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
0.00/0.33	% Computer   : n131.star.cs.uiowa.edu
0.00/0.33	% Model      : x86_64 x86_64
0.00/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.33	% Memory     : 32218.625MB
0.00/0.33	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.33	% CPULimit   : 300
0.00/0.33	% DateTime   : Fri Feb  2 10:04:55 CST 2018
168.46/168.90	% done 16630 iterations in 168.565s
168.46/168.90	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
168.46/168.90	% SZS output start Refutation
168.46/168.90	tff(conj_3, conjecture,
168.46/168.90	  (![N:nat]:
168.46/168.90	     ((![X:hoare_28830079triple(a)]:
168.46/168.90	         (pp(aa(fun(hoare_28830079triple(a),bool),bool,
168.46/168.90	                aa(hoare_28830079triple(a),
168.46/168.90	                   fun(fun(hoare_28830079triple(a),bool),bool),
168.46/168.90	                   member(hoare_28830079triple(a)),X),
168.46/168.90	                tsa)) =>
168.46/168.90	          hoare_1633586161_valid(a,N,X))) | 
168.46/168.90	      (?[X1:hoare_28830079triple(a)]:
168.46/168.90	         ((~hoare_1633586161_valid(a,N,X1)) & 
168.46/168.90	          pp(aa(fun(hoare_28830079triple(a),bool),bool,
168.46/168.90	                aa(hoare_28830079triple(a),
168.46/168.90	                   fun(fun(hoare_28830079triple(a),bool),bool),
168.46/168.90	                   member(hoare_28830079triple(a)),X1),
168.46/168.90	                ga))))))).
168.46/168.90	tff(zf_stmt_0, negated_conjecture,
168.46/168.90	  (~
168.46/168.90	    (![N:nat]:
168.46/168.90	       ((![X:hoare_28830079triple(a)]:
168.46/168.90	           (pp(aa(fun(hoare_28830079triple(a),bool),bool,
168.46/168.90	                  aa(hoare_28830079triple(a),
168.46/168.90	                     fun(fun(hoare_28830079triple(a),bool),bool),
168.46/168.90	                     member(hoare_28830079triple(a)),X),
168.46/168.90	                  tsa)) =>
168.46/168.90	            hoare_1633586161_valid(a,N,X))) | 
168.46/168.90	        (?[X1:hoare_28830079triple(a)]:
168.46/168.90	           ((~hoare_1633586161_valid(a,N,X1)) & 
168.46/168.90	            pp(aa(fun(hoare_28830079triple(a),bool),bool,
168.46/168.90	                  aa(hoare_28830079triple(a),
168.46/168.90	                     fun(fun(hoare_28830079triple(a),bool),bool),
168.46/168.90	                     member(hoare_28830079triple(a)),X1),
168.46/168.90	                  ga)))))))).
168.46/168.90	tff('0', plain,
168.46/168.90	    pp(
168.46/168.90	      aa(fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	        aa(hoare_28830079triple(a), 
168.46/168.90	          fun(fun(hoare_28830079triple(a), bool), bool), 
168.46/168.90	          member(hoare_28830079triple(a)), sk_X11), tsa)),
168.46/168.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
168.46/168.90	tff(help_COMBC_1_1_U, axiom,
168.46/168.90	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
168.46/168.90	     (aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q)))).
168.46/168.90	tff('1', plain,
168.46/168.90	    ![X350 : $tType, X351 : $tType, X352 : $tType, 
168.46/168.90	      X353 : fun(X352, fun(X350, X351)), X354 : X352, X355 : X350]:
168.46/168.90	      aa(X352, X351, combc(X352, X350, X351, X353, X355), X354)
168.46/168.90	       = aa(X350, X351, aa(X352, fun(X350, X351), X353, X354), X355),
168.46/168.90	    inference('cnf', [status(esa)], [help_COMBC_1_1_U])).
168.46/168.90	tff('2', plain,
168.46/168.90	    pp(
168.46/168.90	      aa(hoare_28830079triple(a), bool, 
168.46/168.90	        combc(hoare_28830079triple(a), fun(hoare_28830079triple(a), bool), 
168.46/168.90	          bool, member(hoare_28830079triple(a)), tsa), sk_X11)),
168.46/168.90	    inference('demod', [status(thm)], ['0', '1'])).
168.46/168.90	tff(fact_74_mem__def, axiom,
168.46/168.90	  (![B:$tType,A2:fun(B,bool),X2:B]:
168.46/168.90	     (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X2),A2)) <=>
168.46/168.90	      pp(aa(B,bool,A2,X2))))).
168.46/168.90	tff('3', plain,
168.46/168.90	    ![X262 : $tType, X263 : fun(X262, bool), X264 : X262]:
168.46/168.90	      (pp(aa(X262, bool, X263, X264))
168.46/168.90	       | ~ pp(
168.46/168.90	             aa(fun(X262, bool), bool, 
168.46/168.90	               aa(X262, fun(fun(X262, bool), bool), member(X262), X264), 
168.46/168.90	               X263))),
168.46/168.90	    inference('cnf', [status(esa)], [fact_74_mem__def])).
168.46/168.90	tff('4', plain,
168.46/168.90	    ![X262 : $tType, X263 : fun(X262, bool), X264 : X262]:
168.46/168.90	      (pp(aa(X262, bool, X263, X264))
168.46/168.90	       | ~ pp(
168.46/168.90	             aa(X262, bool, 
168.46/168.90	               combc(X262, fun(X262, bool), bool, member(X262), X263), X264))),
168.46/168.90	    inference('demod', [status(thm)], ['3', '1'])).
168.46/168.90	tff('5', plain,
168.46/168.90	    (~ $true | pp(aa(hoare_28830079triple(a), bool, tsa, sk_X11))),
168.46/168.90	    inference('sup-', [status(thm)], ['2', '4'])).
168.46/168.90	tff('6', plain, pp(aa(hoare_28830079triple(a), bool, tsa, sk_X11)),
168.46/168.90	    inference('simplify', [status(thm)], ['5'])).
168.46/168.90	tff(fact_13_rev__predicate1D, axiom,
168.46/168.90	  (![B:$tType,Q1:fun(B,bool),X2:B,P1:fun(B,bool)]:
168.46/168.90	     (pp(aa(B,bool,P1,X2)) =>
168.46/168.90	      (ord_less_eq(fun(B,bool),P1,Q1) => pp(aa(B,bool,Q1,X2)))))).
168.46/168.90	tff('7', plain,
168.46/168.90	    ![X53 : $tType, X54 : fun(X53, bool), X55 : X53, X56 : fun(X53, bool)]:
168.46/168.90	      (pp(aa(X53, bool, X54, X55))
168.46/168.90	       | ~ pp(aa(X53, bool, X56, X55))
168.46/168.90	       | ~ ord_less_eq(fun(X53, bool), X56, X54)),
168.46/168.90	    inference('cnf', [status(esa)], [fact_13_rev__predicate1D])).
168.46/168.90	tff('8', plain,
168.46/168.90	    ![X0 : fun(hoare_28830079triple(a), bool)]:
168.46/168.90	      (~ $true
168.46/168.90	       | ~ ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, X0)
168.46/168.90	       | pp(aa(hoare_28830079triple(a), bool, X0, sk_X11))),
168.46/168.90	    inference('sup-', [status(thm)], ['6', '7'])).
168.46/168.90	tff('9', plain,
168.46/168.90	    ![X0 : fun(hoare_28830079triple(a), bool)]:
168.46/168.90	      (pp(aa(hoare_28830079triple(a), bool, X0, sk_X11))
168.46/168.90	       | ~ ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, X0)),
168.46/168.90	    inference('simplify', [status(thm)], ['8'])).
168.46/168.90	tff(conj_1, axiom,
168.46/168.90	  (![N1:nat]:
168.46/168.90	     ((![X:hoare_28830079triple(a)]:
168.46/168.90	         (pp(aa(fun(hoare_28830079triple(a),bool),bool,
168.46/168.90	                aa(hoare_28830079triple(a),
168.46/168.90	                   fun(fun(hoare_28830079triple(a),bool),bool),
168.46/168.90	                   member(hoare_28830079triple(a)),X),
168.46/168.90	                ga)) =>
168.46/168.90	          hoare_1633586161_valid(a,N1,X))) =>
168.46/168.90	      (![X1:hoare_28830079triple(a)]:
168.46/168.90	         (pp(aa(fun(hoare_28830079triple(a),bool),bool,
168.46/168.90	                aa(hoare_28830079triple(a),
168.46/168.90	                   fun(fun(hoare_28830079triple(a),bool),bool),
168.46/168.90	                   member(hoare_28830079triple(a)),X1),
168.46/168.90	                ts)) =>
168.46/168.90	          hoare_1633586161_valid(a,N1,X1)))))).
168.46/168.90	tff('10', plain,
168.46/168.90	    ![X356 : hoare_28830079triple(a), X357 : nat]:
168.46/168.90	      (~ pp(
168.46/168.90	           aa(fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	             aa(hoare_28830079triple(a), 
168.46/168.90	               fun(fun(hoare_28830079triple(a), bool), bool), 
168.46/168.90	               member(hoare_28830079triple(a)), X356), ts))
168.46/168.90	       | hoare_1633586161_valid(a, X357, X356)
168.46/168.90	       | pp(
168.46/168.90	           aa(fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	             aa(hoare_28830079triple(a), 
168.46/168.90	               fun(fun(hoare_28830079triple(a), bool), bool), 
168.46/168.90	               member(hoare_28830079triple(a)), sk_X10(X357)), ga))),
168.46/168.90	    inference('cnf', [status(esa)], [conj_1])).
168.46/168.90	tff('11', plain,
168.46/168.90	    ![X356 : hoare_28830079triple(a), X357 : nat]:
168.46/168.90	      (~ pp(
168.46/168.90	           aa(hoare_28830079triple(a), bool, 
168.46/168.90	             combc(hoare_28830079triple(a), 
168.46/168.90	               fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	               member(hoare_28830079triple(a)), ts), X356))
168.46/168.90	       | hoare_1633586161_valid(a, X357, X356)
168.46/168.90	       | pp(
168.46/168.90	           aa(hoare_28830079triple(a), bool, 
168.46/168.90	             combc(hoare_28830079triple(a), 
168.46/168.90	               fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	               member(hoare_28830079triple(a)), ga), sk_X10(X357)))),
168.46/168.90	    inference('demod', [status(thm)], ['10', '1', '1'])).
168.46/168.90	tff('12', plain,
168.46/168.90	    ![X0 : nat]:
168.46/168.90	      (~ $true
168.46/168.90	       | ~ ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, 
168.46/168.90	             combc(hoare_28830079triple(a), 
168.46/168.90	               fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	               member(hoare_28830079triple(a)), ts))
168.46/168.90	       | pp(
168.46/168.90	           aa(hoare_28830079triple(a), bool, 
168.46/168.90	             combc(hoare_28830079triple(a), 
168.46/168.90	               fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	               member(hoare_28830079triple(a)), ga), sk_X10(X0)))
168.46/168.90	       | hoare_1633586161_valid(a, X0, sk_X11)),
168.46/168.90	    inference('sup-', [status(thm)], ['9', '11'])).
168.46/168.90	tff('13', plain,
168.46/168.90	    ![X0 : nat]:
168.46/168.90	      (hoare_1633586161_valid(a, X0, sk_X11)
168.46/168.90	       | pp(
168.46/168.90	           aa(hoare_28830079triple(a), bool, 
168.46/168.90	             combc(hoare_28830079triple(a), 
168.46/168.90	               fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	               member(hoare_28830079triple(a)), ga), sk_X10(X0)))
168.46/168.90	       | ~ ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, 
168.46/168.90	             combc(hoare_28830079triple(a), 
168.46/168.90	               fun(hoare_28830079triple(a), bool), bool, 
168.46/168.90	               member(hoare_28830079triple(a)), ts))),
168.46/168.90	    inference('simplify', [status(thm)], ['12'])).
168.46/168.90	tff(fact_31_subsetI, axiom,
168.46/168.90	  (![B:$tType,B2:fun(B,bool),A2:fun(B,bool)]:
168.46/168.90	     ((![X:B]:
168.46/168.90	         (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X),A2)) =>
168.46/168.90	          pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),X),B2)))) =>
168.46/168.90	      ord_less_eq(fun(B,bool),A2,B2)))).
168.46/168.90	tff('14', plain,
168.46/168.90	    ![X117 : $tType, X118 : fun(X117, bool), X119 : fun(X117, bool)]:
168.46/168.90	      (ord_less_eq(fun(X117, bool), X118, X119)
168.46/168.90	       | pp(
168.46/168.90	           aa(fun(X117, bool), bool, 
168.46/168.90	             aa(X117, fun(fun(X117, bool), bool), member(X117), 
168.46/168.90	               sk_X(X117, X118, X119)), X118))),
168.46/168.90	    inference('cnf', [status(esa)], [fact_31_subsetI])).
168.46/168.90	tff('15', plain,
168.46/168.90	    ![X117 : $tType, X118 : fun(X117, bool), X119 : fun(X117, bool)]:
168.46/168.90	      (ord_less_eq(fun(X117, bool), X118, X119)
168.46/168.90	       | pp(
168.46/168.90	           aa(X117, bool, 
168.46/168.90	             combc(X117, fun(X117, bool), bool, member(X117), X118), 
168.46/168.90	             sk_X(X117, X118, X119)))),
168.46/168.90	    inference('demod', [status(thm)], ['14', '1'])).
168.46/168.90	tff('16', plain,
168.46/168.90	    ![X262 : $tType, X263 : fun(X262, bool), X265 : X262]:
168.46/168.90	      (pp(
168.46/168.90	         aa(fun(X262, bool), bool, 
168.46/168.90	           aa(X262, fun(fun(X262, bool), bool), member(X262), X265), X263))
168.46/168.90	       | ~ pp(aa(X262, bool, X263, X265))),
168.46/168.90	    inference('cnf', [status(esa)], [fact_74_mem__def])).
168.46/168.90	tff('17', plain,
168.46/168.90	    ![X262 : $tType, X263 : fun(X262, bool), X265 : X262]:
168.46/168.90	      (pp(
168.46/168.90	         aa(X262, bool, 
168.46/168.90	           combc(X262, fun(X262, bool), bool, member(X262), X263), X265))
168.46/168.90	       | ~ pp(aa(X262, bool, X263, X265))),
168.46/168.90	    inference('demod', [status(thm)], ['16', '1'])).
168.46/168.90	tff('18', plain,
168.46/168.90	    ![X117 : $tType, X118 : fun(X117, bool), X119 : fun(X117, bool)]:
168.46/168.90	      (ord_less_eq(fun(X117, bool), X118, X119)
168.46/168.90	       | ~ pp(
168.46/168.90	             aa(fun(X117, bool), bool, 
168.46/168.90	               aa(X117, fun(fun(X117, bool), bool), member(X117), 
168.46/168.90	                 sk_X(X117, X118, X119)), X119))),
168.46/168.90	    inference('cnf', [status(esa)], [fact_31_subsetI])).
168.46/168.90	tff('19', plain,
168.46/168.90	    ![X117 : $tType, X118 : fun(X117, bool), X119 : fun(X117, bool)]:
168.46/168.90	      (ord_less_eq(fun(X117, bool), X118, X119)
168.46/168.90	       | ~ pp(
168.46/168.90	             aa(X117, bool, 
168.46/168.90	               combc(X117, fun(X117, bool), bool, member(X117), X119), 
168.46/168.90	               sk_X(X117, X118, X119)))),
168.46/168.90	    inference('demod', [status(thm)], ['18', '1'])).
168.46/168.90	tff('20', plain,
168.46/168.90	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool)]:
168.46/168.90	      (~ $true
168.46/168.90	       | ~ pp(aa(X0, bool, X1, sk_X(X0, X2, X1)))
168.46/168.90	       | ord_less_eq(fun(X0, bool), X2, X1)),
168.46/168.90	    inference('sup-', [status(thm)], ['17', '19'])).
168.46/168.90	tff('21', plain,
168.46/168.90	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool)]:
168.46/168.90	      (ord_less_eq(fun(X0, bool), X2, X1)
168.46/168.90	       | ~ pp(aa(X0, bool, X1, sk_X(X0, X2, X1)))),
168.46/168.90	    inference('simplify', [status(thm)], ['20'])).
168.46/168.90	tff('22', plain,
168.46/168.90	    ![X0 : $tType, X1 : fun(X0, bool)]:
168.46/168.90	      (~ $true
168.46/168.90	       | ord_less_eq(fun(X0, bool), X1, 
168.46/168.90	           combc(X0, fun(X0, bool), bool, member(X0), X1))
168.46/168.90	       | ord_less_eq(fun(X0, bool), X1, 
168.46/168.90	           combc(X0, fun(X0, bool), bool, member(X0), X1))),
168.46/168.90	    inference('sup-', [status(thm)], ['15', '21'])).
168.46/168.90	tff('23', plain,
168.46/168.90	    ![X0 : $tType, X1 : fun(X0, bool)]:
168.46/168.90	      ord_less_eq(fun(X0, bool), X1, 
168.46/168.90	        combc(X0, fun(X0, bool), bool, member(X0), X1)),
168.46/168.90	    inference('simplify', [status(thm)], ['22'])).
168.46/168.90	tff(fact_5_equalityI, axiom,
168.46/168.90	  (![B:$tType,B2:fun(B,bool),A2:fun(B,bool)]:
168.46/168.90	     (ord_less_eq(fun(B,bool),A2,B2) =>
168.46/168.90	      (ord_less_eq(fun(B,bool),B2,A2) => (A2 = B2))))).
168.46/168.90	tff('24', plain,
168.46/168.90	    ![X19 : $tType, X20 : fun(X19, bool), X21 : fun(X19, bool)]:
168.46/168.90	      (~ ord_less_eq(fun(X19, bool), X20, X21)
168.46/168.90	       | X21 = X20
168.46/168.90	       | ~ ord_less_eq(fun(X19, bool), X21, X20)),
168.46/168.90	    inference('cnf', [status(esa)], [fact_5_equalityI])).
168.55/168.90	tff('25', plain,
168.55/168.90	    ![X0 : $tType, X1 : fun(X0, bool)]:
168.55/168.90	      (~ $true
168.55/168.90	       | ~ ord_less_eq(fun(X0, bool), 
168.55/168.90	             combc(X0, fun(X0, bool), bool, member(X0), X1), X1)
168.55/168.90	       | combc(X0, fun(X0, bool), bool, member(X0), X1) = X1),
168.55/168.90	    inference('sup-', [status(thm)], ['23', '24'])).
168.55/168.90	tff('26', plain,
168.55/168.90	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool)]:
168.55/168.90	      (~ $true
168.55/168.90	       | ord_less_eq(fun(X0, bool), X2, X1)
168.55/168.90	       | pp(aa(X0, bool, X2, sk_X(X0, X2, X1)))),
168.55/168.90	    inference('sup-', [status(thm)], ['15', '4'])).
168.55/168.90	tff('27', plain,
168.55/168.90	    ![X0 : $tType, X1 : fun(X0, bool), X2 : fun(X0, bool)]:
168.55/168.90	      (pp(aa(X0, bool, X2, sk_X(X0, X2, X1)))
168.55/168.90	       | ord_less_eq(fun(X0, bool), X2, X1)),
168.55/168.90	    inference('simplify', [status(thm)], ['26'])).
168.55/168.90	tff('28', plain,
168.55/168.90	    ![X0 : $tType, X1 : fun(X0, bool)]:
168.55/168.90	      (~ $true
168.55/168.90	       | ord_less_eq(fun(X0, bool), 
168.55/168.90	           combc(X0, fun(X0, bool), bool, member(X0), X1), X1)
168.55/168.90	       | ord_less_eq(fun(X0, bool), 
168.55/168.90	           combc(X0, fun(X0, bool), bool, member(X0), X1), X1)),
168.55/168.90	    inference('sup-', [status(thm)], ['27', '19'])).
168.55/168.90	tff('29', plain,
168.55/168.90	    ![X0 : $tType, X1 : fun(X0, bool)]:
168.55/168.90	      ord_less_eq(fun(X0, bool), 
168.55/168.90	        combc(X0, fun(X0, bool), bool, member(X0), X1), X1),
168.55/168.90	    inference('simplify', [status(thm)], ['28'])).
168.55/168.90	tff('30', plain,
168.55/168.90	    ![X0 : $tType, X1 : fun(X0, bool)]:
168.55/168.90	      (~ $true
168.55/168.90	       | ~ $true
168.55/168.90	       | combc(X0, fun(X0, bool), bool, member(X0), X1) = X1),
168.55/168.90	    inference('demod', [status(thm)], ['25', '29'])).
168.55/168.90	tff('31', plain,
168.55/168.90	    ![X0 : $tType, X1 : fun(X0, bool)]:
168.55/168.90	      combc(X0, fun(X0, bool), bool, member(X0), X1) = X1,
168.55/168.90	    inference('simplify', [status(thm)], ['30'])).
168.55/168.90	tff(conj_2, axiom, (ord_less_eq(fun(hoare_28830079triple(a),bool),tsa,ts))).
168.55/168.90	tff('32', plain, ord_less_eq(fun(hoare_28830079triple(a), bool), tsa, ts),
168.55/168.90	    inference('cnf', [status(esa)], [conj_2])).
168.55/168.90	tff('33', plain,
168.55/168.90	    ![X0 : nat]:
168.55/168.90	      (hoare_1633586161_valid(a, X0, sk_X11)
168.55/168.90	       | pp(aa(hoare_28830079triple(a), bool, ga, sk_X10(X0)))
168.55/168.90	       | ~ $true),
168.55/168.90	    inference('demod', [status(thm)], ['13', '31', '31', '32'])).
168.55/168.90	tff('34', plain,
168.55/168.90	    ![X0 : nat]:
168.55/168.90	      (pp(aa(hoare_28830079triple(a), bool, ga, sk_X10(X0)))
168.55/168.90	       | hoare_1633586161_valid(a, X0, sk_X11)),
168.55/168.90	    inference('simplify', [status(thm)], ['33'])).
168.55/168.90	tff('35', plain,
168.55/168.90	    ![X358 : hoare_28830079triple(a)]:
168.55/168.90	      (hoare_1633586161_valid(a, sk_N2, X358)
168.55/168.90	       | ~ pp(
168.55/168.90	             aa(fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	               aa(hoare_28830079triple(a), 
168.55/168.90	                 fun(fun(hoare_28830079triple(a), bool), bool), 
168.55/168.90	                 member(hoare_28830079triple(a)), X358), ga))),
168.55/168.90	    inference('cnf', [status(esa)], [zf_stmt_0])).
168.55/168.90	tff('36', plain,
168.55/168.90	    ![X358 : hoare_28830079triple(a)]:
168.55/168.90	      (hoare_1633586161_valid(a, sk_N2, X358)
168.55/168.90	       | ~ pp(
168.55/168.90	             aa(hoare_28830079triple(a), bool, 
168.55/168.90	               combc(hoare_28830079triple(a), 
168.55/168.90	                 fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	                 member(hoare_28830079triple(a)), ga), X358))),
168.55/168.90	    inference('demod', [status(thm)], ['35', '1'])).
168.55/168.90	tff('37', plain,
168.55/168.90	    ![X0 : hoare_28830079triple(a)]:
168.55/168.90	      (~ $true
168.55/168.90	       | ~ pp(aa(hoare_28830079triple(a), bool, ga, X0))
168.55/168.90	       | hoare_1633586161_valid(a, sk_N2, X0)),
168.55/168.90	    inference('sup-', [status(thm)], ['17', '36'])).
168.55/168.90	tff('38', plain,
168.55/168.90	    ![X0 : hoare_28830079triple(a)]:
168.55/168.90	      (hoare_1633586161_valid(a, sk_N2, X0)
168.55/168.90	       | ~ pp(aa(hoare_28830079triple(a), bool, ga, X0))),
168.55/168.90	    inference('simplify', [status(thm)], ['37'])).
168.55/168.90	tff('39', plain,
168.55/168.90	    ![X0 : nat]:
168.55/168.90	      (~ $true
168.55/168.90	       | hoare_1633586161_valid(a, X0, sk_X11)
168.55/168.90	       | hoare_1633586161_valid(a, sk_N2, sk_X10(X0))),
168.55/168.90	    inference('sup-', [status(thm)], ['34', '38'])).
168.55/168.90	tff('40', plain,
168.55/168.90	    ![X0 : nat]:
168.55/168.90	      (hoare_1633586161_valid(a, sk_N2, sk_X10(X0))
168.55/168.90	       | hoare_1633586161_valid(a, X0, sk_X11)),
168.55/168.90	    inference('simplify', [status(thm)], ['39'])).
168.55/168.90	tff(fact_4_subsetD, axiom,
168.55/168.90	  (![B:$tType,C1:B,B2:fun(B,bool),A2:fun(B,bool)]:
168.55/168.90	     (ord_less_eq(fun(B,bool),A2,B2) =>
168.55/168.90	      (pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),A2)) =>
168.55/168.90	       pp(aa(fun(B,bool),bool,aa(B,fun(fun(B,bool),bool),member(B),C1),B2)))))).
168.55/168.90	tff('41', plain,
168.55/168.90	    ![X15 : $tType, X16 : X15, X17 : fun(X15, bool), X18 : fun(X15, bool)]:
168.55/168.90	      (pp(
168.55/168.90	         aa(fun(X15, bool), bool, 
168.55/168.90	           aa(X15, fun(fun(X15, bool), bool), member(X15), X16), X17))
168.55/168.90	       | ~ ord_less_eq(fun(X15, bool), X18, X17)
168.55/168.90	       | ~ pp(
168.55/168.90	             aa(fun(X15, bool), bool, 
168.55/168.90	               aa(X15, fun(fun(X15, bool), bool), member(X15), X16), X18))),
168.55/168.90	    inference('cnf', [status(esa)], [fact_4_subsetD])).
168.55/168.90	tff('42', plain,
168.55/168.90	    ![X0 : hoare_28830079triple(a)]:
168.55/168.90	      (~ $true
168.55/168.90	       | ~ pp(
168.55/168.90	             aa(fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	               aa(hoare_28830079triple(a), 
168.55/168.90	                 fun(fun(hoare_28830079triple(a), bool), bool), 
168.55/168.90	                 member(hoare_28830079triple(a)), X0), tsa))
168.55/168.90	       | pp(
168.55/168.90	           aa(fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	             aa(hoare_28830079triple(a), 
168.55/168.90	               fun(fun(hoare_28830079triple(a), bool), bool), 
168.55/168.90	               member(hoare_28830079triple(a)), X0), ts))),
168.55/168.90	    inference('sup-', [status(thm)], ['32', '41'])).
168.55/168.90	tff('43', plain,
168.55/168.90	    ![X0 : hoare_28830079triple(a)]:
168.55/168.90	      (pp(
168.55/168.90	         aa(fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	           aa(hoare_28830079triple(a), 
168.55/168.90	             fun(fun(hoare_28830079triple(a), bool), bool), 
168.55/168.90	             member(hoare_28830079triple(a)), X0), ts))
168.55/168.90	       | ~ pp(
168.55/168.90	             aa(fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	               aa(hoare_28830079triple(a), 
168.55/168.90	                 fun(fun(hoare_28830079triple(a), bool), bool), 
168.55/168.90	                 member(hoare_28830079triple(a)), X0), tsa))),
168.55/168.90	    inference('simplify', [status(thm)], ['42'])).
168.55/168.90	tff('44', plain,
168.55/168.90	    ![X0 : hoare_28830079triple(a)]:
168.55/168.90	      (pp(
168.55/168.90	         aa(hoare_28830079triple(a), bool, 
168.55/168.90	           combc(hoare_28830079triple(a), 
168.55/168.90	             fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	             member(hoare_28830079triple(a)), ts), X0))
168.55/168.90	       | ~ pp(
168.55/168.90	             aa(hoare_28830079triple(a), bool, 
168.55/168.90	               combc(hoare_28830079triple(a), 
168.55/168.90	                 fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	                 member(hoare_28830079triple(a)), tsa), X0))),
168.55/168.90	    inference('demod', [status(thm)], ['43', '1', '1'])).
168.55/168.90	tff('45', plain,
168.55/168.90	    (~ $true
168.55/168.90	     | pp(
168.55/168.90	         aa(hoare_28830079triple(a), bool, 
168.55/168.90	           combc(hoare_28830079triple(a), 
168.55/168.90	             fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	             member(hoare_28830079triple(a)), ts), sk_X11))),
168.55/168.90	    inference('sup-', [status(thm)], ['2', '44'])).
168.55/168.90	tff('46', plain,
168.55/168.90	    pp(
168.55/168.90	      aa(hoare_28830079triple(a), bool, 
168.55/168.90	        combc(hoare_28830079triple(a), fun(hoare_28830079triple(a), bool), 
168.55/168.90	          bool, member(hoare_28830079triple(a)), ts), sk_X11)),
168.55/168.90	    inference('simplify', [status(thm)], ['45'])).
168.55/168.90	tff('47', plain,
168.55/168.90	    ![X356 : hoare_28830079triple(a), X357 : nat]:
168.55/168.90	      (~ pp(
168.55/168.90	           aa(fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	             aa(hoare_28830079triple(a), 
168.55/168.90	               fun(fun(hoare_28830079triple(a), bool), bool), 
168.55/168.90	               member(hoare_28830079triple(a)), X356), ts))
168.55/168.90	       | hoare_1633586161_valid(a, X357, X356)
168.55/168.90	       | ~ hoare_1633586161_valid(a, X357, sk_X10(X357))),
168.55/168.90	    inference('cnf', [status(esa)], [conj_1])).
168.55/168.90	tff('48', plain,
168.55/168.90	    ![X356 : hoare_28830079triple(a), X357 : nat]:
168.55/168.90	      (~ pp(
168.55/168.90	           aa(hoare_28830079triple(a), bool, 
168.55/168.90	             combc(hoare_28830079triple(a), 
168.55/168.90	               fun(hoare_28830079triple(a), bool), bool, 
168.55/168.90	               member(hoare_28830079triple(a)), ts), X356))
168.55/168.90	       | hoare_1633586161_valid(a, X357, X356)
168.55/168.90	       | ~ hoare_1633586161_valid(a, X357, sk_X10(X357))),
168.55/168.90	    inference('demod', [status(thm)], ['47', '1'])).
168.55/168.90	tff('49', plain,
168.55/168.90	    ![X0 : nat]:
168.55/168.90	      (~ $true
168.55/168.90	       | ~ hoare_1633586161_valid(a, X0, sk_X10(X0))
168.55/168.90	       | hoare_1633586161_valid(a, X0, sk_X11)),
168.55/168.90	    inference('sup-', [status(thm)], ['46', '48'])).
168.55/168.90	tff('50', plain,
168.55/168.90	    ![X0 : nat]:
168.55/168.90	      (hoare_1633586161_valid(a, X0, sk_X11)
168.55/168.90	       | ~ hoare_1633586161_valid(a, X0, sk_X10(X0))),
168.55/168.91	    inference('simplify', [status(thm)], ['49'])).
168.55/168.91	tff('51', plain,
168.55/168.91	    (~ $true
168.55/168.91	     | hoare_1633586161_valid(a, sk_N2, sk_X11)
168.55/168.91	     | hoare_1633586161_valid(a, sk_N2, sk_X11)),
168.55/168.91	    inference('sup-', [status(thm)], ['40', '50'])).
168.55/168.91	tff('52', plain, hoare_1633586161_valid(a, sk_N2, sk_X11),
168.55/168.91	    inference('simplify', [status(thm)], ['51'])).
168.55/168.91	tff('53', plain, ~ hoare_1633586161_valid(a, sk_N2, sk_X11),
168.55/168.91	    inference('cnf', [status(esa)], [zf_stmt_0])).
168.55/168.91	tff('54', plain, ~ $true, inference('sup-', [status(thm)], ['52', '53'])).
168.55/168.91	tff('55', plain, $false, inference('simplify', [status(thm)], ['54'])).
168.55/168.91	
168.55/168.91	% SZS output end Refutation
168.55/168.91	EOF
