0.00/0.00	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : supatvars_int
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --sup-at-vars \
0.00/0.00	  --ho-no-ext-pos \
0.00/0.00	  --ho-no-ext-neg \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.20	% Computer   : n098.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 17:29:39 CST 2018
1.86/2.10	% done 6046 iterations in 1.892s
1.86/2.10	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
1.86/2.10	% SZS output start Refutation
1.92/2.11	tff(cTHM261_B_pme, conjecture,
1.92/2.11	  (![P:(a > $o > $o)]:
1.92/2.11	     ((![Xx:a]:
1.92/2.11	         (?[Xp:(a > $o)]:
1.92/2.11	            ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
1.92/2.11	             P(Xp)))) =>
1.92/2.11	      ((![Xx:a,Xy:a,Xz:a]:
1.92/2.11	          (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
1.92/2.11	            (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
1.92/2.11	           (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
1.92/2.11	       (![Xx:a,Xy:a]:
1.92/2.11	          ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
1.92/2.11	           (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
1.92/2.11	       (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S)))))))).
1.92/2.11	tff(zf_stmt_0, negated_conjecture,
1.92/2.11	  (~
1.92/2.11	    (![P:(a > $o > $o)]:
1.92/2.11	       ((![Xx:a]:
1.92/2.11	           (?[Xp:(a > $o)]:
1.92/2.11	              ((![Xq:(a > $o)]: ((Xq(Xx) & P(Xq)) => (Xq = Xp))) & Xp(Xx) & 
1.92/2.11	               P(Xp)))) =>
1.92/2.11	        ((![Xx:a,Xy:a,Xz:a]:
1.92/2.11	            (((?[S:(a > $o)]: (S(Xz) & S(Xy) & P(S))) & 
1.92/2.11	              (?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S)))) =>
1.92/2.11	             (?[S:(a > $o)]: (S(Xz) & S(Xx) & P(S))))) & 
1.92/2.11	         (![Xx:a,Xy:a]:
1.92/2.11	            ((?[S:(a > $o)]: (S(Xy) & S(Xx) & P(S))) =>
1.92/2.11	             (?[S:(a > $o)]: (S(Xx) & S(Xy) & P(S))))) & 
1.92/2.11	         (![Xx:a]: (?[S:(a > $o)]: (S(Xx) & S(Xx) & P(S))))))))).
1.92/2.11	tff('0', plain, ![X0 : a]: sk_Xp(X0, X0),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('1', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('2', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['1'])).
1.92/2.11	tff('3', plain,
1.92/2.11	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '2'])).
1.92/2.11	tff('4', plain, ![X0 : a]: sk_P(sk_Xp(X0)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('5', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xy1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['3', '4'])).
1.92/2.11	tff('6', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['5'])).
1.92/2.11	tff('7', plain,
1.92/2.11	    ![X0 : a, X1 : a > $o]: (X1 = sk_Xp(X0) | ~ sk_P(X1) | ~ X1(X0)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('8', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.92/2.11	    inference('sup-', [status(thm)], ['6', '7'])).
1.92/2.11	tff('9', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('simplify', [status(thm)], ['8'])).
1.92/2.11	tff('10', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('11', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['10'])).
1.92/2.11	tff('12', plain,
1.92/2.11	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '11'])).
1.92/2.11	tff('13', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xy1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['12', '4'])).
1.92/2.11	tff('14', plain, (sk_S2(sk_Xy1) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['13'])).
1.92/2.11	tff('15', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xx)),
1.92/2.11	    inference('clc', [status(thm)], ['9', '14'])).
1.92/2.11	tff('16', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xx, X1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['15'])).
1.92/2.11	tff('17', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx))
1.92/2.11	       | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['16', '7'])).
1.92/2.11	tff('18', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0) | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['17', '4'])).
1.92/2.11	tff('19', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xx) = sk_Xp(X0) | sk_S2(sk_Xy1) | ~ sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['18'])).
1.92/2.11	tff('20', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S1(sk_Xy)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('21', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['20'])).
1.92/2.11	tff('22', plain,
1.92/2.11	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '21'])).
1.92/2.11	tff('23', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['22', '4'])).
1.92/2.11	tff('24', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['23'])).
1.92/2.11	tff('25', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.92/2.11	    inference('sup-', [status(thm)], ['24', '7'])).
1.92/2.11	tff('26', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('simplify', [status(thm)], ['25'])).
1.92/2.11	tff('27', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('28', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['27'])).
1.92/2.11	tff('29', plain,
1.92/2.11	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '28'])).
1.92/2.11	tff('30', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xy1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['29', '4'])).
1.92/2.11	tff('31', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['30'])).
1.92/2.11	tff('32', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.92/2.11	    inference('sup-', [status(thm)], ['31', '7'])).
1.92/2.11	tff('33', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('simplify', [status(thm)], ['32'])).
1.92/2.11	tff('34', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xy)),
1.92/2.11	    inference('clc', [status(thm)], ['33', '14'])).
1.92/2.11	tff('35', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['34'])).
1.92/2.11	tff('36', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xy))
1.92/2.11	       | sk_Xp(sk_Xy) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['35', '7'])).
1.92/2.11	tff('37', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0) | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['36', '4'])).
1.92/2.11	tff('38', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xy) = sk_Xp(X0) | sk_S2(sk_Xy1) | ~ sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['37'])).
1.92/2.11	tff('39', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (sk_Xp(sk_Xy) = sk_Xp(sk_Xx)
1.92/2.11	       | ~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup+', [status(thm)], ['19', '38'])).
1.92/2.11	tff('40', plain,
1.92/2.11	    ![X0 : a]: (sk_S2(sk_Xy1) | ~ sk_S(X0) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['39'])).
1.92/2.11	tff('41', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xy1) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup-', [status(thm)], ['6', '40'])).
1.92/2.11	tff('42', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('simplify', [status(thm)], ['41'])).
1.92/2.11	tff('43', plain,
1.92/2.11	    (sk_S1 = sk_Xp(sk_Xx) | sk_S2(sk_Xy1) | ~ sk_P(sk_S1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup+', [status(thm)], ['26', '42'])).
1.92/2.11	tff('44', plain, (~ sk_P(sk_S1) | sk_S2(sk_Xy1) | sk_S1 = sk_Xp(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['43'])).
1.92/2.11	tff('45', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('46', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['45'])).
1.92/2.11	tff('47', plain,
1.92/2.11	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '46'])).
1.92/2.11	tff('48', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xy1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['47', '4'])).
1.92/2.11	tff('49', plain, (sk_S2(sk_Xy1) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['48'])).
1.92/2.11	tff('50', plain, (sk_S1 = sk_Xp(sk_Xx) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('clc', [status(thm)], ['44', '49'])).
1.92/2.11	tff('51', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xx, X1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['50'])).
1.92/2.11	tff('52', plain,
1.92/2.11	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup+', [status(thm)], ['16', '51'])).
1.92/2.11	tff('53', plain, ![X0 : a]: (sk_S2(sk_Xy1) | sk_S1(X0) = sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['52'])).
1.92/2.11	tff('54', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S1(sk_Xz)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('55', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['54'])).
1.92/2.11	tff('56', plain,
1.92/2.11	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '55'])).
1.92/2.11	tff('57', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xy1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['56', '4'])).
1.92/2.11	tff('58', plain, (sk_S2(sk_Xy1) | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['57'])).
1.92/2.11	tff('59', plain, (sk_S(sk_Xz) | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup+', [status(thm)], ['53', '58'])).
1.92/2.11	tff('60', plain, (sk_S2(sk_Xy1) | sk_S(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['59'])).
1.92/2.11	tff('61', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xy1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xz)),
1.92/2.11	    inference('sup-', [status(thm)], ['60', '7'])).
1.92/2.11	tff('62', plain, (sk_S = sk_Xp(sk_Xz) | ~ sk_P(sk_S) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('simplify', [status(thm)], ['61'])).
1.92/2.11	tff('63', plain, (sk_S2(sk_Xy1) | sk_S = sk_Xp(sk_Xz)),
1.92/2.11	    inference('clc', [status(thm)], ['62', '14'])).
1.92/2.11	tff('64', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xz, X1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['63'])).
1.92/2.11	tff('65', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xz))
1.92/2.11	       | sk_Xp(sk_Xz) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['64', '7'])).
1.92/2.11	tff('66', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0) | sk_S2(sk_Xy1) | ~ $true | sk_Xp(sk_Xz) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['65', '4'])).
1.92/2.11	tff('67', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xz) = sk_Xp(X0) | sk_S2(sk_Xy1) | ~ sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['66'])).
1.92/2.11	tff('68', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (sk_Xp(sk_Xz) = sk_Xp(sk_Xx)
1.92/2.11	       | ~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup+', [status(thm)], ['19', '67'])).
1.92/2.11	tff('69', plain,
1.92/2.11	    ![X0 : a]: (sk_S2(sk_Xy1) | ~ sk_S(X0) | sk_Xp(sk_Xz) = sk_Xp(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['68'])).
1.92/2.11	tff('70', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xy1) | sk_Xp(sk_Xz) = sk_Xp(sk_Xx) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup-', [status(thm)], ['6', '69'])).
1.92/2.11	tff('71', plain, (sk_Xp(sk_Xz) = sk_Xp(sk_Xx) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('simplify', [status(thm)], ['70'])).
1.92/2.11	tff('72', plain,
1.92/2.11	    ![X1 : a]: (sk_Xp(sk_Xz, X1) = sk_Xp(sk_Xx, X1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['71'])).
1.92/2.11	tff('73', plain, (sk_Xp(sk_Xx, sk_Xz) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup+', [status(thm)], ['72', '0'])).
1.92/2.11	tff('74', plain,
1.92/2.11	    ![X2 : a > $o, X4 : a > $o]:
1.92/2.11	      (~ sk_P(X4)
1.92/2.11	       | ~ X4(sk_Xx)
1.92/2.11	       | ~ X4(sk_Xz)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('75', plain,
1.92/2.11	    ![X2 : a > $o, X4 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ X4(sk_Xz)
1.92/2.11	       | ~ X4(sk_Xx)
1.92/2.11	       | ~ sk_P(X4)),
1.92/2.11	    inference('simplify', [status(thm)], ['74'])).
1.92/2.11	tff('76', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '75'])).
1.92/2.11	tff('77', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | sk_S2(sk_Xy1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['76', '4'])).
1.92/2.11	tff('78', plain,
1.92/2.11	    ![X0 : a > $o]: (sk_S2(sk_Xy1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['77'])).
1.92/2.11	tff('79', plain,
1.92/2.11	    (~ $true
1.92/2.11	     | sk_S2(sk_Xy1)
1.92/2.11	     | ~ sk_P(sk_Xp(sk_Xx))
1.92/2.11	     | ~ sk_Xp(sk_Xx, sk_Xx)
1.92/2.11	     | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup-', [status(thm)], ['73', '78'])).
1.92/2.11	tff('80', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xy1) | ~ $true | ~ $true | sk_S2(sk_Xy1)),
1.92/2.11	    inference('demod', [status(thm)], ['79', '4', '0'])).
1.92/2.11	tff('81', plain, sk_S2(sk_Xy1), inference('simplify', [status(thm)], ['80'])).
1.92/2.11	tff('82', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('sup-', [status(thm)], ['81', '7'])).
1.92/2.11	tff('83', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2)),
1.92/2.11	    inference('simplify', [status(thm)], ['82'])).
1.92/2.11	tff('84', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | ~ sk_P(sk_S2)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['83'])).
1.92/2.11	tff('85', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (sk_S1(sk_Xz)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('86', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['85'])).
1.92/2.11	tff('87', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_S1(sk_Xz)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '86'])).
1.92/2.11	tff('88', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_S1(sk_Xz)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['87', '4'])).
1.92/2.11	tff('89', plain,
1.92/2.11	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['88'])).
1.92/2.11	tff('90', plain,
1.92/2.11	    (~ $true | sk_S1(sk_Xz) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '89'])).
1.92/2.11	tff('91', plain,
1.92/2.11	    (~ $true | sk_S1(sk_Xz) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
1.92/2.11	    inference('demod', [status(thm)], ['90', '4'])).
1.92/2.11	tff('92', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['91'])).
1.92/2.11	tff('93', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('94', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['93'])).
1.92/2.11	tff('95', plain,
1.92/2.11	    (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '94'])).
1.92/2.11	tff('96', plain, (~ $true | sk_P(sk_S1) | sk_S2(sk_Xx1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['95', '4'])).
1.92/2.11	tff('97', plain, (sk_S2(sk_Xx1) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['96'])).
1.92/2.11	tff('98', plain,
1.92/2.11	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('sup-', [status(thm)], ['49', '7'])).
1.92/2.11	tff('99', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['98'])).
1.92/2.11	tff('100', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('101', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['100'])).
1.92/2.11	tff('102', plain,
1.92/2.11	    (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '101'])).
1.92/2.11	tff('103', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S2) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['102', '4'])).
1.92/2.11	tff('104', plain, (sk_P(sk_S2) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['103'])).
1.92/2.11	tff('105', plain, (sk_P(sk_S1) | sk_S2 = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('clc', [status(thm)], ['99', '104'])).
1.92/2.11	tff('106', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | sk_P(sk_S1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['105'])).
1.92/2.11	tff('107', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0)
1.92/2.11	       | sk_P(sk_S1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xy1))
1.92/2.11	       | sk_Xp(sk_Xy1) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['106', '7'])).
1.92/2.11	tff('108', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0) | sk_P(sk_S1) | ~ $true | sk_Xp(sk_Xy1) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['107', '4'])).
1.92/2.11	tff('109', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xy1) = sk_Xp(X0) | sk_P(sk_S1) | ~ sk_S2(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['108'])).
1.92/2.11	tff('110', plain,
1.92/2.11	    (~ $true | sk_P(sk_S1) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['97', '7'])).
1.92/2.11	tff('111', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['110'])).
1.92/2.11	tff('112', plain, (sk_P(sk_S1) | sk_S2 = sk_Xp(sk_Xx1)),
1.92/2.11	    inference('clc', [status(thm)], ['111', '104'])).
1.92/2.11	tff('113', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xx1, X1) | sk_P(sk_S1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['112'])).
1.92/2.11	tff('114', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0)
1.92/2.11	       | sk_P(sk_S1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx1))
1.92/2.11	       | sk_Xp(sk_Xx1) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['113', '7'])).
1.92/2.11	tff('115', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0) | sk_P(sk_S1) | ~ $true | sk_Xp(sk_Xx1) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['114', '4'])).
1.92/2.11	tff('116', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xx1) = sk_Xp(X0) | sk_P(sk_S1) | ~ sk_S2(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['115'])).
1.92/2.11	tff('117', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1)
1.92/2.11	       | ~ sk_S2(X0)
1.92/2.11	       | sk_P(sk_S1)
1.92/2.11	       | ~ sk_S2(X0)
1.92/2.11	       | sk_P(sk_S1)),
1.92/2.11	    inference('sup+', [status(thm)], ['109', '116'])).
1.92/2.11	tff('118', plain,
1.92/2.11	    ![X0 : a]: (sk_P(sk_S1) | ~ sk_S2(X0) | sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('simplify', [status(thm)], ['117'])).
1.92/2.11	tff('119', plain,
1.92/2.11	    (~ $true | sk_P(sk_S1) | sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1) | sk_P(sk_S1)),
1.92/2.11	    inference('sup-', [status(thm)], ['97', '118'])).
1.92/2.11	tff('120', plain, (sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['119'])).
1.92/2.11	tff('121', plain,
1.92/2.11	    ![X1 : a]: (sk_Xp(sk_Xx1, X1) = sk_Xp(sk_Xy1, X1) | sk_P(sk_S1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['120'])).
1.92/2.11	tff('122', plain, (sk_Xp(sk_Xx1, sk_Xy1) | sk_P(sk_S1)),
1.92/2.11	    inference('sup+', [status(thm)], ['121', '0'])).
1.92/2.11	tff('123', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (sk_P(sk_S1)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('124', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['123'])).
1.92/2.11	tff('125', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_P(sk_S1)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '124'])).
1.92/2.11	tff('126', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_P(sk_S1)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['125', '4'])).
1.92/2.11	tff('127', plain,
1.92/2.11	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S1)),
1.92/2.11	    inference('simplify', [status(thm)], ['126'])).
1.92/2.11	tff('128', plain,
1.92/2.11	    (~ $true
1.92/2.11	     | sk_P(sk_S1)
1.92/2.11	     | sk_P(sk_S1)
1.92/2.11	     | ~ sk_P(sk_Xp(sk_Xx1))
1.92/2.11	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['122', '127'])).
1.92/2.11	tff('129', plain, (~ $true | sk_P(sk_S1) | sk_P(sk_S1) | ~ $true | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['128', '4', '0'])).
1.92/2.11	tff('130', plain, sk_P(sk_S1), inference('simplify', [status(thm)], ['129'])).
1.92/2.11	tff('131', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('132', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['131'])).
1.92/2.11	tff('133', plain,
1.92/2.11	    (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '132'])).
1.92/2.11	tff('134', plain, (~ $true | sk_S(sk_Xx) | sk_S2(sk_Xx1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['133', '4'])).
1.92/2.11	tff('135', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['134'])).
1.92/2.11	tff('136', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.92/2.11	    inference('sup-', [status(thm)], ['135', '7'])).
1.92/2.11	tff('137', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('simplify', [status(thm)], ['136'])).
1.92/2.11	tff('138', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('139', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['138'])).
1.92/2.11	tff('140', plain,
1.92/2.11	    (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '139'])).
1.92/2.11	tff('141', plain, (~ $true | sk_P(sk_S) | sk_S2(sk_Xx1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['140', '4'])).
1.92/2.11	tff('142', plain, (sk_S2(sk_Xx1) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['141'])).
1.92/2.11	tff('143', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xx)),
1.92/2.11	    inference('clc', [status(thm)], ['137', '142'])).
1.92/2.11	tff('144', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S1(sk_Xy)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('145', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['144'])).
1.92/2.11	tff('146', plain,
1.92/2.11	    (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '145'])).
1.92/2.11	tff('147', plain, (~ $true | sk_S1(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['146', '4'])).
1.92/2.11	tff('148', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['147'])).
1.92/2.11	tff('149', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.92/2.11	    inference('sup-', [status(thm)], ['148', '7'])).
1.92/2.11	tff('150', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('simplify', [status(thm)], ['149'])).
1.92/2.11	tff('151', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xx, X1) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['143'])).
1.92/2.11	tff('152', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx))
1.92/2.11	       | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['151', '7'])).
1.92/2.11	tff('153', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0) | sk_S2(sk_Xx1) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['152', '4'])).
1.92/2.11	tff('154', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xx) = sk_Xp(X0) | sk_S2(sk_Xx1) | ~ sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['153'])).
1.92/2.11	tff('155', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('156', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['155'])).
1.92/2.11	tff('157', plain,
1.92/2.11	    (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '156'])).
1.92/2.11	tff('158', plain, (~ $true | sk_S(sk_Xy) | sk_S2(sk_Xx1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['157', '4'])).
1.92/2.11	tff('159', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['158'])).
1.92/2.11	tff('160', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xx1) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.92/2.11	    inference('sup-', [status(thm)], ['159', '7'])).
1.92/2.11	tff('161', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('simplify', [status(thm)], ['160'])).
1.92/2.11	tff('162', plain, (sk_S2(sk_Xx1) | sk_S = sk_Xp(sk_Xy)),
1.92/2.11	    inference('clc', [status(thm)], ['161', '142'])).
1.92/2.11	tff('163', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['162'])).
1.92/2.11	tff('164', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xy))
1.92/2.11	       | sk_Xp(sk_Xy) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['163', '7'])).
1.92/2.11	tff('165', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0) | sk_S2(sk_Xx1) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['164', '4'])).
1.92/2.11	tff('166', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xy) = sk_Xp(X0) | sk_S2(sk_Xx1) | ~ sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['165'])).
1.92/2.11	tff('167', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (sk_Xp(sk_Xy) = sk_Xp(sk_Xx)
1.92/2.11	       | ~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ sk_S(X0)
1.92/2.11	       | sk_S2(sk_Xx1)),
1.92/2.11	    inference('sup+', [status(thm)], ['154', '166'])).
1.92/2.11	tff('168', plain,
1.92/2.11	    ![X0 : a]: (sk_S2(sk_Xx1) | ~ sk_S(X0) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['167'])).
1.92/2.11	tff('169', plain,
1.92/2.11	    (~ $true | sk_S2(sk_Xx1) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['135', '168'])).
1.92/2.11	tff('170', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('simplify', [status(thm)], ['169'])).
1.92/2.11	tff('171', plain,
1.92/2.11	    (sk_S1 = sk_Xp(sk_Xx) | sk_S2(sk_Xx1) | ~ sk_P(sk_S1) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('sup+', [status(thm)], ['150', '170'])).
1.92/2.11	tff('172', plain, (~ sk_P(sk_S1) | sk_S2(sk_Xx1) | sk_S1 = sk_Xp(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['171'])).
1.92/2.11	tff('173', plain, (sk_S1 = sk_Xp(sk_Xx) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('clc', [status(thm)], ['172', '97'])).
1.92/2.11	tff('174', plain, (sk_S1 = sk_S | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('sup+', [status(thm)], ['143', '173'])).
1.92/2.11	tff('175', plain, (sk_S2(sk_Xx1) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['174'])).
1.92/2.11	tff('176', plain, (sk_S1 = sk_S | sk_S2(sk_Xy1) | sk_S2(sk_Xy1)),
1.92/2.11	    inference('sup+', [status(thm)], ['15', '50'])).
1.92/2.11	tff('177', plain, (sk_S2(sk_Xy1) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['176'])).
1.92/2.11	tff('178', plain,
1.92/2.11	    (~ $true | sk_S1 = sk_S | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('sup-', [status(thm)], ['177', '7'])).
1.92/2.11	tff('179', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['178'])).
1.92/2.11	tff('180', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('181', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['180'])).
1.92/2.11	tff('182', plain,
1.92/2.11	    (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '181'])).
1.92/2.11	tff('183', plain, (~ $true | sk_S(sk_Xy) | sk_P(sk_S2) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['182', '4'])).
1.92/2.11	tff('184', plain, (sk_P(sk_S2) | sk_S(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['183'])).
1.92/2.11	tff('185', plain,
1.92/2.11	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.92/2.11	    inference('sup-', [status(thm)], ['184', '7'])).
1.92/2.11	tff('186', plain, (sk_S = sk_Xp(sk_Xy) | ~ sk_P(sk_S) | sk_P(sk_S2)),
1.92/2.11	    inference('simplify', [status(thm)], ['185'])).
1.92/2.11	tff('187', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('188', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['187'])).
1.92/2.11	tff('189', plain,
1.92/2.11	    (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '188'])).
1.92/2.11	tff('190', plain, (~ $true | sk_P(sk_S) | sk_P(sk_S2) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['189', '4'])).
1.92/2.11	tff('191', plain, (sk_P(sk_S2) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['190'])).
1.92/2.11	tff('192', plain, (sk_P(sk_S2) | sk_S = sk_Xp(sk_Xy)),
1.92/2.11	    inference('clc', [status(thm)], ['186', '191'])).
1.92/2.11	tff('193', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('194', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S1(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['193'])).
1.92/2.11	tff('195', plain,
1.92/2.11	    (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '194'])).
1.92/2.11	tff('196', plain, (~ $true | sk_S1(sk_Xy) | sk_P(sk_S2) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['195', '4'])).
1.92/2.11	tff('197', plain, (sk_P(sk_S2) | sk_S1(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['196'])).
1.92/2.11	tff('198', plain,
1.92/2.11	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.92/2.11	    inference('sup-', [status(thm)], ['197', '7'])).
1.92/2.11	tff('199', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_P(sk_S2)),
1.92/2.11	    inference('simplify', [status(thm)], ['198'])).
1.92/2.11	tff('200', plain, (sk_S1 = sk_S | sk_P(sk_S2) | sk_P(sk_S2) | ~ sk_P(sk_S1)),
1.92/2.11	    inference('sup+', [status(thm)], ['192', '199'])).
1.92/2.11	tff('201', plain, (~ sk_P(sk_S1) | sk_P(sk_S2) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['200'])).
1.92/2.11	tff('202', plain, (~ $true | sk_P(sk_S2) | sk_S1 = sk_S | sk_P(sk_S2)),
1.92/2.11	    inference('sup-', [status(thm)], ['104', '201'])).
1.92/2.11	tff('203', plain, (sk_S1 = sk_S | sk_P(sk_S2)),
1.92/2.11	    inference('simplify', [status(thm)], ['202'])).
1.92/2.11	tff('204', plain, (sk_S1 = sk_S | sk_S2 = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('clc', [status(thm)], ['179', '203'])).
1.92/2.11	tff('205', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | sk_S1 = sk_S),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['204'])).
1.92/2.11	tff('206', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0)
1.92/2.11	       | sk_S1 = sk_S
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xy1))
1.92/2.11	       | sk_Xp(sk_Xy1) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['205', '7'])).
1.92/2.11	tff('207', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0) | sk_S1 = sk_S | ~ $true | sk_Xp(sk_Xy1) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['206', '4'])).
1.92/2.11	tff('208', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xy1) = sk_Xp(X0) | sk_S1 = sk_S | ~ sk_S2(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['207'])).
1.92/2.11	tff('209', plain,
1.92/2.11	    (~ $true | sk_S1 = sk_S | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['175', '7'])).
1.92/2.11	tff('210', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['209'])).
1.92/2.11	tff('211', plain, (sk_S1 = sk_S | sk_S2 = sk_Xp(sk_Xx1)),
1.92/2.11	    inference('clc', [status(thm)], ['210', '203'])).
1.92/2.11	tff('212', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xx1, X1) | sk_S1 = sk_S),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['211'])).
1.92/2.11	tff('213', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0)
1.92/2.11	       | sk_S1 = sk_S
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx1))
1.92/2.11	       | sk_Xp(sk_Xx1) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['212', '7'])).
1.92/2.11	tff('214', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0) | sk_S1 = sk_S | ~ $true | sk_Xp(sk_Xx1) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['213', '4'])).
1.92/2.11	tff('215', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xx1) = sk_Xp(X0) | sk_S1 = sk_S | ~ sk_S2(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['214'])).
1.92/2.11	tff('216', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1)
1.92/2.11	       | ~ sk_S2(X0)
1.92/2.11	       | sk_S1 = sk_S
1.92/2.11	       | ~ sk_S2(X0)
1.92/2.11	       | sk_S1 = sk_S),
1.92/2.11	    inference('sup+', [status(thm)], ['208', '215'])).
1.92/2.11	tff('217', plain,
1.92/2.11	    ![X0 : a]: (sk_S1 = sk_S | ~ sk_S2(X0) | sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('simplify', [status(thm)], ['216'])).
1.92/2.11	tff('218', plain,
1.92/2.11	    (~ $true | sk_S1 = sk_S | sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1) | sk_S1 = sk_S),
1.92/2.11	    inference('sup-', [status(thm)], ['175', '217'])).
1.92/2.11	tff('219', plain, (sk_Xp(sk_Xx1) = sk_Xp(sk_Xy1) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['218'])).
1.92/2.11	tff('220', plain,
1.92/2.11	    ![X1 : a]: (sk_Xp(sk_Xx1, X1) = sk_Xp(sk_Xy1, X1) | sk_S1 = sk_S),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['219'])).
1.92/2.11	tff('221', plain, (sk_Xp(sk_Xx1, sk_Xy1) | sk_S1 = sk_S),
1.92/2.11	    inference('sup+', [status(thm)], ['220', '0'])).
1.92/2.11	tff('222', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (sk_S(sk_Xy)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('223', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | sk_S(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['222'])).
1.92/2.11	tff('224', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_S(sk_Xy)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '223'])).
1.92/2.11	tff('225', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_S(sk_Xy)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['224', '4'])).
1.92/2.11	tff('226', plain,
1.92/2.11	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['225'])).
1.92/2.11	tff('227', plain,
1.92/2.11	    (~ $true
1.92/2.11	     | sk_S1 = sk_S
1.92/2.11	     | sk_S(sk_Xy)
1.92/2.11	     | ~ sk_P(sk_Xp(sk_Xx1))
1.92/2.11	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['221', '226'])).
1.92/2.11	tff('228', plain, (~ $true | sk_S1 = sk_S | sk_S(sk_Xy) | ~ $true | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['227', '4', '0'])).
1.92/2.11	tff('229', plain, (sk_S(sk_Xy) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['228'])).
1.92/2.11	tff('230', plain,
1.92/2.11	    (~ $true | sk_S1 = sk_S | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xy)),
1.92/2.11	    inference('sup-', [status(thm)], ['229', '7'])).
1.92/2.11	tff('231', plain,
1.92/2.11	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('sup-', [status(thm)], ['14', '7'])).
1.92/2.11	tff('232', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['231'])).
1.92/2.11	tff('233', plain,
1.92/2.11	    ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | sk_P(sk_S) | ~ sk_P(sk_S2)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['232'])).
1.92/2.11	tff('234', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0)
1.92/2.11	       | ~ sk_P(sk_S2)
1.92/2.11	       | sk_P(sk_S)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xy1))
1.92/2.11	       | sk_Xp(sk_Xy1) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['233', '7'])).
1.92/2.11	tff('235', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S2(X0)
1.92/2.11	       | ~ sk_P(sk_S2)
1.92/2.11	       | sk_P(sk_S)
1.92/2.11	       | ~ $true
1.92/2.11	       | sk_Xp(sk_Xy1) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['234', '4'])).
1.92/2.11	tff('236', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (sk_Xp(sk_Xy1) = sk_Xp(X0) | sk_P(sk_S) | ~ sk_P(sk_S2) | ~ sk_S2(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['235'])).
1.92/2.11	tff('237', plain,
1.92/2.11	    ![X0 : a, X1 : a]:
1.92/2.11	      (sk_Xp(sk_Xy1, X1) = sk_Xp(X0, X1)
1.92/2.11	       | ~ sk_S2(X0)
1.92/2.11	       | ~ sk_P(sk_S2)
1.92/2.11	       | sk_P(sk_S)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['236'])).
1.92/2.11	tff('238', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(X0, sk_Xy1) | sk_P(sk_S) | ~ sk_P(sk_S2) | ~ sk_S2(X0)),
1.92/2.11	    inference('sup+', [status(thm)], ['237', '0'])).
1.92/2.11	tff('239', plain,
1.92/2.11	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['142', '7'])).
1.92/2.11	tff('240', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['239'])).
1.92/2.11	tff('241', plain,
1.92/2.11	    ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xx1, X1) | sk_P(sk_S) | ~ sk_P(sk_S2)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['240'])).
1.92/2.11	tff('242', plain,
1.92/2.11	    (sk_S2(sk_Xy1) = $true
1.92/2.11	     | ~ sk_S2(sk_Xx1)
1.92/2.11	     | ~ sk_P(sk_S2)
1.92/2.11	     | sk_P(sk_S)
1.92/2.11	     | ~ sk_P(sk_S2)
1.92/2.11	     | sk_P(sk_S)),
1.92/2.11	    inference('sup+', [status(thm)], ['238', '241'])).
1.92/2.11	tff('243', plain,
1.92/2.11	    (sk_P(sk_S) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1) | sk_S2(sk_Xy1) = $true),
1.92/2.11	    inference('simplify', [status(thm)], ['242'])).
1.92/2.11	tff('244', plain, (sk_S2(sk_Xy1) = $true | ~ sk_S2(sk_Xx1) | sk_P(sk_S)),
1.92/2.11	    inference('clc', [status(thm)], ['243', '191'])).
1.92/2.11	tff('245', plain, (sk_P(sk_S) | sk_S2(sk_Xy1) = $true),
1.92/2.11	    inference('clc', [status(thm)], ['244', '142'])).
1.92/2.11	tff('246', plain,
1.92/2.11	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('sup-', [status(thm)], ['245', '7'])).
1.92/2.11	tff('247', plain, (sk_S2 = sk_Xp(sk_Xy1) | ~ sk_P(sk_S2) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['246'])).
1.92/2.11	tff('248', plain, (sk_P(sk_S) | sk_S2 = sk_Xp(sk_Xy1)),
1.92/2.11	    inference('clc', [status(thm)], ['247', '191'])).
1.92/2.11	tff('249', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xy1, X1) | sk_P(sk_S)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['248'])).
1.92/2.11	tff('250', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (sk_P(sk_S)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('251', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['250'])).
1.92/2.11	tff('252', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_P(sk_S)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '251'])).
1.92/2.11	tff('253', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_P(sk_S)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['252', '4'])).
1.92/2.11	tff('254', plain,
1.92/2.11	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['253'])).
1.92/2.11	tff('255', plain,
1.92/2.11	    (~ $true | sk_P(sk_S) | ~ sk_P(sk_Xp(sk_Xy1)) | ~ sk_Xp(sk_Xy1, sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '254'])).
1.92/2.11	tff('256', plain, (~ $true | sk_P(sk_S) | ~ $true | ~ sk_Xp(sk_Xy1, sk_Xx1)),
1.92/2.11	    inference('demod', [status(thm)], ['255', '4'])).
1.92/2.11	tff('257', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_P(sk_S)),
1.92/2.11	    inference('simplify', [status(thm)], ['256'])).
1.92/2.11	tff('258', plain, (~ sk_S2(sk_Xx1) | sk_P(sk_S) | sk_P(sk_S)),
1.92/2.11	    inference('sup-', [status(thm)], ['249', '257'])).
1.92/2.11	tff('259', plain, (sk_P(sk_S) | ~ sk_S2(sk_Xx1)),
1.92/2.11	    inference('simplify', [status(thm)], ['258'])).
1.92/2.11	tff('260', plain, sk_P(sk_S), inference('clc', [status(thm)], ['259', '142'])).
1.92/2.11	tff('261', plain, (~ $true | sk_S1 = sk_S | ~ $true | sk_S = sk_Xp(sk_Xy)),
1.92/2.11	    inference('demod', [status(thm)], ['230', '260'])).
1.92/2.11	tff('262', plain, (sk_S = sk_Xp(sk_Xy) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['261'])).
1.92/2.11	tff('263', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (sk_S1(sk_Xy)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('264', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | sk_S1(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['263'])).
1.92/2.11	tff('265', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_S1(sk_Xy)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '264'])).
1.92/2.11	tff('266', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_S1(sk_Xy)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['265', '4'])).
1.92/2.11	tff('267', plain,
1.92/2.11	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S1(sk_Xy)),
1.92/2.11	    inference('simplify', [status(thm)], ['266'])).
1.92/2.11	tff('268', plain,
1.92/2.11	    (~ $true
1.92/2.11	     | sk_S1 = sk_S
1.92/2.11	     | sk_S1(sk_Xy)
1.92/2.11	     | ~ sk_P(sk_Xp(sk_Xx1))
1.92/2.11	     | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['221', '267'])).
1.92/2.11	tff('269', plain,
1.92/2.11	    (~ $true | sk_S1 = sk_S | sk_S1(sk_Xy) | ~ $true | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['268', '4', '0'])).
1.92/2.11	tff('270', plain, (sk_S1(sk_Xy) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['269'])).
1.92/2.11	tff('271', plain,
1.92/2.11	    (~ $true | sk_S1 = sk_S | ~ sk_P(sk_S1) | sk_S1 = sk_Xp(sk_Xy)),
1.92/2.11	    inference('sup-', [status(thm)], ['270', '7'])).
1.92/2.11	tff('272', plain, (sk_S1 = sk_Xp(sk_Xy) | ~ sk_P(sk_S1) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['271'])).
1.92/2.11	tff('273', plain,
1.92/2.11	    (sk_S1 = sk_S | sk_S1 = sk_S | sk_S1 = sk_S | ~ sk_P(sk_S1)),
1.92/2.11	    inference('sup+', [status(thm)], ['262', '272'])).
1.92/2.11	tff('274', plain, (~ sk_P(sk_S1) | sk_S1 = sk_S),
1.92/2.11	    inference('simplify', [status(thm)], ['273'])).
1.92/2.11	tff('275', plain, (~ $true | sk_S1 = sk_S),
1.92/2.11	    inference('sup-', [status(thm)], ['130', '274'])).
1.92/2.11	tff('276', plain, sk_S1 = sk_S, inference('simplify', [status(thm)], ['275'])).
1.92/2.11	tff('277', plain, ![X1 : a]: sk_S1(X1) = sk_S(X1),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['276'])).
1.92/2.11	tff('278', plain, (~ sk_Xp(sk_Xy1, sk_Xx1) | sk_S(sk_Xz)),
1.92/2.11	    inference('demod', [status(thm)], ['92', '277'])).
1.92/2.11	tff('279', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xz)),
1.92/2.11	    inference('sup-', [status(thm)], ['84', '278'])).
1.92/2.11	tff('280', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xx, X1) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['173'])).
1.92/2.11	tff('281', plain,
1.92/2.11	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('sup+', [status(thm)], ['151', '280'])).
1.92/2.11	tff('282', plain, ![X0 : a]: (sk_S2(sk_Xx1) | sk_S1(X0) = sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['281'])).
1.92/2.11	tff('283', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S1(sk_Xz)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('284', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['283'])).
1.92/2.11	tff('285', plain,
1.92/2.11	    (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '284'])).
1.92/2.11	tff('286', plain, (~ $true | sk_S1(sk_Xz) | sk_S2(sk_Xx1) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['285', '4'])).
1.92/2.11	tff('287', plain, (sk_S2(sk_Xx1) | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['286'])).
1.92/2.11	tff('288', plain, (sk_S(sk_Xz) | sk_S2(sk_Xx1) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('sup+', [status(thm)], ['282', '287'])).
1.92/2.11	tff('289', plain, (sk_S2(sk_Xx1) | sk_S(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['288'])).
1.92/2.11	tff('290', plain, (sk_S(sk_Xz) | ~ sk_P(sk_S2)),
1.92/2.11	    inference('clc', [status(thm)], ['279', '289'])).
1.92/2.11	tff('291', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('292', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['291'])).
1.92/2.11	tff('293', plain,
1.92/2.11	    (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '292'])).
1.92/2.11	tff('294', plain, (~ $true | sk_S(sk_Xx) | sk_P(sk_S2) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['293', '4'])).
1.92/2.11	tff('295', plain, (sk_P(sk_S2) | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['294'])).
1.92/2.11	tff('296', plain,
1.92/2.11	    (~ $true | sk_P(sk_S2) | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.92/2.11	    inference('sup-', [status(thm)], ['295', '7'])).
1.92/2.11	tff('297', plain, (sk_S = sk_Xp(sk_Xx) | ~ sk_P(sk_S) | sk_P(sk_S2)),
1.92/2.11	    inference('simplify', [status(thm)], ['296'])).
1.92/2.11	tff('298', plain, (sk_P(sk_S2) | sk_S = sk_Xp(sk_Xx)),
1.92/2.11	    inference('clc', [status(thm)], ['297', '191'])).
1.92/2.11	tff('299', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xx, X1) | sk_P(sk_S2)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['298'])).
1.92/2.11	tff('300', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0)
1.92/2.11	       | sk_P(sk_S2)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx))
1.92/2.11	       | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['299', '7'])).
1.92/2.11	tff('301', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0) | sk_P(sk_S2) | ~ $true | sk_Xp(sk_Xx) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['300', '4'])).
1.92/2.11	tff('302', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xx) = sk_Xp(X0) | sk_P(sk_S2) | ~ sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['301'])).
1.92/2.11	tff('303', plain, ![X1 : a]: (sk_S(X1) = sk_Xp(sk_Xy, X1) | sk_P(sk_S2)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['192'])).
1.92/2.11	tff('304', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0)
1.92/2.11	       | sk_P(sk_S2)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xy))
1.92/2.11	       | sk_Xp(sk_Xy) = sk_Xp(X0)),
1.92/2.11	    inference('sup-', [status(thm)], ['303', '7'])).
1.92/2.11	tff('305', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (~ sk_S(X0) | sk_P(sk_S2) | ~ $true | sk_Xp(sk_Xy) = sk_Xp(X0)),
1.92/2.11	    inference('demod', [status(thm)], ['304', '4'])).
1.92/2.11	tff('306', plain,
1.92/2.11	    ![X0 : a]: (sk_Xp(sk_Xy) = sk_Xp(X0) | sk_P(sk_S2) | ~ sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['305'])).
1.92/2.11	tff('307', plain,
1.92/2.11	    ![X0 : a]:
1.92/2.11	      (sk_Xp(sk_Xy) = sk_Xp(sk_Xx)
1.92/2.11	       | ~ sk_S(X0)
1.92/2.11	       | sk_P(sk_S2)
1.92/2.11	       | ~ sk_S(X0)
1.92/2.11	       | sk_P(sk_S2)),
1.92/2.11	    inference('sup+', [status(thm)], ['302', '306'])).
1.92/2.11	tff('308', plain,
1.92/2.11	    ![X0 : a]: (sk_P(sk_S2) | ~ sk_S(X0) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['307'])).
1.92/2.11	tff('309', plain,
1.92/2.11	    (~ $true | sk_P(sk_S2) | sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_P(sk_S2)),
1.92/2.11	    inference('sup-', [status(thm)], ['295', '308'])).
1.92/2.11	tff('310', plain, (sk_Xp(sk_Xy) = sk_Xp(sk_Xx) | sk_P(sk_S2)),
1.92/2.11	    inference('simplify', [status(thm)], ['309'])).
1.92/2.11	tff('311', plain,
1.92/2.11	    (sk_S1 = sk_Xp(sk_Xx) | sk_P(sk_S2) | ~ sk_P(sk_S1) | sk_P(sk_S2)),
1.92/2.11	    inference('sup+', [status(thm)], ['199', '310'])).
1.92/2.11	tff('312', plain, (~ sk_P(sk_S1) | sk_P(sk_S2) | sk_S1 = sk_Xp(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['311'])).
1.92/2.11	tff('313', plain, (sk_S1 = sk_Xp(sk_Xx) | sk_P(sk_S2)),
1.92/2.11	    inference('clc', [status(thm)], ['312', '104'])).
1.92/2.11	tff('314', plain, ![X1 : a]: (sk_S1(X1) = sk_Xp(sk_Xx, X1) | sk_P(sk_S2)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['313'])).
1.92/2.11	tff('315', plain,
1.92/2.11	    ![X0 : a]: (sk_S1(X0) = sk_S(X0) | sk_P(sk_S2) | sk_P(sk_S2)),
1.92/2.11	    inference('sup+', [status(thm)], ['299', '314'])).
1.92/2.11	tff('316', plain, ![X0 : a]: (sk_P(sk_S2) | sk_S1(X0) = sk_S(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['315'])).
1.92/2.11	tff('317', plain,
1.92/2.11	    ![X2 : a > $o]:
1.92/2.11	      (sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(X2) | ~ X2(sk_Xx2) | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('318', plain,
1.92/2.11	    ![X2 : a > $o]: (~ X2(sk_Xx2) | ~ sk_P(X2) | sk_P(sk_S2) | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['317'])).
1.92/2.11	tff('319', plain,
1.92/2.11	    (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '318'])).
1.92/2.11	tff('320', plain, (~ $true | sk_S1(sk_Xz) | sk_P(sk_S2) | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['319', '4'])).
1.92/2.11	tff('321', plain, (sk_P(sk_S2) | sk_S1(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['320'])).
1.92/2.11	tff('322', plain, (sk_S(sk_Xz) | sk_P(sk_S2) | sk_P(sk_S2)),
1.92/2.11	    inference('sup+', [status(thm)], ['316', '321'])).
1.92/2.11	tff('323', plain, (sk_P(sk_S2) | sk_S(sk_Xz)),
1.92/2.11	    inference('simplify', [status(thm)], ['322'])).
1.92/2.11	tff('324', plain, sk_S(sk_Xz),
1.92/2.11	    inference('clc', [status(thm)], ['290', '323'])).
1.92/2.11	tff('325', plain,
1.92/2.11	    ![X2 : a > $o, X4 : a > $o]:
1.92/2.11	      (~ sk_P(X4)
1.92/2.11	       | ~ X4(sk_Xx)
1.92/2.11	       | ~ X4(sk_Xz)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('326', plain,
1.92/2.11	    ![X2 : a > $o, X4 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ X4(sk_Xz)
1.92/2.11	       | ~ X4(sk_Xx)
1.92/2.11	       | ~ sk_P(X4)),
1.92/2.11	    inference('simplify', [status(thm)], ['325'])).
1.92/2.11	tff('327', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '326'])).
1.92/2.11	tff('328', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | sk_S2(sk_Xx1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['327', '4'])).
1.92/2.11	tff('329', plain,
1.92/2.11	    ![X0 : a > $o]: (sk_S2(sk_Xx1) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['328'])).
1.92/2.11	tff('330', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_S2(sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['324', '329'])).
1.92/2.11	tff('331', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (sk_S(sk_Xx)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('332', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['331'])).
1.92/2.11	tff('333', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_S(sk_Xx)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '332'])).
1.92/2.11	tff('334', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | sk_S(sk_Xx)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xy1)
1.92/2.11	       | ~ X0(sk_Xx1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['333', '4'])).
1.92/2.11	tff('335', plain,
1.92/2.11	    ![X0 : a > $o]: (~ X0(sk_Xx1) | ~ X0(sk_Xy1) | ~ sk_P(X0) | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['334'])).
1.92/2.11	tff('336', plain, (~ $true | sk_S(sk_Xx) | ~ sk_P(sk_S2) | ~ sk_S2(sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['81', '335'])).
1.92/2.11	tff('337', plain, (~ sk_S2(sk_Xx1) | ~ sk_P(sk_S2) | sk_S(sk_Xx)),
1.92/2.11	    inference('simplify', [status(thm)], ['336'])).
1.92/2.11	tff('338', plain, (sk_S(sk_Xx) | ~ sk_P(sk_S2)),
1.92/2.11	    inference('clc', [status(thm)], ['337', '135'])).
1.92/2.11	tff('339', plain, sk_S(sk_Xx),
1.92/2.11	    inference('clc', [status(thm)], ['338', '295'])).
1.92/2.11	tff('340', plain, (~ $true | ~ sk_P(sk_S) | sk_S = sk_Xp(sk_Xx)),
1.92/2.11	    inference('sup-', [status(thm)], ['339', '7'])).
1.92/2.11	tff('341', plain, (~ $true | ~ $true | sk_S = sk_Xp(sk_Xx)),
1.92/2.11	    inference('demod', [status(thm)], ['340', '260'])).
1.92/2.11	tff('342', plain, sk_S = sk_Xp(sk_Xx),
1.92/2.11	    inference('simplify', [status(thm)], ['341'])).
1.92/2.11	tff('343', plain, ![X1 : a]: sk_S(X1) = sk_Xp(sk_Xx, X1),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['342'])).
1.92/2.11	tff('344', plain, sk_S(sk_Xx) = $true,
1.92/2.11	    inference('sup+', [status(thm)], ['0', '343'])).
1.92/2.11	tff('345', plain, (~ $true | ~ $true | ~ $true | sk_S2(sk_Xx1)),
1.92/2.11	    inference('demod', [status(thm)], ['330', '260', '344'])).
1.92/2.11	tff('346', plain, sk_S2(sk_Xx1),
1.92/2.11	    inference('simplify', [status(thm)], ['345'])).
1.92/2.11	tff('347', plain, (~ $true | ~ sk_P(sk_S2) | sk_S2 = sk_Xp(sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['346', '7'])).
1.92/2.11	tff('348', plain, (sk_S2 = sk_Xp(sk_Xx1) | ~ sk_P(sk_S2)),
1.92/2.11	    inference('simplify', [status(thm)], ['347'])).
1.92/2.11	tff('349', plain, ![X1 : a]: (sk_S2(X1) = sk_Xp(sk_Xx1, X1) | ~ sk_P(sk_S2)),
1.92/2.11	    inference('ho_complete_eq', [status(thm)], ['348'])).
1.92/2.11	tff('350', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o, X4 : a > $o]:
1.92/2.11	      (~ sk_P(X4)
1.92/2.11	       | ~ X4(sk_Xx)
1.92/2.11	       | ~ X4(sk_Xz)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('351', plain,
1.92/2.11	    ![X2 : a > $o, X3 : a > $o, X4 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X3(sk_Xx1)
1.92/2.11	       | ~ X3(sk_Xy1)
1.92/2.11	       | ~ sk_P(X3)
1.92/2.11	       | ~ X4(sk_Xz)
1.92/2.11	       | ~ X4(sk_Xx)
1.92/2.11	       | ~ sk_P(X4)),
1.92/2.11	    inference('simplify', [status(thm)], ['350'])).
1.92/2.11	tff('352', plain,
1.92/2.11	    ![X0 : a > $o, X1 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | ~ sk_P(X1)
1.92/2.11	       | ~ X1(sk_Xy1)
1.92/2.11	       | ~ X1(sk_Xx1)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '351'])).
1.92/2.11	tff('353', plain,
1.92/2.11	    ![X0 : a > $o, X1 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | ~ sk_P(X1)
1.92/2.11	       | ~ X1(sk_Xy1)
1.92/2.11	       | ~ X1(sk_Xx1)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['352', '4'])).
1.92/2.11	tff('354', plain,
1.92/2.11	    ![X0 : a > $o, X1 : a > $o]:
1.92/2.11	      (~ X1(sk_Xx1)
1.92/2.11	       | ~ X1(sk_Xy1)
1.92/2.11	       | ~ sk_P(X1)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ sk_P(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['353'])).
1.92/2.11	tff('355', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ sk_S2(sk_Xy1)
1.92/2.11	       | ~ sk_P(sk_S2)
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx1))
1.92/2.11	       | ~ sk_Xp(sk_Xx1, sk_Xx1)),
1.92/2.11	    inference('sup-', [status(thm)], ['349', '354'])).
1.92/2.11	tff('356', plain,
1.92/2.11	    ![X2 : a > $o, X4 : a > $o]:
1.92/2.11	      (~ sk_P(X4)
1.92/2.11	       | ~ X4(sk_Xx)
1.92/2.11	       | ~ X4(sk_Xz)
1.92/2.11	       | sk_P(sk_S2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | ~ X2(sk_Xx2)
1.92/2.11	       | ~ X2(sk_Xx2)),
1.92/2.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
1.92/2.11	tff('357', plain,
1.92/2.11	    ![X2 : a > $o, X4 : a > $o]:
1.92/2.11	      (~ X2(sk_Xx2)
1.92/2.11	       | ~ sk_P(X2)
1.92/2.11	       | sk_P(sk_S2)
1.92/2.11	       | ~ X4(sk_Xz)
1.92/2.11	       | ~ X4(sk_Xx)
1.92/2.11	       | ~ sk_P(X4)),
1.92/2.11	    inference('simplify', [status(thm)], ['356'])).
1.92/2.11	tff('358', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | sk_P(sk_S2)
1.92/2.11	       | ~ sk_P(sk_Xp(sk_Xx2))),
1.92/2.11	    inference('sup-', [status(thm)], ['0', '357'])).
1.92/2.11	tff('359', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | sk_P(sk_S2)
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['358', '4'])).
1.92/2.11	tff('360', plain,
1.92/2.11	    ![X0 : a > $o]: (sk_P(sk_S2) | ~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['359'])).
1.92/2.11	tff('361', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx) | sk_P(sk_S2)),
1.92/2.11	    inference('sup-', [status(thm)], ['324', '360'])).
1.92/2.11	tff('362', plain, (~ $true | ~ $true | ~ $true | sk_P(sk_S2)),
1.92/2.11	    inference('demod', [status(thm)], ['361', '260', '344'])).
1.92/2.11	tff('363', plain, sk_P(sk_S2), inference('simplify', [status(thm)], ['362'])).
1.92/2.11	tff('364', plain,
1.92/2.11	    ![X0 : a > $o]:
1.92/2.11	      (~ $true
1.92/2.11	       | ~ $true
1.92/2.11	       | ~ sk_P(X0)
1.92/2.11	       | ~ X0(sk_Xx)
1.92/2.11	       | ~ X0(sk_Xz)
1.92/2.11	       | ~ $true
1.92/2.11	       | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['355', '81', '363', '4', '0'])).
1.92/2.11	tff('365', plain, ![X0 : a > $o]: (~ X0(sk_Xz) | ~ X0(sk_Xx) | ~ sk_P(X0)),
1.92/2.11	    inference('simplify', [status(thm)], ['364'])).
1.92/2.11	tff('366', plain, (~ $true | ~ sk_P(sk_S) | ~ sk_S(sk_Xx)),
1.92/2.11	    inference('sup-', [status(thm)], ['324', '365'])).
1.92/2.11	tff('367', plain, (~ $true | ~ $true | ~ $true),
1.92/2.11	    inference('demod', [status(thm)], ['366', '260', '344'])).
1.92/2.11	tff('368', plain, $false, inference('simplify', [status(thm)], ['367'])).
1.92/2.11	
1.92/2.11	% SZS output end Refutation
1.92/2.11	EOF
