%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC190+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:02:52 PM UTC 2026
% Result : Theorem 3.34s 1.47s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 16
% Syntax : Number of formulae : 124 ( 24 unt; 9 def)
% Number of atoms : 456 ( 46 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 580 ( 248 ~; 247 |; 47 &)
% ( 12 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 88 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ~ ssList(X7)
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0
| X4 = X5 ) ) ) )
| ! [X8] :
( ssItem(X8)
=> ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X2,X9) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ~ ssList(X7)
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0
| X4 = X5 ) ) ) )
| ! [X8] :
( ssItem(X8)
=> ? [X9] :
( ssItem(X9)
& X8 != X9
& memberP(X2,X9) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ssList(X7)
& app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) = X0
& X4 != X5 )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
& ? [X8] :
( ! [X9] :
( ~ ssItem(X9)
| X8 = X9
| ~ memberP(X2,X9) )
& ssItem(X8) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f121,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ssList(sK7)
& sK0 = app(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)),sK7)
& sK4 != sK5
& ssList(sK6)
& ssItem(sK5)
& ssItem(sK4)
& ! [X9] :
( ~ ssItem(X9)
| sK8 = X9
| ~ memberP(sK2,X9) )
& ssItem(sK8)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X8,sK8)],[f98]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f119]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f128]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,cons(X1,X5)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f130]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK13(X0,X1))
& ssList(sK14(X0,X1))
& app(sK13(X0,X1),cons(X1,sK14(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f131]) ).
fof(f137,plain,
! [X9] :
( ~ memberP(sK2,X9)
| sK8 = X9
| ~ ssItem(X9) ),
inference(cnf_transformation,[],[f121]) ).
fof(f138,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f121]) ).
fof(f139,plain,
ssItem(sK5),
inference(cnf_transformation,[],[f121]) ).
fof(f140,plain,
ssList(sK6),
inference(cnf_transformation,[],[f121]) ).
fof(f141,plain,
sK4 != sK5,
inference(cnf_transformation,[],[f121]) ).
fof(f142,plain,
sK0 = app(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)),sK7),
inference(cnf_transformation,[],[f121]) ).
fof(f143,plain,
ssList(sK7),
inference(cnf_transformation,[],[f121]) ).
fof(f144,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f121]) ).
fof(f157,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f162,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f168,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f169,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f176,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f180,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f181,plain,
sK2 = app(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)),sK7),
inference(definition_unfolding,[],[f142,f144]) ).
fof(f184,definition,
~ sP15(sK4),
introduced(definition,[new_symbols(definition,[sP15])],[inequality_splitting_name_introduction]) ).
fof(f185,plain,
sP15(sK5),
inference(inequality_splitting,[],[f141,f184]) ).
fof(f198,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f180]) ).
fof(f204,plain,
( sK2 = app(app(sK6,cons(sK4,nil)),app(cons(sK5,nil),sK7))
| ~ ssList(sK7)
| ~ ssList(cons(sK5,nil))
| ~ ssList(app(sK6,cons(sK4,nil))) ),
inference(superposition,[],[f181,f162]) ).
fof(f216,plain,
! [X0] :
( memberP(sK2,X0)
| ~ memberP(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)),X0)
| ~ ssList(sK7)
| ~ ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| ~ ssItem(X0) ),
inference(superposition,[],[f176,f181]) ).
fof(f223,plain,
! [X0] :
( memberP(sK2,X0)
| ~ memberP(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)),X0)
| ~ ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f216,f143]) ).
fof(f234,plain,
( sK2 = app(app(sK6,cons(sK4,nil)),app(cons(sK5,nil),sK7))
| ~ ssList(cons(sK5,nil))
| ~ ssList(app(sK6,cons(sK4,nil))) ),
inference(forward_subsumption_resolution,[],[f204,f143]) ).
fof(f236,definition,
( spl22_1
<=> ssList(app(sK6,cons(sK4,nil))) ),
introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition]) ).
fof(f237,plain,
( ssList(app(sK6,cons(sK4,nil)))
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f238,plain,
( ~ ssList(app(sK6,cons(sK4,nil)))
| spl22_1 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f240,definition,
( spl22_2
<=> ssList(cons(sK5,nil)) ),
introduced(definition,[new_symbols(definition,[spl22_2])],[avatar_definition]) ).
fof(f241,plain,
( ssList(cons(sK5,nil))
| ~ spl22_2 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f242,plain,
( ~ ssList(cons(sK5,nil))
| spl22_2 ),
inference(avatar_component_clause,[],[f240]) ).
fof(f259,definition,
( spl22_6
<=> ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil))) ),
introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition]) ).
fof(f260,plain,
( ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| ~ spl22_6 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( ~ ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| spl22_6 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f294,definition,
( spl22_14
<=> ! [X0] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl22_14])],[avatar_definition]) ).
fof(f295,plain,
( ! [X0] :
( ~ memberP(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)),X0)
| ~ ssItem(X0)
| memberP(sK2,X0) )
| ~ spl22_14 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f296,plain,
( ~ spl22_6
| spl22_14 ),
inference(avatar_split_clause,[],[f223,f294,f259]) ).
fof(f324,definition,
( spl22_21
<=> sK2 = app(app(sK6,cons(sK4,nil)),app(cons(sK5,nil),sK7)) ),
introduced(definition,[new_symbols(definition,[spl22_21])],[avatar_definition]) ).
fof(f326,plain,
( sK2 = app(app(sK6,cons(sK4,nil)),app(cons(sK5,nil),sK7))
| ~ spl22_21 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f329,plain,
( ~ spl22_1
| ~ spl22_2
| spl22_21 ),
inference(avatar_split_clause,[],[f234,f324,f240,f236]) ).
fof(f331,definition,
( spl22_22
<=> ssList(cons(sK4,nil)) ),
introduced(definition,[new_symbols(definition,[spl22_22])],[avatar_definition]) ).
fof(f332,plain,
( ssList(cons(sK4,nil))
| ~ spl22_22 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f333,plain,
( ~ ssList(cons(sK4,nil))
| spl22_22 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f352,plain,
( ~ ssItem(sK5)
| ~ ssList(nil)
| spl22_2 ),
inference(resolution,[],[f242,f157]) ).
fof(f354,plain,
( ~ ssList(nil)
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f352,f139]) ).
fof(f355,plain,
( $false
| spl22_2 ),
inference(forward_subsumption_resolution,[],[f354,f169]) ).
fof(f356,plain,
spl22_2,
inference(avatar_contradiction_clause,[],[f355]) ).
fof(f358,plain,
( ~ ssItem(sK4)
| ~ ssList(nil)
| spl22_22 ),
inference(resolution,[],[f333,f157]) ).
fof(f360,plain,
( ~ ssList(nil)
| spl22_22 ),
inference(forward_subsumption_resolution,[],[f358,f138]) ).
fof(f361,plain,
( $false
| spl22_22 ),
inference(forward_subsumption_resolution,[],[f360,f169]) ).
fof(f362,plain,
spl22_22,
inference(avatar_contradiction_clause,[],[f361]) ).
fof(f364,plain,
( ~ ssList(cons(sK4,nil))
| ~ ssList(sK6)
| spl22_1 ),
inference(resolution,[],[f238,f168]) ).
fof(f367,plain,
( ~ ssList(sK6)
| spl22_1
| ~ spl22_22 ),
inference(forward_subsumption_resolution,[],[f364,f332]) ).
fof(f368,plain,
( $false
| spl22_1
| ~ spl22_22 ),
inference(forward_subsumption_resolution,[],[f367,f140]) ).
fof(f369,plain,
( spl22_1
| ~ spl22_22 ),
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f373,plain,
( ~ ssList(cons(sK5,nil))
| ~ ssList(app(sK6,cons(sK4,nil)))
| spl22_6 ),
inference(resolution,[],[f261,f168]) ).
fof(f379,plain,
( ~ ssList(app(sK6,cons(sK4,nil)))
| ~ spl22_2
| spl22_6 ),
inference(forward_subsumption_resolution,[],[f373,f241]) ).
fof(f381,plain,
( $false
| ~ spl22_1
| ~ spl22_2
| spl22_6 ),
inference(forward_subsumption_resolution,[],[f379,f237]) ).
fof(f382,plain,
( ~ spl22_1
| ~ spl22_2
| spl22_6 ),
inference(avatar_contradiction_clause,[],[f381]) ).
fof(f450,plain,
( ! [X0] :
( memberP(sK2,X0)
| ~ memberP(app(sK6,cons(sK4,nil)),X0)
| ~ ssList(app(cons(sK5,nil),sK7))
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ ssItem(X0) )
| ~ spl22_21 ),
inference(superposition,[],[f176,f326]) ).
fof(f456,plain,
( ! [X0] :
( memberP(sK2,X0)
| ~ memberP(app(sK6,cons(sK4,nil)),X0)
| ~ ssList(app(cons(sK5,nil),sK7))
| ~ ssItem(X0) )
| ~ spl22_1
| ~ spl22_21 ),
inference(forward_subsumption_resolution,[],[f450,f237]) ).
fof(f488,definition,
( spl22_27
<=> ! [X0] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(app(sK6,cons(sK4,nil)),X0) ) ),
introduced(definition,[new_symbols(definition,[spl22_27])],[avatar_definition]) ).
fof(f489,plain,
( ! [X0] :
( ~ memberP(app(sK6,cons(sK4,nil)),X0)
| ~ ssItem(X0)
| memberP(sK2,X0) )
| ~ spl22_27 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f563,definition,
( spl22_40
<=> ssList(app(cons(sK5,nil),sK7)) ),
introduced(definition,[new_symbols(definition,[spl22_40])],[avatar_definition]) ).
fof(f565,plain,
( ~ ssList(app(cons(sK5,nil),sK7))
| spl22_40 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f571,plain,
( ~ spl22_40
| spl22_27
| ~ spl22_1
| ~ spl22_21 ),
inference(avatar_split_clause,[],[f456,f324,f236,f488,f563]) ).
fof(f606,plain,
( ~ ssList(sK7)
| ~ ssList(cons(sK5,nil))
| spl22_40 ),
inference(resolution,[],[f565,f168]) ).
fof(f609,plain,
( ~ ssList(cons(sK5,nil))
| spl22_40 ),
inference(forward_subsumption_resolution,[],[f606,f143]) ).
fof(f610,plain,
( $false
| ~ spl22_2
| spl22_40 ),
inference(forward_subsumption_resolution,[],[f609,f241]) ).
fof(f611,plain,
( ~ spl22_2
| spl22_40 ),
inference(avatar_contradiction_clause,[],[f610]) ).
fof(f885,plain,
( ~ ssItem(sK5)
| memberP(sK2,sK5)
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| ~ spl22_14 ),
inference(resolution,[],[f295,f198]) ).
fof(f890,plain,
( ~ ssItem(sK5)
| memberP(sK2,sK5)
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ ssList(nil)
| ~ ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| ~ spl22_14 ),
inference(duplicate_literal_removal,[],[f885]) ).
fof(f893,plain,
( memberP(sK2,sK5)
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ ssList(nil)
| ~ ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| ~ spl22_14 ),
inference(forward_subsumption_resolution,[],[f890,f139]) ).
fof(f895,plain,
( memberP(sK2,sK5)
| ~ ssList(nil)
| ~ ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| ~ spl22_1
| ~ spl22_14 ),
inference(forward_subsumption_resolution,[],[f893,f237]) ).
fof(f897,plain,
( memberP(sK2,sK5)
| ~ ssList(app(app(sK6,cons(sK4,nil)),cons(sK5,nil)))
| ~ spl22_1
| ~ spl22_14 ),
inference(forward_subsumption_resolution,[],[f895,f169]) ).
fof(f898,plain,
( memberP(sK2,sK5)
| ~ spl22_1
| ~ spl22_6
| ~ spl22_14 ),
inference(forward_subsumption_resolution,[],[f897,f260]) ).
fof(f899,plain,
( sK5 = sK8
| ~ ssItem(sK5)
| ~ spl22_1
| ~ spl22_6
| ~ spl22_14 ),
inference(resolution,[],[f898,f137]) ).
fof(f900,plain,
( sK5 = sK8
| ~ spl22_1
| ~ spl22_6
| ~ spl22_14 ),
inference(forward_subsumption_resolution,[],[f899,f139]) ).
fof(f1297,plain,
( ~ ssItem(sK4)
| memberP(sK2,sK4)
| ~ ssList(sK6)
| ~ ssList(nil)
| ~ ssItem(sK4)
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ spl22_27 ),
inference(resolution,[],[f489,f198]) ).
fof(f1300,plain,
( ~ ssItem(sK4)
| memberP(sK2,sK4)
| ~ ssList(sK6)
| ~ ssList(nil)
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ spl22_27 ),
inference(duplicate_literal_removal,[],[f1297]) ).
fof(f1303,plain,
( memberP(sK2,sK4)
| ~ ssList(sK6)
| ~ ssList(nil)
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ spl22_27 ),
inference(forward_subsumption_resolution,[],[f1300,f138]) ).
fof(f1306,plain,
( memberP(sK2,sK4)
| ~ ssList(nil)
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ spl22_27 ),
inference(forward_subsumption_resolution,[],[f1303,f140]) ).
fof(f1309,plain,
( memberP(sK2,sK4)
| ~ ssList(app(sK6,cons(sK4,nil)))
| ~ spl22_27 ),
inference(forward_subsumption_resolution,[],[f1306,f169]) ).
fof(f1310,plain,
( memberP(sK2,sK4)
| ~ spl22_1
| ~ spl22_27 ),
inference(forward_subsumption_resolution,[],[f1309,f237]) ).
fof(f1311,plain,
( sK4 = sK8
| ~ ssItem(sK4)
| ~ spl22_1
| ~ spl22_27 ),
inference(resolution,[],[f1310,f137]) ).
fof(f1312,plain,
( sK4 = sK8
| ~ spl22_1
| ~ spl22_27 ),
inference(forward_subsumption_resolution,[],[f1311,f138]) ).
fof(f1320,plain,
( sK4 = sK5
| ~ spl22_1
| ~ spl22_6
| ~ spl22_14
| ~ spl22_27 ),
inference(superposition,[],[f900,f1312]) ).
fof(f1397,plain,
( sP15(sK4)
| ~ spl22_1
| ~ spl22_6
| ~ spl22_14
| ~ spl22_27 ),
inference(superposition,[],[f185,f1320]) ).
fof(f1427,plain,
( $false
| ~ spl22_1
| ~ spl22_6
| ~ spl22_14
| ~ spl22_27 ),
inference(forward_subsumption_resolution,[],[f1397,f184]) ).
fof(f1428,plain,
( ~ spl22_1
| ~ spl22_6
| ~ spl22_14
| ~ spl22_27 ),
inference(avatar_contradiction_clause,[],[f1427]) ).
cnf(s5,plain,
( ~ spl22_6
| spl22_14 ),
inference(sat_conversion,[],[f296]) ).
cnf(s16,plain,
( ~ spl22_1
| ~ spl22_2
| spl22_21 ),
inference(sat_conversion,[],[f329]) ).
cnf(s19,plain,
spl22_2,
inference(sat_conversion,[],[f356]) ).
cnf(s20,plain,
spl22_22,
inference(sat_conversion,[],[f362]) ).
cnf(s21,plain,
( spl22_1
| ~ spl22_22 ),
inference(sat_conversion,[],[f369]) ).
cnf(s22,plain,
( ~ spl22_1
| ~ spl22_2
| spl22_6 ),
inference(sat_conversion,[],[f382]) ).
cnf(s40,plain,
( ~ spl22_1
| ~ spl22_21
| spl22_27
| ~ spl22_40 ),
inference(sat_conversion,[],[f571]) ).
cnf(s53,plain,
( ~ spl22_2
| spl22_40 ),
inference(sat_conversion,[],[f611]) ).
cnf(s80,plain,
( ~ spl22_1
| ~ spl22_6
| ~ spl22_14
| ~ spl22_27 ),
inference(sat_conversion,[],[f1428]) ).
cnf(s96,plain,
spl22_1,
inference(rat,[],[s21,s20]) ).
cnf(s99,plain,
spl22_40,
inference(rat,[],[s53,s19]) ).
cnf(s100,plain,
spl22_6,
inference(rat,[],[s22,s96,s19]) ).
cnf(s104,plain,
spl22_21,
inference(rat,[],[s16,s19,s96]) ).
cnf(s112,plain,
spl22_27,
inference(rat,[],[s40,s99,s96,s104]) ).
cnf(s113,plain,
~ spl22_14,
inference(rat,[],[s80,s100,s96,s112]) ).
cnf(s121,plain,
$false,
inference(rat,[],[s5,s113,s100]) ).
fof(f1429,plain,
$false,
inference(avatar_sat_refutation,[],[s121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC190+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 08:21:52 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.34/1.47 % (206169)Detected formulas, will run a generic FOF schedule.
% 3.34/1.47 % (206280)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1408754360:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/1.47 % (206276)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2529159431:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/1.47 % (206277)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=811328847:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/1.47 % (206275)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=4056877579:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/1.47 % (206279)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=370147608:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/1.47 % (206281)dis-21_1_sil=8000:lcm=predicate:random_seed=2551945125:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.34/1.47 % (206278)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2382445142:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/1.47 % (206280)Instruction limit reached!
% 3.34/1.47 % (206280)------------------------------
% 3.34/1.47 % (206280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.47 % (206280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.47 % (206280)CaDiCaL version: 2.1.3
% 3.34/1.47 % (206280)Termination reason: Instruction limit
% 3.34/1.47 % (206280)Termination phase: Saturation
% 3.34/1.47 % (206280)Time elapsed: 0.053 s
% 3.34/1.47 % (206280)Peak memory usage: 90 MB
% 3.34/1.47 % (206280)Instructions burned: 142 (million)
% 3.34/1.47 % (206278)First to succeed.
% 3.34/1.47 % (206278)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-206169"
% 3.34/1.47 % (206279)Instruction limit reached!
% 3.34/1.47 % (206279)------------------------------
% 3.34/1.47 % (206279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.47 % (206279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.47 % (206279)CaDiCaL version: 2.1.3
% 3.34/1.47 % (206279)Termination reason: Instruction limit
% 3.34/1.47 % (206279)Termination phase: Saturation
% 3.34/1.47 % (206279)Time elapsed: 0.074 s
% 3.34/1.47 % (206279)Peak memory usage: 88 MB
% 3.34/1.47 % (206279)Instructions burned: 119 (million)
% 3.34/1.47 % (206281)Instruction limit reached!
% 3.34/1.47 % (206281)------------------------------
% 3.34/1.47 % (206281)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.47 % (206281)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.47 % (206281)CaDiCaL version: 2.1.3
% 3.34/1.47 % (206281)Termination reason: Instruction limit
% 3.34/1.47 % (206281)Termination phase: Saturation
% 3.34/1.47 % (206281)Time elapsed: 0.085 s
% 3.34/1.47 % (206281)Peak memory usage: 91 MB
% 3.34/1.47 % (206281)Instructions burned: 129 (million)
% 3.34/1.47 % (206293)lrs+10_1_sil=8000:sp=occurrence:random_seed=852518647:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.34/1.47 % (206293)Also succeeded, but the first one will report.
% 3.34/1.47 % (206310)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3670089896:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.34/1.47 % (206318)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1960815110:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.34/1.47 % (206278)Refutation found. Thanks to Tanya!
% 3.34/1.47 % SZS status Theorem for theBenchmark
% 3.34/1.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.80 % (206278)------------------------------
% 0.19/1.80 % (206278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.80 % (206278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.80 % (206278)CaDiCaL version: 2.1.3
% 0.19/1.80 % (206278)Termination reason: Refutation
% 0.19/1.80 % (206278)Time elapsed: 0.032 s
% 0.19/1.80 % (206278)Peak memory usage: 90 MB
% 0.19/1.80 % (206278)Instructions burned: 46 (million)
% 0.19/1.80 % (206278)------------------------------
% 0.19/1.80 % (206278)------------------------------
% 0.19/1.80 % (206169)Success in time 0.611 s
% 0.19/1.80 % Vampire exiting
%------------------------------------------------------------------------------