ~ sk_P(sk_Xp(sk_Xx))
1.34/1.55	     | ~ sk_Xp(sk_Xx, sk_Xx)
1.34/1.55	     | sk_S2(sk_Xy1)),
1.34/1.55	    inference('sup-', [status(thm)], ['107', '112'])).
1.34/1.55	tff('114', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xy1) | ~ $true | ~ $true | sk_S2(sk_Xy1)),
1.34/1.55	    inference('demod', [status(thm)], ['113', '4', '0'])).
1.34/1.55	tff('115', plain, sk_S2(sk_Xy1),
1.34/1.55	    inference('simplify', [status(thm)], ['114'])).
1.34/1.55	tff('116', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (sk_P(sk_S)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('117', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['116'])).
1.34/1.55	tff('118', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_P(sk_S)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '117'])).
1.34/1.55	tff('119', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_P(sk_S)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['118', '4'])).
1.34/1.55	tff('120', plain,
1.34/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['119'])).
1.34/1.55	tff('121', plain, (~ $true | sk_P(sk_S) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['115', '120'])).
1.34/1.55	tff('122', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['121'])).
1.34/1.55	tff('123', plain, (sk_P(sk_S) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('clc', [status(thm)], ['122', '24'])).
1.34/1.55	tff('124', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('125', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['124'])).
1.34/1.55	tff('126', plain,
1.34/1.55	    (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '125'])).
1.34/1.55	tff('127', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['126', '4'])).
1.34/1.55	tff('128', plain, (sk_P(sk_S2) | sk_P(sk_S)),
1.34/1.55	    inference('simplify', [status(thm)], ['127'])).
1.34/1.55	tff('129', plain, sk_P(sk_S), inference('clc', [status(thm)], ['123', '128'])).
1.34/1.55	tff('130', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (sk_S(sk_Xx)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('131', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['130'])).
1.34/1.55	tff('132', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_S(sk_Xx)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '131'])).
1.34/1.55	tff('133', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_S(sk_Xx)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['132', '4'])).
1.34/1.55	tff('134', plain,
1.34/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['133'])).
1.34/1.55	tff('135', plain, (~ $true | sk_S(sk_Xx) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['115', '134'])).
1.34/1.55	tff('136', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['135'])).
1.34/1.55	tff('137', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('138', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['137'])).
1.34/1.55	tff('139', plain,
1.34/1.55	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '138'])).
1.34/1.55	tff('140', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['139', '4'])).
1.34/1.55	tff('141', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['140'])).
1.34/1.55	tff('142', plain, (sk_S(sk_Xx) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('clc', [status(thm)], ['136', '141'])).
1.34/1.55	tff('143', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('144', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['143'])).
1.34/1.55	tff('145', plain,
1.34/1.55	    (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '144'])).
1.34/1.55	tff('146', plain, (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['145', '4'])).
1.34/1.55	tff('147', plain, (sk_P(sk_S2) | sk_S(sk_Xx)),
1.34/1.55	    inference('simplify', [status(thm)], ['146'])).
1.34/1.55	tff('148', plain, sk_S(sk_Xx),
1.34/1.55	    inference('clc', [status(thm)], ['142', '147'])).
1.34/1.55	tff('149', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.34/1.55	    inference('sup-', [status(thm)], ['148', '17'])).
1.34/1.55	tff('150', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xx)),
1.34/1.55	    inference('demod', [status(thm)], ['149', '129'])).
1.34/1.55	tff('151', plain, sk_S = sk_Xp(sk_Xx),
1.34/1.55	    inference('simplify', [status(thm)], ['150'])).
1.34/1.55	tff('152', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xx, X1),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['151'])).
1.34/1.55	tff('153', plain, sk_S(sk_Xx) = $true,
1.34/1.55	    inference('sup+', [status(thm)], ['0', '152'])).
1.34/1.55	tff('154', plain,
1.34/1.55	    (~ $true | sk_S2(sk_Xx1) | ~ $true | ~ $true | sk_S2(sk_Xx1)),
1.34/1.55	    inference('demod', [status(thm)], ['45', '129', '153'])).
1.34/1.55	tff('155', plain, sk_S2(sk_Xx1),
1.34/1.55	    inference('simplify', [status(thm)], ['154'])).
1.34/1.55	tff('156', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['155', '17'])).
1.34/1.55	tff('157', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('simplify', [status(thm)], ['156'])).
1.34/1.55	tff('158', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xx1, X1) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['157'])).
1.34/1.55	tff('159', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (sk_S1(sk_Xz)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('160', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | sk_S1(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['159'])).
1.34/1.55	tff('161', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_S1(sk_Xz)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '160'])).
1.34/1.55	tff('162', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_S1(sk_Xz)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['161', '4'])).
1.34/1.55	tff('163', plain,
1.34/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['162'])).
1.34/1.55	tff('164', plain,
1.34/1.55	    (~ sk_S2(sk_Xy1)
1.34/1.55	     | ~ sk_P(sk_S2)
1.34/1.55	     | sk_S1(sk_Xz)
1.34/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.34/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['158', '163'])).
1.34/1.55	tff('165', plain,
1.34/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_S1(sk_Xz) | ~ $true | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['164', '115', '4', '0'])).
1.34/1.55	tff('166', plain, (sk_S1(sk_Xz) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('simplify', [status(thm)], ['165'])).
1.34/1.55	tff('167', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('168', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S1(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['167'])).
1.34/1.55	tff('169', plain,
1.34/1.55	    (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '168'])).
1.34/1.55	tff('170', plain, (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['169', '4'])).
1.34/1.55	tff('171', plain, (sk_P(sk_S2) | sk_S1(sk_Xz)),
1.34/1.55	    inference('simplify', [status(thm)], ['170'])).
1.34/1.55	tff('172', plain, sk_S1(sk_Xz),
1.34/1.55	    inference('clc', [status(thm)], ['166', '171'])).
1.34/1.55	tff('173', plain,
1.34/1.55	    ![X0 : a]: (~ sk_S(X0) | ~ sk_P(sk_Xp(sk_Xx)) | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.34/1.55	    inference('sup-', [status(thm)], ['152', '17'])).
1.34/1.55	tff('174', plain, ![X0 : a]: (~ sk_S(X0) | ~ $true | sk_S = sk_Xp(X0)),
1.34/1.55	    inference('demod', [status(thm)], ['173', '151', '129', '151'])).
1.34/1.55	tff('175', plain, ![X0 : a]: (sk_S = sk_Xp(X0) | ~ sk_S(X0)),
1.34/1.55	    inference('simplify', [status(thm)], ['174'])).
1.34/1.55	tff('176', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (sk_S1(sk_Xy)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('177', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | sk_S1(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['176'])).
1.34/1.55	tff('178', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_S1(sk_Xy)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '177'])).
1.34/1.55	tff('179', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_S1(sk_Xy)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['178', '4'])).
1.34/1.55	tff('180', plain,
1.34/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['179'])).
1.34/1.55	tff('181', plain,
1.34/1.55	    (~ sk_S2(sk_Xy1)
1.34/1.55	     | ~ sk_P(sk_S2)
1.34/1.55	     | sk_S1(sk_Xy)
1.34/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.34/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['158', '180'])).
1.34/1.55	tff('182', plain,
1.34/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_S1(sk_Xy) | ~ $true | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['181', '115', '4', '0'])).
1.34/1.55	tff('183', plain, (sk_S1(sk_Xy) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('simplify', [status(thm)], ['182'])).
1.34/1.55	tff('184', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('185', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S1(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['184'])).
1.34/1.55	tff('186', plain,
1.34/1.55	    (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '185'])).
1.34/1.55	tff('187', plain, (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['186', '4'])).
1.34/1.55	tff('188', plain, (sk_P(sk_S2) | sk_S1(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['187'])).
1.34/1.55	tff('189', plain, sk_S1(sk_Xy),
1.34/1.55	    inference('clc', [status(thm)], ['183', '188'])).
1.34/1.55	tff('190', plain, (~ $true | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.34/1.55	    inference('sup-', [status(thm)], ['189', '17'])).
1.34/1.55	tff('191', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['190'])).
1.34/1.55	tff('192', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (sk_P(sk_S1)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('193', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['192'])).
1.34/1.55	tff('194', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_P(sk_S1)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '193'])).
1.34/1.55	tff('195', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_P(sk_S1)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['194', '4'])).
1.34/1.55	tff('196', plain,
1.34/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['195'])).
1.34/1.55	tff('197', plain,
1.34/1.55	    (~ sk_S2(sk_Xy1)
1.34/1.55	     | ~ sk_P(sk_S2)
1.34/1.55	     | sk_P(sk_S1)
1.34/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.34/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['158', '196'])).
1.34/1.55	tff('198', plain,
1.34/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_P(sk_S1) | ~ $true | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['197', '115', '4', '0'])).
1.34/1.55	tff('199', plain, (sk_P(sk_S1) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('simplify', [status(thm)], ['198'])).
1.34/1.55	tff('200', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('201', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['200'])).
1.34/1.55	tff('202', plain,
1.34/1.55	    (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '201'])).
1.34/1.55	tff('203', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['202', '4'])).
1.34/1.55	tff('204', plain, (sk_P(sk_S2) | sk_P(sk_S1)),
1.34/1.55	    inference('simplify', [status(thm)], ['203'])).
1.34/1.55	tff('205', plain, sk_P(sk_S1),
1.34/1.55	    inference('clc', [status(thm)], ['199', '204'])).
1.34/1.55	tff('206', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['191', '205'])).
1.34/1.55	tff('207', plain, sk_S1 = sk_Xp(sk_Xy),
1.34/1.55	    inference('simplify', [status(thm)], ['206'])).
1.34/1.55	tff('208', plain, (sk_S1 = sk_S | ~ sk_S(sk_Xy)),
1.34/1.55	    inference('sup+', [status(thm)], ['175', '207'])).
1.34/1.55	tff('209', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (sk_S(sk_Xy)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('210', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | sk_S(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['209'])).
1.34/1.55	tff('211', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_S(sk_Xy)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '210'])).
1.34/1.55	tff('212', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | sk_S(sk_Xy)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xy1)
1.34/1.55	       | ~ X0(sk_Xx1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['211', '4'])).
1.34/1.55	tff('213', plain,
1.34/1.55	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['212'])).
1.34/1.55	tff('214', plain,
1.34/1.55	    (~ sk_S2(sk_Xy1)
1.34/1.55	     | ~ sk_P(sk_S2)
1.34/1.55	     | sk_S(sk_Xy)
1.34/1.55	     | ~ sk_P(sk_Xp(sk_Xx1))
1.34/1.55	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['158', '213'])).
1.34/1.55	tff('215', plain,
1.34/1.55	    (~ $true | ~ sk_P(sk_S2) | sk_S(sk_Xy) | ~ $true | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['214', '115', '4', '0'])).
1.34/1.55	tff('216', plain, (sk_S(sk_Xy) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('simplify', [status(thm)], ['215'])).
1.34/1.55	tff('217', plain,
1.34/1.55	    ![X2 : a > $o]:
1.34/1.55	      (sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('218', plain,
1.34/1.55	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['217'])).
1.34/1.55	tff('219', plain,
1.34/1.55	    (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '218'])).
1.34/1.55	tff('220', plain, (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['219', '4'])).
1.34/1.55	tff('221', plain, (sk_P(sk_S2) | sk_S(sk_Xy)),
1.34/1.55	    inference('simplify', [status(thm)], ['220'])).
1.34/1.55	tff('222', plain, sk_S(sk_Xy),
1.34/1.55	    inference('clc', [status(thm)], ['216', '221'])).
1.34/1.55	tff('223', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.34/1.55	    inference('sup-', [status(thm)], ['222', '17'])).
1.34/1.55	tff('224', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xy)),
1.34/1.55	    inference('demod', [status(thm)], ['223', '129'])).
1.34/1.55	tff('225', plain, sk_S = sk_Xp(sk_Xy),
1.34/1.55	    inference('simplify', [status(thm)], ['224'])).
1.34/1.55	tff('226', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xy, X1),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['225'])).
1.34/1.55	tff('227', plain, sk_S(sk_Xy) = $true,
1.34/1.55	    inference('sup+', [status(thm)], ['0', '226'])).
1.34/1.55	tff('228', plain, (sk_S1 = sk_S | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['208', '227'])).
1.34/1.55	tff('229', plain, sk_S1 = sk_S, inference('simplify', [status(thm)], ['228'])).
1.34/1.55	tff('230', plain, ![X1 : a]: sk_S1(X1) = sk_S(X1),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['229'])).
1.34/1.55	tff('231', plain, sk_S(sk_Xz),
1.34/1.55	    inference('demod', [status(thm)], ['172', '230'])).
1.34/1.55	tff('232', plain, (sk_S2(sk_Xx1) = $true | ~ sk_P(sk_S2)),
1.34/1.55	    inference('sup+', [status(thm)], ['0', '158'])).
1.34/1.55	tff('233', plain,
1.34/1.55	    (~ $true | ~ sk_P(sk_S2) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['232', '17'])).
1.34/1.55	tff('234', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2)),
1.34/1.55	    inference('simplify', [status(thm)], ['233'])).
1.34/1.55	tff('235', plain,
1.34/1.55	    ![X2 : a > $o, X4 : a > $o]:
1.34/1.55	      (~ sk_P(X4)
1.34/1.55	       | ~ X4(sk_Xx)
1.34/1.55	       | ~ X4(sk_Xz)
1.34/1.55	       | sk_P(sk_S2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('236', plain,
1.34/1.55	    ![X2 : a > $o, X4 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | sk_P(sk_S2)
1.34/1.55	       | ~ X4(sk_Xz)
1.34/1.55	       | ~ X4(sk_Xx)
1.34/1.55	       | ~ sk_P(X4)),
1.34/1.55	    inference('simplify', [status(thm)], ['235'])).
1.34/1.55	tff('237', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | sk_P(sk_S2)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '236'])).
1.34/1.55	tff('238', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | sk_P(sk_S2)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['237', '4'])).
1.34/1.55	tff('239', plain,
1.34/1.55	    ![X0 : a > $o]: (sk_P(sk_S2) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.34/1.55	    inference('simplify', [status(thm)], ['238'])).
1.34/1.55	tff('240', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_P(sk_S2)),
1.34/1.55	    inference('sup-', [status(thm)], ['231', '239'])).
1.34/1.55	tff('241', plain, (~ $true | ~ $true | ~ $true | sk_P(sk_S2)),
1.34/1.55	    inference('demod', [status(thm)], ['240', '129', '153'])).
1.34/1.55	tff('242', plain, sk_P(sk_S2), inference('simplify', [status(thm)], ['241'])).
1.34/1.55	tff('243', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['234', '242'])).
1.34/1.55	tff('244', plain, sk_S2 = sk_Xp(sk_Xx1),
1.34/1.55	    inference('simplify', [status(thm)], ['243'])).
1.34/1.55	tff('245', plain, ![X1 : a]: sk_S2(X1) = sk_Xp(sk_Xx1, X1),
1.34/1.55	    inference('ho_complete_eq', [status(thm)], ['244'])).
1.34/1.55	tff('246', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o, X4 : a > $o]:
1.34/1.55	      (~ sk_P(X4)
1.34/1.55	       | ~ X4(sk_Xx)
1.34/1.55	       | ~ X4(sk_Xz)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X2(sk_Xx2)
1.34/1.55	       | ~ X2(sk_Xx2)),
1.34/1.55	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.34/1.55	tff('247', plain,
1.34/1.55	    ![X2 : a > $o, X3 : a > $o, X4 : a > $o]:
1.34/1.55	      (~ X2(sk_Xx2)
1.34/1.55	       | ~ sk_P(X2)
1.34/1.55	       | ~ X3(sk_Xx1)
1.34/1.55	       | ~ X3(sk_Xy1)
1.34/1.55	       | ~ sk_P(X3)
1.34/1.55	       | ~ X4(sk_Xz)
1.34/1.55	       | ~ X4(sk_Xx)
1.34/1.55	       | ~ sk_P(X4)),
1.34/1.55	    inference('simplify', [status(thm)], ['246'])).
1.34/1.55	tff('248', plain,
1.34/1.55	    ![X0 : a > $o, X1 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | ~ sk_P(X1)
1.34/1.55	       | ~ X1(sk_Xy1)
1.34/1.55	       | ~ X1(sk_Xx1)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.34/1.55	    inference('sup-', [status(thm)], ['0', '247'])).
1.34/1.55	tff('249', plain,
1.34/1.55	    ![X0 : a > $o, X1 : a > $o]:
1.34/1.55	      (~ $true
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | ~ sk_P(X1)
1.34/1.55	       | ~ X1(sk_Xy1)
1.34/1.55	       | ~ X1(sk_Xx1)
1.34/1.55	       | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['248', '4'])).
1.34/1.55	tff('250', plain,
1.34/1.55	    ![X0 : a > $o, X1 : a > $o]:
1.34/1.55	      (~ X1(sk_Xx1)
1.34/1.55	       | ~ X1(sk_Xy1)
1.34/1.55	       | ~ sk_P(X1)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ sk_P(X0)),
1.34/1.55	    inference('simplify', [status(thm)], ['249'])).
1.34/1.55	tff('251', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ sk_S2(sk_Xy1)
1.34/1.55	       | ~ sk_P(X0)
1.34/1.55	       | ~ X0(sk_Xx)
1.34/1.55	       | ~ X0(sk_Xz)
1.34/1.55	       | ~ sk_P(sk_Xp(sk_Xx1))
1.34/1.55	       | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.34/1.55	    inference('sup-', [status(thm)], ['245', '250'])).
1.34/1.55	tff('252', plain, sk_S2(sk_Xx1) = $true,
1.34/1.55	    inference('sup+', [status(thm)], ['0', '245'])).
1.34/1.55	tff('253', plain,
1.34/1.55	    ![X0 : a > $o]:
1.34/1.55	      (~ $true | ~ sk_P(X0) | ~ X0(sk_Xx) | ~ X0(sk_Xz) | ~ $true | ~ $true),
1.34/1.55	    inference('demod', [status(thm)],
1.34/1.55	              ['251', '115', '244', '242', '245', '252'])).
1.34/1.55	tff('254', plain, ![X0 : a > $o]: (~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.34/1.55	    inference('simplify', [status(thm)], ['253'])).
1.34/1.55	tff('255', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx)),
1.34/1.55	    inference('sup-', [status(thm)], ['231', '254'])).
1.34/1.55	tff('256', plain, (~ $true | ~ $true | ~ $true),
1.34/1.55	    inference('demod', [status(thm)], ['255', '129', '153'])).
1.34/1.55	tff('257', plain, $false, inference('simplify', [status(thm)], ['256'])).
1.34/1.55	
1.34/1.55	% SZS output end Refutation
1.34/1.55	EOF
