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    : purification_ext
0.00/0.00	% Ordering    : kbo
0.00/0.00	% Command    : 
0.00/0.00	#!/bin/sh
0.00/0.00	
0.00/0.00	./zipperposition.native ${1:+"$1"} \
0.00/0.00	  -i tptp \
0.00/0.00	  -o tptp \
0.00/0.00	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.00	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.00	  --no-avatar \
0.00/0.00	  --ho \
0.00/0.00	  --force-ho \
0.00/0.00	  --no-ho-elim-pred-var \
0.00/0.00	  --ho-general-ext-pos \
0.00/0.00	  --no-ho-unif \
0.00/0.00	  --no-induction \
0.00/0.00	  --no-unif-pattern \
0.00/0.00	  --ord $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
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   : n104.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 10:05:08 CST 2018
217.98/218.23	% done 16944 iterations in 218.024s
217.98/218.23	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
217.98/218.23	% SZS output start Refutation
217.98/218.23	tff(conj_3, conjecture,
217.98/218.23	  (![N:nat]:
217.98/218.23	     ((![X:hoare_28830079triple(a)]:
217.98/218.23	         (pp(aa(fun(hoare_28830079triple(a),bool),bool,
217.98/218.23	                aa(hoare_28830079triple(a),
217.98/218.23	                   fun(fun(hoare_28830079triple(a),bool),bool),
217.98/218.23	                   member(hoare_28830079triple(a)),X),
217.98/218.23	                tsa)) =>
217.98/218.23	          hoare_1633586161_valid(a,N,X))) | 
217.98/218.23	      (?[X1:hoare_28830079triple(a)]:
217.98/218.23	         ((~hoare_1633586161_valid(a,N,X1)) & 
217.98/218.23	          pp(aa(fun(hoare_28830079triple(a),bool),bool,
217.98/218.23	                aa(hoare_28830079triple(a),
217.98/218.23	                   fun(fun(hoare_28830079triple(a),bool),bool),
217.98/218.23	                   member(hoare_28830079triple(a)),X1),
217.98/218.23	                ga))))))).
217.98/218.23	tff(zf_stmt_0, negated_conjecture,
217.98/218.23	  (~
217.98/218.23	    (![N:nat]:
217.98/218.23	       ((![X:hoare_28830079triple(a)]:
217.98/218.23	           (pp(aa(fun(hoare_28830079triple(a),bool),bool,
217.98/218.23	                  aa(hoare_28830079triple(a),
217.98/218.23	                     fun(fun(hoare_28830079triple(a),bool),bool),
217.98/218.23	                     member(hoare_28830079triple(a)),X),
217.98/218.23	                  tsa)) =>
217.98/218.23	            hoare_1633586161_valid(a,N,X))) | 
217.98/218.23	        (?[X1:hoare_28830079triple(a)]:
217.98/218.23	           ((~hoare_1633586161_valid(a,N,X1)) & 
217.98/218.23	            pp(aa(fun(hoare_28830079triple(a),bool),bool,
217.98/218.23	                  aa(hoare_28830079triple(a),
217.98/218.23	                     fun(fun(hoare_28830079triple(a),bool),bool),
217.98/218.23	                     member(hoare_28830079triple(a)),X1),
217.98/218.23	                  ga)))))))).
217.98/218.23	tff('0', plain,
217.98/218.23	    pp(
217.98/218.23	      aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	        aa(hoare_28830079triple(a), 
217.98/218.23	          fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	          member(hoare_28830079triple(a)), sk_X11), tsa)),
217.98/218.23	    inference('cnf', [status(esa)], [zf_stmt_0])).
217.98/218.23	tff(help_COMBC_1_1_U, axiom,
217.98/218.23	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
217.98/218.23	     (aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q)))).
217.98/218.23	tff('1', plain,
217.98/218.23	    ![X350 : $tType, X351 : $tType, X352 : $tType, 
217.98/218.23	      X353 : fun(X352, fun(X350, X351)), X354 : X352, X355 : X350]:
217.98/218.23	      aa(X352, X351, combc(X352, X350, X351, X353, X355), X354)
217.98/218.23	       = aa(X350, X351, aa(X352, fun(X350, X351), X353, X354), X355),
217.98/218.23	    inference('cnf', [status(esa)], [help_COMBC_1_1_U])).
217.98/218.23	tff('2', plain,
217.98/218.23	    pp(
217.98/218.23	      aa(hoare_28830079triple(a), bool, 
217.98/218.23	        combc(hoare_28830079triple(a), fun(hoare_28830079triple(a), bool), 
217.98/218.23	          bool, member(hoare_28830079triple(a)), tsa), sk_X11)),
217.98/218.23	    inference('demod', [status(thm)], ['0', '1'])).
217.98/218.23	tff(fact_74_mem__def, axiom,
217.98/218.23	  (![B:$tType,A2:fun(B,bool),X2:B]:
217.98/218.23	     (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X2),A2)) <=>
217.98/218.23	      pp(aa(B,bool,A2,X2))))).
217.98/218.23	tff('3', plain,
217.98/218.23	    ![X262 : $tType, X263 : fun(X262, bool), X264 : X262]:
217.98/218.23	      (pp(aa(X262, bool, X263, X264))
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(fun(X262, bool), bool, 
217.98/218.23	               aa(X262, fun(fun(X262, bool), bool), member(X262), X264), 
217.98/218.23	               X263))),
217.98/218.23	    inference('cnf', [status(esa)], [fact_74_mem__def])).
217.98/218.23	tff('4', plain,
217.98/218.23	    ![X262 : $tType, X263 : fun(X262, bool), X264 : X262]:
217.98/218.23	      (pp(aa(X262, bool, X263, X264))
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(X262, bool, 
217.98/218.23	               combc(X262, fun(X262, bool), bool, member(X262), X263), X264))),
217.98/218.23	    inference('demod', [status(thm)], ['3', '1'])).
217.98/218.23	tff('5', plain,
217.98/218.23	    (~ $true | pp(aa(hoare_28830079triple(a), bool, tsa, sk_X11))),
217.98/218.23	    inference('sup-', [status(thm)], ['2', '4'])).
217.98/218.23	tff('6', plain, pp(aa(hoare_28830079triple(a), bool, tsa, sk_X11)),
217.98/218.23	    inference('simplify', [status(thm)], ['5'])).
217.98/218.23	tff(fact_13_rev__predicate1D, axiom,
217.98/218.23	  (![B:$tType,Q1:fun(B,bool),X2:B,P1:fun(B,bool)]:
217.98/218.23	     (pp(aa(B,bool,P1,X2)) =>
217.98/218.23	      (ord_less_eq(fun(B,bool),P1,Q1) => pp(aa(B,bool,Q1,X2)))))).
217.98/218.23	tff('7', plain,
217.98/218.23	    ![X53 : $tType, X54 : fun(X53, bool), X55 : X53, X56 : fun(X53, bool)]:
217.98/218.23	      (pp(aa(X53, bool, X54, X55))
217.98/218.23	       | ~ pp(aa(X53, bool, X56, X55))
217.98/218.23	       | ~ ord_less_eq(fun(X53, bool), X56, X54)),
217.98/218.23	    inference('cnf', [status(esa)], [fact_13_rev__predicate1D])).
217.98/218.23	tff('8', plain,
217.98/218.23	    ![X0 : fun(hoare_28830079triple(a), bool)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ~ ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, X0)
217.98/218.23	       | pp(aa(hoare_28830079triple(a), bool, X0, sk_X11))),
217.98/218.23	    inference('sup-', [status(thm)], ['6', '7'])).
217.98/218.23	tff('9', plain,
217.98/218.23	    ![X0 : fun(hoare_28830079triple(a), bool)]:
217.98/218.23	      (pp(aa(hoare_28830079triple(a), bool, X0, sk_X11))
217.98/218.23	       | ~ ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, X0)),
217.98/218.23	    inference('simplify', [status(thm)], ['8'])).
217.98/218.23	tff(conj_1, axiom,
217.98/218.23	  (![N1:nat]:
217.98/218.23	     ((![X:hoare_28830079triple(a)]:
217.98/218.23	         (pp(aa(fun(hoare_28830079triple(a),bool),bool,
217.98/218.23	                aa(hoare_28830079triple(a),
217.98/218.23	                   fun(fun(hoare_28830079triple(a),bool),bool),
217.98/218.23	                   member(hoare_28830079triple(a)),X),
217.98/218.23	                ga)) =>
217.98/218.23	          hoare_1633586161_valid(a,N1,X))) =>
217.98/218.23	      (![X1:hoare_28830079triple(a)]:
217.98/218.23	         (pp(aa(fun(hoare_28830079triple(a),bool),bool,
217.98/218.23	                aa(hoare_28830079triple(a),
217.98/218.23	                   fun(fun(hoare_28830079triple(a),bool),bool),
217.98/218.23	                   member(hoare_28830079triple(a)),X1),
217.98/218.23	                ts)) =>
217.98/218.23	          hoare_1633586161_valid(a,N1,X1)))))).
217.98/218.23	tff('10', plain,
217.98/218.23	    ![X356 : hoare_28830079triple(a), X357 : nat]:
217.98/218.23	      (~ pp(
217.98/218.23	           aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	             aa(hoare_28830079triple(a), 
217.98/218.23	               fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	               member(hoare_28830079triple(a)), X356), ts))
217.98/218.23	       | hoare_1633586161_valid(a, X357, X356)
217.98/218.23	       | pp(
217.98/218.23	           aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	             aa(hoare_28830079triple(a), 
217.98/218.23	               fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	               member(hoare_28830079triple(a)), sk_X10(X357)), ga))),
217.98/218.23	    inference('cnf', [status(esa)], [conj_1])).
217.98/218.23	tff('11', plain,
217.98/218.23	    ![X356 : hoare_28830079triple(a), X357 : nat]:
217.98/218.23	      (~ pp(
217.98/218.23	           aa(hoare_28830079triple(a), bool, 
217.98/218.23	             combc(hoare_28830079triple(a), 
217.98/218.23	               fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               member(hoare_28830079triple(a)), ts), X356))
217.98/218.23	       | hoare_1633586161_valid(a, X357, X356)
217.98/218.23	       | pp(
217.98/218.23	           aa(hoare_28830079triple(a), bool, 
217.98/218.23	             combc(hoare_28830079triple(a), 
217.98/218.23	               fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               member(hoare_28830079triple(a)), ga), sk_X10(X357)))),
217.98/218.23	    inference('demod', [status(thm)], ['10', '1', '1'])).
217.98/218.23	tff('12', plain,
217.98/218.23	    ![X0 : nat]:
217.98/218.23	      (~ $true
217.98/218.23	       | ~ ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, 
217.98/218.23	             combc(hoare_28830079triple(a), 
217.98/218.23	               fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               member(hoare_28830079triple(a)), ts))
217.98/218.23	       | pp(
217.98/218.23	           aa(hoare_28830079triple(a), bool, 
217.98/218.23	             combc(hoare_28830079triple(a), 
217.98/218.23	               fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               member(hoare_28830079triple(a)), ga), sk_X10(X0)))
217.98/218.23	       | hoare_1633586161_valid(a, X0, sk_X11)),
217.98/218.23	    inference('sup-', [status(thm)], ['9', '11'])).
217.98/218.23	tff('13', plain,
217.98/218.23	    ![X0 : nat]:
217.98/218.23	      (hoare_1633586161_valid(a, X0, sk_X11)
217.98/218.23	       | pp(
217.98/218.23	           aa(hoare_28830079triple(a), bool, 
217.98/218.23	             combc(hoare_28830079triple(a), 
217.98/218.23	               fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               member(hoare_28830079triple(a)), ga), sk_X10(X0)))
217.98/218.23	       | ~ ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, 
217.98/218.23	             combc(hoare_28830079triple(a), 
217.98/218.23	               fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               member(hoare_28830079triple(a)), ts))),
217.98/218.23	    inference('simplify', [status(thm)], ['12'])).
217.98/218.23	tff(fact_31_subsetI, axiom,
217.98/218.23	  (![B:$tType,B2:fun(B,bool),A2:fun(B,bool)]:
217.98/218.23	     ((![X:B]:
217.98/218.23	         (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X),A2)) =>
217.98/218.23	          pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X),B2)))) =>
217.98/218.23	      ord_less_eq(fun(B,bool),A2,B2)))).
217.98/218.23	tff('14', plain,
217.98/218.23	    ![X117 : $tType, X118 : fun(X117, bool), X119 : fun(X117, bool)]:
217.98/218.23	      (ord_less_eq(fun(X117, bool), X118, X119)
217.98/218.23	       | pp(
217.98/218.23	           aa(fun(X117, bool), bool, 
217.98/218.23	             aa(X117, fun(fun(X117, bool), bool), member(X117), 
217.98/218.23	               sk_X(X117, X118, X119)), X118))),
217.98/218.23	    inference('cnf', [status(esa)], [fact_31_subsetI])).
217.98/218.23	tff('15', plain,
217.98/218.23	    ![X117 : $tType, X118 : fun(X117, bool), X119 : fun(X117, bool)]:
217.98/218.23	      (ord_less_eq(fun(X117, bool), X118, X119)
217.98/218.23	       | pp(
217.98/218.23	           aa(X117, bool, 
217.98/218.23	             combc(X117, fun(X117, bool), bool, member(X117), X118), 
217.98/218.23	             sk_X(X117, X118, X119)))),
217.98/218.23	    inference('demod', [status(thm)], ['14', '1'])).
217.98/218.23	tff('16', plain,
217.98/218.23	    ![X262 : $tType, X263 : fun(X262, bool), X265 : X262]:
217.98/218.23	      (pp(
217.98/218.23	         aa(fun(X262, bool), bool, 
217.98/218.23	           aa(X262, fun(fun(X262, bool), bool), member(X262), X265), X263))
217.98/218.23	       | ~ pp(aa(X262, bool, X263, X265))),
217.98/218.23	    inference('cnf', [status(esa)], [fact_74_mem__def])).
217.98/218.23	tff('17', plain,
217.98/218.23	    ![X262 : $tType, X263 : fun(X262, bool), X265 : X262]:
217.98/218.23	      (pp(
217.98/218.23	         aa(X262, bool, 
217.98/218.23	           combc(X262, fun(X262, bool), bool, member(X262), X263), X265))
217.98/218.23	       | ~ pp(aa(X262, bool, X263, X265))),
217.98/218.23	    inference('demod', [status(thm)], ['16', '1'])).
217.98/218.23	tff('18', plain,
217.98/218.23	    ![X117 : $tType, X118 : fun(X117, bool), X119 : fun(X117, bool)]:
217.98/218.23	      (ord_less_eq(fun(X117, bool), X118, X119)
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(fun(X117, bool), bool, 
217.98/218.23	               aa(X117, fun(fun(X117, bool), bool), member(X117), 
217.98/218.23	                 sk_X(X117, X118, X119)), X119))),
217.98/218.23	    inference('cnf', [status(esa)], [fact_31_subsetI])).
217.98/218.23	tff('19', plain,
217.98/218.23	    ![X117 : $tType, X118 : fun(X117, bool), X119 : fun(X117, bool)]:
217.98/218.23	      (ord_less_eq(fun(X117, bool), X118, X119)
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(X117, bool, 
217.98/218.23	               combc(X117, fun(X117, bool), bool, member(X117), X119), 
217.98/218.23	               sk_X(X117, X118, X119)))),
217.98/218.23	    inference('demod', [status(thm)], ['18', '1'])).
217.98/218.23	tff('20', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ~ pp(aa(X0, bool, X1, sk_X(X0, X2, X1)))
217.98/218.23	       | ord_less_eq(fun(X0, bool), X2, X1)),
217.98/218.23	    inference('sup-', [status(thm)], ['17', '19'])).
217.98/218.23	tff('21', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool)]:
217.98/218.23	      (ord_less_eq(fun(X0, bool), X2, X1)
217.98/218.23	       | ~ pp(aa(X0, bool, X1, sk_X(X0, X2, X1)))),
217.98/218.23	    inference('simplify', [status(thm)], ['20'])).
217.98/218.23	tff('22', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ord_less_eq(fun(X0, bool), X1, 
217.98/218.23	           combc(X0, fun(X0, bool), bool, member(X0), X1))
217.98/218.23	       | ord_less_eq(fun(X0, bool), X1, 
217.98/218.23	           combc(X0, fun(X0, bool), bool, member(X0), X1))),
217.98/218.23	    inference('sup-', [status(thm)], ['15', '21'])).
217.98/218.23	tff('23', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool)]:
217.98/218.23	      ord_less_eq(fun(X0, bool), X1, 
217.98/218.23	        combc(X0, fun(X0, bool), bool, member(X0), X1)),
217.98/218.23	    inference('simplify', [status(thm)], ['22'])).
217.98/218.23	tff(fact_5_equalityI, axiom,
217.98/218.23	  (![B:$tType,B2:fun(B,bool),A2:fun(B,bool)]:
217.98/218.23	     (ord_less_eq(fun(B,bool),A2,B2) =>
217.98/218.23	      (ord_less_eq(fun(B,bool),B2,A2) => (A2 = B2))))).
217.98/218.23	tff('24', plain,
217.98/218.23	    ![X19 : $tType, X20 : fun(X19, bool), X21 : fun(X19, bool)]:
217.98/218.23	      (~ ord_less_eq(fun(X19, bool), X20, X21)
217.98/218.23	       | X21 = X20
217.98/218.23	       | ~ ord_less_eq(fun(X19, bool), X21, X20)),
217.98/218.23	    inference('cnf', [status(esa)], [fact_5_equalityI])).
217.98/218.23	tff('25', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ~ ord_less_eq(fun(X0, bool), 
217.98/218.23	             combc(X0, fun(X0, bool), bool, member(X0), X1), X1)
217.98/218.23	       | combc(X0, fun(X0, bool), bool, member(X0), X1) = X1),
217.98/218.23	    inference('sup-', [status(thm)], ['23', '24'])).
217.98/218.23	tff('26', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ord_less_eq(fun(X0, bool), X2, X1)
217.98/218.23	       | pp(aa(X0, bool, X2, sk_X(X0, X2, X1)))),
217.98/218.23	    inference('sup-', [status(thm)], ['15', '4'])).
217.98/218.23	tff('27', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool)]:
217.98/218.23	      (pp(aa(X0, bool, X2, sk_X(X0, X2, X1)))
217.98/218.23	       | ord_less_eq(fun(X0, bool), X2, X1)),
217.98/218.23	    inference('simplify', [status(thm)], ['26'])).
217.98/218.23	tff('28', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ord_less_eq(fun(X0, bool), 
217.98/218.23	           combc(X0, fun(X0, bool), bool, member(X0), X1), X1)
217.98/218.23	       | ord_less_eq(fun(X0, bool), 
217.98/218.23	           combc(X0, fun(X0, bool), bool, member(X0), X1), X1)),
217.98/218.23	    inference('sup-', [status(thm)], ['27', '19'])).
217.98/218.23	tff('29', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool)]:
217.98/218.23	      ord_less_eq(fun(X0, bool), 
217.98/218.23	        combc(X0, fun(X0, bool), bool, member(X0), X1), X1),
217.98/218.23	    inference('simplify', [status(thm)], ['28'])).
217.98/218.23	tff('30', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ~ $true
217.98/218.23	       | combc(X0, fun(X0, bool), bool, member(X0), X1) = X1),
217.98/218.23	    inference('demod', [status(thm)], ['25', '29'])).
217.98/218.23	tff('31', plain,
217.98/218.23	    ![X0 : $tType, X1 : fun(X0, bool)]:
217.98/218.23	      combc(X0, fun(X0, bool), bool, member(X0), X1) = X1,
217.98/218.23	    inference('simplify', [status(thm)], ['30'])).
217.98/218.23	tff(conj_2, axiom, (ord_less_eq(fun(hoare_28830079triple(a),bool),tsa,ts))).
217.98/218.23	tff('32', plain, ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, ts),
217.98/218.23	    inference('cnf', [status(esa)], [conj_2])).
217.98/218.23	tff('33', plain,
217.98/218.23	    ![X0 : nat]:
217.98/218.23	      (hoare_1633586161_valid(a, X0, sk_X11)
217.98/218.23	       | pp(aa(hoare_28830079triple(a), bool, ga, sk_X10(X0)))
217.98/218.23	       | ~ $true),
217.98/218.23	    inference('demod', [status(thm)], ['13', '31', '31', '32'])).
217.98/218.23	tff('34', plain,
217.98/218.23	    ![X0 : nat]:
217.98/218.23	      (pp(aa(hoare_28830079triple(a), bool, ga, sk_X10(X0)))
217.98/218.23	       | hoare_1633586161_valid(a, X0, sk_X11)),
217.98/218.23	    inference('simplify', [status(thm)], ['33'])).
217.98/218.23	tff('35', plain,
217.98/218.23	    ![X358 : hoare_28830079triple(a)]:
217.98/218.23	      (hoare_1633586161_valid(a, sk_N2, X358)
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               aa(hoare_28830079triple(a), 
217.98/218.23	                 fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	                 member(hoare_28830079triple(a)), X358), ga))),
217.98/218.23	    inference('cnf', [status(esa)], [zf_stmt_0])).
217.98/218.23	tff('36', plain,
217.98/218.23	    ![X358 : hoare_28830079triple(a)]:
217.98/218.23	      (hoare_1633586161_valid(a, sk_N2, X358)
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(hoare_28830079triple(a), bool, 
217.98/218.23	               combc(hoare_28830079triple(a), 
217.98/218.23	                 fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	                 member(hoare_28830079triple(a)), ga), X358))),
217.98/218.23	    inference('demod', [status(thm)], ['35', '1'])).
217.98/218.23	tff('37', plain,
217.98/218.23	    ![X0 : hoare_28830079triple(a)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ~ pp(aa(hoare_28830079triple(a), bool, ga, X0))
217.98/218.23	       | hoare_1633586161_valid(a, sk_N2, X0)),
217.98/218.23	    inference('sup-', [status(thm)], ['17', '36'])).
217.98/218.23	tff('38', plain,
217.98/218.23	    ![X0 : hoare_28830079triple(a)]:
217.98/218.23	      (hoare_1633586161_valid(a, sk_N2, X0)
217.98/218.23	       | ~ pp(aa(hoare_28830079triple(a), bool, ga, X0))),
217.98/218.23	    inference('simplify', [status(thm)], ['37'])).
217.98/218.23	tff('39', plain,
217.98/218.23	    ![X0 : nat]:
217.98/218.23	      (~ $true
217.98/218.23	       | hoare_1633586161_valid(a, X0, sk_X11)
217.98/218.23	       | hoare_1633586161_valid(a, sk_N2, sk_X10(X0))),
217.98/218.23	    inference('sup-', [status(thm)], ['34', '38'])).
217.98/218.23	tff('40', plain,
217.98/218.23	    ![X0 : nat]:
217.98/218.23	      (hoare_1633586161_valid(a, sk_N2, sk_X10(X0))
217.98/218.23	       | hoare_1633586161_valid(a, X0, sk_X11)),
217.98/218.23	    inference('simplify', [status(thm)], ['39'])).
217.98/218.23	tff(fact_4_subsetD, axiom,
217.98/218.23	  (![B:$tType,C1:B,B2:fun(B,bool),A2:fun(B,bool)]:
217.98/218.23	     (ord_less_eq(fun(B,bool),A2,B2) =>
217.98/218.23	      (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A2)) =>
217.98/218.23	       pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B2)))))).
217.98/218.23	tff('41', plain,
217.98/218.23	    ![X15 : $tType, X16 : X15, X17 : fun(X15, bool), X18 : fun(X15, bool)]:
217.98/218.23	      (pp(
217.98/218.23	         aa(fun(X15, bool), bool, 
217.98/218.23	           aa(X15, fun(fun(X15, bool), bool), member(X15), X16), X17))
217.98/218.23	       | ~ ord_less_eq(fun(X15, bool), X18, X17)
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(fun(X15, bool), bool, 
217.98/218.23	               aa(X15, fun(fun(X15, bool), bool), member(X15), X16), X18))),
217.98/218.23	    inference('cnf', [status(esa)], [fact_4_subsetD])).
217.98/218.23	tff('42', plain,
217.98/218.23	    ![X0 : hoare_28830079triple(a)]:
217.98/218.23	      (~ $true
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               aa(hoare_28830079triple(a), 
217.98/218.23	                 fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	                 member(hoare_28830079triple(a)), X0), tsa))
217.98/218.23	       | pp(
217.98/218.23	           aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	             aa(hoare_28830079triple(a), 
217.98/218.23	               fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	               member(hoare_28830079triple(a)), X0), ts))),
217.98/218.23	    inference('sup-', [status(thm)], ['32', '41'])).
217.98/218.23	tff('43', plain,
217.98/218.23	    ![X0 : hoare_28830079triple(a)]:
217.98/218.23	      (pp(
217.98/218.23	         aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	           aa(hoare_28830079triple(a), 
217.98/218.23	             fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	             member(hoare_28830079triple(a)), X0), ts))
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               aa(hoare_28830079triple(a), 
217.98/218.23	                 fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	                 member(hoare_28830079triple(a)), X0), tsa))),
217.98/218.23	    inference('simplify', [status(thm)], ['42'])).
217.98/218.23	tff('44', plain,
217.98/218.23	    ![X0 : hoare_28830079triple(a)]:
217.98/218.23	      (pp(
217.98/218.23	         aa(hoare_28830079triple(a), bool, 
217.98/218.23	           combc(hoare_28830079triple(a), 
217.98/218.23	             fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	             member(hoare_28830079triple(a)), ts), X0))
217.98/218.23	       | ~ pp(
217.98/218.23	             aa(hoare_28830079triple(a), bool, 
217.98/218.23	               combc(hoare_28830079triple(a), 
217.98/218.23	                 fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	                 member(hoare_28830079triple(a)), tsa), X0))),
217.98/218.23	    inference('demod', [status(thm)], ['43', '1', '1'])).
217.98/218.23	tff('45', plain,
217.98/218.23	    (~ $true
217.98/218.23	     | pp(
217.98/218.23	         aa(hoare_28830079triple(a), bool, 
217.98/218.23	           combc(hoare_28830079triple(a), 
217.98/218.23	             fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	             member(hoare_28830079triple(a)), ts), sk_X11))),
217.98/218.23	    inference('sup-', [status(thm)], ['2', '44'])).
217.98/218.23	tff('46', plain,
217.98/218.23	    pp(
217.98/218.23	      aa(hoare_28830079triple(a), bool, 
217.98/218.23	        combc(hoare_28830079triple(a), fun(hoare_28830079triple(a), bool), 
217.98/218.23	          bool, member(hoare_28830079triple(a)), ts), sk_X11)),
217.98/218.23	    inference('simplify', [status(thm)], ['45'])).
217.98/218.23	tff('47', plain,
217.98/218.23	    ![X356 : hoare_28830079triple(a), X357 : nat]:
217.98/218.23	      (~ pp(
217.98/218.23	           aa(fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	             aa(hoare_28830079triple(a), 
217.98/218.23	               fun(fun(hoare_28830079triple(a), bool), bool), 
217.98/218.23	               member(hoare_28830079triple(a)), X356), ts))
217.98/218.23	       | hoare_1633586161_valid(a, X357, X356)
217.98/218.23	       | ~ hoare_1633586161_valid(a, X357, sk_X10(X357))),
217.98/218.23	    inference('cnf', [status(esa)], [conj_1])).
217.98/218.23	tff('48', plain,
217.98/218.23	    ![X356 : hoare_28830079triple(a), X357 : nat]:
217.98/218.23	      (~ pp(
217.98/218.23	           aa(hoare_28830079triple(a), bool, 
217.98/218.23	             combc(hoare_28830079triple(a), 
217.98/218.23	               fun(hoare_28830079triple(a), bool), bool, 
217.98/218.23	               member(hoare_28830079triple(a)), ts), X356))
217.98/218.23	       | hoare_1633586161_valid(a, X357, X356)
217.98/218.23	       | ~ hoare_1633586161_valid(a, X357, sk_X10(X357))),
217.98/218.23	    inference('demod', [status(thm)], ['47', '1'])).
217.98/218.23	tff('49', plain,
217.98/218.23	    ![X0 : nat]:
217.98/218.23	      (~ $true
217.98/218.23	       | ~ hoare_1633586161_valid(a, X0, sk_X10(X0))
217.98/218.23	       | hoare_1633586161_valid(a, X0, sk_X11)),
217.98/218.23	    inference('sup-', [status(thm)], ['46', '48'])).
217.98/218.23	tff('50', plain,
217.98/218.23	    ![X0 : nat]:
217.98/218.23	      (hoare_1633586161_valid(a, X0, sk_X11)
217.98/218.23	       | ~ hoare_1633586161_valid(a, X0, sk_X10(X0))),
217.98/218.23	    inference('simplify', [status(thm)], ['49'])).
217.98/218.23	tff('51', plain,
217.98/218.23	    (~ $true
217.98/218.23	     | hoare_1633586161_valid(a, sk_N2, sk_X11)
217.98/218.23	     | hoare_1633586161_valid(a, sk_N2, sk_X11)),
217.98/218.23	    inference('sup-', [status(thm)], ['40', '50'])).
217.98/218.23	tff('52', plain, hoare_1633586161_valid(a, sk_N2, sk_X11),
217.98/218.23	    inference('simplify', [status(thm)], ['51'])).
217.98/218.23	tff('53', plain, ~ hoare_1633586161_valid(a, sk_N2, sk_X11),
217.98/218.23	    inference('cnf', [status(esa)], [zf_stmt_0])).
217.98/218.23	tff('54', plain, ~ $true, inference('sup-', [status(thm)], ['52', '53'])).
217.98/218.23	tff('55', plain, $false, inference('simplify', [status(thm)], ['54'])).
217.98/218.23	
217.98/218.23	% SZS output end Refutation
217.98/218.24	EOF
