%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC004+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 : n019.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 01:01:59 PM UTC 2026
% Result : Theorem 2.50s 1.30s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 99 ( 12 unt; 7 def)
% Number of atoms : 384 ( 66 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 484 ( 199 ~; 180 |; 77 &)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 7 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn 126 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
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(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0
& neq(X5,nil) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X3
| app(X8,X9) != X2 ) ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X4,X5),X6) = X1
& app(X4,X6) = X0
& neq(X5,nil) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X3
| app(X8,X9) != X2 ) ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,definition,
! [X1,X0,X3,X2] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ~ sP0(X1,X0,X3,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f121,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP0(X1,X0,X3,X2)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f120]) ).
fof(f122,plain,
! [X1,X0,X3,X2] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X1
| app(X4,X6) != X0
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X3
& app(X8,X9) = X2
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ~ sP0(X1,X0,X3,X2) ),
inference(nnf_transformation,[],[f120]) ).
fof(f123,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1
| ~ neq(X5,nil) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X2
& app(X8,X9) = X3
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) ) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f122]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssList(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1
| ~ neq(X5,nil) ) ) )
& app(app(sK2(X2,X3),cons(sK1(X2,X3),nil)),sK3(X2,X3)) = X2
& app(sK2(X2,X3),sK3(X2,X3)) = X3
& ssList(sK3(X2,X3))
& ssList(sK2(X2,X3))
& ssItem(sK1(X2,X3)) )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X7,sK1(X2,X3)),skolemize(X8,sK2(X2,X3)),skolemize(X9,sK3(X2,X3))],[f123]) ).
fof(f125,plain,
( sK5 = sK7
& sK4 = sK6
& ( sP0(sK5,sK4,sK7,sK6)
| ( neq(sK5,nil)
& ~ neq(sK7,nil) ) )
& ssList(sK7)
& ssList(sK6)
& ssList(sK5)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f121]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK2(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK3(X2,X3)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f135,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(sK2(X2,X3),sK3(X2,X3)) = X3 ),
inference(cnf_transformation,[],[f124]) ).
fof(f136,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(app(sK2(X2,X3),cons(sK1(X2,X3),nil)),sK3(X2,X3)) = X2 ),
inference(cnf_transformation,[],[f124]) ).
fof(f137,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X4,X5),X6) != X0
| app(X4,X6) != X1
| ~ neq(X5,nil)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f124]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| neq(X0,nil) ),
inference(cnf_transformation,[],[f124]) ).
fof(f143,plain,
( sP0(sK5,sK4,sK7,sK6)
| ~ neq(sK7,nil) ),
inference(cnf_transformation,[],[f125]) ).
fof(f144,plain,
( sP0(sK5,sK4,sK7,sK6)
| neq(sK5,nil) ),
inference(cnf_transformation,[],[f125]) ).
fof(f145,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f125]) ).
fof(f146,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f125]) ).
fof(f150,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f157,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f170,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f173,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f174,plain,
( sP0(sK7,sK6,sK7,sK6)
| neq(sK7,nil) ),
inference(definition_unfolding,[],[f144,f146,f145,f146]) ).
fof(f175,plain,
( sP0(sK7,sK6,sK7,sK6)
| ~ neq(sK7,nil) ),
inference(definition_unfolding,[],[f143,f146,f145]) ).
fof(f178,plain,
! [X2,X3,X1,X6,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(X4,X6) != X1
| ~ neq(X5,nil)
| ~ sP0(app(app(X4,X5),X6),X1,X2,X3) ),
inference(equality_resolution,[],[f137]) ).
fof(f179,plain,
! [X2,X3,X6,X4,X5] :
( ~ sP0(app(app(X4,X5),X6),app(X4,X6),X2,X3)
| ~ ssList(X5)
| ~ ssList(X6)
| ~ neq(X5,nil)
| ~ ssList(X4) ),
inference(equality_resolution,[],[f178]) ).
fof(f188,definition,
( spl12_1
<=> neq(sK7,nil) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f192,definition,
( spl12_2
<=> sP0(sK7,sK6,sK7,sK6) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f194,plain,
( sP0(sK7,sK6,sK7,sK6)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f195,plain,
( ~ spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f175,f192,f188]) ).
fof(f196,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f174,f192,f188]) ).
fof(f203,plain,
( neq(sK7,nil)
| ~ spl12_2 ),
inference(resolution,[],[f138,f194]) ).
fof(f204,plain,
( spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f203,f192,f188]) ).
fof(f217,plain,
( ssItem(sK1(sK7,sK6))
| ~ spl12_2 ),
inference(resolution,[],[f132,f194]) ).
fof(f218,plain,
( ssList(sK2(sK7,sK6))
| ~ spl12_2 ),
inference(resolution,[],[f133,f194]) ).
fof(f219,plain,
( ssList(sK3(sK7,sK6))
| ~ spl12_2 ),
inference(resolution,[],[f134,f194]) ).
fof(f358,plain,
( sK6 = app(sK2(sK7,sK6),sK3(sK7,sK6))
| ~ spl12_2 ),
inference(resolution,[],[f135,f194]) ).
fof(f584,plain,
( sK7 = app(app(sK2(sK7,sK6),cons(sK1(sK7,sK6),nil)),sK3(sK7,sK6))
| ~ spl12_2 ),
inference(resolution,[],[f136,f194]) ).
fof(f2069,definition,
( spl12_87
<=> neq(cons(sK1(sK7,sK6),nil),nil) ),
introduced(definition,[new_symbols(definition,[spl12_87])],[avatar_definition]) ).
fof(f2070,plain,
( neq(cons(sK1(sK7,sK6),nil),nil)
| ~ spl12_87 ),
inference(avatar_component_clause,[],[f2069]) ).
fof(f2071,plain,
( ~ neq(cons(sK1(sK7,sK6),nil),nil)
| spl12_87 ),
inference(avatar_component_clause,[],[f2069]) ).
fof(f2073,definition,
( spl12_88
<=> ssList(cons(sK1(sK7,sK6),nil)) ),
introduced(definition,[new_symbols(definition,[spl12_88])],[avatar_definition]) ).
fof(f2074,plain,
( ssList(cons(sK1(sK7,sK6),nil))
| ~ spl12_88 ),
inference(avatar_component_clause,[],[f2073]) ).
fof(f2075,plain,
( ~ ssList(cons(sK1(sK7,sK6),nil))
| spl12_88 ),
inference(avatar_component_clause,[],[f2073]) ).
fof(f2077,definition,
( spl12_89
<=> ! [X0,X1] : ~ sP0(sK7,sK6,X0,X1) ),
introduced(definition,[new_symbols(definition,[spl12_89])],[avatar_definition]) ).
fof(f2078,plain,
( ! [X0,X1] : ~ sP0(sK7,sK6,X0,X1)
| ~ spl12_89 ),
inference(avatar_component_clause,[],[f2077]) ).
fof(f2141,plain,
( ~ ssItem(sK1(sK7,sK6))
| ~ ssList(nil)
| spl12_88 ),
inference(resolution,[],[f2075,f157]) ).
fof(f2142,plain,
( ~ ssList(nil)
| ~ spl12_2
| spl12_88 ),
inference(forward_subsumption_resolution,[],[f2141,f217]) ).
fof(f2143,plain,
( $false
| ~ spl12_2
| spl12_88 ),
inference(forward_subsumption_resolution,[],[f2142,f173]) ).
fof(f2144,plain,
( ~ spl12_2
| spl12_88 ),
inference(avatar_contradiction_clause,[],[f2143]) ).
fof(f2187,definition,
( spl12_90
<=> nil = cons(sK1(sK7,sK6),nil) ),
introduced(definition,[new_symbols(definition,[spl12_90])],[avatar_definition]) ).
fof(f2188,plain,
( nil != cons(sK1(sK7,sK6),nil)
| spl12_90 ),
inference(avatar_component_clause,[],[f2187]) ).
fof(f2189,plain,
( nil = cons(sK1(sK7,sK6),nil)
| ~ spl12_90 ),
inference(avatar_component_clause,[],[f2187]) ).
fof(f2351,plain,
( nil = cons(sK1(sK7,sK6),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK1(sK7,sK6),nil))
| spl12_87 ),
inference(resolution,[],[f2071,f170]) ).
fof(f2571,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK1(sK7,sK6),nil))
| spl12_87
| spl12_90 ),
inference(forward_subsumption_resolution,[],[f2351,f2188]) ).
fof(f2573,plain,
( ~ ssList(cons(sK1(sK7,sK6),nil))
| spl12_87
| spl12_90 ),
inference(forward_subsumption_resolution,[],[f2571,f173]) ).
fof(f2579,plain,
( $false
| spl12_87
| ~ spl12_88
| spl12_90 ),
inference(forward_subsumption_resolution,[],[f2573,f2074]) ).
fof(f2580,plain,
( spl12_87
| ~ spl12_88
| spl12_90 ),
inference(avatar_contradiction_clause,[],[f2579]) ).
fof(f2590,plain,
( ! [X0,X1] :
( ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ ssList(cons(sK1(sK7,sK6),nil))
| ~ ssList(sK3(sK7,sK6))
| ~ neq(cons(sK1(sK7,sK6),nil),nil)
| ~ ssList(sK2(sK7,sK6)) )
| ~ spl12_2 ),
inference(superposition,[],[f179,f584]) ).
fof(f2591,plain,
( ! [X0,X1] :
( ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ ssList(sK3(sK7,sK6))
| ~ neq(cons(sK1(sK7,sK6),nil),nil)
| ~ ssList(sK2(sK7,sK6)) )
| ~ spl12_2
| ~ spl12_88 ),
inference(forward_subsumption_resolution,[],[f2590,f2074]) ).
fof(f2597,plain,
( ! [X0,X1] :
( ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ neq(cons(sK1(sK7,sK6),nil),nil)
| ~ ssList(sK2(sK7,sK6)) )
| ~ spl12_2
| ~ spl12_88 ),
inference(forward_subsumption_resolution,[],[f2591,f219]) ).
fof(f2603,plain,
( ! [X0,X1] :
( ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ ssList(sK2(sK7,sK6)) )
| ~ spl12_2
| ~ spl12_87
| ~ spl12_88 ),
inference(forward_subsumption_resolution,[],[f2597,f2070]) ).
fof(f2609,plain,
( ! [X0,X1] : ~ sP0(sK7,app(sK2(sK7,sK6),sK3(sK7,sK6)),X0,X1)
| ~ spl12_2
| ~ spl12_87
| ~ spl12_88 ),
inference(forward_subsumption_resolution,[],[f2603,f218]) ).
fof(f2615,plain,
( ! [X0,X1] : ~ sP0(sK7,sK6,X0,X1)
| ~ spl12_2
| ~ spl12_87
| ~ spl12_88 ),
inference(forward_demodulation,[],[f2609,f358]) ).
fof(f2621,plain,
( spl12_89
| ~ spl12_2
| ~ spl12_87
| ~ spl12_88 ),
inference(avatar_split_clause,[],[f2615,f2073,f2069,f192,f2077]) ).
fof(f2633,plain,
( $false
| ~ spl12_2
| ~ spl12_89 ),
inference(resolution,[],[f2078,f194]) ).
fof(f2634,plain,
( ~ spl12_2
| ~ spl12_89 ),
inference(avatar_contradiction_clause,[],[f2633]) ).
fof(f3580,plain,
( nil != nil
| ~ ssItem(sK1(sK7,sK6))
| ~ ssList(nil)
| ~ spl12_90 ),
inference(superposition,[],[f150,f2189]) ).
fof(f3588,plain,
( ~ ssItem(sK1(sK7,sK6))
| ~ ssList(nil)
| ~ spl12_90 ),
inference(trivial_inequality_removal,[],[f3580]) ).
fof(f3590,plain,
( ~ ssList(nil)
| ~ spl12_2
| ~ spl12_90 ),
inference(forward_subsumption_resolution,[],[f3588,f217]) ).
fof(f3594,plain,
( $false
| ~ spl12_2
| ~ spl12_90 ),
inference(forward_subsumption_resolution,[],[f3590,f173]) ).
fof(f3595,plain,
( ~ spl12_2
| ~ spl12_90 ),
inference(avatar_contradiction_clause,[],[f3594]) ).
cnf(s1,plain,
( ~ spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f195]) ).
cnf(s2,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f196]) ).
cnf(s3,plain,
( spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f204]) ).
cnf(s87,plain,
( ~ spl12_2
| spl12_88 ),
inference(sat_conversion,[],[f2144]) ).
cnf(s110,plain,
( spl12_87
| ~ spl12_88
| spl12_90 ),
inference(sat_conversion,[],[f2580]) ).
cnf(s111,plain,
( ~ spl12_2
| ~ spl12_87
| ~ spl12_88
| spl12_89 ),
inference(sat_conversion,[],[f2621]) ).
cnf(s112,plain,
( ~ spl12_2
| ~ spl12_89 ),
inference(sat_conversion,[],[f2634]) ).
cnf(s131,plain,
( ~ spl12_2
| ~ spl12_90 ),
inference(sat_conversion,[],[f3595]) ).
cnf(s167,plain,
spl12_1,
inference(rat,[],[s2,s3]) ).
cnf(s171,plain,
spl12_2,
inference(rat,[],[s1,s167]) ).
cnf(s175,plain,
~ spl12_90,
inference(rat,[],[s131,s171]) ).
cnf(s176,plain,
~ spl12_89,
inference(rat,[],[s112,s171]) ).
cnf(s177,plain,
spl12_88,
inference(rat,[],[s87,s171]) ).
cnf(s180,plain,
spl12_87,
inference(rat,[],[s110,s175,s177]) ).
cnf(s186,plain,
$false,
inference(rat,[],[s111,s176,s171,s177,s180]) ).
fof(f3599,plain,
$false,
inference(avatar_sat_refutation,[],[s186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC004+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 07:24:19 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.50/1.30 % (3825433)Detected formulas, will run a generic FOF schedule.
% 2.50/1.30 % (3825444)dis-21_1_sil=8000:lcm=predicate:random_seed=655348990: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)
% 2.50/1.30 % (3825440)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=138889445:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.50/1.30 % (3825439)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=3568206298:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.50/1.30 % (3825438)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=3419148739:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.50/1.30 % (3825441)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1562916037:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.50/1.30 % (3825442)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3337830395:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.50/1.30 % (3825443)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2242914886:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.50/1.30 % (3825444)Instruction limit reached!
% 2.50/1.30 % (3825444)------------------------------
% 2.50/1.30 % (3825444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.30 % (3825444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.30 % (3825444)CaDiCaL version: 2.1.3
% 2.50/1.30 % (3825444)Termination reason: Instruction limit
% 2.50/1.30 % (3825444)Termination phase: Saturation
% 2.50/1.30 % (3825444)Time elapsed: 0.043 s
% 2.50/1.30 % (3825444)Peak memory usage: 90 MB
% 2.50/1.30 % (3825444)Instructions burned: 139 (million)
% 2.50/1.30 % (3825441)Instruction limit reached!
% 2.50/1.30 % (3825441)------------------------------
% 2.50/1.30 % (3825441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.30 % (3825442)Instruction limit reached!
% 2.50/1.30 % (3825442)------------------------------
% 2.50/1.30 % (3825442)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.30 % (3825442)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.30 % (3825441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.30 % (3825442)CaDiCaL version: 2.1.3
% 2.50/1.30 % (3825441)CaDiCaL version: 2.1.3
% 2.50/1.30 % (3825442)Termination reason: Instruction limit
% 2.50/1.30 % (3825442)Termination phase: Saturation
% 2.50/1.30 % (3825442)Time elapsed: 0.070 s
% 2.50/1.30 % (3825441)Termination reason: Instruction limit
% 2.50/1.30 % (3825441)Termination phase: Saturation
% 2.50/1.30 % (3825442)Peak memory usage: 89 MB
% 2.50/1.30 % (3825441)Time elapsed: 0.070 s
% 2.50/1.30 % (3825442)Instructions burned: 120 (million)
% 2.50/1.30 % (3825441)Peak memory usage: 89 MB
% 2.50/1.30 % (3825441)Instructions burned: 110 (million)
% 2.50/1.30 % (3825443)Instruction limit reached!
% 2.50/1.30 % (3825443)------------------------------
% 2.50/1.30 % (3825443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.30 % (3825443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.30 % (3825443)CaDiCaL version: 2.1.3
% 2.50/1.30 % (3825443)Termination reason: Instruction limit
% 2.50/1.30 % (3825443)Termination phase: Saturation
% 2.50/1.30 % (3825443)Time elapsed: 0.092 s
% 2.50/1.30 % (3825443)Peak memory usage: 90 MB
% 2.50/1.30 % (3825443)Instructions burned: 140 (million)
% 2.50/1.30 % (3825452)lrs+10_1_sil=8000:sp=occurrence:random_seed=1755646962:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.50/1.30 % (3825452)First to succeed.
% 2.50/1.30 % (3825452)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3825433"
% 2.50/1.30 % (3825454)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3347036070:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.50/1.30 % (3825453)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3335227512:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.50/1.30 % (3825455)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=265551272:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 2.50/1.30 % (3825453)Instruction limit reached!
% 2.50/1.30 % (3825453)------------------------------
% 2.50/1.30 % (3825453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.50/1.30 % (3825453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.50/1.30 % (3825453)CaDiCaL version: 2.1.3
% 2.50/1.30 % (3825453)Termination reason: Instruction limit
% 2.50/1.30 % (3825453)Termination phase: Saturation
% 2.50/1.30 % (3825453)Time elapsed: 0.073 s
% 2.50/1.30 % (3825453)Peak memory usage: 92 MB
% 2.50/1.30 % (3825453)Instructions burned: 158 (million)
% 2.50/1.30 % (3825452)Refutation found. Thanks to Tanya!
% 2.50/1.30 % SZS status Theorem for theBenchmark
% 2.50/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.49 % (3825452)------------------------------
% 3.71/1.49 % (3825452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.49 % (3825452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.49 % (3825452)CaDiCaL version: 2.1.3
% 3.71/1.49 % (3825452)Termination reason: Refutation
% 3.71/1.49 % (3825452)Time elapsed: 0.039 s
% 3.71/1.49 % (3825452)Peak memory usage: 91 MB
% 3.71/1.49 % (3825452)Instructions burned: 116 (million)
% 3.71/1.49 % (3825452)------------------------------
% 3.71/1.49 % (3825452)------------------------------
% 3.71/1.49 % (3825433)Success in time 0.446 s
% 3.71/1.49 % Vampire exiting
%------------------------------------------------------------------------------