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_ext
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 $2  \
0.00/0.00	  --simultaneous-sup false \
0.00/0.00	  --ho-purify ext \
0.00/0.00	  --ho-ext-axiom \
0.00/0.00	  --restrict-hidden-sup-at-vars \
0.00/0.00	  --ho-prim-enum none \
0.00/0.00	  --no-max-vars \
0.00/0.00	  --dont-select-ho-var-lits \
0.00/0.00	  --no-fool
0.00/0.19	% Computer   : n172.star.cs.uiowa.edu
0.00/0.19	% Model      : x86_64 x86_64
0.00/0.19	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.00/0.19	% Memory     : 32218.625MB
0.00/0.19	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.00/0.19	% CPULimit   : 300
0.00/0.19	% DateTime   : Fri Feb  2 07:27:53 CST 2018
203.69/203.97	% done 4233 iterations in 203.773s
203.69/203.97	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
203.69/203.97	% SZS output start Refutation
203.69/203.97	tff(help_COMBC_1_1_U, axiom,
203.69/203.97	  (![A:$tType,C:$tType,B:$tType,R:A,Q:B,P:fun(A,fun(B,C))]:
203.69/203.97	     (aa(A,C,combc(A,B,C,P,Q),R) = aa(B,C,aa(A,fun(B,C),P,R),Q)))).
203.69/203.97	tff('0', plain,
203.69/203.97	    ![X361 : $tType, X362 : $tType, X363 : $tType, 
203.69/203.97	      X364 : fun(X363, fun(X361, X362)), X365 : X363, X366 : X361]:
203.69/203.97	      aa(X363, X362, combc(X363, X361, X362, X364, X366), X365)
203.69/203.97	       = aa(X361, X362, aa(X363, fun(X361, X362), X364, X365), X366),
203.69/203.97	    inference('cnf', [status(esa)], [help_COMBC_1_1_U])).
203.69/203.97	tff(fact_57_foldl__Cons, axiom,
203.69/203.97	  (![A:$tType,B:$tType,Xs:list(B),X:B,Aa:A,F:fun(A,fun(B,A))]:
203.69/203.97	     (foldl(A,B,F,Aa,cons(B,X,Xs)) =
203.69/203.97	      foldl(A,B,F,aa(B,A,aa(A,fun(B,A),F,Aa),X),Xs)))).
203.69/203.97	tff('1', plain,
203.69/203.97	    ![X199 : $tType, X200 : $tType, X201 : fun(X199, fun(X200, X199)), 
203.69/203.97	      X202 : X199, X203 : X200, X204 : list(X200)]:
203.69/203.97	      foldl(X199, X200, X201, X202, cons(X200, X203, X204))
203.69/203.97	       = foldl(X199, X200, X201, 
203.69/203.97	           aa(X200, X199, aa(X199, fun(X200, X199), X201, X202), X203), X204),
203.69/203.97	    inference('cnf', [status(esa)], [fact_57_foldl__Cons])).
203.69/203.97	tff('2', plain,
203.69/203.97	    ![X0 : $tType, X1 : X0, X2 : $tType, X3 : X2, X4 : fun(X0, fun(X2, X0)), 
203.69/203.97	      X5 : list(X2)]:
203.69/203.97	      foldl(X0, X2, X4, X1, cons(X2, X3, X5))
203.69/203.97	       = foldl(X0, X2, X4, aa(X0, X0, combc(X0, X2, X0, X4, X3), X1), X5),
203.69/203.97	    inference('sup+', [status(thm)], ['0', '1'])).
203.69/203.97	tff(fact_3_beta, axiom,
203.69/203.97	  (![T:dB,S2:dB]:
203.69/203.97	     pp(aa(dB,bool,
203.69/203.97	           aa(dB,fun(dB,bool),beta,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(S2)),T)),
203.69/203.97	           subst(S2,T,zero_zero(nat)))))).
203.69/203.97	tff('3', plain,
203.69/203.97	    ![X0 : dB, X1 : dB]:
203.69/203.97	      pp(
203.69/203.97	        aa(dB, bool, 
203.69/203.97	          aa(dB, fun(dB, bool), beta, 
203.69/203.97	            aa(dB, dB, aa(dB, fun(dB, dB), app, abs(X0)), X1)), 
203.69/203.97	          subst(X0, X1, zero_zero(nat)))),
203.69/203.97	    inference('cnf', [status(esa)], [fact_3_beta])).
203.69/203.97	tff('4', plain,
203.69/203.97	    ![X0 : dB, X1 : dB]:
203.69/203.97	      pp(
203.69/203.97	        aa(dB, bool, 
203.69/203.97	          aa(dB, fun(dB, bool), beta, 
203.69/203.97	            aa(dB, dB, combc(dB, dB, dB, app, X1), abs(X0))), 
203.69/203.97	          subst(X0, X1, zero_zero(nat)))),
203.69/203.97	    inference('sup+', [status(thm)], ['0', '3'])).
203.69/203.97	tff(help_fFalse_1_1_T, axiom, (![P:bool]: ((P = fFalse) | (P = fTrue)))).
203.69/203.97	tff('5', plain, ![X373 : bool]: (X373 = fFalse | X373 = fTrue),
203.69/203.97	    inference('cnf', [status(esa)], [help_fFalse_1_1_T])).
203.69/203.97	tff(fact_10_apps__preserves__beta, axiom,
203.69/203.97	  (![Ss1:list(dB),S:dB,Ra:dB]:
203.69/203.97	     (pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,Ra),S)) =>
203.69/203.97	      pp(aa(dB,bool,aa(dB,fun(dB,bool),beta,foldl(dB,dB,app,Ra,Ss1)),
203.69/203.97	            foldl(dB,dB,app,S,Ss1)))))).
203.69/203.97	tff('6', plain,
203.69/203.97	    ![X23 : dB, X24 : list(dB), X25 : dB]:
203.69/203.97	      (pp(
203.69/203.97	         aa(dB, bool, 
203.69/203.97	           aa(dB, fun(dB, bool), beta, foldl(dB, dB, app, X23, X24)), 
203.69/203.97	           foldl(dB, dB, app, X25, X24)))
203.69/203.97	       | ~ pp(aa(dB, bool, aa(dB, fun(dB, bool), beta, X23), X25))),
203.69/203.97	    inference('cnf', [status(esa)], [fact_10_apps__preserves__beta])).
203.69/203.97	tff('7', plain,
203.69/203.97	    ![X0 : list(dB), X1 : dB, X2 : dB]:
203.69/203.97	      (pp(fFalse)
203.69/203.97	       | aa(dB, bool, 
203.69/203.97	           aa(dB, fun(dB, bool), beta, foldl(dB, dB, app, X2, X0)), 
203.69/203.97	           foldl(dB, dB, app, X1, X0))
203.69/203.97	          = fTrue
203.69/203.97	       | ~ pp(aa(dB, bool, aa(dB, fun(dB, bool), beta, X2), X1))),
203.69/203.97	    inference('sup+', [status(thm)], ['5', '6'])).
203.69/203.97	tff(fact_70_typings_Osimps_I1_J, axiom,
203.69/203.97	  (![Ts2:list(type),Eb:fun(nat,type)]:
203.69/203.97	     (pp(aa(list(type),bool,typings(Eb,nil(dB)),Ts2)) <=> (Ts2 = nil(type))))).
203.69/203.97	tff('8', plain,
203.69/203.97	    ![X255 : list(type), X257 : fun(nat, type)]:
203.69/203.97	      (pp(aa(list(type), bool, typings(X257, nil(dB)), X255))
203.69/203.97	       | X255 != nil(type)),
203.69/203.97	    inference('cnf', [status(esa)], [fact_70_typings_Osimps_I1_J])).
203.69/203.97	tff('9', plain,
203.69/203.97	    ![X257 : fun(nat, type)]:
203.69/203.97	      pp(aa(list(type), bool, typings(X257, nil(dB)), nil(type))),
203.69/203.97	    inference('simplify', [status(thm)], ['8'])).
203.69/203.97	tff('10', plain,
203.69/203.97	    ![X0 : bool, X1 : bool]: (X1 = X0 | X0 = fFalse | X1 = fFalse),
203.69/203.97	    inference('sup+', [status(thm)], ['5', '5'])).
203.69/203.97	tff(help_pp_1_1_U, axiom, (~pp(fFalse))).
203.69/203.97	tff('11', plain, ~ pp(fFalse),
203.69/203.97	    inference('cnf', [status(esa)], [help_pp_1_1_U])).
203.69/203.97	tff('12', plain, ![X0 : bool, X1 : bool]: (~ pp(X0) | X1 = fFalse | X1 = X0),
203.69/203.97	    inference('sup-', [status(thm)], ['10', '11'])).
203.69/203.97	tff('13', plain,
203.69/203.97	    ![X0 : fun(nat, type), X1 : bool]:
203.69/203.97	      (~ $true
203.69/203.97	       | X1 = aa(list(type), bool, typings(X0, nil(dB)), nil(type))
203.69/203.97	       | X1 = fFalse),
203.69/203.97	    inference('sup-', [status(thm)], ['9', '12'])).
203.69/203.97	tff('14', plain,
203.69/203.97	    ![X0 : fun(nat, type), X1 : bool]:
203.69/203.97	      (X1 = fFalse
203.69/203.97	       | X1 = aa(list(type), bool, typings(X0, nil(dB)), nil(type))),
203.69/203.97	    inference('simplify', [status(thm)], ['13'])).
203.69/203.97	tff(conj_0, conjecture,
203.69/203.97	  (pp(aa(dB,bool,
203.69/203.97	         aa(dB,fun(dB,bool),beta,
203.69/203.97	            foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),
203.69/203.97	         foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))))).
203.69/203.97	tff(zf_stmt_0, negated_conjecture,
203.69/203.97	  (~
203.69/203.97	    pp(aa(dB,bool,
203.69/203.97	          aa(dB,fun(dB,bool),beta,
203.69/203.97	             foldl(dB,dB,app,aa(dB,dB,aa(dB,fun(dB,dB),app,abs(r)),a),as)),
203.69/203.97	          foldl(dB,dB,app,subst(r,a,zero_zero(nat)),as))))).
203.69/203.97	tff('15', plain,
203.69/203.97	    ~ pp(
203.69/203.97	        aa(dB, bool, 
203.69/203.97	          aa(dB, fun(dB, bool), beta, 
203.69/203.97	            foldl(dB, dB, app, 
203.69/203.97	              aa(dB, dB, aa(dB, fun(dB, dB), app, abs(r)), a), as)), 
203.69/203.97	          foldl(dB, dB, app, subst(r, a, zero_zero(nat)), as))),
203.69/203.97	    inference('cnf', [status(esa)], [zf_stmt_0])).
203.69/203.97	tff('16', plain,
203.69/203.97	    ~ pp(
203.69/203.97	        aa(dB, bool, 
203.69/203.97	          aa(dB, fun(dB, bool), beta, 
203.69/203.97	            foldl(dB, dB, app, abs(r), cons(dB, a, as))), 
203.69/203.97	          foldl(dB, dB, app, subst(r, a, zero_zero(nat)), as))),
203.69/203.97	    inference('demod', [status(thm)], ['15', '1'])).
203.69/203.97	tff('17', plain,
203.69/203.97	    ![X0 : fun(nat, type)]:
203.69/203.97	      (~ pp(aa(list(type), bool, typings(X0, nil(dB)), nil(type)))
203.69/203.97	       | aa(dB, bool, 
203.69/203.97	           aa(dB, fun(dB, bool), beta, 
203.69/203.97	             foldl(dB, dB, app, abs(r), cons(dB, a, as))), 
203.69/203.97	           foldl(dB, dB, app, subst(r, a, zero_zero(nat)), as))
203.69/203.97	          = fFalse),
203.69/203.97	    inference('sup-', [status(thm)], ['14', '16'])).
203.69/203.97	tff('18', plain,
203.69/203.97	    (~ $true
203.69/203.97	     | aa(dB, bool, 
203.69/203.97	         aa(dB, fun(dB, bool), beta, 
203.69/203.97	           foldl(dB, dB, app, abs(r), cons(dB, a, as))), 
203.69/203.97	         foldl(dB, dB, app, subst(r, a, zero_zero(nat)), as))
203.69/203.97	        = fFalse),
203.69/203.97	    inference('demod', [status(thm)], ['17', '9'])).
203.69/203.97	tff('19', plain,
203.69/203.97	    aa(dB, bool, 
203.69/203.97	      aa(dB, fun(dB, bool), beta, 
203.69/203.97	        foldl(dB, dB, app, abs(r), cons(dB, a, as))), 
203.69/203.97	      foldl(dB, dB, app, subst(r, a, zero_zero(nat)), as))
203.69/203.97	     = fFalse,
203.69/203.97	    inference('simplify', [status(thm)], ['18'])).
203.69/203.97	tff('20', plain,
203.69/203.97	    ![X0 : list(dB), X1 : dB, X2 : dB]:
203.69/203.97	      (pp(
203.69/203.97	         aa(dB, bool, 
203.69/203.97	           aa(dB, fun(dB, bool), beta, 
203.69/203.97	             foldl(dB, dB, app, abs(r), cons(dB, a, as))), 
203.69/203.97	           foldl(dB, dB, app, subst(r, a, zero_zero(nat)), as)))
203.69/203.97	       | aa(dB, bool, 
203.69/203.97	           aa(dB, fun(dB, bool), beta, foldl(dB, dB, app, X2, X0)), 
203.69/203.97	           foldl(dB, dB, app, X1, X0))
203.69/203.97	          = fTrue
203.69/203.97	       | ~ pp(aa(dB, bool, aa(dB, fun(dB, bool), beta, X2), X1))),
203.69/203.97	    inference('demod', [status(thm)], ['7', '19'])).
203.69/203.97	tff('21', plain,
203.69/203.97	    ![X0 : list(dB), X1 : dB, X2 : dB]:
203.69/203.97	      (~ pp(aa(dB, bool, aa(dB, fun(dB, bool), beta, X2), X1))
203.69/203.97	       | aa(dB, bool, 
203.69/203.97	           aa(dB, fun(dB, bool), beta, foldl(dB, dB, app, X2, X0)), 
203.69/203.97	           foldl(dB, dB, app, X1, X0))
203.69/203.97	          = fTrue),
203.69/203.97	    inference('clc', [status(thm)], ['20', '16'])).
203.69/203.97	tff('22', plain,
203.69/203.97	    ![X0 : dB, X1 : dB, X2 : list(dB)]:
203.69/203.97	      (~ $true
203.69/203.97	       | aa(dB, bool, 
203.69/203.97	           aa(dB, fun(dB, bool), beta, 
203.69/203.97	             foldl(dB, dB, app, 
203.69/203.97	               aa(dB, dB, combc(dB, dB, dB, app, X0), abs(X1)), X2)), 
203.69/203.97	           foldl(dB, dB, app, subst(X1, X0, zero_zero(nat)), X2))
203.69/203.97	          = fTrue),
203.69/203.97	    inference('sup-', [status(thm)], ['4', '21'])).
203.69/203.97	tff('23', plain,
203.69/203.97	    ![X0 : dB, X1 : dB, X2 : list(dB)]:
203.69/203.97	      aa(dB, bool, 
203.69/203.97	        aa(dB, fun(dB, bool), beta, 
203.69/203.97	          foldl(dB, dB, app, 
203.69/203.97	            aa(dB, dB, combc(dB, dB, dB, app, X0), abs(X1)), X2)), 
203.69/203.97	        foldl(dB, dB, app, subst(X1, X0, zero_zero(nat)), X2))
203.69/203.97	       = fTrue,
203.69/203.97	    inference('simplify', [status(thm)], ['22'])).
203.69/203.97	tff('24', plain,
203.69/203.97	    ![X0 : list(dB), X1 : dB, X2 : dB]:
203.69/203.97	      aa(dB, bool, 
203.69/203.97	        aa(dB, fun(dB, bool), beta, 
203.69/203.97	          foldl(dB, dB, app, abs(X2), cons(dB, X1, X0))), 
203.69/203.97	        foldl(dB, dB, app, subst(X2, X1, zero_zero(nat)), X0))
203.69/203.97	       = fTrue,
203.69/203.97	    inference('sup+', [status(thm)], ['2', '23'])).
203.69/203.97	tff(help_pp_2_1_U, axiom, (pp(fTrue))).
203.69/203.97	tff('25', plain, pp(fTrue), inference('cnf', [status(esa)], [help_pp_2_1_U])).
203.69/203.97	tff('26', plain,
203.69/203.97	    ![X0 : list(dB), X1 : dB, X2 : dB]:
203.69/203.97	      pp(
203.69/203.97	        aa(dB, bool, 
203.69/203.97	          aa(dB, fun(dB, bool), beta, 
203.69/203.97	            foldl(dB, dB, app, abs(X2), cons(dB, X1, X0))), 
203.69/203.97	          foldl(dB, dB, app, subst(X2, X1, zero_zero(nat)), X0))),
203.69/203.97	    inference('sup+', [status(thm)], ['24', '25'])).
203.69/203.97	tff('27', plain, ~ $true, inference('sup-', [status(thm)], ['26', '16'])).
203.69/203.97	tff('28', plain, $false, inference('simplify', [status(thm)], ['27'])).
203.69/203.97	
203.69/203.97	% SZS output end Refutation
203.69/203.98	EOF
