0.00/0.01	% File    : /export/starexec/sandbox/benchmark/theBenchmark.p
0.00/0.01	% app-encoded or not : original
0.00/0.01	% Variant    : fo
0.00/0.01	% Ordering    : rpo6
0.00/0.01	% Command    : 
0.00/0.01	#!/bin/sh
0.00/0.01	
0.00/0.01	./zipperposition.native ${1:+"$1"} \
0.00/0.01	  -i tptp \
0.00/0.01	  -o tptp \
0.00/0.01	  --timeout "$STAREXEC_WALLCLOCK_LIMIT" \
0.00/0.01	  --mem-limit "$STAREXEC_MAX_MEM" \
0.00/0.01	  --no-ho \
0.00/0.01	  --no-avatar \
0.00/0.01	  --no-induction \
0.00/0.01	  --no-unif-pattern \
0.00/0.01	  --ord $2 \
0.00/0.01	  --simultaneous-sup false \
0.00/0.01	  --no-max-vars \
0.00/0.01	  --no-fool
0.00/0.20	% Computer   : n183.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 06:48:24 CST 2018
13.90/14.12	% done 3836 iterations in 13.917s
13.90/14.12	% SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
13.90/14.12	% SZS output start Refutation
13.90/14.13	tff(conj_1, axiom,
13.90/14.13	  (pp(aa(dB,bool,it,
13.90/14.13	         aa(dB,dB,
13.90/14.13	            aa(dB,fun(dB,dB),app,
13.90/14.13	               foldl(dB,dB,app,subst(r,s,zero_zero(nat)),ss)),
13.90/14.13	            var(i)))))).
13.90/14.13	tff('0', plain,
13.90/14.13	    pp(
13.90/14.13	      aa(dB, bool, it, 
13.90/14.13	        aa(dB, dB, 
13.90/14.13	          aa(dB, fun(dB, dB), app, 
13.90/14.13	            foldl(dB, dB, app, subst(r, s, zero_zero(nat)), ss)), var(i)))),
13.90/14.13	    inference('cnf', [status(esa)], [conj_1])).
13.90/14.13	tff(fact_9_App__eq__foldl__conv, axiom,
13.90/14.13	  (![Ts:list(dB),Ta:dB,S:dB,R:dB]:
13.90/14.13	     ((aa(dB,dB,aa(dB,fun(dB,dB),app,R),S) = foldl(dB,dB,app,Ta,Ts)) <=>
13.90/14.13	      (((Ts != nil(dB)) =>
13.90/14.13	        (?[Ss2:list(dB)]:
13.90/14.13	           ((R = foldl(dB,dB,app,Ta,Ss2)) & 
13.90/14.13	            (Ts = append(dB,Ss2,cons(dB,S,nil(dB))))))) & 
13.90/14.13	       ((Ts = nil(dB)) => (aa(dB,dB,aa(dB,fun(dB,dB),app,R),S) = Ta)))))).
13.90/14.13	tff('1', plain,
13.90/14.13	    ![X35 : list(dB), X37 : dB, X38 : dB, X39 : dB, X40 : list(dB)]:
13.90/14.13	      (aa(dB, dB, aa(dB, fun(dB, dB), app, X39), X37)
13.90/14.13	        = foldl(dB, dB, app, X38, X35)
13.90/14.13	       | X35 = nil(dB)
13.90/14.13	       | X39 != foldl(dB, dB, app, X38, X40)
13.90/14.13	       | X35 != append(dB, X40, cons(dB, X37, nil(dB)))),
13.90/14.13	    inference('cnf', [status(esa)], [fact_9_App__eq__foldl__conv])).
13.90/14.13	tff('2', plain,
13.90/14.13	    ![X37 : dB, X38 : dB, X40 : list(dB)]:
13.90/14.13	      (append(dB, X40, cons(dB, X37, nil(dB))) = nil(dB)
13.90/14.13	       | aa(dB, dB, aa(dB, fun(dB, dB), app, foldl(dB, dB, app, X38, X40)), 
13.90/14.13	           X37)
13.90/14.13	          = foldl(dB, dB, app, X38, append(dB, X40, cons(dB, X37, nil(dB))))),
13.90/14.13	    inference('simplify', [status(thm)], ['1'])).
13.90/14.13	tff(fact_88_rotate__simps, axiom,
13.90/14.13	  (![A1:$tType,B:$tType,Xs:list(B),X:B]:
13.90/14.13	     ((rotate1(B,cons(B,X,Xs)) = append(B,Xs,cons(B,X,nil(B)))) & 
13.90/14.13	      (rotate1(A1,nil(A1)) = nil(A1))))).
13.90/14.13	tff('3', plain,
13.90/14.13	    ![X362 : $tType, X363 : list(X362), X364 : X362]:
13.90/14.13	      rotate1(X362, cons(X362, X364, X363))
13.90/14.13	       = append(X362, X363, cons(X362, X364, nil(X362))),
13.90/14.13	    inference('cnf', [status(esa)], [fact_88_rotate__simps])).
13.90/14.13	tff(fact_90_rotate1__is__Nil__conv, axiom,
13.90/14.13	  (![A1:$tType,Xs1:list(A1)]:
13.90/14.13	     ((rotate1(A1,Xs1) = nil(A1)) <=> (Xs1 = nil(A1))))).
13.90/14.13	tff('4', plain,
13.90/14.13	    ![X371 : $tType, X372 : list(X371)]:
13.90/14.13	      (X372 = nil(X371) | rotate1(X371, X372) != nil(X371)),
13.90/14.13	    inference('cnf', [status(esa)], [fact_90_rotate1__is__Nil__conv])).
13.90/14.13	tff('5', plain,
13.90/14.13	    ![X0 : $tType, X1 : X0, X2 : list(X0)]:
13.90/14.13	      (append(X0, X2, cons(X0, X1, nil(X0))) != nil(X0)
13.90/14.13	       | cons(X0, X1, X2) = nil(X0)),
13.90/14.13	    inference('sup-', [status(thm)], ['3', '4'])).
13.90/14.13	tff(fact_33_list_Osimps_I3_J, axiom,
13.90/14.13	  (![A1:$tType,List2:list(A1),A5:A1]: (cons(A1,A5,List2) != nil(A1)))).
13.90/14.13	tff('6', plain,
13.90/14.13	    ![X138 : $tType, X139 : X138, X140 : list(X138)]:
13.90/14.13	      cons(X138, X139, X140) != nil(X138),
13.90/14.13	    inference('cnf', [status(esa)], [fact_33_list_Osimps_I3_J])).
13.90/14.13	tff('7', plain,
13.90/14.13	    ![X0 : $tType, X1 : X0, X2 : list(X0)]:
13.90/14.13	      append(X0, X2, cons(X0, X1, nil(X0))) != nil(X0),
13.90/14.13	    inference('simplify_reflect-', [status(thm)], ['5', '6'])).
13.90/14.13	tff('8', plain,
13.90/14.13	    ![X37 : dB, X38 : dB, X40 : list(dB)]:
13.90/14.13	      aa(dB, dB, aa(dB, fun(dB, dB), app, foldl(dB, dB, app, X38, X40)), X37)
13.90/14.13	       = foldl(dB, dB, app, X38, append(dB, X40, cons(dB, X37, nil(dB)))),
13.90/14.13	    inference('simplify_reflect-', [status(thm)], ['2', '7'])).
13.90/14.13	tff(fact_2_Beta, axiom,
13.90/14.13	  (![Ss1:list(dB),S:dB,R:dB]:
13.90/14.13	     (pp(aa(dB,bool,it,foldl(dB,dB,app,subst(R,S,zero_zero(nat)),Ss1))) =>
13.90/14.13	      (pp(aa(dB,bool,it,S)) =>
13.90/14.13	       pp(aa(dB,bool,it,
13.90/14.13	             foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(R)),S),Ss1))))))).
13.90/14.13	tff('9', plain,
13.90/14.13	    ![X4 : dB, X5 : dB, X6 : list(dB)]:
13.90/14.13	      (~ pp(aa(dB, bool, it, X4))
13.90/14.13	       | ~ pp(
13.90/14.13	             aa(dB, bool, it, 
13.90/14.13	               foldl(dB, dB, app, subst(X5, X4, zero_zero(nat)), X6)))
13.90/14.13	       | pp(
13.90/14.13	           aa(dB, bool, it, 
13.90/14.13	             foldl(dB, dB, app, 
13.90/14.13	               aa(dB, dB, aa(dB, fun(dB, dB), app, abs(X5)), X4), X6)))),
13.90/14.13	    inference('cnf', [status(esa)], [fact_2_Beta])).
13.90/14.13	tff('10', plain,
13.90/14.13	    ![X0 : dB, X1 : list(dB), X2 : dB, X3 : dB]:
13.90/14.13	      (~ pp(
13.90/14.13	           aa(dB, bool, it, 
13.90/14.13	             aa(dB, dB, 
13.90/14.13	               aa(dB, fun(dB, dB), app, 
13.90/14.13	                 foldl(dB, dB, app, subst(X3, X2, zero_zero(nat)), X1)), X0)))
13.90/14.13	       | pp(
13.90/14.13	           aa(dB, bool, it, 
13.90/14.13	             foldl(dB, dB, app, 
13.90/14.13	               aa(dB, dB, aa(dB, fun(dB, dB), app, abs(X3)), X2), 
13.90/14.13	               append(dB, X1, cons(dB, X0, nil(dB))))))
13.90/14.13	       | ~ pp(aa(dB, bool, it, X2))),
13.90/14.13	    inference('sup-', [status(thm)], ['8', '9'])).
13.90/14.13	tff('11', plain,
13.90/14.13	    ![X0 : dB, X1 : list(dB), X2 : dB, X3 : dB]:
13.90/14.13	      (~ pp(
13.90/14.13	           aa(dB, bool, it, 
13.90/14.13	             aa(dB, dB, 
13.90/14.13	               aa(dB, fun(dB, dB), app, 
13.90/14.13	                 foldl(dB, dB, app, subst(X3, X2, zero_zero(nat)), X1)), X0)))
13.90/14.13	       | pp(
13.90/14.13	           aa(dB, bool, it, 
13.90/14.13	             aa(dB, dB, 
13.90/14.13	               aa(dB, fun(dB, dB), app, 
13.90/14.13	                 foldl(dB, dB, app, 
13.90/14.13	                   aa(dB, dB, aa(dB, fun(dB, dB), app, abs(X3)), X2), X1)), 
13.90/14.13	               X0)))
13.90/14.13	       | ~ pp(aa(dB, bool, it, X2))),
13.90/14.13	    inference('demod', [status(thm)], ['10', '8'])).
13.90/14.13	tff(fact_39_foldl__Cons, axiom,
13.90/14.13	  (![A1:$tType,B:$tType,Xs1:list(B),X1:B,A:A1,F:fun(A1,fun(B,A1))]:
13.90/14.13	     (foldl(A1,B,F,A,cons(B,X1,Xs1)) =
13.90/14.13	      foldl(A1,B,F,aa(B,A1,aa(A1,fun(B,A1),F,A),X1),Xs1)))).
13.90/14.13	tff('12', plain,
13.90/14.13	    ![X157 : $tType, X158 : $tType, X159 : fun(X157, fun(X158, X157)), 
13.90/14.13	      X160 : X157, X161 : X158, X162 : list(X158)]:
13.90/14.13	      foldl(X157, X158, X159, X160, cons(X158, X161, X162))
13.90/14.13	       = foldl(X157, X158, X159, 
13.90/14.13	           aa(X158, X157, aa(X157, fun(X158, X157), X159, X160), X161), X162),
13.90/14.13	    inference('cnf', [status(esa)], [fact_39_foldl__Cons])).
13.90/14.13	tff(fact_40_foldl__Nil, axiom,
13.90/14.13	  (![B:$tType,A1:$tType,A:A1,F:fun(A1,fun(B,A1))]:
13.90/14.13	     (foldl(A1,B,F,A,nil(B)) = A))).
13.90/14.13	tff('13', plain,
13.90/14.13	    ![X163 : $tType, X164 : X163, X165 : $tType, 
13.90/14.13	      X166 : fun(X163, fun(X165, X163))]:
13.90/14.13	      foldl(X163, X165, X166, X164, nil(X165)) = X164,
13.90/14.13	    inference('cnf', [status(esa)], [fact_40_foldl__Nil])).
13.90/14.13	tff('14', plain,
13.90/14.13	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : X0, X4 : fun(X0, fun(X1, X0))]:
13.90/14.13	      foldl(X0, X1, X4, X3, cons(X1, X2, nil(X1)))
13.90/14.13	       = aa(X1, X0, aa(X0, fun(X1, X0), X4, X3), X2),
13.90/14.13	    inference('sup+', [status(thm)], ['12', '13'])).
13.90/14.13	tff(fact_28_foldl__append, axiom,
13.90/14.13	  (![A1:$tType,B:$tType,Ys2:list(B),Xs1:list(B),A:A1,F:fun(A1,fun(B,A1))]:
13.90/14.13	     (foldl(A1,B,F,A,append(B,Xs1,Ys2)) =
13.90/14.13	      foldl(A1,B,F,foldl(A1,B,F,A,Xs1),Ys2)))).
13.90/14.13	tff('15', plain,
13.90/14.13	    ![X112 : $tType, X113 : $tType, X114 : fun(X112, fun(X113, X112)), 
13.90/14.13	      X115 : X112, X116 : list(X113), X117 : list(X113)]:
13.90/14.13	      foldl(X112, X113, X114, X115, append(X113, X116, X117))
13.90/14.13	       = foldl(X112, X113, X114, foldl(X112, X113, X114, X115, X116), X117),
13.90/14.13	    inference('cnf', [status(esa)], [fact_28_foldl__append])).
13.90/14.13	tff('16', plain,
13.90/14.13	    ![X0 : $tType, X1 : $tType, X2 : X1, X3 : X0, X4 : fun(X0, fun(X1, X0)), 
13.90/14.13	      X5 : list(X1)]:
13.90/14.13	      foldl(X0, X1, X4, X3, append(X1, cons(X1, X2, nil(X1)), X5))
13.90/14.13	       = foldl(X0, X1, X4, aa(X1, X0, aa(X0, fun(X1, X0), X4, X3), X2), X5),
13.90/14.13	    inference('sup+', [status(thm)], ['14', '15'])).
13.90/14.13	tff('17', plain,
13.90/14.13	    ![X0 : dB, X1 : list(dB), X2 : dB, X3 : dB]:
13.90/14.13	      (~ pp(
13.90/14.13	           aa(dB, bool, it, 
13.90/14.13	             aa(dB, dB, 
13.90/14.13	               aa(dB, fun(dB, dB), app, 
13.90/14.13	                 foldl(dB, dB, app, subst(X3, X2, zero_zero(nat)), X1)), X0)))
13.90/14.13	       | pp(
13.90/14.13	           aa(dB, bool, it, 
13.90/14.13	             aa(dB, dB, 
13.90/14.13	               aa(dB, fun(dB, dB), app, 
13.90/14.13	                 foldl(dB, dB, app, abs(X3), 
13.90/14.13	                   append(dB, cons(dB, X2, nil(dB)), X1))), X0)))
13.90/14.13	       | ~ pp(aa(dB, bool, it, X2))),
13.90/14.13	    inference('demod', [status(thm)], ['11', '16'])).
13.90/14.13	tff('18', plain,
13.90/14.13	    (~ $true
13.90/14.13	     | ~ pp(aa(dB, bool, it, s))
13.90/14.13	     | pp(
13.90/14.13	         aa(dB, bool, it, 
13.90/14.13	           aa(dB, dB, 
13.90/14.13	             aa(dB, fun(dB, dB), app, 
13.90/14.13	               foldl(dB, dB, app, abs(r), 
13.90/14.13	                 append(dB, cons(dB, s, nil(dB)), ss))), var(i))))),
13.90/14.13	    inference('sup-', [status(thm)], ['0', '17'])).
13.90/14.13	tff(conj_2, axiom, (pp(aa(dB,bool,it,s)))).
13.90/14.13	tff('19', plain, pp(aa(dB, bool, it, s)),
13.90/14.13	    inference('cnf', [status(esa)], [conj_2])).
13.90/14.13	tff('20', plain,
13.90/14.13	    (~ $true
13.90/14.13	     | ~ $true
13.90/14.13	     | pp(
13.90/14.13	         aa(dB, bool, it, 
13.90/14.13	           aa(dB, dB, 
13.90/14.13	             aa(dB, fun(dB, dB), app, 
13.90/14.13	               foldl(dB, dB, app, abs(r), 
13.90/14.13	                 append(dB, cons(dB, s, nil(dB)), ss))), var(i))))),
13.90/14.13	    inference('demod', [status(thm)], ['18', '19'])).
13.90/14.13	tff('21', plain,
13.90/14.13	    pp(
13.90/14.13	      aa(dB, bool, it, 
13.90/14.13	        aa(dB, dB, 
13.90/14.13	          aa(dB, fun(dB, dB), app, 
13.90/14.13	            foldl(dB, dB, app, abs(r), append(dB, cons(dB, s, nil(dB)), ss))), 
13.90/14.13	          var(i)))),
13.90/14.13	    inference('simplify', [status(thm)], ['20'])).
13.90/14.13	tff(conj_4, conjecture,
13.90/14.13	  (pp(aa(dB,bool,it,
13.90/14.13	         foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),s),
13.90/14.13	               append(dB,ss,cons(dB,var(i),nil(dB)))))))).
13.90/14.13	tff(zf_stmt_0, negated_conjecture,
13.90/14.13	  (~
13.90/14.13	    pp(aa(dB,bool,it,
13.90/14.13	          foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),s),
13.90/14.13	                append(dB,ss,cons(dB,var(i),nil(dB)))))))).
13.90/14.13	tff('22', plain,
13.90/14.13	    ~ pp(
13.90/14.13	        aa(dB, bool, it, 
13.90/14.13	          foldl(dB, dB, app, 
13.90/14.13	            aa(dB, dB, aa(dB, fun(dB, dB), app, abs(r)), s), 
13.90/14.13	            append(dB, ss, cons(dB, var(i), nil(dB)))))),
13.90/14.13	    inference('cnf', [status(esa)], [zf_stmt_0])).
13.90/14.13	tff('23', plain,
13.90/14.13	    ~ pp(
13.90/14.13	        aa(dB, bool, it, 
13.90/14.13	          aa(dB, dB, 
13.90/14.13	            aa(dB, fun(dB, dB), app, 
13.90/14.13	              foldl(dB, dB, app, 
13.90/14.13	                aa(dB, dB, aa(dB, fun(dB, dB), app, abs(r)), s), ss)), 
13.90/14.13	            var(i)))),
13.90/14.13	    inference('demod', [status(thm)], ['22', '8'])).
13.90/14.13	tff(fact_38_append__Nil, axiom,
13.90/14.13	  (![A1:$tType,Ys:list(A1)]: (append(A1,nil(A1),Ys) = Ys))).
13.90/14.13	tff('24', plain,
13.90/14.13	    ![X155 : $tType, X156 : list(X155)]: append(X155, nil(X155), X156) = X156,
13.90/14.13	    inference('cnf', [status(esa)], [fact_38_append__Nil])).
13.90/14.13	tff('25', plain,
13.90/14.13	    ![X0 : dB, X1 : dB]:
13.90/14.13	      aa(dB, dB, aa(dB, fun(dB, dB), app, foldl(dB, dB, app, X1, nil(dB))), 
13.90/14.13	        X0)
13.90/14.13	       = foldl(dB, dB, app, X1, cons(dB, X0, nil(dB))),
13.90/14.13	    inference('sup+', [status(thm)], ['24', '8'])).
13.90/14.13	tff('26', plain,
13.90/14.13	    ![X0 : dB, X1 : dB]:
13.90/14.13	      aa(dB, dB, aa(dB, fun(dB, dB), app, X1), X0)
13.90/14.13	       = foldl(dB, dB, app, X1, cons(dB, X0, nil(dB))),
13.90/14.13	    inference('demod', [status(thm)], ['25', '13'])).
13.90/14.13	tff('27', plain,
13.90/14.13	    ![X0 : dB, X1 : dB, X2 : list(dB)]:
13.90/14.13	      foldl(dB, dB, app, X1, append(dB, cons(dB, X0, nil(dB)), X2))
13.90/14.13	       = foldl(dB, dB, app, aa(dB, dB, aa(dB, fun(dB, dB), app, X1), X0), X2),
13.90/14.13	    inference('sup+', [status(thm)], ['26', '15'])).
13.90/14.13	tff('28', plain,
13.90/14.13	    ~ pp(
13.90/14.13	        aa(dB, bool, it, 
13.90/14.13	          aa(dB, dB, 
13.90/14.13	            aa(dB, fun(dB, dB), app, 
13.90/14.13	              foldl(dB, dB, app, abs(r), 
13.90/14.13	                append(dB, cons(dB, s, nil(dB)), ss))), var(i)))),
13.90/14.13	    inference('demod', [status(thm)], ['23', '27'])).
13.90/14.13	tff('29', plain, ~ $true, inference('sup-', [status(thm)], ['21', '28'])).
13.90/14.13	tff('30', plain, $false, inference('simplify', [status(thm)], ['29'])).
13.90/14.13	
13.90/14.13	% SZS output end Refutation
13.90/14.13	EOF
