0.00/0.00	% File    : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.00/0.00	% app-encoded or not : original
0.00/0.00	% Variant    : purification_int
0.00/0.00	% Ordering    : rpo6
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 int \
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   : n077.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 07:10:23 CST 2018
5.91/6.11	% done 1366 iterations in 5.904s
5.91/6.11	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
5.91/6.11	% SZS output start Refutation
5.91/6.11	tff(fact_4_argsT, axiom,
5.91/6.11	  (pp(aa(list(type),bool,typings(shift(type,e,i,t),as),ts)))).
5.91/6.11	tff('0', plain,
5.91/6.11	    pp(aa(list(type), bool, typings(shift(type, e, i, t), as), ts)),
5.91/6.11	    inference('cnf', [status(esa)], [fact_4_argsT])).
5.91/6.11	tff(fact_6_substs__lemma, axiom,
5.91/6.11	  (![Tsa:list(type),Ts:list(dB),Ib:nat,Ta1:type,Ub:dB,Eb:fun(nat,type)]:
5.91/6.11	     (pp(aa(type,bool,aa(dB,fun(type,bool),typing(Eb),Ub),Ta1)) =>
5.91/6.11	      (pp(aa(list(type),bool,typings(shift(type,Eb,Ib,Ta1),Ts),Tsa)) =>
5.91/6.11	       pp(aa(list(type),bool,
5.91/6.11	             typings(Eb,
5.91/6.11	                     map(dB,dB,
5.91/6.11	                         combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,Ub),Ib),
5.91/6.11	                         Ts)),
5.91/6.11	             Tsa)))))).
5.91/6.11	tff('1', plain,
5.91/6.11	    ![X2 : fun(nat, type), X3 : nat, X4 : type, X5 : list(dB), 
5.91/6.11	      X6 : list(type), X7 : dB]:
5.91/6.11	      (~ pp(aa(list(type), bool, typings(shift(type, X2, X3, X4), X5), X6))
5.91/6.11	       | pp(
5.91/6.11	           aa(list(type), bool, 
5.91/6.11	             typings(X2, 
5.91/6.11	               map(dB, dB, 
5.91/6.11	                 combc(dB, nat, dB, combc(dB, dB, fun(nat, dB), subst, X7), 
5.91/6.11	                   X3), X5)), X6))
5.91/6.11	       | ~ pp(aa(type, bool, aa(dB, fun(type, bool), typing(X2), X7), X4))),
5.91/6.11	    inference('cnf', [status(esa)], [fact_6_substs__lemma])).
5.91/6.11	tff('2', plain,
5.91/6.11	    ![X0 : dB]:
5.91/6.11	      (~ $true
5.91/6.11	       | ~ pp(aa(type, bool, aa(dB, fun(type, bool), typing(e), X0), t))
5.91/6.11	       | pp(
5.91/6.11	           aa(list(type), bool, 
5.91/6.11	             typings(e, 
5.91/6.11	               map(dB, dB, 
5.91/6.11	                 combc(dB, nat, dB, combc(dB, dB, fun(nat, dB), subst, X0), 
5.91/6.11	                   i), as)), ts))),
5.91/6.11	    inference('sup-', [status(thm)], ['0', '1'])).
5.91/6.11	tff('3', plain,
5.91/6.11	    ![X0 : dB]:
5.91/6.11	      (pp(
5.91/6.11	         aa(list(type), bool, 
5.91/6.11	           typings(e, 
5.91/6.11	             map(dB, dB, 
5.91/6.11	               combc(dB, nat, dB, combc(dB, dB, fun(nat, dB), subst, X0), i), 
5.91/6.11	               as)), ts))
5.91/6.11	       | ~ pp(aa(type, bool, aa(dB, fun(type, bool), typing(e), X0), t))),
5.91/6.11	    inference('simplify', [status(thm)], ['2'])).
5.91/6.11	tff(conj_0, conjecture,
5.91/6.11	  (pp(aa(list(type),bool,
5.91/6.11	         typings(e,
5.91/6.11	                 map(dB,dB,
5.91/6.11	                     combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),
5.91/6.11	         ts)))).
5.91/6.11	tff(zf_stmt_0, negated_conjecture,
5.91/6.11	  (~
5.91/6.11	    pp(aa(list(type),bool,
5.91/6.11	          typings(e,
5.91/6.11	                  map(dB,dB,
5.91/6.11	                      combc(dB,nat,dB,combc(dB,dB,fun(nat,dB),subst,u),i),as)),
5.91/6.11	          ts)))).
5.91/6.11	tff('4', plain,
5.91/6.11	    ~ pp(
5.91/6.11	        aa(list(type), bool, 
5.91/6.11	          typings(e, 
5.91/6.11	            map(dB, dB, 
5.91/6.11	              combc(dB, nat, dB, combc(dB, dB, fun(nat, dB), subst, u), i), 
5.91/6.11	              as)), ts)),
5.91/6.11	    inference('cnf', [status(esa)], [zf_stmt_0])).
5.91/6.11	tff('5', plain,
5.91/6.11	    (~ $true | ~ pp(aa(type, bool, aa(dB, fun(type, bool), typing(e), u), t))),
5.91/6.11	    inference('sup-', [status(thm)], ['3', '4'])).
5.91/6.11	tff(help_COMBC_1_1_U, axiom,
5.91/6.11	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
5.91/6.11	     (aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q)))).
5.91/6.11	tff('6', plain,
5.91/6.11	    ![X313 : $tType, X314 : $tType, X315 : $tType, 
5.91/6.11	      X316 : fun(X315, fun(X313, X314)), X317 : X315, X318 : X313]:
5.91/6.11	      aa(X315, X314, combc(X315, X313, X314, X316, X318), X317)
5.91/6.11	       = aa(X313, X314, aa(X315, fun(X313, X314), X316, X317), X318),
5.91/6.11	    inference('cnf', [status(esa)], [help_COMBC_1_1_U])).
5.91/6.11	tff(fact_0_uT, axiom,
5.91/6.11	  (pp(aa(type,bool,aa(dB,fun(type,bool),typing(e),u),t)))).
5.91/6.11	tff('7', plain, pp(aa(type, bool, aa(dB, fun(type, bool), typing(e), u), t)),
5.91/6.11	    inference('cnf', [status(esa)], [fact_0_uT])).
5.91/6.11	tff(help_fFalse_1_1_T, axiom, (![P:bool]: ((P = fFalse) | (P = fTrue)))).
5.91/6.11	tff('8', plain, ![X333 : bool]: (X333 = fFalse | X333 = fTrue),
5.91/6.11	    inference('cnf', [status(esa)], [help_fFalse_1_1_T])).
5.91/6.11	tff(help_pp_1_1_U, axiom, (~pp(fFalse))).
5.91/6.11	tff('9', plain, ~ pp(fFalse),
5.91/6.11	    inference('cnf', [status(esa)], [help_pp_1_1_U])).
5.91/6.11	tff('10', plain, ![X0 : bool]: (~ pp(X0) | X0 = fTrue),
5.91/6.11	    inference('sup-', [status(thm)], ['8', '9'])).
5.91/6.11	tff('11', plain,
5.91/6.11	    (~ $true
5.91/6.11	     | aa(type, bool, aa(dB, fun(type, bool), typing(e), u), t) = fTrue),
5.91/6.11	    inference('sup-', [status(thm)], ['7', '10'])).
5.91/6.11	tff('12', plain,
5.91/6.11	    aa(type, bool, aa(dB, fun(type, bool), typing(e), u), t) = fTrue,
5.91/6.11	    inference('simplify', [status(thm)], ['11'])).
5.91/6.11	tff(fact_3_uIT, axiom, (pp(aa(dB,bool,it,u)))).
5.91/6.11	tff('13', plain, pp(aa(dB, bool, it, u)),
5.91/6.11	    inference('cnf', [status(esa)], [fact_3_uIT])).
5.91/6.11	tff('14', plain, (~ $true | aa(dB, bool, it, u) = fTrue),
5.91/6.11	    inference('sup-', [status(thm)], ['13', '10'])).
5.91/6.11	tff('15', plain, aa(dB, bool, it, u) = fTrue,
5.91/6.11	    inference('simplify', [status(thm)], ['14'])).
5.91/6.11	tff('16', plain,
5.91/6.11	    aa(dB, bool, it, u)
5.91/6.11	     = aa(type, bool, aa(dB, fun(type, bool), typing(e), u), t),
5.91/6.11	    inference('sup+', [status(thm)], ['12', '15'])).
5.91/6.11	tff('17', plain,
5.91/6.11	    aa(dB, bool, it, u)
5.91/6.11	     = aa(dB, bool, combc(dB, type, bool, typing(e), t), u),
5.91/6.11	    inference('demod', [status(thm)], ['16', '6'])).
5.91/6.11	tff(fact_27_varT, axiom,
5.91/6.11	  (pp(aa(type,bool,aa(dB,fun(type,bool),typing(shift(type,e,i,t)),var(n)),
5.91/6.11	         aa(type,type,aa(type,fun(type,type),fun1,t2),
5.91/6.11	            foldr(type,type,fun1,ts,t1)))))).
5.91/6.11	tff('18', plain,
5.91/6.11	    pp(
5.91/6.11	      aa(type, bool, 
5.91/6.11	        aa(dB, fun(type, bool), typing(shift(type, e, i, t)), var(n)), 
5.91/6.11	        aa(type, type, aa(type, fun(type, type), fun1, t2), 
5.91/6.11	          foldr(type, type, fun1, ts, t1)))),
5.91/6.11	    inference('cnf', [status(esa)], [fact_27_varT])).
5.91/6.11	tff(fact_1_True, axiom, (n = i)).
5.91/6.11	tff('19', plain, n = i, inference('cnf', [status(esa)], [fact_1_True])).
5.91/6.11	tff(fact_29_T, axiom,
5.91/6.11	  (t =
5.91/6.11	   aa(type,type,aa(type,fun(type,type),fun1,t2),foldr(type,type,fun1,ts,t1)))).
5.91/6.11	tff('20', plain,
5.91/6.11	    t
5.91/6.11	     = aa(type, type, aa(type, fun(type, type), fun1, t2), 
5.91/6.11	         foldr(type, type, fun1, ts, t1)),
5.91/6.11	    inference('cnf', [status(esa)], [fact_29_T])).
5.91/6.11	tff('21', plain,
5.91/6.11	    t
5.91/6.11	     = aa(type, type, 
5.91/6.11	         combc(type, type, type, fun1, foldr(type, type, fun1, ts, t1)), t2),
5.91/6.11	    inference('demod', [status(thm)], ['20', '6'])).
5.91/6.11	tff('22', plain,
5.91/6.11	    pp(
5.91/6.11	      aa(type, bool, 
5.91/6.11	        aa(dB, fun(type, bool), typing(shift(type, e, i, t)), var(i)), t)),
5.91/6.11	    inference('demod', [status(thm)], ['18', '19', '6', '21'])).
5.91/6.11	tff(fact_38_Var__IT, axiom, (![N1:nat]: pp(aa(dB,bool,it,var(N1))))).
5.91/6.11	tff('23', plain, ![X66 : nat]: pp(aa(dB, bool, it, var(X66))),
5.91/6.11	    inference('cnf', [status(esa)], [fact_38_Var__IT])).
5.91/6.11	tff('24', plain, ![X0 : nat]: (~ $true | aa(dB, bool, it, var(X0)) = fTrue),
5.91/6.11	    inference('sup-', [status(thm)], ['23', '10'])).
5.91/6.11	tff('25', plain, ![X0 : nat]: aa(dB, bool, it, var(X0)) = fTrue,
5.91/6.11	    inference('simplify', [status(thm)], ['24'])).
5.91/6.11	tff('26', plain,
5.91/6.11	    ![X0 : nat]: aa(dB, bool, it, var(X0)) = aa(dB, bool, it, u),
5.91/6.11	    inference('demod', [status(thm)], ['25', '15'])).
5.91/6.11	tff('27', plain,
5.91/6.11	    ![X333 : bool]: (X333 = fFalse | X333 = aa(dB, bool, it, u)),
5.91/6.11	    inference('demod', [status(thm)], ['8', '15'])).
5.91/6.11	tff('28', plain,
5.91/6.11	    ![X0 : nat, X1 : bool]: (X1 = aa(dB, bool, it, var(X0)) | X1 = fFalse),
5.91/6.11	    inference('sup+', [status(thm)], ['26', '27'])).
5.91/6.11	tff('29', plain,
5.91/6.11	    ![X0 : bool, X1 : nat]: (aa(dB, bool, it, var(X1)) = X0 | X0 = fFalse),
5.91/6.11	    inference('sup+', [status(thm)], ['27', '26'])).
5.91/6.11	tff('30', plain,
5.91/6.11	    ![X0 : nat]:
5.91/6.11	      (~ pp(aa(dB, bool, it, var(X0)))
5.91/6.11	       | aa(list(type), bool, 
5.91/6.11	           typings(e, 
5.91/6.11	             map(dB, dB, 
5.91/6.11	               combc(dB, nat, dB, combc(dB, dB, fun(nat, dB), subst, u), i), 
5.91/6.11	               as)), ts)
5.91/6.11	          = fFalse),
5.91/6.11	    inference('sup-', [status(thm)], ['29', '4'])).
5.91/6.11	tff('31', plain,
5.91/6.11	    (~ $true
5.91/6.11	     | aa(list(type), bool, 
5.91/6.11	         typings(e, 
5.91/6.11	           map(dB, dB, 
5.91/6.11	             combc(dB, nat, dB, combc(dB, dB, fun(nat, dB), subst, u), i), 
5.91/6.11	             as)), ts)
5.91/6.11	        = fFalse),
5.91/6.11	    inference('demod', [status(thm)], ['30', '23'])).
5.91/6.11	tff('32', plain,
5.91/6.11	    aa(list(type), bool, 
5.91/6.11	      typings(e, 
5.91/6.11	        map(dB, dB, 
5.91/6.11	          combc(dB, nat, dB, combc(dB, dB, fun(nat, dB), subst, u), i), as)), 
5.91/6.11	      ts)
5.91/6.11	     = fFalse,
5.91/6.11	    inference('simplify', [status(thm)], ['31'])).
5.91/6.11	tff('33', plain,
5.91/6.11	    ![X0 : nat, X1 : bool]:
5.91/6.11	      (X1 = aa(dB, bool, it, var(X0))
5.91/6.11	       | X1
5.91/6.11	          = aa(list(type), bool, 
5.91/6.11	              typings(e, 
5.91/6.11	                map(dB, dB, 
5.91/6.11	                  combc(dB, nat, dB, combc(dB, dB, fun(nat, dB), subst, u), 
5.91/6.11	                    i), as)), ts)),
5.91/6.11	    inference('demod', [status(thm)], ['28', '32'])).
5.91/6.11	tff('34', plain,
5.91/6.11	    ![X0 : bool, X1 : nat]: (~ pp(X0) | X0 = aa(dB, bool, it, var(X1))),
5.91/6.11	    inference('sup-', [status(thm)], ['33', '4'])).
5.91/6.11	tff('35', plain,
5.91/6.11	    ![X0 : nat]:
5.91/6.11	      (~ $true
5.91/6.11	       | aa(type, bool, 
5.91/6.11	           aa(dB, fun(type, bool), typing(shift(type, e, i, t)), var(i)), t)
5.91/6.11	          = aa(dB, bool, it, var(X0))),
5.91/6.11	    inference('sup-', [status(thm)], ['22', '34'])).
5.91/6.11	tff('36', plain,
5.91/6.11	    ![X0 : nat]:
5.91/6.11	      aa(type, bool, 
5.91/6.11	        aa(dB, fun(type, bool), typing(shift(type, e, i, t)), var(i)), t)
5.91/6.11	       = aa(dB, bool, it, var(X0)),
5.91/6.11	    inference('simplify', [status(thm)], ['35'])).
5.91/6.11	tff('37', plain,
5.91/6.11	    aa(type, bool, 
5.91/6.11	      aa(dB, fun(type, bool), typing(shift(type, e, i, t)), var(i)), t)
5.91/6.11	     = aa(dB, bool, it, u),
5.91/6.11	    inference('sup+', [status(thm)], ['36', '26'])).
5.91/6.11	tff('38', plain,
5.91/6.11	    aa(type, bool, 
5.91/6.11	      aa(dB, fun(type, bool), typing(shift(type, e, i, t)), var(i)), t)
5.91/6.11	     = aa(dB, bool, combc(dB, type, bool, typing(e), t), u),
5.91/6.11	    inference('demod', [status(thm)], ['17', '37'])).
5.91/6.11	tff(fact_44_shift__eq, axiom,
5.91/6.11	  (![A:$tType,Ta1:A,Eb:fun(nat,A),J1:nat,Ib:nat]:
5.91/6.11	     ((Ib = J1) => (aa(nat,A,shift(A,Eb,Ib,Ta1),J1) = Ta1)))).
5.91/6.11	tff('39', plain,
5.91/6.11	    ![X87 : $tType, X88 : X87, X89 : fun(nat, X87), X90 : nat, X91 : nat]:
5.91/6.11	      (aa(nat, X87, shift(X87, X89, X90, X88), X91) = X88 | X90 != X91),
5.91/6.11	    inference('cnf', [status(esa)], [fact_44_shift__eq])).
5.91/6.11	tff('40', plain,
5.91/6.11	    ![X87 : $tType, X88 : X87, X89 : fun(nat, X87), X91 : nat]:
5.91/6.11	      aa(nat, X87, shift(X87, X89, X91, X88), X91) = X88,
5.91/6.11	    inference('simplify', [status(thm)], ['39'])).
5.91/6.11	tff(fact_23_typing_OVar, axiom,
5.91/6.11	  (![Ta1:type,X1:nat,Env:fun(nat,type)]:
5.91/6.11	     ((aa(nat,type,Env,X1) = Ta1) =>
5.91/6.11	      pp(aa(type,bool,aa(dB,fun(type,bool),typing(Env),var(X1)),Ta1))))).
5.91/6.11	tff('41', plain,
5.91/6.11	    ![X48 : fun(nat, type), X49 : nat, X50 : type]:
5.91/6.11	      (pp(
5.91/6.11	         aa(type, bool, aa(dB, fun(type, bool), typing(X48), var(X49)), X50))
5.91/6.11	       | aa(nat, type, X48, X49) != X50),
5.91/6.11	    inference('cnf', [status(esa)], [fact_23_typing_OVar])).
5.91/6.11	tff('42', plain,
5.91/6.11	    ![X48 : fun(nat, type), X49 : nat]:
5.91/6.11	      pp(
5.91/6.11	        aa(type, bool, aa(dB, fun(type, bool), typing(X48), var(X49)), 
5.91/6.11	          aa(nat, type, X48, X49))),
5.91/6.11	    inference('simplify', [status(thm)], ['41'])).
5.91/6.11	tff('43', plain,
5.91/6.11	    ![X0 : type, X1 : nat, X2 : fun(nat, type)]:
5.91/6.11	      pp(
5.91/6.11	        aa(type, bool, 
5.91/6.11	          aa(dB, fun(type, bool), typing(shift(type, X2, X1, X0)), var(X1)), 
5.91/6.11	          X0)),
5.91/6.11	    inference('sup+', [status(thm)], ['40', '42'])).
5.91/6.11	tff('44', plain, (~ $true | ~ $true),
5.91/6.11	    inference('demod', [status(thm)], ['5', '6', '38', '43'])).
5.91/6.11	tff('45', plain, $false, inference('simplify', [status(thm)], ['44'])).
5.91/6.11	
5.91/6.11	% SZS output end Refutation
5.91/6.11	EOF
