TSTP Solution File: SWC044+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC044+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 : n016.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 : Tue Apr 30 15:47:43 EDT 2024
% Result : Theorem 0.22s 0.42s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 104
% Syntax : Number of formulae : 333 ( 91 unt; 0 def)
% Number of atoms : 965 ( 292 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 962 ( 330 ~; 354 |; 159 &)
% ( 68 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 76 ( 74 usr; 57 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 314 ( 261 !; 53 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f985,plain,
$false,
inference(avatar_sat_refutation,[],[f700,f705,f710,f715,f720,f725,f730,f735,f740,f745,f750,f755,f759,f763,f767,f771,f775,f779,f783,f787,f791,f795,f799,f803,f807,f811,f815,f823,f827,f832,f836,f840,f844,f848,f852,f856,f860,f864,f868,f874,f893,f898,f903,f907,f911,f915,f919,f923,f927,f931,f945,f949,f953,f957,f961,f965,f984]) ).
fof(f984,plain,
( ~ spl69_1
| spl69_12
| ~ spl69_11
| ~ spl69_39 ),
inference(avatar_split_clause,[],[f886,f866,f747,f752,f697]) ).
fof(f697,plain,
( spl69_1
<=> ssList(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_1])]) ).
fof(f752,plain,
( spl69_12
<=> sK20 = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl69_12])]) ).
fof(f747,plain,
( spl69_11
<=> rearsegP(sK21,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_11])]) ).
fof(f866,plain,
( spl69_39
<=> ! [X0] :
( sK21 = X0
| ~ rearsegP(sK21,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_39])]) ).
fof(f886,plain,
( sK20 = sK21
| ~ ssList(sK20)
| ~ spl69_11
| ~ spl69_39 ),
inference(resolution,[],[f867,f749]) ).
fof(f749,plain,
( rearsegP(sK21,sK20)
| ~ spl69_11 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f867,plain,
( ! [X0] :
( ~ rearsegP(sK21,X0)
| sK21 = X0
| ~ ssList(X0) )
| ~ spl69_39 ),
inference(avatar_component_clause,[],[f866]) ).
fof(f965,plain,
spl69_56,
inference(avatar_split_clause,[],[f661,f963]) ).
fof(f963,plain,
( spl69_56
<=> ! [X0,X1] :
( sK21 = X1
| app(X0,X1) != sK21
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_56])]) ).
fof(f661,plain,
! [X0,X1] :
( sK21 = X1
| app(X0,X1) != sK21
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f582,f600,f600]) ).
fof(f600,plain,
nil = sK21,
inference(definition_unfolding,[],[f378,f379]) ).
fof(f379,plain,
sK19 = sK21,
inference(cnf_transformation,[],[f254]) ).
fof(f254,plain,
( nil != sK18
& rearsegP(sK21,sK20)
& sK18 = sK20
& sK19 = sK21
& nil = sK19
& ssList(sK21)
& ssList(sK20)
& ssList(sK19)
& ssList(sK18) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21])],[f99,f253,f252,f251,f250]) ).
fof(f250,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil != X0
& rearsegP(X3,X2)
& X0 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil != sK18
& rearsegP(X3,X2)
& sK18 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK18) ) ),
introduced(choice_axiom,[]) ).
fof(f251,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil != sK18
& rearsegP(X3,X2)
& sK18 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( nil != sK18
& rearsegP(X3,X2)
& sK18 = X2
& sK19 = X3
& nil = sK19
& ssList(X3) )
& ssList(X2) )
& ssList(sK19) ) ),
introduced(choice_axiom,[]) ).
fof(f252,plain,
( ? [X2] :
( ? [X3] :
( nil != sK18
& rearsegP(X3,X2)
& sK18 = X2
& sK19 = X3
& nil = sK19
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( nil != sK18
& rearsegP(X3,sK20)
& sK18 = sK20
& sK19 = X3
& nil = sK19
& ssList(X3) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
( ? [X3] :
( nil != sK18
& rearsegP(X3,sK20)
& sK18 = sK20
& sK19 = X3
& nil = sK19
& ssList(X3) )
=> ( nil != sK18
& rearsegP(sK21,sK20)
& sK18 = sK20
& sK19 = sK21
& nil = sK19
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil != X0
& rearsegP(X3,X2)
& X0 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil != X0
& rearsegP(X3,X2)
& X0 = X2
& X1 = X3
& nil = X1
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil = X0
| ~ rearsegP(X3,X2)
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil = X0
| ~ rearsegP(X3,X2)
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f378,plain,
nil = sK19,
inference(cnf_transformation,[],[f254]) ).
fof(f582,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f370]) ).
fof(f370,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f369]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f961,plain,
spl69_55,
inference(avatar_split_clause,[],[f660,f959]) ).
fof(f959,plain,
( spl69_55
<=> ! [X0,X1] :
( sK21 = X0
| app(X0,X1) != sK21
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_55])]) ).
fof(f660,plain,
! [X0,X1] :
( sK21 = X0
| app(X0,X1) != sK21
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f583,f600,f600]) ).
fof(f583,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f370]) ).
fof(f957,plain,
spl69_54,
inference(avatar_split_clause,[],[f641,f955]) ).
fof(f955,plain,
( spl69_54
<=> ! [X0] :
( cons(hd(X0),tl(X0)) = X0
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_54])]) ).
fof(f641,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f460,f600]) ).
fof(f460,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f154]) ).
fof(f154,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(f953,plain,
spl69_53,
inference(avatar_split_clause,[],[f636,f951]) ).
fof(f951,plain,
( spl69_53
<=> ! [X0] :
( cons(sK23(X0),sK22(X0)) = X0
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_53])]) ).
fof(f636,plain,
! [X0] :
( cons(sK23(X0),sK22(X0)) = X0
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f457,f600]) ).
fof(f457,plain,
! [X0] :
( cons(sK23(X0),sK22(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0] :
( ( cons(sK23(X0),sK22(X0)) = X0
& ssItem(sK23(X0))
& ssList(sK22(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f149,f275,f274]) ).
fof(f274,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK22(X0)) = X0
& ssItem(X2) )
& ssList(sK22(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f275,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK22(X0)) = X0
& ssItem(X2) )
=> ( cons(sK23(X0),sK22(X0)) = X0
& ssItem(sK23(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f148]) ).
fof(f148,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(f949,plain,
spl69_52,
inference(avatar_split_clause,[],[f626,f947]) ).
fof(f947,plain,
( spl69_52
<=> ! [X0,X1] :
( sP2(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| sK21 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_52])]) ).
fof(f626,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| sK21 = X0 ),
inference(definition_unfolding,[],[f442,f600]) ).
fof(f442,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f270]) ).
fof(f270,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f269]) ).
fof(f269,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f945,plain,
spl69_51,
inference(avatar_split_clause,[],[f621,f943]) ).
fof(f943,plain,
( spl69_51
<=> ! [X0,X1] :
( sP0(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| sK21 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_51])]) ).
fof(f621,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| sK21 = X0 ),
inference(definition_unfolding,[],[f434,f600]) ).
fof(f434,plain,
! [X0,X1] :
( sP0(X0,X1)
| ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f266]) ).
fof(f266,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f265]) ).
fof(f265,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f931,plain,
spl69_50,
inference(avatar_split_clause,[],[f670,f929]) ).
fof(f929,plain,
( spl69_50
<=> ! [X1] :
( singletonP(cons(X1,sK21))
| ~ ssItem(X1)
| ~ ssList(cons(X1,sK21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_50])]) ).
fof(f670,plain,
! [X1] :
( singletonP(cons(X1,sK21))
| ~ ssItem(X1)
| ~ ssList(cons(X1,sK21)) ),
inference(equality_resolution,[],[f646]) ).
fof(f646,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,sK21) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f467,f600]) ).
fof(f467,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK26(X0),nil) = X0
& ssItem(sK26(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f282,f283]) ).
fof(f283,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK26(X0),nil) = X0
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f282,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f281]) ).
fof(f281,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,[],[f160]) ).
fof(f160,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(f927,plain,
spl69_49,
inference(avatar_split_clause,[],[f647,f925]) ).
fof(f925,plain,
( spl69_49
<=> ! [X0] :
( cons(sK26(X0),sK21) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_49])]) ).
fof(f647,plain,
! [X0] :
( cons(sK26(X0),sK21) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f466,f600]) ).
fof(f466,plain,
! [X0] :
( cons(sK26(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f923,plain,
spl69_48,
inference(avatar_split_clause,[],[f644,f921]) ).
fof(f921,plain,
( spl69_48
<=> ! [X0] :
( tl(X0) = sK25(X0)
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_48])]) ).
fof(f644,plain,
! [X0] :
( tl(X0) = sK25(X0)
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f464,f600]) ).
fof(f464,plain,
! [X0] :
( tl(X0) = sK25(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ( tl(X0) = sK25(X0)
& ssList(sK25(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f159,f279]) ).
fof(f279,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK25(X0)
& ssList(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f158]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
fof(f919,plain,
spl69_47,
inference(avatar_split_clause,[],[f642,f917]) ).
fof(f917,plain,
( spl69_47
<=> ! [X0] :
( hd(X0) = sK24(X0)
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_47])]) ).
fof(f642,plain,
! [X0] :
( hd(X0) = sK24(X0)
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f462,f600]) ).
fof(f462,plain,
! [X0] :
( hd(X0) = sK24(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0] :
( ( hd(X0) = sK24(X0)
& ssItem(sK24(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f157,f277]) ).
fof(f277,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK24(X0)
& ssItem(sK24(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f156]) ).
fof(f156,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(f915,plain,
spl69_46,
inference(avatar_split_clause,[],[f628,f913]) ).
fof(f913,plain,
( spl69_46
<=> ! [X0,X1] :
( lt(X1,hd(X0))
| sK21 = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_46])]) ).
fof(f628,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| sK21 = X0
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f440,f600]) ).
fof(f440,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f911,plain,
spl69_45,
inference(avatar_split_clause,[],[f623,f909]) ).
fof(f909,plain,
( spl69_45
<=> ! [X0,X1] :
( leq(X1,hd(X0))
| sK21 = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_45])]) ).
fof(f623,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| sK21 = X0
| ~ sP0(X0,X1) ),
inference(definition_unfolding,[],[f432,f600]) ).
fof(f432,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f907,plain,
spl69_44,
inference(avatar_split_clause,[],[f654,f905]) ).
fof(f905,plain,
( spl69_44
<=> ! [X0,X1] :
( cons(X1,X0) != sK21
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_44])]) ).
fof(f654,plain,
! [X0,X1] :
( cons(X1,X0) != sK21
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f554,f600]) ).
fof(f554,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f903,plain,
spl69_43,
inference(avatar_split_clause,[],[f598,f900]) ).
fof(f900,plain,
( spl69_43
<=> ssItem(sK68) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_43])]) ).
fof(f598,plain,
ssItem(sK68),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
( sK67 != sK68
& ssItem(sK68)
& ssItem(sK67) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f2,f372,f371]) ).
fof(f371,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK67 != X1
& ssItem(X1) )
& ssItem(sK67) ) ),
introduced(choice_axiom,[]) ).
fof(f372,plain,
( ? [X1] :
( sK67 != X1
& ssItem(X1) )
=> ( sK67 != sK68
& ssItem(sK68) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f898,plain,
spl69_42,
inference(avatar_split_clause,[],[f597,f895]) ).
fof(f895,plain,
( spl69_42
<=> ssItem(sK67) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_42])]) ).
fof(f597,plain,
ssItem(sK67),
inference(cnf_transformation,[],[f373]) ).
fof(f893,plain,
( spl69_41
| ~ spl69_1
| ~ spl69_27 ),
inference(avatar_split_clause,[],[f818,f813,f697,f890]) ).
fof(f890,plain,
( spl69_41
<=> sK20 = app(sK21,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_41])]) ).
fof(f813,plain,
( spl69_27
<=> ! [X0] :
( app(sK21,X0) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_27])]) ).
fof(f818,plain,
( sK20 = app(sK21,sK20)
| ~ spl69_1
| ~ spl69_27 ),
inference(resolution,[],[f814,f699]) ).
fof(f699,plain,
( ssList(sK20)
| ~ spl69_1 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f814,plain,
( ! [X0] :
( ~ ssList(X0)
| app(sK21,X0) = X0 )
| ~ spl69_27 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f874,plain,
( spl69_40
| ~ spl69_2
| ~ spl69_26 ),
inference(avatar_split_clause,[],[f817,f809,f702,f871]) ).
fof(f871,plain,
( spl69_40
<=> sK21 = app(sK21,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_40])]) ).
fof(f702,plain,
( spl69_2
<=> ssList(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_2])]) ).
fof(f809,plain,
( spl69_26
<=> ! [X0] :
( app(X0,sK21) = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_26])]) ).
fof(f817,plain,
( sK21 = app(sK21,sK21)
| ~ spl69_2
| ~ spl69_26 ),
inference(resolution,[],[f810,f704]) ).
fof(f704,plain,
( ssList(sK21)
| ~ spl69_2 ),
inference(avatar_component_clause,[],[f702]) ).
fof(f810,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,sK21) = X0 )
| ~ spl69_26 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f868,plain,
spl69_39,
inference(avatar_split_clause,[],[f653,f866]) ).
fof(f653,plain,
! [X0] :
( sK21 = X0
| ~ rearsegP(sK21,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f551,f600,f600]) ).
fof(f551,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f864,plain,
spl69_38,
inference(avatar_split_clause,[],[f651,f862]) ).
fof(f862,plain,
( spl69_38
<=> ! [X0] :
( sK21 = X0
| ~ frontsegP(sK21,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_38])]) ).
fof(f651,plain,
! [X0] :
( sK21 = X0
| ~ frontsegP(sK21,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f549,f600,f600]) ).
fof(f549,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f860,plain,
spl69_37,
inference(avatar_split_clause,[],[f649,f858]) ).
fof(f858,plain,
( spl69_37
<=> ! [X0] :
( sK21 = X0
| ~ segmentP(sK21,X0)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_37])]) ).
fof(f649,plain,
! [X0] :
( sK21 = X0
| ~ segmentP(sK21,X0)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f547,f600,f600]) ).
fof(f547,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f175]) ).
fof(f175,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f856,plain,
spl69_36,
inference(avatar_split_clause,[],[f645,f854]) ).
fof(f854,plain,
( spl69_36
<=> ! [X0] :
( ssList(sK25(X0))
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_36])]) ).
fof(f645,plain,
! [X0] :
( ssList(sK25(X0))
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f463,f600]) ).
fof(f463,plain,
! [X0] :
( ssList(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f852,plain,
spl69_35,
inference(avatar_split_clause,[],[f643,f850]) ).
fof(f850,plain,
( spl69_35
<=> ! [X0] :
( ssItem(sK24(X0))
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_35])]) ).
fof(f643,plain,
! [X0] :
( ssItem(sK24(X0))
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f461,f600]) ).
fof(f461,plain,
! [X0] :
( ssItem(sK24(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f848,plain,
spl69_34,
inference(avatar_split_clause,[],[f640,f846]) ).
fof(f846,plain,
( spl69_34
<=> ! [X0] :
( ssList(tl(X0))
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_34])]) ).
fof(f640,plain,
! [X0] :
( ssList(tl(X0))
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f459,f600]) ).
fof(f459,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f844,plain,
spl69_33,
inference(avatar_split_clause,[],[f639,f842]) ).
fof(f842,plain,
( spl69_33
<=> ! [X0] :
( ssItem(hd(X0))
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_33])]) ).
fof(f639,plain,
! [X0] :
( ssItem(hd(X0))
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f458,f600]) ).
fof(f458,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f150]) ).
fof(f150,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(f840,plain,
spl69_32,
inference(avatar_split_clause,[],[f638,f838]) ).
fof(f838,plain,
( spl69_32
<=> ! [X0] :
( ssList(sK22(X0))
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_32])]) ).
fof(f638,plain,
! [X0] :
( ssList(sK22(X0))
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f455,f600]) ).
fof(f455,plain,
! [X0] :
( ssList(sK22(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f836,plain,
spl69_31,
inference(avatar_split_clause,[],[f637,f834]) ).
fof(f834,plain,
( spl69_31
<=> ! [X0] :
( ssItem(sK23(X0))
| sK21 = X0
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_31])]) ).
fof(f637,plain,
! [X0] :
( ssItem(sK23(X0))
| sK21 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f456,f600]) ).
fof(f456,plain,
! [X0] :
( ssItem(sK23(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f832,plain,
( spl69_30
| ~ spl69_1
| ~ spl69_26 ),
inference(avatar_split_clause,[],[f816,f809,f697,f829]) ).
fof(f829,plain,
( spl69_30
<=> sK20 = app(sK20,sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_30])]) ).
fof(f816,plain,
( sK20 = app(sK20,sK21)
| ~ spl69_1
| ~ spl69_26 ),
inference(resolution,[],[f810,f699]) ).
fof(f827,plain,
spl69_29,
inference(avatar_split_clause,[],[f629,f825]) ).
fof(f825,plain,
( spl69_29
<=> ! [X0,X1] :
( strictorderedP(X0)
| sK21 = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_29])]) ).
fof(f629,plain,
! [X0,X1] :
( strictorderedP(X0)
| sK21 = X0
| ~ sP2(X0,X1) ),
inference(definition_unfolding,[],[f439,f600]) ).
fof(f439,plain,
! [X0,X1] :
( strictorderedP(X0)
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f823,plain,
spl69_28,
inference(avatar_split_clause,[],[f624,f821]) ).
fof(f821,plain,
( spl69_28
<=> ! [X0,X1] :
( totalorderedP(X0)
| sK21 = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_28])]) ).
fof(f624,plain,
! [X0,X1] :
( totalorderedP(X0)
| sK21 = X0
| ~ sP0(X0,X1) ),
inference(definition_unfolding,[],[f431,f600]) ).
fof(f431,plain,
! [X0,X1] :
( totalorderedP(X0)
| nil = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f815,plain,
spl69_27,
inference(avatar_split_clause,[],[f635,f813]) ).
fof(f635,plain,
! [X0] :
( app(sK21,X0) = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f454,f600]) ).
fof(f454,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,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(f811,plain,
spl69_26,
inference(avatar_split_clause,[],[f634,f809]) ).
fof(f634,plain,
! [X0] :
( app(X0,sK21) = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f453,f600]) ).
fof(f453,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,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(f807,plain,
spl69_25,
inference(avatar_split_clause,[],[f620,f805]) ).
fof(f805,plain,
( spl69_25
<=> ! [X0] :
( strictorderedP(cons(X0,sK21))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_25])]) ).
fof(f620,plain,
! [X0] :
( strictorderedP(cons(X0,sK21))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f402,f600]) ).
fof(f402,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
fof(f803,plain,
spl69_24,
inference(avatar_split_clause,[],[f619,f801]) ).
fof(f801,plain,
( spl69_24
<=> ! [X0] :
( totalorderedP(cons(X0,sK21))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_24])]) ).
fof(f619,plain,
! [X0] :
( totalorderedP(cons(X0,sK21))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f401,f600]) ).
fof(f401,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,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(f799,plain,
spl69_23,
inference(avatar_split_clause,[],[f618,f797]) ).
fof(f797,plain,
( spl69_23
<=> ! [X0] :
( totalorderP(cons(X0,sK21))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_23])]) ).
fof(f618,plain,
! [X0] :
( totalorderP(cons(X0,sK21))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f400,f600]) ).
fof(f400,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
fof(f795,plain,
spl69_22,
inference(avatar_split_clause,[],[f617,f793]) ).
fof(f793,plain,
( spl69_22
<=> ! [X0] :
( cyclefreeP(cons(X0,sK21))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_22])]) ).
fof(f617,plain,
! [X0] :
( cyclefreeP(cons(X0,sK21))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f399,f600]) ).
fof(f399,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ssItem(X0)
=> cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
fof(f791,plain,
spl69_21,
inference(avatar_split_clause,[],[f616,f789]) ).
fof(f789,plain,
( spl69_21
<=> ! [X0] :
( equalelemsP(cons(X0,sK21))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_21])]) ).
fof(f616,plain,
! [X0] :
( equalelemsP(cons(X0,sK21))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f398,f600]) ).
fof(f398,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,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) ).
fof(f787,plain,
spl69_20,
inference(avatar_split_clause,[],[f615,f785]) ).
fof(f785,plain,
( spl69_20
<=> ! [X0] :
( strictorderP(cons(X0,sK21))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_20])]) ).
fof(f615,plain,
! [X0] :
( strictorderP(cons(X0,sK21))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f397,f600]) ).
fof(f397,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
fof(f783,plain,
spl69_19,
inference(avatar_split_clause,[],[f614,f781]) ).
fof(f781,plain,
( spl69_19
<=> ! [X0] :
( duplicatefreeP(cons(X0,sK21))
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_19])]) ).
fof(f614,plain,
! [X0] :
( duplicatefreeP(cons(X0,sK21))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f396,f600]) ).
fof(f396,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f779,plain,
spl69_18,
inference(avatar_split_clause,[],[f633,f777]) ).
fof(f777,plain,
( spl69_18
<=> ! [X0] :
( rearsegP(X0,sK21)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_18])]) ).
fof(f633,plain,
! [X0] :
( rearsegP(X0,sK21)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f450,f600]) ).
fof(f450,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f775,plain,
spl69_17,
inference(avatar_split_clause,[],[f632,f773]) ).
fof(f773,plain,
( spl69_17
<=> ! [X0] :
( frontsegP(X0,sK21)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_17])]) ).
fof(f632,plain,
! [X0] :
( frontsegP(X0,sK21)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f448,f600]) ).
fof(f448,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f771,plain,
spl69_16,
inference(avatar_split_clause,[],[f631,f769]) ).
fof(f769,plain,
( spl69_16
<=> ! [X0] :
( segmentP(X0,sK21)
| ~ ssList(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_16])]) ).
fof(f631,plain,
! [X0] :
( segmentP(X0,sK21)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f447,f600]) ).
fof(f447,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f767,plain,
spl69_15,
inference(avatar_split_clause,[],[f613,f765]) ).
fof(f765,plain,
( spl69_15
<=> ! [X0] :
( ~ memberP(sK21,X0)
| ~ ssItem(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_15])]) ).
fof(f613,plain,
! [X0] :
( ~ memberP(sK21,X0)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f392,f600]) ).
fof(f392,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,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(f763,plain,
spl69_14,
inference(avatar_split_clause,[],[f668,f761]) ).
fof(f761,plain,
( spl69_14
<=> ! [X1] : sP2(sK21,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_14])]) ).
fof(f668,plain,
! [X1] : sP2(sK21,X1),
inference(equality_resolution,[],[f627]) ).
fof(f627,plain,
! [X0,X1] :
( sP2(X0,X1)
| sK21 != X0 ),
inference(definition_unfolding,[],[f441,f600]) ).
fof(f441,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f271]) ).
fof(f759,plain,
spl69_13,
inference(avatar_split_clause,[],[f666,f757]) ).
fof(f757,plain,
( spl69_13
<=> ! [X1] : sP0(sK21,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_13])]) ).
fof(f666,plain,
! [X1] : sP0(sK21,X1),
inference(equality_resolution,[],[f622]) ).
fof(f622,plain,
! [X0,X1] :
( sP0(X0,X1)
| sK21 != X0 ),
inference(definition_unfolding,[],[f433,f600]) ).
fof(f433,plain,
! [X0,X1] :
( sP0(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f267]) ).
fof(f755,plain,
~ spl69_12,
inference(avatar_split_clause,[],[f601,f752]) ).
fof(f601,plain,
sK20 != sK21,
inference(definition_unfolding,[],[f382,f600,f380]) ).
fof(f380,plain,
sK18 = sK20,
inference(cnf_transformation,[],[f254]) ).
fof(f382,plain,
nil != sK18,
inference(cnf_transformation,[],[f254]) ).
fof(f750,plain,
spl69_11,
inference(avatar_split_clause,[],[f381,f747]) ).
fof(f381,plain,
rearsegP(sK21,sK20),
inference(cnf_transformation,[],[f254]) ).
fof(f745,plain,
spl69_10,
inference(avatar_split_clause,[],[f611,f742]) ).
fof(f742,plain,
( spl69_10
<=> totalorderedP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_10])]) ).
fof(f611,plain,
totalorderedP(sK21),
inference(definition_unfolding,[],[f390,f600]) ).
fof(f390,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f740,plain,
spl69_9,
inference(avatar_split_clause,[],[f610,f737]) ).
fof(f737,plain,
( spl69_9
<=> strictorderedP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_9])]) ).
fof(f610,plain,
strictorderedP(sK21),
inference(definition_unfolding,[],[f389,f600]) ).
fof(f389,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
fof(f735,plain,
spl69_8,
inference(avatar_split_clause,[],[f609,f732]) ).
fof(f732,plain,
( spl69_8
<=> totalorderP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_8])]) ).
fof(f609,plain,
totalorderP(sK21),
inference(definition_unfolding,[],[f388,f600]) ).
fof(f388,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f730,plain,
spl69_7,
inference(avatar_split_clause,[],[f608,f727]) ).
fof(f727,plain,
( spl69_7
<=> strictorderP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_7])]) ).
fof(f608,plain,
strictorderP(sK21),
inference(definition_unfolding,[],[f387,f600]) ).
fof(f387,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
fof(f725,plain,
spl69_6,
inference(avatar_split_clause,[],[f607,f722]) ).
fof(f722,plain,
( spl69_6
<=> duplicatefreeP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_6])]) ).
fof(f607,plain,
duplicatefreeP(sK21),
inference(definition_unfolding,[],[f386,f600]) ).
fof(f386,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f720,plain,
spl69_5,
inference(avatar_split_clause,[],[f606,f717]) ).
fof(f717,plain,
( spl69_5
<=> cyclefreeP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_5])]) ).
fof(f606,plain,
cyclefreeP(sK21),
inference(definition_unfolding,[],[f385,f600]) ).
fof(f385,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
fof(f715,plain,
spl69_4,
inference(avatar_split_clause,[],[f605,f712]) ).
fof(f712,plain,
( spl69_4
<=> equalelemsP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_4])]) ).
fof(f605,plain,
equalelemsP(sK21),
inference(definition_unfolding,[],[f384,f600]) ).
fof(f384,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(f710,plain,
~ spl69_3,
inference(avatar_split_clause,[],[f604,f707]) ).
fof(f707,plain,
( spl69_3
<=> singletonP(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl69_3])]) ).
fof(f604,plain,
~ singletonP(sK21),
inference(definition_unfolding,[],[f383,f600]) ).
fof(f383,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f705,plain,
spl69_2,
inference(avatar_split_clause,[],[f377,f702]) ).
fof(f377,plain,
ssList(sK21),
inference(cnf_transformation,[],[f254]) ).
fof(f700,plain,
spl69_1,
inference(avatar_split_clause,[],[f376,f697]) ).
fof(f376,plain,
ssList(sK20),
inference(cnf_transformation,[],[f254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SWC044+1 : TPTP v8.1.2. Released v2.4.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 04:46:56 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (25176)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (25177)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39 % (25179)WARNING: value z3 for option sas not known
% 0.22/0.39 % (25178)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39 % (25180)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39 % (25182)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)
% 0.22/0.39 % (25183)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)
% 0.22/0.39 % (25181)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)
% 0.22/0.39 % (25179)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)
% 0.22/0.40 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.41 TRYING [3]
% 0.22/0.41 % (25181)First to succeed.
% 0.22/0.41 TRYING [1]
% 0.22/0.42 TRYING [2]
% 0.22/0.42 % (25179)Also succeeded, but the first one will report.
% 0.22/0.42 % (25182)Also succeeded, but the first one will report.
% 0.22/0.42 % (25181)Refutation found. Thanks to Tanya!
% 0.22/0.42 % SZS status Theorem for theBenchmark
% 0.22/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.42 % (25181)------------------------------
% 0.22/0.42 % (25181)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.42 % (25181)Termination reason: Refutation
% 0.22/0.42
% 0.22/0.42 % (25181)Memory used [KB]: 1405
% 0.22/0.42 % (25181)Time elapsed: 0.026 s
% 0.22/0.42 % (25181)Instructions burned: 30 (million)
% 0.22/0.42 % (25181)------------------------------
% 0.22/0.42 % (25181)------------------------------
% 0.22/0.42 % (25176)Success in time 0.056 s
%------------------------------------------------------------------------------