TSTP Solution File: ITP006+2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP006+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 06:56:44 EDT 2024
% Result : Theorem 3.49s 0.88s
% Output : Refutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 23
% Syntax : Number of formulae : 88 ( 18 unt; 0 def)
% Number of atoms : 557 ( 24 equ)
% Maximal formula atoms : 38 ( 6 avg)
% Number of connectives : 698 ( 229 ~; 211 |; 135 &)
% ( 36 <=>; 85 =>; 0 <=; 2 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 316 ( 258 !; 58 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7569,plain,
$false,
inference(subsumption_resolution,[],[f7545,f334]) ).
fof(f334,plain,
~ p(c_2Ebool_2EF),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_false_p) ).
fof(f7545,plain,
p(c_2Ebool_2EF),
inference(superposition,[],[f7168,f7493]) ).
fof(f7493,plain,
c_2Ebool_2EF = ap(sK37,ap(sK35,sK38(sK34,sK35,sK37))),
inference(resolution,[],[f7176,f6615]) ).
fof(f6615,plain,
mem(sK38(sK34,sK35,sK37),sK34),
inference(subsumption_resolution,[],[f6614,f5288]) ).
fof(f5288,plain,
sP9(sK34,sK33),
inference(resolution,[],[f5285,f359]) ).
fof(f359,plain,
! [X2,X3,X0,X1] :
( ~ sP10(X0,X1,X2,X3)
| sP9(X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( ! [X5] :
( sP5(X1,X5,X0,X4)
| ~ mem(X5,arr(X1,bool)) )
| ~ mem(X4,arr(X0,X1)) )
& ! [X6] :
( ! [X7] :
( sP3(X1,X7,X0,X6)
| ~ mem(X7,arr(X1,bool)) )
| ~ mem(X6,arr(X0,X1)) )
& sP9(X0,X1)
& sP8(X0,X1)
& sP7(X1,X0,X3,X2)
& sP6(X1,X0,X3,X2) )
| ~ sP10(X0,X1,X2,X3) ),
inference(rectify,[],[f206]) ).
fof(f206,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( ! [X5] :
( sP5(X1,X5,X0,X4)
| ~ mem(X5,arr(X1,bool)) )
| ~ mem(X4,arr(X0,X1)) )
& ! [X8] :
( ! [X9] :
( sP3(X1,X9,X0,X8)
| ~ mem(X9,arr(X1,bool)) )
| ~ mem(X8,arr(X0,X1)) )
& sP9(X0,X1)
& sP8(X0,X1)
& sP7(X1,X0,X3,X2)
& sP6(X1,X0,X3,X2) )
| ~ sP10(X0,X1,X2,X3) ),
inference(nnf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0,X1,X2,X3] :
( ( ! [X4] :
( ! [X5] :
( sP5(X1,X5,X0,X4)
| ~ mem(X5,arr(X1,bool)) )
| ~ mem(X4,arr(X0,X1)) )
& ! [X8] :
( ! [X9] :
( sP3(X1,X9,X0,X8)
| ~ mem(X9,arr(X1,bool)) )
| ~ mem(X8,arr(X0,X1)) )
& sP9(X0,X1)
& sP8(X0,X1)
& sP7(X1,X0,X3,X2)
& sP6(X1,X0,X3,X2) )
| ~ sP10(X0,X1,X2,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f5285,plain,
sP10(sK34,sK33,sK35,sK36),
inference(subsumption_resolution,[],[f5279,f327]) ).
fof(f327,plain,
ne(sK34),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),sK37))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),sK36))
& ! [X5] :
( p(ap(sK36,X5))
| ~ p(ap(sK37,X5))
| ~ mem(X5,sK33) )
& mem(sK37,arr(sK33,bool))
& mem(sK36,arr(sK33,bool))
& mem(sK35,arr(sK34,sK33))
& ne(sK34)
& ne(sK33) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36,sK37])],[f107,f203,f202,f201,f200,f199]) ).
fof(f199,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,X0) )
& mem(X4,arr(X0,bool)) )
& mem(X3,arr(X0,bool)) )
& mem(X2,arr(X1,X0)) )
& ne(X1) )
& ne(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,sK33),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,sK33),X2),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,sK33) )
& mem(X4,arr(sK33,bool)) )
& mem(X3,arr(sK33,bool)) )
& mem(X2,arr(X1,sK33)) )
& ne(X1) )
& ne(sK33) ) ),
introduced(choice_axiom,[]) ).
fof(f200,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,sK33),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,sK33),X2),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,sK33) )
& mem(X4,arr(sK33,bool)) )
& mem(X3,arr(sK33,bool)) )
& mem(X2,arr(X1,sK33)) )
& ne(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),X2),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,sK33) )
& mem(X4,arr(sK33,bool)) )
& mem(X3,arr(sK33,bool)) )
& mem(X2,arr(sK34,sK33)) )
& ne(sK34) ) ),
introduced(choice_axiom,[]) ).
fof(f201,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),X2),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,sK33) )
& mem(X4,arr(sK33,bool)) )
& mem(X3,arr(sK33,bool)) )
& mem(X2,arr(sK34,sK33)) )
=> ( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,sK33) )
& mem(X4,arr(sK33,bool)) )
& mem(X3,arr(sK33,bool)) )
& mem(sK35,arr(sK34,sK33)) ) ),
introduced(choice_axiom,[]) ).
fof(f202,plain,
( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,sK33) )
& mem(X4,arr(sK33,bool)) )
& mem(X3,arr(sK33,bool)) )
=> ( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),sK36))
& ! [X5] :
( p(ap(sK36,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,sK33) )
& mem(X4,arr(sK33,bool)) )
& mem(sK36,arr(sK33,bool)) ) ),
introduced(choice_axiom,[]) ).
fof(f203,plain,
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),sK36))
& ! [X5] :
( p(ap(sK36,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,sK33) )
& mem(X4,arr(sK33,bool)) )
=> ( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),sK37))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),sK36))
& ! [X5] :
( p(ap(sK36,X5))
| ~ p(ap(sK37,X5))
| ~ mem(X5,sK33) )
& mem(sK37,arr(sK33,bool)) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,X0) )
& mem(X4,arr(X0,bool)) )
& mem(X3,arr(X0,bool)) )
& mem(X2,arr(X1,X0)) )
& ne(X1) )
& ne(X0) ),
inference(flattening,[],[f106]) ).
fof(f106,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4))
& p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
& ! [X5] :
( p(ap(X3,X5))
| ~ p(ap(X4,X5))
| ~ mem(X5,X0) )
& mem(X4,arr(X0,bool)) )
& mem(X3,arr(X0,bool)) )
& mem(X2,arr(X1,X0)) )
& ne(X1) )
& ne(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
~ ! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X1,X0))
=> ! [X3] :
( mem(X3,arr(X0,bool))
=> ! [X4] :
( mem(X4,arr(X0,bool))
=> ( ! [X5] :
( mem(X5,X0)
=> ( p(ap(X4,X5))
=> p(ap(X3,X5)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X3))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X1,X0),X2),X4)) ) ) ) ) ) ) ),
inference(rectify,[],[f53]) ).
fof(f53,negated_conjecture,
~ ! [X8] :
( ne(X8)
=> ! [X9] :
( ne(X9)
=> ! [X19] :
( mem(X19,arr(X9,X8))
=> ! [X20] :
( mem(X20,arr(X8,bool))
=> ! [X44] :
( mem(X44,arr(X8,bool))
=> ( ! [X45] :
( mem(X45,X8)
=> ( p(ap(X44,X45))
=> p(ap(X20,X45)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X8),X19),X20))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X8),X19),X44)) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f52]) ).
fof(f52,conjecture,
! [X8] :
( ne(X8)
=> ! [X9] :
( ne(X9)
=> ! [X19] :
( mem(X19,arr(X9,X8))
=> ! [X20] :
( mem(X20,arr(X8,bool))
=> ! [X44] :
( mem(X44,arr(X8,bool))
=> ( ! [X45] :
( mem(X45,X8)
=> ( p(ap(X44,X45))
=> p(ap(X20,X45)) ) )
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X8),X19),X20))
=> p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X9,X8),X19),X44)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT) ).
fof(f5279,plain,
( sP10(sK34,sK33,sK35,sK36)
| ~ ne(sK34) ),
inference(resolution,[],[f5277,f328]) ).
fof(f328,plain,
mem(sK35,arr(sK34,sK33)),
inference(cnf_transformation,[],[f204]) ).
fof(f5277,plain,
! [X0,X1] :
( ~ mem(X1,arr(X0,sK33))
| sP10(X0,sK33,X1,sK36)
| ~ ne(X0) ),
inference(subsumption_resolution,[],[f5265,f326]) ).
fof(f326,plain,
ne(sK33),
inference(cnf_transformation,[],[f204]) ).
fof(f5265,plain,
! [X0,X1] :
( sP10(X0,sK33,X1,sK36)
| ~ mem(X1,arr(X0,sK33))
| ~ ne(sK33)
| ~ ne(X0) ),
inference(resolution,[],[f396,f329]) ).
fof(f329,plain,
mem(sK36,arr(sK33,bool)),
inference(cnf_transformation,[],[f204]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( ~ mem(X3,arr(X1,bool))
| sP10(X0,X1,X2,X3)
| ~ mem(X2,arr(X0,X1))
| ~ ne(X1)
| ~ ne(X0) ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( sP10(X0,X1,X2,X3)
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(definition_folding,[],[f120,f167,f166,f165,f164,f163,f162,f161,f160,f159,f158,f157]) ).
fof(f157,plain,
! [X2,X3,X0,X1] :
( sP0(X2,X3,X0,X1)
<=> ! [X20] :
( ? [X21] :
( p(ap(X3,ap(X2,X21)))
& mem(X21,X0) )
| ~ p(ap(X3,X20))
| ~ mem(X20,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( sP1(X2,X3,X0,X1)
<=> ! [X18] :
( ? [X19] :
( ~ p(ap(X3,ap(X2,X19)))
& mem(X19,X0) )
| p(ap(X3,X18))
| ~ mem(X18,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f159,plain,
! [X8,X0,X9,X1] :
( sP2(X8,X0,X9,X1)
<=> ! [X10] :
( ? [X11] :
( ap(X8,X11) = X10
& mem(X11,X0) )
| ~ p(ap(X9,X10))
| ~ mem(X10,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f160,plain,
! [X1,X9,X0,X8] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X8),X9))
<=> sP2(X8,X0,X9,X1) )
| ~ sP3(X1,X9,X0,X8) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f161,plain,
! [X4,X0,X5,X1] :
( sP4(X4,X0,X5,X1)
<=> ! [X6] :
( ? [X7] :
( ap(X4,X7) = X6
& mem(X7,X0) )
| p(ap(X5,X6))
| ~ mem(X6,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f162,plain,
! [X1,X5,X0,X4] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X4),X5))
<=> sP4(X4,X0,X5,X1) )
| ~ sP5(X1,X5,X0,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f163,plain,
! [X1,X0,X3,X2] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
<=> sP0(X2,X3,X0,X1) )
| ~ sP6(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f164,plain,
! [X1,X0,X3,X2] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
<=> sP1(X2,X3,X0,X1) )
| ~ sP7(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f165,plain,
! [X0,X1] :
( ! [X15] :
( ! [X16] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X15),X16))
<=> ! [X17] :
( p(ap(X16,ap(X15,X17)))
| ~ mem(X17,X0) ) )
| ~ mem(X16,arr(X1,bool)) )
| ~ mem(X15,arr(X0,X1)) )
| ~ sP8(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f166,plain,
! [X0,X1] :
( ! [X12] :
( ! [X13] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
<=> ! [X14] :
( ~ p(ap(X13,ap(X12,X14)))
| ~ mem(X14,X0) ) )
| ~ mem(X13,arr(X1,bool)) )
| ~ mem(X12,arr(X0,X1)) )
| ~ sP9(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ! [X4] :
( ! [X5] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X4),X5))
<=> ! [X6] :
( ? [X7] :
( ap(X4,X7) = X6
& mem(X7,X0) )
| p(ap(X5,X6))
| ~ mem(X6,X1) ) )
| ~ mem(X5,arr(X1,bool)) )
| ~ mem(X4,arr(X0,X1)) )
& ! [X8] :
( ! [X9] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X8),X9))
<=> ! [X10] :
( ? [X11] :
( ap(X8,X11) = X10
& mem(X11,X0) )
| ~ p(ap(X9,X10))
| ~ mem(X10,X1) ) )
| ~ mem(X9,arr(X1,bool)) )
| ~ mem(X8,arr(X0,X1)) )
& ! [X12] :
( ! [X13] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
<=> ! [X14] :
( ~ p(ap(X13,ap(X12,X14)))
| ~ mem(X14,X0) ) )
| ~ mem(X13,arr(X1,bool)) )
| ~ mem(X12,arr(X0,X1)) )
& ! [X15] :
( ! [X16] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X15),X16))
<=> ! [X17] :
( p(ap(X16,ap(X15,X17)))
| ~ mem(X17,X0) ) )
| ~ mem(X16,arr(X1,bool)) )
| ~ mem(X15,arr(X0,X1)) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
<=> ! [X18] :
( ? [X19] :
( ~ p(ap(X3,ap(X2,X19)))
& mem(X19,X0) )
| p(ap(X3,X18))
| ~ mem(X18,X1) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
<=> ! [X20] :
( ? [X21] :
( p(ap(X3,ap(X2,X21)))
& mem(X21,X0) )
| ~ p(ap(X3,X20))
| ~ mem(X20,X1) ) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ! [X4] :
( ! [X5] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X4),X5))
<=> ! [X6] :
( ? [X7] :
( ap(X4,X7) = X6
& mem(X7,X0) )
| p(ap(X5,X6))
| ~ mem(X6,X1) ) )
| ~ mem(X5,arr(X1,bool)) )
| ~ mem(X4,arr(X0,X1)) )
& ! [X8] :
( ! [X9] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X8),X9))
<=> ! [X10] :
( ? [X11] :
( ap(X8,X11) = X10
& mem(X11,X0) )
| ~ p(ap(X9,X10))
| ~ mem(X10,X1) ) )
| ~ mem(X9,arr(X1,bool)) )
| ~ mem(X8,arr(X0,X1)) )
& ! [X12] :
( ! [X13] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
<=> ! [X14] :
( ~ p(ap(X13,ap(X12,X14)))
| ~ mem(X14,X0) ) )
| ~ mem(X13,arr(X1,bool)) )
| ~ mem(X12,arr(X0,X1)) )
& ! [X15] :
( ! [X16] :
( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X15),X16))
<=> ! [X17] :
( p(ap(X16,ap(X15,X17)))
| ~ mem(X17,X0) ) )
| ~ mem(X16,arr(X1,bool)) )
| ~ mem(X15,arr(X0,X1)) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
<=> ! [X18] :
( ? [X19] :
( ~ p(ap(X3,ap(X2,X19)))
& mem(X19,X0) )
| p(ap(X3,X18))
| ~ mem(X18,X1) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
<=> ! [X20] :
( ? [X21] :
( p(ap(X3,ap(X2,X21)))
& mem(X21,X0) )
| ~ p(ap(X3,X20))
| ~ mem(X20,X1) ) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) )
| ~ ne(X1) )
| ~ ne(X0) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ne(X0)
=> ! [X1] :
( ne(X1)
=> ! [X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ( ! [X4] :
( mem(X4,arr(X0,X1))
=> ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X0,X1),X4),X5))
<=> ! [X6] :
( mem(X6,X1)
=> ( ~ p(ap(X5,X6))
=> ? [X7] :
( ap(X4,X7) = X6
& mem(X7,X0) ) ) ) ) ) )
& ! [X8] :
( mem(X8,arr(X0,X1))
=> ! [X9] :
( mem(X9,arr(X1,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X0,X1),X8),X9))
<=> ! [X10] :
( mem(X10,X1)
=> ( p(ap(X9,X10))
=> ? [X11] :
( ap(X8,X11) = X10
& mem(X11,X0) ) ) ) ) ) )
& ! [X12] :
( mem(X12,arr(X0,X1))
=> ! [X13] :
( mem(X13,arr(X1,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
<=> ! [X14] :
( mem(X14,X0)
=> ~ p(ap(X13,ap(X12,X14))) ) ) ) )
& ! [X15] :
( mem(X15,arr(X0,X1))
=> ! [X16] :
( mem(X16,arr(X1,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X0,X1),X15),X16))
<=> ! [X17] :
( mem(X17,X0)
=> p(ap(X16,ap(X15,X17))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X0,X1),X2),X3))
<=> ! [X18] :
( mem(X18,X1)
=> ( ~ p(ap(X3,X18))
=> ? [X19] :
( ~ p(ap(X3,ap(X2,X19)))
& mem(X19,X0) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X0,X1),X2),X3))
<=> ! [X20] :
( mem(X20,X1)
=> ( p(ap(X3,X20))
=> ? [X21] :
( p(ap(X3,ap(X2,X21)))
& mem(X21,X0) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X8] :
( ne(X8)
=> ! [X9] :
( ne(X9)
=> ! [X19] :
( mem(X19,arr(X8,X9))
=> ! [X20] :
( mem(X20,arr(X9,bool))
=> ( ! [X35] :
( mem(X35,arr(X8,X9))
=> ! [X36] :
( mem(X36,arr(X9,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(X8,X9),X35),X36))
<=> ! [X37] :
( mem(X37,X9)
=> ( ~ p(ap(X36,X37))
=> ? [X38] :
( ap(X35,X38) = X37
& mem(X38,X8) ) ) ) ) ) )
& ! [X31] :
( mem(X31,arr(X8,X9))
=> ! [X32] :
( mem(X32,arr(X9,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(X8,X9),X31),X32))
<=> ! [X33] :
( mem(X33,X9)
=> ( p(ap(X32,X33))
=> ? [X34] :
( ap(X31,X34) = X33
& mem(X34,X8) ) ) ) ) ) )
& ! [X28] :
( mem(X28,arr(X8,X9))
=> ! [X29] :
( mem(X29,arr(X9,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X8,X9),X28),X29))
<=> ! [X30] :
( mem(X30,X8)
=> ~ p(ap(X29,ap(X28,X30))) ) ) ) )
& ! [X25] :
( mem(X25,arr(X8,X9))
=> ! [X26] :
( mem(X26,arr(X9,bool))
=> ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(X8,X9),X25),X26))
<=> ! [X27] :
( mem(X27,X8)
=> p(ap(X26,ap(X25,X27))) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(X8,X9),X19),X20))
<=> ! [X23] :
( mem(X23,X9)
=> ( ~ p(ap(X20,X23))
=> ? [X24] :
( ~ p(ap(X20,ap(X19,X24)))
& mem(X24,X8) ) ) ) )
& ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(X8,X9),X19),X20))
<=> ! [X21] :
( mem(X21,X9)
=> ( p(ap(X20,X21))
=> ? [X22] :
( p(ap(X20,ap(X19,X22)))
& mem(X22,X8) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2EquantHeuristics_2EGUESS__REWRITES) ).
fof(f6614,plain,
( mem(sK38(sK34,sK35,sK37),sK34)
| ~ sP9(sK34,sK33) ),
inference(subsumption_resolution,[],[f6613,f328]) ).
fof(f6613,plain,
( mem(sK38(sK34,sK35,sK37),sK34)
| ~ mem(sK35,arr(sK34,sK33))
| ~ sP9(sK34,sK33) ),
inference(subsumption_resolution,[],[f6432,f330]) ).
fof(f330,plain,
mem(sK37,arr(sK33,bool)),
inference(cnf_transformation,[],[f204]) ).
fof(f6432,plain,
( mem(sK38(sK34,sK35,sK37),sK34)
| ~ mem(sK37,arr(sK33,bool))
| ~ mem(sK35,arr(sK34,sK33))
| ~ sP9(sK34,sK33) ),
inference(resolution,[],[f363,f333]) ).
fof(f333,plain,
~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),sK37)),
inference(cnf_transformation,[],[f204]) ).
fof(f363,plain,
! [X2,X3,X0,X1] :
( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| mem(sK38(X0,X2,X3),X0)
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ( p(ap(X3,ap(X2,sK38(X0,X2,X3))))
& mem(sK38(X0,X2,X3),X0) ) )
& ( ! [X5] :
( ~ p(ap(X3,ap(X2,X5)))
| ~ mem(X5,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3)) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) )
| ~ sP9(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f209,f210]) ).
fof(f210,plain,
! [X0,X2,X3] :
( ? [X4] :
( p(ap(X3,ap(X2,X4)))
& mem(X4,X0) )
=> ( p(ap(X3,ap(X2,sK38(X0,X2,X3))))
& mem(sK38(X0,X2,X3),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f209,plain,
! [X0,X1] :
( ! [X2] :
( ! [X3] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ? [X4] :
( p(ap(X3,ap(X2,X4)))
& mem(X4,X0) ) )
& ( ! [X5] :
( ~ p(ap(X3,ap(X2,X5)))
| ~ mem(X5,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3)) ) )
| ~ mem(X3,arr(X1,bool)) )
| ~ mem(X2,arr(X0,X1)) )
| ~ sP9(X0,X1) ),
inference(rectify,[],[f208]) ).
fof(f208,plain,
! [X0,X1] :
( ! [X12] :
( ! [X13] :
( ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13))
| ? [X14] :
( p(ap(X13,ap(X12,X14)))
& mem(X14,X0) ) )
& ( ! [X14] :
( ~ p(ap(X13,ap(X12,X14)))
| ~ mem(X14,X0) )
| ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X12),X13)) ) )
| ~ mem(X13,arr(X1,bool)) )
| ~ mem(X12,arr(X0,X1)) )
| ~ sP9(X0,X1) ),
inference(nnf_transformation,[],[f166]) ).
fof(f7176,plain,
! [X0] :
( ~ mem(X0,sK34)
| c_2Ebool_2EF = ap(sK37,ap(sK35,X0)) ),
inference(subsumption_resolution,[],[f7048,f719]) ).
fof(f719,plain,
! [X0] :
( mem(ap(sK35,X0),sK33)
| ~ mem(X0,sK34) ),
inference(resolution,[],[f550,f328]) ).
fof(f550,plain,
! [X2,X3,X0,X1] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2] :
( ! [X3] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( mem(X2,arr(X0,X1))
=> ! [X3] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ap_tp) ).
fof(f7048,plain,
! [X0] :
( ~ mem(X0,sK34)
| ~ mem(ap(sK35,X0),sK33)
| c_2Ebool_2EF = ap(sK37,ap(sK35,X0)) ),
inference(resolution,[],[f7044,f787]) ).
fof(f787,plain,
! [X0] :
( p(ap(sK36,X0))
| ~ mem(X0,sK33)
| c_2Ebool_2EF = ap(sK37,X0) ),
inference(duplicate_literal_removal,[],[f784]) ).
fof(f784,plain,
! [X0] :
( c_2Ebool_2EF = ap(sK37,X0)
| ~ mem(X0,sK33)
| p(ap(sK36,X0))
| ~ mem(X0,sK33) ),
inference(resolution,[],[f736,f331]) ).
fof(f331,plain,
! [X5] :
( ~ p(ap(sK37,X5))
| p(ap(sK36,X5))
| ~ mem(X5,sK33) ),
inference(cnf_transformation,[],[f204]) ).
fof(f736,plain,
! [X0] :
( p(ap(sK37,X0))
| c_2Ebool_2EF = ap(sK37,X0)
| ~ mem(X0,sK33) ),
inference(resolution,[],[f721,f692]) ).
fof(f692,plain,
! [X0] :
( ~ mem(X0,bool)
| c_2Ebool_2EF = X0
| p(X0) ),
inference(subsumption_resolution,[],[f686,f334]) ).
fof(f686,plain,
! [X0] :
( p(c_2Ebool_2EF)
| p(X0)
| c_2Ebool_2EF = X0
| ~ mem(X0,bool) ),
inference(resolution,[],[f431,f338]) ).
fof(f338,plain,
mem(c_2Ebool_2EF,bool),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
fof(f431,plain,
! [X0,X1] :
( ~ mem(X1,bool)
| p(X1)
| p(X0)
| X0 = X1
| ~ mem(X0,bool) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X1)
| p(X0) ) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(nnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ( p(X0)
<~> p(X1) )
| ~ mem(X1,bool) )
| ~ mem(X0,bool) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( mem(X0,bool)
=> ! [X1] :
( mem(X1,bool)
=> ( ( p(X0)
<=> p(X1) )
=> X0 = X1 ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X4] :
( mem(X4,bool)
=> ! [X5] :
( mem(X5,bool)
=> ( ( p(X4)
<=> p(X5) )
=> X4 = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',boolext) ).
fof(f721,plain,
! [X0] :
( mem(ap(sK37,X0),bool)
| ~ mem(X0,sK33) ),
inference(resolution,[],[f550,f330]) ).
fof(f7044,plain,
! [X0] :
( ~ p(ap(sK36,ap(sK35,X0)))
| ~ mem(X0,sK34) ),
inference(subsumption_resolution,[],[f7043,f5288]) ).
fof(f7043,plain,
! [X0] :
( ~ mem(X0,sK34)
| ~ p(ap(sK36,ap(sK35,X0)))
| ~ sP9(sK34,sK33) ),
inference(subsumption_resolution,[],[f7042,f328]) ).
fof(f7042,plain,
! [X0] :
( ~ mem(X0,sK34)
| ~ p(ap(sK36,ap(sK35,X0)))
| ~ mem(sK35,arr(sK34,sK33))
| ~ sP9(sK34,sK33) ),
inference(subsumption_resolution,[],[f7029,f329]) ).
fof(f7029,plain,
! [X0] :
( ~ mem(X0,sK34)
| ~ p(ap(sK36,ap(sK35,X0)))
| ~ mem(sK36,arr(sK33,bool))
| ~ mem(sK35,arr(sK34,sK33))
| ~ sP9(sK34,sK33) ),
inference(resolution,[],[f362,f332]) ).
fof(f332,plain,
p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(sK34,sK33),sK35),sK36)),
inference(cnf_transformation,[],[f204]) ).
fof(f362,plain,
! [X2,X3,X0,X1,X5] :
( ~ p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ~ mem(X5,X0)
| ~ p(ap(X3,ap(X2,X5)))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
fof(f7168,plain,
p(ap(sK37,ap(sK35,sK38(sK34,sK35,sK37)))),
inference(subsumption_resolution,[],[f7167,f5288]) ).
fof(f7167,plain,
( p(ap(sK37,ap(sK35,sK38(sK34,sK35,sK37))))
| ~ sP9(sK34,sK33) ),
inference(subsumption_resolution,[],[f7166,f328]) ).
fof(f7166,plain,
( p(ap(sK37,ap(sK35,sK38(sK34,sK35,sK37))))
| ~ mem(sK35,arr(sK34,sK33))
| ~ sP9(sK34,sK33) ),
inference(subsumption_resolution,[],[f7149,f330]) ).
fof(f7149,plain,
( p(ap(sK37,ap(sK35,sK38(sK34,sK35,sK37))))
| ~ mem(sK37,arr(sK33,bool))
| ~ mem(sK35,arr(sK34,sK33))
| ~ sP9(sK34,sK33) ),
inference(resolution,[],[f364,f333]) ).
fof(f364,plain,
! [X2,X3,X0,X1] :
( p(ap(X3,ap(X2,sK38(X0,X2,X3))))
| p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(X0,X1),X2),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X2,arr(X0,X1))
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f211]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.14 % Problem : ITP006+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.06/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.37 % Computer : n012.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8042.1875MB
% 0.12/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri May 3 19:01:53 EDT 2024
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % (16072)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.39 % (16075)WARNING: value z3 for option sas not known
% 0.12/0.39 % (16075)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.39 % (16079)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.39 % (16076)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.39 % (16074)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.39 % (16080)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.39 % (16077)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.39 % (16073)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.42 TRYING [1]
% 0.18/0.42 TRYING [2]
% 0.18/0.45 TRYING [3]
% 0.18/0.50 TRYING [1]
% 0.18/0.51 TRYING [2]
% 0.18/0.56 TRYING [4]
% 1.85/0.63 TRYING [3]
% 3.49/0.88 % (16075)First to succeed.
% 3.49/0.88 % (16075)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16072"
% 3.49/0.88 % (16075)Refutation found. Thanks to Tanya!
% 3.49/0.88 % SZS status Theorem for theBenchmark
% 3.49/0.88 % SZS output start Proof for theBenchmark
% See solution above
% 3.49/0.89 % (16075)------------------------------
% 3.49/0.89 % (16075)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.49/0.89 % (16075)Termination reason: Refutation
% 3.49/0.89
% 3.49/0.89 % (16075)Memory used [KB]: 8548
% 3.49/0.89 % (16075)Time elapsed: 0.492 s
% 3.49/0.89 % (16075)Instructions burned: 966 (million)
% 3.49/0.89 % (16072)Success in time 0.504 s
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