TSTP Solution File: SWC239+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC239+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n023.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 10:18:23 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 73
% Syntax : Number of formulae : 367 ( 31 unt; 0 def)
% Number of atoms : 1379 ( 319 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 1636 ( 624 ~; 637 |; 265 &)
% ( 44 <=>; 66 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 33 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 383 ( 297 !; 86 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3662,plain,
$false,
inference(avatar_sat_refutation,[],[f791,f794,f890,f899,f1149,f1153,f1468,f1472,f1487,f1491,f1563,f1567,f1647,f1651,f1771,f1775,f1875,f1879,f1889,f1906,f2210,f2214,f2259,f2264,f2581,f2621,f3402,f3455,f3661]) ).
fof(f3661,plain,
~ spl73_1,
inference(avatar_contradiction_clause,[],[f3660]) ).
fof(f3660,plain,
( $false
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f3659,f414]) ).
fof(f414,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f3659,plain,
( ~ ssList(nil)
| ~ spl73_1 ),
inference(trivial_inequality_removal,[],[f3658]) ).
fof(f3658,plain,
( sK22 != sK22
| ~ ssList(nil)
| ~ spl73_1 ),
inference(superposition,[],[f3655,f682]) ).
fof(f682,plain,
sK22 = app(sK22,nil),
inference(resolution,[],[f476,f396]) ).
fof(f396,plain,
ssList(sK22),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
( ( ( nil = sK24
& nil = sK25 )
| sP1(sK25,sK24) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK22
& sK22 = sK24
& sK23 = sK25
& ssList(sK25)
& ssList(sK24)
& ssList(sK23)
& ssList(sK22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24,sK25])],[f262,f266,f265,f264,f263]) ).
fof(f263,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP1(X3,X2) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP1(X3,X2) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK22
& sK22 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f264,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP1(X3,X2) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK22
& sK22 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP1(X3,X2) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK22
& sK22 = X2
& sK23 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f265,plain,
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP1(X3,X2) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK22
& sK22 = X2
& sK23 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ( nil = sK24
& nil = X3 )
| sP1(X3,sK24) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK22
& sK22 = sK24
& sK23 = X3
& ssList(X3) )
& ssList(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f266,plain,
( ? [X3] :
( ( ( nil = sK24
& nil = X3 )
| sP1(X3,sK24) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK22
& sK22 = sK24
& sK23 = X3
& ssList(X3) )
=> ( ( ( nil = sK24
& nil = sK25 )
| sP1(sK25,sK24) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK22
& sK22 = sK24
& sK23 = sK25
& ssList(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f262,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP1(X3,X2) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(rectify,[],[f226]) ).
fof(f226,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| sP1(X3,X2) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f100,f225,f224]) ).
fof(f224,plain,
! [X6,X8,X7] :
( ? [X9] :
( ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X8,X9)
& memberP(X7,X9)
& ssItem(X9) )
| ~ sP0(X6,X8,X7) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f225,plain,
! [X3,X2] :
( ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
| ~ sP1(X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ? [X9] :
( ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X8,X9)
& memberP(X7,X9)
& ssItem(X9) )
| app(app(X7,cons(X6,nil)),X8) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) ) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ? [X9] :
( ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X8,X9)
& memberP(X7,X9)
& ssItem(X9) )
| app(app(X7,cons(X6,nil)),X8) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ! [X9] :
( ssItem(X9)
=> ( leq(X6,X9)
| ~ lt(X6,X9)
| ~ memberP(X8,X9)
| ~ memberP(X7,X9) ) )
& app(app(X7,cons(X6,nil)),X8) = X0
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ( ? [X9] :
( leq(X8,X9)
& memberP(X3,X9)
& X8 != X9
& ssItem(X9) )
| ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil != X2
| nil != X3 )
& ! [X8] :
( ssItem(X8)
=> ( ? [X9] :
( leq(X8,X9)
& memberP(X3,X9)
& X8 != X9
& ssItem(X9) )
| ~ memberP(X3,X8)
| cons(X8,nil) != X2 ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f476,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f3655,plain,
( ! [X0] :
( sK22 != app(sK22,X0)
| ~ ssList(X0) )
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f3651,f414]) ).
fof(f3651,plain,
( ! [X0] :
( sK22 != app(sK22,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl73_1 ),
inference(superposition,[],[f3327,f709]) ).
fof(f709,plain,
sK22 = app(nil,sK22),
inference(resolution,[],[f477,f396]) ).
fof(f477,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f3327,plain,
( ! [X0,X1] :
( sK22 != app(app(X0,sK22),X1)
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f3322,f785]) ).
fof(f785,plain,
( ssItem(sK20(sK23,sK22))
| ~ spl73_1 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f784,plain,
( spl73_1
<=> ssItem(sK20(sK23,sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_1])]) ).
fof(f3322,plain,
! [X0,X1] :
( sK22 != app(app(X0,sK22),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK20(sK23,sK22)) ),
inference(superposition,[],[f3273,f770]) ).
fof(f770,plain,
sK22 = cons(sK20(sK23,sK22),nil),
inference(resolution,[],[f388,f667]) ).
fof(f667,plain,
sP1(sK23,sK22),
inference(forward_demodulation,[],[f666,f400]) ).
fof(f400,plain,
sK23 = sK25,
inference(cnf_transformation,[],[f267]) ).
fof(f666,plain,
sP1(sK25,sK22),
inference(forward_demodulation,[],[f665,f401]) ).
fof(f401,plain,
sK22 = sK24,
inference(cnf_transformation,[],[f267]) ).
fof(f665,plain,
sP1(sK25,sK24),
inference(subsumption_resolution,[],[f664,f402]) ).
fof(f402,plain,
nil != sK22,
inference(cnf_transformation,[],[f267]) ).
fof(f664,plain,
( nil = sK22
| sP1(sK25,sK24) ),
inference(forward_demodulation,[],[f405,f401]) ).
fof(f405,plain,
( nil = sK24
| sP1(sK25,sK24) ),
inference(cnf_transformation,[],[f267]) ).
fof(f388,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| cons(sK20(X0,X1),nil) = X1 ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0,X1] :
( ( ! [X3] :
( ~ leq(sK20(X0,X1),X3)
| ~ memberP(X0,X3)
| sK20(X0,X1) = X3
| ~ ssItem(X3) )
& memberP(X0,sK20(X0,X1))
& cons(sK20(X0,X1),nil) = X1
& ssItem(sK20(X0,X1)) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f255,f256]) ).
fof(f256,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X0,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X0,X2)
& cons(X2,nil) = X1
& ssItem(X2) )
=> ( ! [X3] :
( ~ leq(sK20(X0,X1),X3)
| ~ memberP(X0,X3)
| sK20(X0,X1) = X3
| ~ ssItem(X3) )
& memberP(X0,sK20(X0,X1))
& cons(sK20(X0,X1),nil) = X1
& ssItem(sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f255,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X0,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X0,X2)
& cons(X2,nil) = X1
& ssItem(X2) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f254]) ).
fof(f254,plain,
! [X3,X2] :
( ? [X4] :
( ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2
& ssItem(X4) )
| ~ sP1(X3,X2) ),
inference(nnf_transformation,[],[f225]) ).
fof(f3273,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(subsumption_resolution,[],[f403,f830]) ).
fof(f830,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ ssItem(X0) ),
inference(subsumption_resolution,[],[f829,f391]) ).
fof(f391,plain,
! [X2,X0,X1] :
( ssItem(sK21(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ( ~ leq(X0,sK21(X0,X1,X2))
& lt(X0,sK21(X0,X1,X2))
& memberP(X1,sK21(X0,X1,X2))
& memberP(X2,sK21(X0,X1,X2))
& ssItem(sK21(X0,X1,X2)) )
| ~ sP0(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f259,f260]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ leq(X0,X3)
& lt(X0,X3)
& memberP(X1,X3)
& memberP(X2,X3)
& ssItem(X3) )
=> ( ~ leq(X0,sK21(X0,X1,X2))
& lt(X0,sK21(X0,X1,X2))
& memberP(X1,sK21(X0,X1,X2))
& memberP(X2,sK21(X0,X1,X2))
& ssItem(sK21(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ leq(X0,X3)
& lt(X0,X3)
& memberP(X1,X3)
& memberP(X2,X3)
& ssItem(X3) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f258]) ).
fof(f258,plain,
! [X6,X8,X7] :
( ? [X9] :
( ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X8,X9)
& memberP(X7,X9)
& ssItem(X9) )
| ~ sP0(X6,X8,X7) ),
inference(nnf_transformation,[],[f224]) ).
fof(f829,plain,
! [X2,X0,X1] :
( ~ ssItem(sK21(X0,X1,X2))
| ~ ssItem(X0)
| ~ sP0(X0,X1,X2) ),
inference(subsumption_resolution,[],[f828,f395]) ).
fof(f395,plain,
! [X2,X0,X1] :
( ~ leq(X0,sK21(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
fof(f828,plain,
! [X2,X0,X1] :
( leq(X0,sK21(X0,X1,X2))
| ~ ssItem(sK21(X0,X1,X2))
| ~ ssItem(X0)
| ~ sP0(X0,X1,X2) ),
inference(resolution,[],[f438,f394]) ).
fof(f394,plain,
! [X2,X0,X1] :
( lt(X0,sK21(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
fof(f438,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).
fof(f403,plain,
! [X6,X4,X5] :
( sP0(X4,X6,X5)
| app(app(X5,cons(X4,nil)),X6) != sK22
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f267]) ).
fof(f3455,plain,
( ~ spl73_31
| spl73_32
| ~ spl73_23 ),
inference(avatar_split_clause,[],[f3092,f2252,f3452,f3448]) ).
fof(f3448,plain,
( spl73_31
<=> rearsegP(sK23,cons(sK72,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_31])]) ).
fof(f3452,plain,
( spl73_32
<=> sK23 = cons(sK72,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_32])]) ).
fof(f2252,plain,
( spl73_23
<=> ssList(cons(sK72,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_23])]) ).
fof(f3092,plain,
( sK23 = cons(sK72,sK23)
| ~ rearsegP(sK23,cons(sK72,sK23))
| ~ spl73_23 ),
inference(subsumption_resolution,[],[f3091,f397]) ).
fof(f397,plain,
ssList(sK23),
inference(cnf_transformation,[],[f267]) ).
fof(f3091,plain,
( sK23 = cons(sK72,sK23)
| ~ rearsegP(sK23,cons(sK72,sK23))
| ~ ssList(sK23)
| ~ spl73_23 ),
inference(subsumption_resolution,[],[f3088,f2998]) ).
fof(f2998,plain,
( ssList(cons(sK72,sK23))
| ~ spl73_23 ),
inference(subsumption_resolution,[],[f2997,f2253]) ).
fof(f2253,plain,
( ssList(cons(sK72,nil))
| ~ spl73_23 ),
inference(avatar_component_clause,[],[f2252]) ).
fof(f2997,plain,
( ssList(cons(sK72,sK23))
| ~ ssList(cons(sK72,nil)) ),
inference(subsumption_resolution,[],[f2988,f397]) ).
fof(f2988,plain,
( ssList(cons(sK72,sK23))
| ~ ssList(sK23)
| ~ ssList(cons(sK72,nil)) ),
inference(superposition,[],[f586,f2845]) ).
fof(f2845,plain,
cons(sK72,sK23) = app(cons(sK72,nil),sK23),
inference(resolution,[],[f1949,f621]) ).
fof(f621,plain,
ssItem(sK72),
inference(cnf_transformation,[],[f386]) ).
fof(f386,plain,
( sK71 != sK72
& ssItem(sK72)
& ssItem(sK71) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72])],[f2,f385,f384]) ).
fof(f384,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK71 != X1
& ssItem(X1) )
& ssItem(sK71) ) ),
introduced(choice_axiom,[]) ).
fof(f385,plain,
( ? [X1] :
( sK71 != X1
& ssItem(X1) )
=> ( sK71 != sK72
& ssItem(sK72) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f1949,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK23) = app(cons(X0,nil),sK23) ),
inference(resolution,[],[f581,f397]) ).
fof(f581,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f586,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f3088,plain,
( sK23 = cons(sK72,sK23)
| ~ rearsegP(sK23,cons(sK72,sK23))
| ~ ssList(cons(sK72,sK23))
| ~ ssList(sK23)
| ~ spl73_23 ),
inference(resolution,[],[f3006,f590]) ).
fof(f590,plain,
! [X0,X1] :
( ~ rearsegP(X1,X0)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f3006,plain,
( rearsegP(cons(sK72,sK23),sK23)
| ~ spl73_23 ),
inference(subsumption_resolution,[],[f3005,f397]) ).
fof(f3005,plain,
( rearsegP(cons(sK72,sK23),sK23)
| ~ ssList(sK23)
| ~ spl73_23 ),
inference(subsumption_resolution,[],[f2991,f2253]) ).
fof(f2991,plain,
( rearsegP(cons(sK72,sK23),sK23)
| ~ ssList(cons(sK72,nil))
| ~ ssList(sK23) ),
inference(superposition,[],[f2260,f2845]) ).
fof(f2260,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f645,f586]) ).
fof(f645,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f597]) ).
fof(f597,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK67(X0,X1),X1) = X0
& ssList(sK67(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f370,f371]) ).
fof(f371,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK67(X0,X1),X1) = X0
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f370,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f3402,plain,
( ~ spl73_29
| spl73_30
| ~ spl73_21 ),
inference(avatar_split_clause,[],[f2977,f2203,f3399,f3395]) ).
fof(f3395,plain,
( spl73_29
<=> rearsegP(sK23,cons(sK71,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_29])]) ).
fof(f3399,plain,
( spl73_30
<=> sK23 = cons(sK71,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_30])]) ).
fof(f2203,plain,
( spl73_21
<=> ssList(cons(sK71,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_21])]) ).
fof(f2977,plain,
( sK23 = cons(sK71,sK23)
| ~ rearsegP(sK23,cons(sK71,sK23))
| ~ spl73_21 ),
inference(subsumption_resolution,[],[f2976,f397]) ).
fof(f2976,plain,
( sK23 = cons(sK71,sK23)
| ~ rearsegP(sK23,cons(sK71,sK23))
| ~ ssList(sK23)
| ~ spl73_21 ),
inference(subsumption_resolution,[],[f2973,f2928]) ).
fof(f2928,plain,
( ssList(cons(sK71,sK23))
| ~ spl73_21 ),
inference(subsumption_resolution,[],[f2927,f2204]) ).
fof(f2204,plain,
( ssList(cons(sK71,nil))
| ~ spl73_21 ),
inference(avatar_component_clause,[],[f2203]) ).
fof(f2927,plain,
( ssList(cons(sK71,sK23))
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2918,f397]) ).
fof(f2918,plain,
( ssList(cons(sK71,sK23))
| ~ ssList(sK23)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f586,f2844]) ).
fof(f2844,plain,
cons(sK71,sK23) = app(cons(sK71,nil),sK23),
inference(resolution,[],[f1949,f620]) ).
fof(f620,plain,
ssItem(sK71),
inference(cnf_transformation,[],[f386]) ).
fof(f2973,plain,
( sK23 = cons(sK71,sK23)
| ~ rearsegP(sK23,cons(sK71,sK23))
| ~ ssList(cons(sK71,sK23))
| ~ ssList(sK23)
| ~ spl73_21 ),
inference(resolution,[],[f2936,f590]) ).
fof(f2936,plain,
( rearsegP(cons(sK71,sK23),sK23)
| ~ spl73_21 ),
inference(subsumption_resolution,[],[f2935,f397]) ).
fof(f2935,plain,
( rearsegP(cons(sK71,sK23),sK23)
| ~ ssList(sK23)
| ~ spl73_21 ),
inference(subsumption_resolution,[],[f2921,f2204]) ).
fof(f2921,plain,
( rearsegP(cons(sK71,sK23),sK23)
| ~ ssList(cons(sK71,nil))
| ~ ssList(sK23) ),
inference(superposition,[],[f2260,f2844]) ).
fof(f2621,plain,
( ~ spl73_27
| spl73_28
| ~ spl73_23
| ~ spl73_24 ),
inference(avatar_split_clause,[],[f2330,f2256,f2252,f2618,f2614]) ).
fof(f2614,plain,
( spl73_27
<=> rearsegP(sK22,cons(sK72,sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_27])]) ).
fof(f2618,plain,
( spl73_28
<=> sK22 = cons(sK72,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_28])]) ).
fof(f2256,plain,
( spl73_24
<=> ssList(cons(sK72,sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_24])]) ).
fof(f2330,plain,
( sK22 = cons(sK72,sK22)
| ~ rearsegP(sK22,cons(sK72,sK22))
| ~ spl73_23
| ~ spl73_24 ),
inference(subsumption_resolution,[],[f2329,f396]) ).
fof(f2329,plain,
( sK22 = cons(sK72,sK22)
| ~ rearsegP(sK22,cons(sK72,sK22))
| ~ ssList(sK22)
| ~ spl73_23
| ~ spl73_24 ),
inference(subsumption_resolution,[],[f2328,f2258]) ).
fof(f2258,plain,
( ssList(cons(sK72,sK22))
| ~ spl73_24 ),
inference(avatar_component_clause,[],[f2256]) ).
fof(f2328,plain,
( sK22 = cons(sK72,sK22)
| ~ rearsegP(sK22,cons(sK72,sK22))
| ~ ssList(cons(sK72,sK22))
| ~ ssList(sK22)
| ~ spl73_23 ),
inference(resolution,[],[f2324,f590]) ).
fof(f2324,plain,
( rearsegP(cons(sK72,sK22),sK22)
| ~ spl73_23 ),
inference(subsumption_resolution,[],[f2323,f396]) ).
fof(f2323,plain,
( rearsegP(cons(sK72,sK22),sK22)
| ~ ssList(sK22)
| ~ spl73_23 ),
inference(subsumption_resolution,[],[f2314,f2253]) ).
fof(f2314,plain,
( rearsegP(cons(sK72,sK22),sK22)
| ~ ssList(cons(sK72,nil))
| ~ ssList(sK22) ),
inference(superposition,[],[f2260,f2139]) ).
fof(f2139,plain,
cons(sK72,sK22) = app(cons(sK72,nil),sK22),
inference(resolution,[],[f1948,f621]) ).
fof(f1948,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK22) = app(cons(X0,nil),sK22) ),
inference(resolution,[],[f581,f396]) ).
fof(f2581,plain,
( ~ spl73_25
| spl73_26
| ~ spl73_21
| ~ spl73_22 ),
inference(avatar_split_clause,[],[f2327,f2207,f2203,f2578,f2574]) ).
fof(f2574,plain,
( spl73_25
<=> rearsegP(sK22,cons(sK71,sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_25])]) ).
fof(f2578,plain,
( spl73_26
<=> sK22 = cons(sK71,sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_26])]) ).
fof(f2207,plain,
( spl73_22
<=> ssList(cons(sK71,sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_22])]) ).
fof(f2327,plain,
( sK22 = cons(sK71,sK22)
| ~ rearsegP(sK22,cons(sK71,sK22))
| ~ spl73_21
| ~ spl73_22 ),
inference(subsumption_resolution,[],[f2326,f396]) ).
fof(f2326,plain,
( sK22 = cons(sK71,sK22)
| ~ rearsegP(sK22,cons(sK71,sK22))
| ~ ssList(sK22)
| ~ spl73_21
| ~ spl73_22 ),
inference(subsumption_resolution,[],[f2325,f2209]) ).
fof(f2209,plain,
( ssList(cons(sK71,sK22))
| ~ spl73_22 ),
inference(avatar_component_clause,[],[f2207]) ).
fof(f2325,plain,
( sK22 = cons(sK71,sK22)
| ~ rearsegP(sK22,cons(sK71,sK22))
| ~ ssList(cons(sK71,sK22))
| ~ ssList(sK22)
| ~ spl73_21 ),
inference(resolution,[],[f2322,f590]) ).
fof(f2322,plain,
( rearsegP(cons(sK71,sK22),sK22)
| ~ spl73_21 ),
inference(subsumption_resolution,[],[f2321,f396]) ).
fof(f2321,plain,
( rearsegP(cons(sK71,sK22),sK22)
| ~ ssList(sK22)
| ~ spl73_21 ),
inference(subsumption_resolution,[],[f2313,f2204]) ).
fof(f2313,plain,
( rearsegP(cons(sK71,sK22),sK22)
| ~ ssList(cons(sK71,nil))
| ~ ssList(sK22) ),
inference(superposition,[],[f2260,f2138]) ).
fof(f2138,plain,
cons(sK71,sK22) = app(cons(sK71,nil),sK22),
inference(resolution,[],[f1948,f620]) ).
fof(f2264,plain,
spl73_23,
inference(avatar_contradiction_clause,[],[f2263]) ).
fof(f2263,plain,
( $false
| spl73_23 ),
inference(subsumption_resolution,[],[f2262,f414]) ).
fof(f2262,plain,
( ~ ssList(nil)
| spl73_23 ),
inference(subsumption_resolution,[],[f2261,f621]) ).
fof(f2261,plain,
( ~ ssItem(sK72)
| ~ ssList(nil)
| spl73_23 ),
inference(resolution,[],[f2254,f576]) ).
fof(f576,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f2254,plain,
( ~ ssList(cons(sK72,nil))
| spl73_23 ),
inference(avatar_component_clause,[],[f2252]) ).
fof(f2259,plain,
( ~ spl73_23
| spl73_24 ),
inference(avatar_split_clause,[],[f2250,f2256,f2252]) ).
fof(f2250,plain,
( ssList(cons(sK72,sK22))
| ~ ssList(cons(sK72,nil)) ),
inference(subsumption_resolution,[],[f2246,f396]) ).
fof(f2246,plain,
( ssList(cons(sK72,sK22))
| ~ ssList(sK22)
| ~ ssList(cons(sK72,nil)) ),
inference(superposition,[],[f586,f2139]) ).
fof(f2214,plain,
spl73_21,
inference(avatar_contradiction_clause,[],[f2213]) ).
fof(f2213,plain,
( $false
| spl73_21 ),
inference(subsumption_resolution,[],[f2212,f414]) ).
fof(f2212,plain,
( ~ ssList(nil)
| spl73_21 ),
inference(subsumption_resolution,[],[f2211,f620]) ).
fof(f2211,plain,
( ~ ssItem(sK71)
| ~ ssList(nil)
| spl73_21 ),
inference(resolution,[],[f2205,f576]) ).
fof(f2205,plain,
( ~ ssList(cons(sK71,nil))
| spl73_21 ),
inference(avatar_component_clause,[],[f2203]) ).
fof(f2210,plain,
( ~ spl73_21
| spl73_22 ),
inference(avatar_split_clause,[],[f2201,f2207,f2203]) ).
fof(f2201,plain,
( ssList(cons(sK71,sK22))
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2197,f396]) ).
fof(f2197,plain,
( ssList(cons(sK71,sK22))
| ~ ssList(sK22)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f586,f2138]) ).
fof(f1906,plain,
( spl73_19
| ~ spl73_20 ),
inference(avatar_contradiction_clause,[],[f1905]) ).
fof(f1905,plain,
( $false
| spl73_19
| ~ spl73_20 ),
inference(subsumption_resolution,[],[f1902,f413]) ).
fof(f413,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f1902,plain,
( ~ totalorderedP(nil)
| spl73_19
| ~ spl73_20 ),
inference(superposition,[],[f1883,f1888]) ).
fof(f1888,plain,
( nil = sK26(sK22)
| ~ spl73_20 ),
inference(avatar_component_clause,[],[f1886]) ).
fof(f1886,plain,
( spl73_20
<=> nil = sK26(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_20])]) ).
fof(f1883,plain,
( ~ totalorderedP(sK26(sK22))
| spl73_19 ),
inference(avatar_component_clause,[],[f1882]) ).
fof(f1882,plain,
( spl73_19
<=> totalorderedP(sK26(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_19])]) ).
fof(f1889,plain,
( spl73_19
| spl73_20
| ~ spl73_17 ),
inference(avatar_split_clause,[],[f1880,f1868,f1886,f1882]) ).
fof(f1868,plain,
( spl73_17
<=> sP2(sK26(sK22),hd(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_17])]) ).
fof(f1880,plain,
( nil = sK26(sK22)
| totalorderedP(sK26(sK22))
| ~ spl73_17 ),
inference(resolution,[],[f1870,f454]) ).
fof(f454,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f279]) ).
fof(f279,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f278]) ).
fof(f278,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f1870,plain,
( sP2(sK26(sK22),hd(sK22))
| ~ spl73_17 ),
inference(avatar_component_clause,[],[f1868]) ).
fof(f1879,plain,
( ~ spl73_1
| ~ spl73_5
| ~ spl73_13
| spl73_18 ),
inference(avatar_contradiction_clause,[],[f1878]) ).
fof(f1878,plain,
( $false
| ~ spl73_1
| ~ spl73_5
| ~ spl73_13
| spl73_18 ),
inference(subsumption_resolution,[],[f1877,f1280]) ).
fof(f1280,plain,
( ssItem(hd(sK22))
| ~ spl73_1
| ~ spl73_5 ),
inference(superposition,[],[f1143,f1278]) ).
fof(f1278,plain,
( hd(sK22) = sK30(sK22)
| ~ spl73_1
| ~ spl73_5 ),
inference(forward_demodulation,[],[f1260,f1123]) ).
fof(f1123,plain,
( sK22 = cons(sK30(sK22),nil)
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f1122,f396]) ).
fof(f1122,plain,
( sK22 = cons(sK30(sK22),nil)
| ~ ssList(sK22)
| ~ spl73_1 ),
inference(resolution,[],[f1121,f489]) ).
fof(f489,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK30(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK30(X0),nil) = X0
& ssItem(sK30(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f295,f296]) ).
fof(f296,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK30(X0),nil) = X0
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f295,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f1121,plain,
( singletonP(sK22)
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f1120,f396]) ).
fof(f1120,plain,
( ~ ssList(sK22)
| singletonP(sK22)
| ~ spl73_1 ),
inference(forward_demodulation,[],[f1119,f770]) ).
fof(f1119,plain,
( singletonP(sK22)
| ~ ssList(cons(sK20(sK23,sK22),nil))
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f1117,f785]) ).
fof(f1117,plain,
( singletonP(sK22)
| ~ ssItem(sK20(sK23,sK22))
| ~ ssList(cons(sK20(sK23,sK22),nil)) ),
inference(superposition,[],[f631,f770]) ).
fof(f631,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f490]) ).
fof(f490,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f1260,plain,
( sK30(sK22) = hd(cons(sK30(sK22),nil))
| ~ spl73_5 ),
inference(resolution,[],[f1026,f1143]) ).
fof(f1026,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,nil)) = X0 ),
inference(resolution,[],[f580,f414]) ).
fof(f580,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f1143,plain,
( ssItem(sK30(sK22))
| ~ spl73_5 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1142,plain,
( spl73_5
<=> ssItem(sK30(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_5])]) ).
fof(f1877,plain,
( ~ ssItem(hd(sK22))
| ~ spl73_13
| spl73_18 ),
inference(subsumption_resolution,[],[f1876,f1641]) ).
fof(f1641,plain,
( ssList(sK26(sK22))
| ~ spl73_13 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f1640,plain,
( spl73_13
<=> ssList(sK26(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_13])]) ).
fof(f1876,plain,
( ~ ssList(sK26(sK22))
| ~ ssItem(hd(sK22))
| spl73_18 ),
inference(resolution,[],[f1874,f458]) ).
fof(f458,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f229]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f228,f227]) ).
fof(f228,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).
fof(f1874,plain,
( ~ sP3(hd(sK22),sK26(sK22))
| spl73_18 ),
inference(avatar_component_clause,[],[f1872]) ).
fof(f1872,plain,
( spl73_18
<=> sP3(hd(sK22),sK26(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_18])]) ).
fof(f1875,plain,
( spl73_17
| ~ spl73_18
| ~ spl73_1
| ~ spl73_7
| ~ spl73_13 ),
inference(avatar_split_clause,[],[f1755,f1640,f1461,f784,f1872,f1868]) ).
fof(f1461,plain,
( spl73_7
<=> ssItem(sK27(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_7])]) ).
fof(f1755,plain,
( ~ sP3(hd(sK22),sK26(sK22))
| sP2(sK26(sK22),hd(sK22))
| ~ spl73_1
| ~ spl73_7
| ~ spl73_13 ),
inference(forward_demodulation,[],[f1754,f1695]) ).
fof(f1695,plain,
( hd(sK22) = sK27(sK22)
| ~ spl73_7
| ~ spl73_13 ),
inference(forward_demodulation,[],[f1673,f1430]) ).
fof(f1430,plain,
sK22 = cons(sK27(sK22),sK26(sK22)),
inference(subsumption_resolution,[],[f1397,f402]) ).
fof(f1397,plain,
( nil = sK22
| sK22 = cons(sK27(sK22),sK26(sK22)) ),
inference(resolution,[],[f480,f396]) ).
fof(f480,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK27(X0),sK26(X0)) = X0 ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ( cons(sK27(X0),sK26(X0)) = X0
& ssItem(sK27(X0))
& ssList(sK26(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f150,f288,f287]) ).
fof(f287,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK26(X0)) = X0
& ssItem(X2) )
& ssList(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f288,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK26(X0)) = X0
& ssItem(X2) )
=> ( cons(sK27(X0),sK26(X0)) = X0
& ssItem(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f1673,plain,
( sK27(sK22) = hd(cons(sK27(sK22),sK26(sK22)))
| ~ spl73_7
| ~ spl73_13 ),
inference(resolution,[],[f1659,f1462]) ).
fof(f1462,plain,
( ssItem(sK27(sK22))
| ~ spl73_7 ),
inference(avatar_component_clause,[],[f1461]) ).
fof(f1659,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK26(sK22))) = X0 )
| ~ spl73_13 ),
inference(resolution,[],[f1641,f580]) ).
fof(f1754,plain,
( sP2(sK26(sK22),hd(sK22))
| ~ sP3(sK27(sK22),sK26(sK22))
| ~ spl73_1
| ~ spl73_7
| ~ spl73_13 ),
inference(forward_demodulation,[],[f1446,f1695]) ).
fof(f1446,plain,
( sP2(sK26(sK22),sK27(sK22))
| ~ sP3(sK27(sK22),sK26(sK22))
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f1438,f802]) ).
fof(f802,plain,
( totalorderedP(sK22)
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f777,f785]) ).
fof(f777,plain,
( totalorderedP(sK22)
| ~ ssItem(sK20(sK23,sK22)) ),
inference(superposition,[],[f425,f770]) ).
fof(f425,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f1438,plain,
( ~ totalorderedP(sK22)
| sP2(sK26(sK22),sK27(sK22))
| ~ sP3(sK27(sK22),sK26(sK22)) ),
inference(superposition,[],[f451,f1430]) ).
fof(f451,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f228]) ).
fof(f1775,plain,
( spl73_4
| spl73_15 ),
inference(avatar_contradiction_clause,[],[f1774]) ).
fof(f1774,plain,
( $false
| spl73_4
| spl73_15 ),
inference(subsumption_resolution,[],[f1773,f397]) ).
fof(f1773,plain,
( ~ ssList(sK23)
| spl73_4
| spl73_15 ),
inference(subsumption_resolution,[],[f1772,f888]) ).
fof(f888,plain,
( nil != sK23
| spl73_4 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f887,plain,
( spl73_4
<=> nil = sK23 ),
introduced(avatar_definition,[new_symbols(naming,[spl73_4])]) ).
fof(f1772,plain,
( nil = sK23
| ~ ssList(sK23)
| spl73_15 ),
inference(resolution,[],[f1766,f478]) ).
fof(f478,plain,
! [X0] :
( ssList(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f1766,plain,
( ~ ssList(sK26(sK23))
| spl73_15 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f1764,plain,
( spl73_15
<=> ssList(sK26(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_15])]) ).
fof(f1771,plain,
( ~ spl73_15
| spl73_16
| spl73_4
| ~ spl73_9 ),
inference(avatar_split_clause,[],[f1762,f1480,f887,f1768,f1764]) ).
fof(f1768,plain,
( spl73_16
<=> memberP(sK23,sK27(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_16])]) ).
fof(f1480,plain,
( spl73_9
<=> ssItem(sK27(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_9])]) ).
fof(f1762,plain,
( memberP(sK23,sK27(sK23))
| ~ ssList(sK26(sK23))
| spl73_4
| ~ spl73_9 ),
inference(subsumption_resolution,[],[f1457,f1481]) ).
fof(f1481,plain,
( ssItem(sK27(sK23))
| ~ spl73_9 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f1457,plain,
( memberP(sK23,sK27(sK23))
| ~ ssList(sK26(sK23))
| ~ ssItem(sK27(sK23))
| spl73_4 ),
inference(superposition,[],[f653,f1431]) ).
fof(f1431,plain,
( sK23 = cons(sK27(sK23),sK26(sK23))
| spl73_4 ),
inference(subsumption_resolution,[],[f1398,f888]) ).
fof(f1398,plain,
( nil = sK23
| sK23 = cons(sK27(sK23),sK26(sK23)) ),
inference(resolution,[],[f480,f397]) ).
fof(f653,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f625]) ).
fof(f625,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f446]) ).
fof(f446,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f273]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f1651,plain,
spl73_13,
inference(avatar_contradiction_clause,[],[f1650]) ).
fof(f1650,plain,
( $false
| spl73_13 ),
inference(subsumption_resolution,[],[f1649,f396]) ).
fof(f1649,plain,
( ~ ssList(sK22)
| spl73_13 ),
inference(subsumption_resolution,[],[f1648,f402]) ).
fof(f1648,plain,
( nil = sK22
| ~ ssList(sK22)
| spl73_13 ),
inference(resolution,[],[f1642,f478]) ).
fof(f1642,plain,
( ~ ssList(sK26(sK22))
| spl73_13 ),
inference(avatar_component_clause,[],[f1640]) ).
fof(f1647,plain,
( ~ spl73_13
| spl73_14
| ~ spl73_7 ),
inference(avatar_split_clause,[],[f1638,f1461,f1644,f1640]) ).
fof(f1644,plain,
( spl73_14
<=> memberP(sK22,sK27(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_14])]) ).
fof(f1638,plain,
( memberP(sK22,sK27(sK22))
| ~ ssList(sK26(sK22))
| ~ spl73_7 ),
inference(subsumption_resolution,[],[f1445,f1462]) ).
fof(f1445,plain,
( memberP(sK22,sK27(sK22))
| ~ ssList(sK26(sK22))
| ~ ssItem(sK27(sK22)) ),
inference(superposition,[],[f653,f1430]) ).
fof(f1567,plain,
( spl73_4
| spl73_11 ),
inference(avatar_contradiction_clause,[],[f1566]) ).
fof(f1566,plain,
( $false
| spl73_4
| spl73_11 ),
inference(subsumption_resolution,[],[f1565,f397]) ).
fof(f1565,plain,
( ~ ssList(sK23)
| spl73_4
| spl73_11 ),
inference(subsumption_resolution,[],[f1564,f888]) ).
fof(f1564,plain,
( nil = sK23
| ~ ssList(sK23)
| spl73_11 ),
inference(resolution,[],[f1558,f481]) ).
fof(f481,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f1558,plain,
( ~ ssItem(hd(sK23))
| spl73_11 ),
inference(avatar_component_clause,[],[f1556]) ).
fof(f1556,plain,
( spl73_11
<=> ssItem(hd(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_11])]) ).
fof(f1563,plain,
( ~ spl73_11
| ~ spl73_12
| spl73_4 ),
inference(avatar_split_clause,[],[f1554,f887,f1560,f1556]) ).
fof(f1560,plain,
( spl73_12
<=> sK23 = tl(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_12])]) ).
fof(f1554,plain,
( sK23 != tl(sK23)
| ~ ssItem(hd(sK23))
| spl73_4 ),
inference(subsumption_resolution,[],[f1553,f397]) ).
fof(f1553,plain,
( sK23 != tl(sK23)
| ~ ssItem(hd(sK23))
| ~ ssList(sK23)
| spl73_4 ),
inference(inner_rewriting,[],[f1551]) ).
fof(f1551,plain,
( sK23 != tl(sK23)
| ~ ssItem(hd(sK23))
| ~ ssList(tl(sK23))
| spl73_4 ),
inference(superposition,[],[f578,f1537]) ).
fof(f1537,plain,
( sK23 = cons(hd(sK23),tl(sK23))
| spl73_4 ),
inference(subsumption_resolution,[],[f1503,f888]) ).
fof(f1503,plain,
( nil = sK23
| sK23 = cons(hd(sK23),tl(sK23)) ),
inference(resolution,[],[f483,f397]) ).
fof(f483,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f578,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f1491,plain,
( spl73_4
| spl73_9 ),
inference(avatar_contradiction_clause,[],[f1490]) ).
fof(f1490,plain,
( $false
| spl73_4
| spl73_9 ),
inference(subsumption_resolution,[],[f1489,f397]) ).
fof(f1489,plain,
( ~ ssList(sK23)
| spl73_4
| spl73_9 ),
inference(subsumption_resolution,[],[f1488,f888]) ).
fof(f1488,plain,
( nil = sK23
| ~ ssList(sK23)
| spl73_9 ),
inference(resolution,[],[f1482,f479]) ).
fof(f479,plain,
! [X0] :
( ssItem(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f1482,plain,
( ~ ssItem(sK27(sK23))
| spl73_9 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f1487,plain,
( ~ spl73_9
| ~ spl73_10
| spl73_4 ),
inference(avatar_split_clause,[],[f1459,f887,f1484,f1480]) ).
fof(f1484,plain,
( spl73_10
<=> sK23 = sK26(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_10])]) ).
fof(f1459,plain,
( sK23 != sK26(sK23)
| ~ ssItem(sK27(sK23))
| spl73_4 ),
inference(subsumption_resolution,[],[f1458,f397]) ).
fof(f1458,plain,
( sK23 != sK26(sK23)
| ~ ssItem(sK27(sK23))
| ~ ssList(sK23)
| spl73_4 ),
inference(inner_rewriting,[],[f1456]) ).
fof(f1456,plain,
( sK23 != sK26(sK23)
| ~ ssItem(sK27(sK23))
| ~ ssList(sK26(sK23))
| spl73_4 ),
inference(superposition,[],[f578,f1431]) ).
fof(f1472,plain,
spl73_7,
inference(avatar_contradiction_clause,[],[f1471]) ).
fof(f1471,plain,
( $false
| spl73_7 ),
inference(subsumption_resolution,[],[f1470,f396]) ).
fof(f1470,plain,
( ~ ssList(sK22)
| spl73_7 ),
inference(subsumption_resolution,[],[f1469,f402]) ).
fof(f1469,plain,
( nil = sK22
| ~ ssList(sK22)
| spl73_7 ),
inference(resolution,[],[f1463,f479]) ).
fof(f1463,plain,
( ~ ssItem(sK27(sK22))
| spl73_7 ),
inference(avatar_component_clause,[],[f1461]) ).
fof(f1468,plain,
( ~ spl73_7
| ~ spl73_8 ),
inference(avatar_split_clause,[],[f1449,f1465,f1461]) ).
fof(f1465,plain,
( spl73_8
<=> sK22 = sK26(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_8])]) ).
fof(f1449,plain,
( sK22 != sK26(sK22)
| ~ ssItem(sK27(sK22)) ),
inference(subsumption_resolution,[],[f1448,f396]) ).
fof(f1448,plain,
( sK22 != sK26(sK22)
| ~ ssItem(sK27(sK22))
| ~ ssList(sK22) ),
inference(inner_rewriting,[],[f1444]) ).
fof(f1444,plain,
( sK22 != sK26(sK22)
| ~ ssItem(sK27(sK22))
| ~ ssList(sK26(sK22)) ),
inference(superposition,[],[f578,f1430]) ).
fof(f1153,plain,
( ~ spl73_1
| spl73_5 ),
inference(avatar_contradiction_clause,[],[f1152]) ).
fof(f1152,plain,
( $false
| ~ spl73_1
| spl73_5 ),
inference(subsumption_resolution,[],[f1151,f396]) ).
fof(f1151,plain,
( ~ ssList(sK22)
| ~ spl73_1
| spl73_5 ),
inference(subsumption_resolution,[],[f1150,f1121]) ).
fof(f1150,plain,
( ~ singletonP(sK22)
| ~ ssList(sK22)
| spl73_5 ),
inference(resolution,[],[f1144,f488]) ).
fof(f488,plain,
! [X0] :
( ssItem(sK30(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f1144,plain,
( ~ ssItem(sK30(sK22))
| spl73_5 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1149,plain,
( ~ spl73_5
| spl73_6
| ~ spl73_1 ),
inference(avatar_split_clause,[],[f1140,f784,f1146,f1142]) ).
fof(f1146,plain,
( spl73_6
<=> memberP(sK22,sK30(sK22)) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_6])]) ).
fof(f1140,plain,
( memberP(sK22,sK30(sK22))
| ~ ssItem(sK30(sK22))
| ~ spl73_1 ),
inference(subsumption_resolution,[],[f1139,f414]) ).
fof(f1139,plain,
( memberP(sK22,sK30(sK22))
| ~ ssList(nil)
| ~ ssItem(sK30(sK22))
| ~ spl73_1 ),
inference(superposition,[],[f653,f1123]) ).
fof(f899,plain,
~ spl73_4,
inference(avatar_contradiction_clause,[],[f898]) ).
fof(f898,plain,
( $false
| ~ spl73_4 ),
inference(subsumption_resolution,[],[f892,f736]) ).
fof(f736,plain,
! [X0] : ~ sP1(nil,X0),
inference(subsumption_resolution,[],[f735,f387]) ).
fof(f387,plain,
! [X0,X1] :
( ssItem(sK20(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f257]) ).
fof(f735,plain,
! [X0] :
( ~ sP1(nil,X0)
| ~ ssItem(sK20(nil,X0)) ),
inference(resolution,[],[f389,f415]) ).
fof(f415,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f389,plain,
! [X0,X1] :
( memberP(X0,sK20(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f257]) ).
fof(f892,plain,
( sP1(nil,sK22)
| ~ spl73_4 ),
inference(superposition,[],[f667,f889]) ).
fof(f889,plain,
( nil = sK23
| ~ spl73_4 ),
inference(avatar_component_clause,[],[f887]) ).
fof(f890,plain,
( spl73_3
| spl73_4 ),
inference(avatar_split_clause,[],[f849,f887,f883]) ).
fof(f883,plain,
( spl73_3
<=> hd(sK23) = sK28(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_3])]) ).
fof(f849,plain,
( nil = sK23
| hd(sK23) = sK28(sK23) ),
inference(resolution,[],[f485,f397]) ).
fof(f485,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK28(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0] :
( ( hd(X0) = sK28(X0)
& ssItem(sK28(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f158,f290]) ).
fof(f290,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK28(X0)
& ssItem(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
fof(f794,plain,
spl73_1,
inference(avatar_contradiction_clause,[],[f793]) ).
fof(f793,plain,
( $false
| spl73_1 ),
inference(subsumption_resolution,[],[f792,f667]) ).
fof(f792,plain,
( ~ sP1(sK23,sK22)
| spl73_1 ),
inference(resolution,[],[f786,f387]) ).
fof(f786,plain,
( ~ ssItem(sK20(sK23,sK22))
| spl73_1 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f791,plain,
( ~ spl73_1
| spl73_2 ),
inference(avatar_split_clause,[],[f771,f788,f784]) ).
fof(f788,plain,
( spl73_2
<=> equalelemsP(sK22) ),
introduced(avatar_definition,[new_symbols(naming,[spl73_2])]) ).
fof(f771,plain,
( equalelemsP(sK22)
| ~ ssItem(sK20(sK23,sK22)) ),
inference(superposition,[],[f419,f770]) ).
fof(f419,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC239+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36 % Computer : n023.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri May 3 20:26:53 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % (18324)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (18327)WARNING: value z3 for option sas not known
% 0.13/0.38 % (18328)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (18329)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)
% 0.13/0.38 % (18331)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)
% 0.13/0.38 % (18330)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)
% 0.13/0.38 % (18326)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (18327)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)
% 0.13/0.39 % (18325)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 TRYING [1]
% 0.21/0.40 TRYING [2]
% 0.21/0.41 TRYING [1]
% 0.21/0.41 TRYING [2]
% 0.21/0.41 TRYING [3]
% 0.21/0.42 TRYING [3]
% 0.21/0.46 TRYING [4]
% 0.21/0.47 TRYING [4]
% 0.21/0.50 % (18327)First to succeed.
% 0.21/0.50 % (18327)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18324"
% 0.21/0.51 % (18327)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (18327)------------------------------
% 0.21/0.51 % (18327)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.51 % (18327)Termination reason: Refutation
% 0.21/0.51
% 0.21/0.51 % (18327)Memory used [KB]: 3157
% 0.21/0.51 % (18327)Time elapsed: 0.120 s
% 0.21/0.51 % (18327)Instructions burned: 269 (million)
% 0.21/0.51 % (18324)Success in time 0.134 s
%------------------------------------------------------------------------------