%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC310+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 01:03:24 PM UTC 2026
% Result : Theorem 3.10s 1.07s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 27
% Syntax : Number of formulae : 168 ( 24 unt; 19 def)
% Number of atoms : 614 ( 109 equ)
% Maximal formula atoms : 27 ( 3 avg)
% Number of connectives : 799 ( 353 ~; 357 |; 53 &)
% ( 16 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 15 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 101 ( 0 sgn 87 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) != X2 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssList(X6)
& X0 = X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X1) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X1) = X9
& neq(nil,X1) )
& neq(nil,X1) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) != X2 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssList(X6)
& X0 = X6
& ? [X7] :
( ssList(X7)
& ? [X8] :
( ssList(X8)
& tl(X1) = X7
& app(X7,X8) = X6
& ? [X9] :
( ssItem(X9)
& cons(X9,nil) = X8
& hd(X1) = X9
& neq(nil,X1) )
& neq(nil,X1) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) = X2 )
& ssItem(X4) )
| ~ neq(X3,nil) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssList(X6)
| X0 != X6
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| tl(X1) != X7
| app(X7,X8) != X6
| ! [X9] :
( ~ ssItem(X9)
| cons(X9,nil) != X8
| hd(X1) != X9
| ~ neq(nil,X1) )
| ~ neq(nil,X1) ) ) ) ) ) )
& 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(f109,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f137,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ( nil = sK2
| nil != sK3 )
& ( ( ssList(sK5)
& sK3 = app(cons(sK4,nil),sK5)
& sK2 = app(sK5,cons(sK4,nil))
& ssItem(sK4) )
| ~ neq(sK3,nil) )
& ( ( nil = sK1
& nil != sK0 )
| ( neq(sK1,nil)
& ! [X6] :
( ~ ssList(X6)
| sK0 != X6
| ! [X7] :
( ~ ssList(X7)
| ! [X8] :
( ~ ssList(X8)
| tl(sK1) != X7
| app(X7,X8) != X6
| ! [X9] :
( ~ ssItem(X9)
| cons(X9,nil) != X8
| hd(sK1) != X9
| ~ neq(nil,sK1) )
| ~ neq(nil,sK1) ) ) ) ) )
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f98]) ).
fof(f142,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f147,plain,
ssList(sK1),
inference(cnf_transformation,[],[f137]) ).
fof(f150,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f137]) ).
fof(f151,plain,
! [X8,X6,X9,X7] :
( nil = sK1
| ~ ssList(X6)
| sK0 != X6
| ~ ssList(X7)
| ~ ssList(X8)
| tl(sK1) != X7
| app(X7,X8) != X6
| ~ ssItem(X9)
| cons(X9,nil) != X8
| hd(sK1) != X9
| ~ neq(nil,sK1)
| ~ neq(nil,sK1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f152,plain,
( nil = sK1
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f137]) ).
fof(f153,plain,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f137]) ).
fof(f154,plain,
( sK2 = app(sK5,cons(sK4,nil))
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f137]) ).
fof(f155,plain,
( sK3 = app(cons(sK4,nil),sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f137]) ).
fof(f156,plain,
( ssList(sK5)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f137]) ).
fof(f157,plain,
( nil = sK2
| nil != sK3 ),
inference(cnf_transformation,[],[f137]) ).
fof(f158,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f137]) ).
fof(f159,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f137]) ).
fof(f171,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f177,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f182,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f183,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f184,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f187,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f191,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f198,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f200,plain,
( nil = sK3
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f152,f159,f159]) ).
fof(f201,plain,
! [X8,X6,X9,X7] :
( nil = sK3
| ~ ssList(X6)
| sK2 != X6
| ~ ssList(X7)
| ~ ssList(X8)
| tl(sK3) != X7
| app(X7,X8) != X6
| ~ ssItem(X9)
| cons(X9,nil) != X8
| hd(sK3) != X9
| ~ neq(nil,sK3)
| ~ neq(nil,sK3) ),
inference(definition_unfolding,[],[f151,f159,f158,f159,f159,f159,f159]) ).
fof(f202,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f150,f158,f159]) ).
fof(f204,plain,
ssList(sK3),
inference(definition_unfolding,[],[f147,f159]) ).
fof(f206,definition,
~ sP12(nil),
introduced(definition,[new_symbols(definition,[sP12])],[inequality_splitting_name_introduction]) ).
fof(f207,plain,
( nil = sK2
| sP12(sK3) ),
inference(inequality_splitting,[],[f157,f206]) ).
fof(f208,definition,
~ sP13(sK2),
introduced(definition,[new_symbols(definition,[sP13])],[inequality_splitting_name_introduction]) ).
fof(f209,definition,
~ sP14(tl(sK3)),
introduced(definition,[new_symbols(definition,[sP14])],[inequality_splitting_name_introduction]) ).
fof(f210,definition,
~ sP15(hd(sK3)),
introduced(definition,[new_symbols(definition,[sP15])],[inequality_splitting_name_introduction]) ).
fof(f211,plain,
! [X8,X6,X9,X7] :
( nil = sK3
| ~ ssList(X6)
| sP13(X6)
| ~ ssList(X7)
| ~ ssList(X8)
| sP14(X7)
| app(X7,X8) != X6
| ~ ssItem(X9)
| cons(X9,nil) != X8
| sP15(X9)
| ~ neq(nil,sK3)
| ~ neq(nil,sK3) ),
inference(inequality_splitting,[],[f201,f210,f209,f208]) ).
fof(f212,definition,
~ sP16(nil),
introduced(definition,[new_symbols(definition,[sP16])],[inequality_splitting_name_introduction]) ).
fof(f213,plain,
( sP16(sK2)
| neq(sK3,nil) ),
inference(inequality_splitting,[],[f202,f212]) ).
fof(f230,plain,
! [X8,X9,X7] :
( nil = sK3
| ~ ssList(app(X7,X8))
| sP13(app(X7,X8))
| ~ ssList(X7)
| ~ ssList(X8)
| sP14(X7)
| ~ ssItem(X9)
| cons(X9,nil) != X8
| sP15(X9)
| ~ neq(nil,sK3)
| ~ neq(nil,sK3) ),
inference(equality_resolution,[],[f211]) ).
fof(f231,plain,
! [X9,X7] :
( nil = sK3
| ~ ssList(app(X7,cons(X9,nil)))
| sP13(app(X7,cons(X9,nil)))
| ~ ssList(X7)
| ~ ssList(cons(X9,nil))
| sP14(X7)
| ~ ssItem(X9)
| sP15(X9)
| ~ neq(nil,sK3)
| ~ neq(nil,sK3) ),
inference(equality_resolution,[],[f230]) ).
fof(f234,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f183]) ).
fof(f236,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f234]) ).
fof(f239,plain,
! [X9,X7] :
( nil = sK3
| ~ ssList(app(X7,cons(X9,nil)))
| sP13(app(X7,cons(X9,nil)))
| ~ ssList(X7)
| ~ ssList(cons(X9,nil))
| sP14(X7)
| ~ ssItem(X9)
| sP15(X9)
| ~ neq(nil,sK3) ),
inference(duplicate_literal_removal,[],[f231]) ).
fof(f242,definition,
( spl27_1
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f244,plain,
( neq(sK3,nil)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f246,definition,
( spl27_2
<=> sP16(sK2) ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f248,plain,
( sP16(sK2)
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f249,plain,
( spl27_1
| spl27_2 ),
inference(avatar_split_clause,[],[f213,f246,f242]) ).
fof(f250,plain,
! [X9,X7] :
( nil = sK3
| sP13(app(X7,cons(X9,nil)))
| ~ ssList(X7)
| ~ ssList(cons(X9,nil))
| sP14(X7)
| ~ ssItem(X9)
| sP15(X9)
| ~ neq(nil,sK3) ),
inference(forward_subsumption_resolution,[],[f239,f182]) ).
fof(f252,definition,
( spl27_3
<=> nil = sK3 ),
introduced(definition,[new_symbols(definition,[spl27_3])],[avatar_definition]) ).
fof(f253,plain,
( nil != sK3
| spl27_3 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f254,plain,
( nil = sK3
| ~ spl27_3 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f255,plain,
( spl27_1
| spl27_3 ),
inference(avatar_split_clause,[],[f200,f252,f242]) ).
fof(f257,definition,
( spl27_4
<=> ssItem(sK4) ),
introduced(definition,[new_symbols(definition,[spl27_4])],[avatar_definition]) ).
fof(f259,plain,
( ssItem(sK4)
| ~ spl27_4 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f260,plain,
( ~ spl27_1
| spl27_4 ),
inference(avatar_split_clause,[],[f153,f257,f242]) ).
fof(f262,definition,
( spl27_5
<=> sK2 = app(sK5,cons(sK4,nil)) ),
introduced(definition,[new_symbols(definition,[spl27_5])],[avatar_definition]) ).
fof(f264,plain,
( sK2 = app(sK5,cons(sK4,nil))
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f265,plain,
( ~ spl27_1
| spl27_5 ),
inference(avatar_split_clause,[],[f154,f262,f242]) ).
fof(f267,definition,
( spl27_6
<=> sK3 = app(cons(sK4,nil),sK5) ),
introduced(definition,[new_symbols(definition,[spl27_6])],[avatar_definition]) ).
fof(f269,plain,
( sK3 = app(cons(sK4,nil),sK5)
| ~ spl27_6 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f270,plain,
( ~ spl27_1
| spl27_6 ),
inference(avatar_split_clause,[],[f155,f267,f242]) ).
fof(f272,definition,
( spl27_7
<=> ssList(sK5) ),
introduced(definition,[new_symbols(definition,[spl27_7])],[avatar_definition]) ).
fof(f274,plain,
( ssList(sK5)
| ~ spl27_7 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f275,plain,
( ~ spl27_1
| spl27_7 ),
inference(avatar_split_clause,[],[f156,f272,f242]) ).
fof(f277,definition,
( spl27_8
<=> sP12(sK3) ),
introduced(definition,[new_symbols(definition,[spl27_8])],[avatar_definition]) ).
fof(f279,plain,
( sP12(sK3)
| ~ spl27_8 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f281,definition,
( spl27_9
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl27_9])],[avatar_definition]) ).
fof(f283,plain,
( nil = sK2
| ~ spl27_9 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f284,plain,
( spl27_8
| spl27_9 ),
inference(avatar_split_clause,[],[f207,f281,f277]) ).
fof(f286,definition,
( spl27_10
<=> neq(nil,sK3) ),
introduced(definition,[new_symbols(definition,[spl27_10])],[avatar_definition]) ).
fof(f288,plain,
( ~ neq(nil,sK3)
| spl27_10 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f298,definition,
( spl27_13
<=> ! [X9,X7] :
( sP13(app(X7,cons(X9,nil)))
| sP15(X9)
| ~ ssItem(X9)
| sP14(X7)
| ~ ssList(cons(X9,nil))
| ~ ssList(X7) ) ),
introduced(definition,[new_symbols(definition,[spl27_13])],[avatar_definition]) ).
fof(f299,plain,
( ! [X9,X7] :
( sP13(app(X7,cons(X9,nil)))
| sP15(X9)
| ~ ssItem(X9)
| sP14(X7)
| ~ ssList(cons(X9,nil))
| ~ ssList(X7) )
| ~ spl27_13 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f300,plain,
( ~ spl27_10
| spl27_13
| spl27_3 ),
inference(avatar_split_clause,[],[f250,f252,f298,f286]) ).
fof(f301,plain,
( sP12(nil)
| ~ spl27_3
| ~ spl27_8 ),
inference(forward_demodulation,[],[f279,f254]) ).
fof(f303,plain,
( $false
| ~ spl27_3
| ~ spl27_8 ),
inference(forward_subsumption_resolution,[],[f301,f206]) ).
fof(f304,plain,
( ~ spl27_3
| ~ spl27_8 ),
inference(avatar_contradiction_clause,[],[f303]) ).
fof(f323,plain,
( sP16(nil)
| ~ spl27_2
| ~ spl27_9 ),
inference(superposition,[],[f248,f283]) ).
fof(f327,plain,
( $false
| ~ spl27_2
| ~ spl27_9 ),
inference(forward_subsumption_resolution,[],[f323,f212]) ).
fof(f328,plain,
( ~ spl27_2
| ~ spl27_9 ),
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f331,plain,
( ~ neq(nil,app(cons(sK4,nil),sK5))
| ~ spl27_6
| spl27_10 ),
inference(forward_demodulation,[],[f288,f269]) ).
fof(f354,definition,
( spl27_14
<=> ssList(cons(sK4,nil)) ),
introduced(definition,[new_symbols(definition,[spl27_14])],[avatar_definition]) ).
fof(f355,plain,
( ssList(cons(sK4,nil))
| ~ spl27_14 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f356,plain,
( ~ ssList(cons(sK4,nil))
| spl27_14 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f368,plain,
( ~ sP13(app(sK5,cons(sK4,nil)))
| ~ spl27_5 ),
inference(superposition,[],[f208,f264]) ).
fof(f370,plain,
( ~ ssItem(sK4)
| ~ ssList(nil)
| spl27_14 ),
inference(resolution,[],[f356,f171]) ).
fof(f372,plain,
( ~ ssList(nil)
| ~ spl27_4
| spl27_14 ),
inference(forward_subsumption_resolution,[],[f370,f259]) ).
fof(f373,plain,
( $false
| ~ spl27_4
| spl27_14 ),
inference(forward_subsumption_resolution,[],[f372,f187]) ).
fof(f374,plain,
( ~ spl27_4
| spl27_14 ),
inference(avatar_contradiction_clause,[],[f373]) ).
fof(f375,plain,
( ssList(app(cons(sK4,nil),sK5))
| ~ spl27_6 ),
inference(superposition,[],[f204,f269]) ).
fof(f376,plain,
( ~ sP14(tl(app(cons(sK4,nil),sK5)))
| ~ spl27_6 ),
inference(superposition,[],[f209,f269]) ).
fof(f377,plain,
( ~ sP15(hd(app(cons(sK4,nil),sK5)))
| ~ spl27_6 ),
inference(superposition,[],[f210,f269]) ).
fof(f381,plain,
( nil != app(cons(sK4,nil),sK5)
| spl27_3
| ~ spl27_6 ),
inference(superposition,[],[f253,f269]) ).
fof(f399,plain,
( nil = app(cons(sK4,nil),sK5)
| ~ ssList(app(cons(sK4,nil),sK5))
| ~ ssList(nil)
| ~ spl27_6
| spl27_10 ),
inference(resolution,[],[f331,f184]) ).
fof(f404,plain,
( ~ ssList(app(cons(sK4,nil),sK5))
| ~ ssList(nil)
| spl27_3
| ~ spl27_6
| spl27_10 ),
inference(forward_subsumption_resolution,[],[f399,f381]) ).
fof(f407,plain,
( ~ ssList(nil)
| spl27_3
| ~ spl27_6
| spl27_10 ),
inference(forward_subsumption_resolution,[],[f404,f375]) ).
fof(f417,plain,
( $false
| spl27_3
| ~ spl27_6
| spl27_10 ),
inference(forward_subsumption_resolution,[],[f407,f187]) ).
fof(f418,plain,
( spl27_3
| ~ spl27_6
| spl27_10 ),
inference(avatar_contradiction_clause,[],[f417]) ).
fof(f463,plain,
( sP15(sK4)
| ~ ssItem(sK4)
| sP14(sK5)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5)
| ~ spl27_5
| ~ spl27_13 ),
inference(resolution,[],[f368,f299]) ).
fof(f466,plain,
( sP15(sK4)
| sP14(sK5)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_5
| ~ spl27_13 ),
inference(forward_subsumption_resolution,[],[f463,f259]) ).
fof(f467,plain,
( sP15(sK4)
| sP14(sK5)
| ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_5
| ~ spl27_13
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f466,f355]) ).
fof(f468,plain,
( sP15(sK4)
| sP14(sK5)
| ~ spl27_4
| ~ spl27_5
| ~ spl27_7
| ~ spl27_13
| ~ spl27_14 ),
inference(forward_subsumption_resolution,[],[f467,f274]) ).
fof(f470,definition,
( spl27_26
<=> sP14(sK5) ),
introduced(definition,[new_symbols(definition,[spl27_26])],[avatar_definition]) ).
fof(f472,plain,
( sP14(sK5)
| ~ spl27_26 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f474,definition,
( spl27_27
<=> sP15(sK4) ),
introduced(definition,[new_symbols(definition,[spl27_27])],[avatar_definition]) ).
fof(f476,plain,
( sP15(sK4)
| ~ spl27_27 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f477,plain,
( spl27_26
| spl27_27
| ~ spl27_4
| ~ spl27_5
| ~ spl27_7
| ~ spl27_13
| ~ spl27_14 ),
inference(avatar_split_clause,[],[f468,f354,f298,f272,f262,f257,f474,f470]) ).
fof(f504,plain,
( ~ sP14(tl(cons(sK4,sK5)))
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl27_6 ),
inference(superposition,[],[f376,f177]) ).
fof(f509,plain,
( ~ sP14(tl(cons(sK4,sK5)))
| ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_6 ),
inference(forward_subsumption_resolution,[],[f504,f259]) ).
fof(f511,plain,
( ~ sP14(tl(cons(sK4,sK5)))
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f509,f274]) ).
fof(f522,plain,
( ~ sP15(hd(cons(sK4,sK5)))
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl27_6 ),
inference(superposition,[],[f377,f177]) ).
fof(f527,plain,
( ~ sP15(hd(cons(sK4,sK5)))
| ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_6 ),
inference(forward_subsumption_resolution,[],[f522,f259]) ).
fof(f529,plain,
( ~ sP15(hd(cons(sK4,sK5)))
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7 ),
inference(forward_subsumption_resolution,[],[f527,f274]) ).
fof(f535,plain,
( ~ sP14(sK5)
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7 ),
inference(superposition,[],[f511,f198]) ).
fof(f537,plain,
( ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_26 ),
inference(forward_subsumption_resolution,[],[f535,f472]) ).
fof(f538,plain,
( ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_26 ),
inference(forward_subsumption_resolution,[],[f537,f259]) ).
fof(f539,plain,
( $false
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_26 ),
inference(forward_subsumption_resolution,[],[f538,f274]) ).
fof(f540,plain,
( ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_26 ),
inference(avatar_contradiction_clause,[],[f539]) ).
fof(f574,plain,
( ~ sP15(sK4)
| ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7 ),
inference(superposition,[],[f529,f191]) ).
fof(f576,plain,
( ~ ssItem(sK4)
| ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_27 ),
inference(forward_subsumption_resolution,[],[f574,f476]) ).
fof(f577,plain,
( ~ ssList(sK5)
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_27 ),
inference(forward_subsumption_resolution,[],[f576,f259]) ).
fof(f578,plain,
( $false
| ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_27 ),
inference(forward_subsumption_resolution,[],[f577,f274]) ).
fof(f579,plain,
( ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_27 ),
inference(avatar_contradiction_clause,[],[f578]) ).
fof(f636,plain,
( neq(nil,nil)
| ~ spl27_1
| ~ spl27_3 ),
inference(superposition,[],[f244,f254]) ).
fof(f658,plain,
( ~ ssList(nil)
| ~ spl27_1
| ~ spl27_3 ),
inference(resolution,[],[f636,f236]) ).
fof(f660,plain,
( $false
| ~ spl27_1
| ~ spl27_3 ),
inference(forward_subsumption_resolution,[],[f658,f187]) ).
fof(f661,plain,
( ~ spl27_1
| ~ spl27_3 ),
inference(avatar_contradiction_clause,[],[f660]) ).
cnf(s1,plain,
( spl27_1
| spl27_2 ),
inference(sat_conversion,[],[f249]) ).
cnf(s2,plain,
( spl27_1
| spl27_3 ),
inference(sat_conversion,[],[f255]) ).
cnf(s3,plain,
( ~ spl27_1
| spl27_4 ),
inference(sat_conversion,[],[f260]) ).
cnf(s4,plain,
( ~ spl27_1
| spl27_5 ),
inference(sat_conversion,[],[f265]) ).
cnf(s5,plain,
( ~ spl27_1
| spl27_6 ),
inference(sat_conversion,[],[f270]) ).
cnf(s6,plain,
( ~ spl27_1
| spl27_7 ),
inference(sat_conversion,[],[f275]) ).
cnf(s7,plain,
( spl27_8
| spl27_9 ),
inference(sat_conversion,[],[f284]) ).
cnf(s9,plain,
( spl27_3
| ~ spl27_10
| spl27_13 ),
inference(sat_conversion,[],[f300]) ).
cnf(s10,plain,
( ~ spl27_3
| ~ spl27_8 ),
inference(sat_conversion,[],[f304]) ).
cnf(s11,plain,
( ~ spl27_2
| ~ spl27_9 ),
inference(sat_conversion,[],[f328]) ).
cnf(s13,plain,
( ~ spl27_4
| spl27_14 ),
inference(sat_conversion,[],[f374]) ).
cnf(s16,plain,
( spl27_3
| ~ spl27_6
| spl27_10 ),
inference(sat_conversion,[],[f418]) ).
cnf(s19,plain,
( ~ spl27_4
| ~ spl27_5
| ~ spl27_7
| ~ spl27_13
| ~ spl27_14
| spl27_26
| spl27_27 ),
inference(sat_conversion,[],[f477]) ).
cnf(s22,plain,
( ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_26 ),
inference(sat_conversion,[],[f540]) ).
cnf(s25,plain,
( ~ spl27_4
| ~ spl27_6
| ~ spl27_7
| ~ spl27_27 ),
inference(sat_conversion,[],[f579]) ).
cnf(s35,plain,
( ~ spl27_1
| ~ spl27_3 ),
inference(sat_conversion,[],[f661]) ).
cnf(s37,plain,
spl27_1,
inference(rat,[],[s7,s11,s10,s1,s2]) ).
cnf(s38,plain,
~ spl27_3,
inference(rat,[],[s35,s37]) ).
cnf(s39,plain,
spl27_7,
inference(rat,[],[s6,s37]) ).
cnf(s40,plain,
spl27_6,
inference(rat,[],[s5,s37]) ).
cnf(s41,plain,
spl27_5,
inference(rat,[],[s4,s37]) ).
cnf(s42,plain,
spl27_4,
inference(rat,[],[s3,s37]) ).
cnf(s43,plain,
spl27_10,
inference(rat,[],[s16,s38,s40]) ).
cnf(s44,plain,
~ spl27_27,
inference(rat,[],[s25,s40,s39,s42]) ).
cnf(s45,plain,
~ spl27_26,
inference(rat,[],[s22,s40,s39,s42]) ).
cnf(s46,plain,
spl27_14,
inference(rat,[],[s13,s42]) ).
cnf(s47,plain,
spl27_13,
inference(rat,[],[s9,s38,s43]) ).
cnf(s48,plain,
$false,
inference(rat,[],[s19,s44,s45,s42,s41,s39,s46,s47]) ).
fof(f663,plain,
$false,
inference(avatar_sat_refutation,[],[s48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC310+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.17 % Computer : n016.cluster.edu
% 0.12/0.17 % Model : x86_64 x86_64
% 0.12/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.17 % Memory : 8046.5625MB
% 0.12/0.17 % OS : Linux 6.8.0-71-generic
% 0.12/0.17 % CPULimit : 300
% 0.12/0.17 % WCLimit : 300
% 0.12/0.17 % DateTime : Mon Sep 28 09:05:18 UTC 2026
% 0.12/0.17 % CPUTime :
% 0.12/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.21 Running first-order theorem proving
% 0.12/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.10/1.07 % (3492531)Detected formulas, will run a generic FOF schedule.
% 3.10/1.07 % (3492540)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2783387217:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.10/1.07 % (3492540)Instruction limit reached!
% 3.10/1.07 % (3492540)------------------------------
% 3.10/1.07 % (3492540)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.07 % (3492540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.07 % (3492540)CaDiCaL version: 2.1.3
% 3.10/1.07 % (3492540)Termination reason: Instruction limit
% 3.10/1.07 % (3492540)Termination phase: Saturation
% 3.10/1.07 % (3492540)Time elapsed: 0.037 s
% 3.10/1.07 % (3492540)Peak memory usage: 88 MB
% 3.10/1.07 % (3492540)Instructions burned: 122 (million)
% 3.10/1.07 % (3492541)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3043689241:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.10/1.07 % (3492537)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=2302729311:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.10/1.07 % (3492538)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=3608249043:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.10/1.07 % (3492536)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=323694158:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.10/1.07 % (3492539)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=917887055:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.10/1.07 % (3492542)dis-21_1_sil=8000:lcm=predicate:random_seed=996625025: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)
% 3.10/1.07 % (3492539)First to succeed.
% 3.10/1.07 % (3492539)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3492531"
% 3.10/1.07 % (3492541)Also succeeded, but the first one will report.
% 3.10/1.07 % (3492542)Instruction limit reached!
% 3.10/1.07 % (3492542)------------------------------
% 3.10/1.07 % (3492542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.07 % (3492542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.07 % (3492542)CaDiCaL version: 2.1.3
% 3.10/1.07 % (3492542)Termination reason: Instruction limit
% 3.10/1.07 % (3492542)Termination phase: Saturation
% 3.10/1.07 % (3492542)Time elapsed: 0.074 s
% 3.10/1.07 % (3492542)Peak memory usage: 90 MB
% 3.10/1.07 % (3492542)Instructions burned: 130 (million)
% 3.10/1.07 % (3492545)lrs+10_1_sil=8000:sp=occurrence:random_seed=1151568201:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.10/1.07 % (3492545)Instruction limit reached!
% 3.10/1.07 % (3492545)------------------------------
% 3.10/1.07 % (3492545)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.07 % (3492545)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.07 % (3492545)CaDiCaL version: 2.1.3
% 3.10/1.07 % (3492545)Termination reason: Instruction limit
% 3.10/1.07 % (3492545)Termination phase: Saturation
% 3.10/1.07 % (3492545)Time elapsed: 0.089 s
% 3.10/1.07 % (3492545)Peak memory usage: 92 MB
% 3.10/1.07 % (3492545)Instructions burned: 287 (million)
% 3.10/1.07 % (3492551)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3721573044:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.10/1.07 % (3492553)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1223450876:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.10/1.07 % (3492539)Refutation found. Thanks to Tanya!
% 3.10/1.07 % SZS status Theorem for theBenchmark
% 3.10/1.07 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.29 % (3492539)------------------------------
% 3.58/1.29 % (3492539)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.29 % (3492539)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.29 % (3492539)CaDiCaL version: 2.1.3
% 3.58/1.29 % (3492539)Termination reason: Refutation
% 3.58/1.29 % (3492539)Time elapsed: 0.013 s
% 3.58/1.29 % (3492539)Peak memory usage: 90 MB
% 3.58/1.29 % (3492539)Instructions burned: 17 (million)
% 3.58/1.29 % (3492539)------------------------------
% 3.58/1.29 % (3492539)------------------------------
% 3.58/1.29 % (3492531)Success in time 0.422 s
% 3.58/1.29 % Vampire exiting
%------------------------------------------------------------------------------