%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC080+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 : n011.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 01:02:20 PM UTC 2026
% Result : Theorem 4.61s 1.90s
% Output : Refutation 8.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 116 ( 22 unt; 10 def)
% Number of atoms : 425 ( 38 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 550 ( 241 ~; 231 |; 53 &)
% ( 14 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 62 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
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)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ frontsegP(X3,X5)
| ~ frontsegP(X2,X5) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ frontsegP(X3,X5)
| ~ frontsegP(X2,X5) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ? [X5] :
( ssList(X5)
& neq(X5,nil)
& frontsegP(X3,X5)
& frontsegP(X2,X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f111,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f137,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f140,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ( ( neq(sK1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4) )
& ssList(sK4)
& neq(sK4,nil)
& frontsegP(sK3,sK4)
& frontsegP(sK2,sK4) )
| ( neq(sK1,nil)
& ~ neq(sK3,nil) ) )
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4)],[f98]) ).
fof(f146,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f111]) ).
fof(f147,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X1,X3) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f146]) ).
fof(f148,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ( ssList(sK5(X0,X1))
& app(X1,sK5(X0,X1)) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1))],[f147]) ).
fof(f150,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f151,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f150]) ).
fof(f152,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK6(X0,X1))
& ssList(sK7(X0,X1))
& app(app(sK6(X0,X1),X1),sK7(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X4,sK6(X0,X1)),skolemize(X5,sK7(X0,X1))],[f151]) ).
fof(f157,plain,
ssList(sK0),
inference(cnf_transformation,[],[f140]) ).
fof(f158,plain,
ssList(sK1),
inference(cnf_transformation,[],[f140]) ).
fof(f160,plain,
( frontsegP(sK2,sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f140]) ).
fof(f162,plain,
( frontsegP(sK3,sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f140]) ).
fof(f164,plain,
( neq(sK4,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f140]) ).
fof(f166,plain,
( ssList(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f140]) ).
fof(f168,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK1,X4)
| ~ segmentP(sK0,X4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f140]) ).
fof(f171,plain,
( neq(sK1,nil)
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f140]) ).
fof(f172,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f140]) ).
fof(f173,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f140]) ).
fof(f179,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f190,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK5(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f191,plain,
! [X0,X1] :
( ssList(sK5(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f203,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f223,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f226,plain,
( neq(sK3,nil)
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f171,f173,f173]) ).
fof(f229,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK3,X4)
| ~ segmentP(sK2,X4)
| ~ neq(sK3,nil) ),
inference(definition_unfolding,[],[f168,f173,f172]) ).
fof(f234,plain,
ssList(sK3),
inference(definition_unfolding,[],[f158,f173]) ).
fof(f235,plain,
ssList(sK2),
inference(definition_unfolding,[],[f157,f172]) ).
fof(f242,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f203]) ).
fof(f249,plain,
neq(sK3,nil),
inference(duplicate_literal_removal,[],[f226]) ).
fof(f252,definition,
( spl12_1
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f255,definition,
( spl12_2
<=> frontsegP(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f256,plain,
( frontsegP(sK2,sK4)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f257,plain,
( ~ spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f160,f255,f252]) ).
fof(f261,definition,
( spl12_3
<=> frontsegP(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f262,plain,
( frontsegP(sK3,sK4)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( ~ spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f162,f261,f252]) ).
fof(f266,definition,
( spl12_4
<=> neq(sK4,nil) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f267,plain,
( neq(sK4,nil)
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f268,plain,
( ~ spl12_1
| spl12_4 ),
inference(avatar_split_clause,[],[f164,f266,f252]) ).
fof(f271,definition,
( spl12_5
<=> ssList(sK4) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f272,plain,
( ssList(sK4)
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f273,plain,
( ~ spl12_1
| spl12_5 ),
inference(avatar_split_clause,[],[f166,f271,f252]) ).
fof(f276,definition,
( spl12_6
<=> ! [X4] :
( ~ ssList(X4)
| ~ segmentP(sK2,X4)
| ~ segmentP(sK3,X4)
| ~ neq(X4,nil) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f277,plain,
( ! [X4] :
( ~ segmentP(sK3,X4)
| ~ segmentP(sK2,X4)
| ~ ssList(X4)
| ~ neq(X4,nil) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f278,plain,
( ~ spl12_1
| spl12_6 ),
inference(avatar_split_clause,[],[f229,f276,f252]) ).
fof(f280,plain,
spl12_1,
inference(avatar_split_clause,[],[f249,f252]) ).
fof(f281,plain,
( sK3 = app(sK4,sK5(sK3,sK4))
| ~ ssList(sK4)
| ~ ssList(sK3)
| ~ spl12_3 ),
inference(resolution,[],[f190,f262]) ).
fof(f282,plain,
( sK2 = app(sK4,sK5(sK2,sK4))
| ~ ssList(sK4)
| ~ ssList(sK2)
| ~ spl12_2 ),
inference(resolution,[],[f190,f256]) ).
fof(f283,plain,
( sK2 = app(sK4,sK5(sK2,sK4))
| ~ ssList(sK2)
| ~ spl12_2
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f282,f272]) ).
fof(f284,plain,
( sK3 = app(sK4,sK5(sK3,sK4))
| ~ ssList(sK3)
| ~ spl12_3
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f281,f272]) ).
fof(f285,plain,
( sK2 = app(sK4,sK5(sK2,sK4))
| ~ spl12_2
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f283,f235]) ).
fof(f286,plain,
( sK3 = app(sK4,sK5(sK3,sK4))
| ~ spl12_3
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f284,f234]) ).
fof(f292,definition,
( spl12_7
<=> ssList(sK5(sK3,sK4)) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f293,plain,
( ~ ssList(sK5(sK3,sK4))
| spl12_7 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f299,definition,
( spl12_9
<=> ssList(sK5(sK2,sK4)) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f300,plain,
( ~ ssList(sK5(sK2,sK4))
| spl12_9 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f307,plain,
( ~ frontsegP(sK3,sK4)
| ~ ssList(sK4)
| ~ ssList(sK3)
| spl12_7 ),
inference(resolution,[],[f191,f293]) ).
fof(f308,plain,
( ~ frontsegP(sK2,sK4)
| ~ ssList(sK4)
| ~ ssList(sK2)
| spl12_9 ),
inference(resolution,[],[f191,f300]) ).
fof(f311,plain,
( ~ ssList(sK4)
| ~ ssList(sK2)
| ~ spl12_2
| spl12_9 ),
inference(forward_subsumption_resolution,[],[f308,f256]) ).
fof(f312,plain,
( ~ ssList(sK4)
| ~ ssList(sK3)
| ~ spl12_3
| spl12_7 ),
inference(forward_subsumption_resolution,[],[f307,f262]) ).
fof(f313,plain,
( ~ ssList(sK2)
| ~ spl12_2
| ~ spl12_5
| spl12_9 ),
inference(forward_subsumption_resolution,[],[f311,f272]) ).
fof(f314,plain,
( ~ ssList(sK3)
| ~ spl12_3
| ~ spl12_5
| spl12_7 ),
inference(forward_subsumption_resolution,[],[f312,f272]) ).
fof(f315,plain,
( $false
| ~ spl12_2
| ~ spl12_5
| spl12_9 ),
inference(forward_subsumption_resolution,[],[f313,f235]) ).
fof(f316,plain,
( ~ spl12_2
| ~ spl12_5
| spl12_9 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f317,plain,
( $false
| ~ spl12_3
| ~ spl12_5
| spl12_7 ),
inference(forward_subsumption_resolution,[],[f314,f234]) ).
fof(f318,plain,
( ~ spl12_3
| ~ spl12_5
| spl12_7 ),
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f322,plain,
( sK4 = app(nil,sK4)
| ~ spl12_5 ),
inference(resolution,[],[f223,f272]) ).
fof(f336,plain,
( ! [X0] :
( ~ ssList(app(sK4,X0))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK4)
| segmentP(app(sK4,X0),sK4) )
| ~ spl12_5 ),
inference(superposition,[],[f242,f322]) ).
fof(f337,plain,
( ! [X0] :
( ~ ssList(app(sK4,X0))
| ~ ssList(X0)
| ~ ssList(sK4)
| segmentP(app(sK4,X0),sK4) )
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f336,f179]) ).
fof(f338,plain,
( ! [X0] :
( segmentP(app(sK4,X0),sK4)
| ~ ssList(X0)
| ~ ssList(app(sK4,X0)) )
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f337,f272]) ).
fof(f339,plain,
( segmentP(sK2,sK4)
| ~ ssList(sK5(sK2,sK4))
| ~ ssList(sK2)
| ~ spl12_2
| ~ spl12_5 ),
inference(superposition,[],[f338,f285]) ).
fof(f340,plain,
( segmentP(sK3,sK4)
| ~ ssList(sK5(sK3,sK4))
| ~ ssList(sK3)
| ~ spl12_3
| ~ spl12_5 ),
inference(superposition,[],[f338,f286]) ).
fof(f341,plain,
( segmentP(sK3,sK4)
| ~ ssList(sK5(sK3,sK4))
| ~ spl12_3
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f340,f234]) ).
fof(f342,plain,
( segmentP(sK2,sK4)
| ~ ssList(sK5(sK2,sK4))
| ~ spl12_2
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f339,f235]) ).
fof(f344,definition,
( spl12_11
<=> segmentP(sK3,sK4) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
fof(f345,plain,
( segmentP(sK3,sK4)
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f346,plain,
( ~ spl12_7
| spl12_11
| ~ spl12_3
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f341,f271,f261,f344,f292]) ).
fof(f348,definition,
( spl12_12
<=> segmentP(sK2,sK4) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
fof(f349,plain,
( segmentP(sK2,sK4)
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f350,plain,
( ~ spl12_9
| spl12_12
| ~ spl12_2
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f342,f271,f255,f348,f299]) ).
fof(f352,plain,
( ~ segmentP(sK2,sK4)
| ~ ssList(sK4)
| ~ neq(sK4,nil)
| ~ spl12_6
| ~ spl12_11 ),
inference(resolution,[],[f345,f277]) ).
fof(f354,plain,
( ~ ssList(sK4)
| ~ neq(sK4,nil)
| ~ spl12_6
| ~ spl12_11
| ~ spl12_12 ),
inference(forward_subsumption_resolution,[],[f352,f349]) ).
fof(f355,plain,
( ~ neq(sK4,nil)
| ~ spl12_5
| ~ spl12_6
| ~ spl12_11
| ~ spl12_12 ),
inference(forward_subsumption_resolution,[],[f354,f272]) ).
fof(f356,plain,
( $false
| ~ spl12_4
| ~ spl12_5
| ~ spl12_6
| ~ spl12_11
| ~ spl12_12 ),
inference(forward_subsumption_resolution,[],[f355,f267]) ).
fof(f357,plain,
( ~ spl12_4
| ~ spl12_5
| ~ spl12_6
| ~ spl12_11
| ~ spl12_12 ),
inference(avatar_contradiction_clause,[],[f356]) ).
cnf(s1,plain,
( ~ spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f257]) ).
cnf(s3,plain,
( ~ spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f263]) ).
cnf(s5,plain,
( ~ spl12_1
| spl12_4 ),
inference(sat_conversion,[],[f268]) ).
cnf(s7,plain,
( ~ spl12_1
| spl12_5 ),
inference(sat_conversion,[],[f273]) ).
cnf(s9,plain,
( ~ spl12_1
| spl12_6 ),
inference(sat_conversion,[],[f278]) ).
cnf(s11,plain,
spl12_1,
inference(sat_conversion,[],[f280]) ).
cnf(s16,plain,
( ~ spl12_2
| ~ spl12_5
| spl12_9 ),
inference(sat_conversion,[],[f316]) ).
cnf(s17,plain,
( ~ spl12_3
| ~ spl12_5
| spl12_7 ),
inference(sat_conversion,[],[f318]) ).
cnf(s18,plain,
( ~ spl12_3
| ~ spl12_5
| ~ spl12_7
| spl12_11 ),
inference(sat_conversion,[],[f346]) ).
cnf(s19,plain,
( ~ spl12_2
| ~ spl12_5
| ~ spl12_9
| spl12_12 ),
inference(sat_conversion,[],[f350]) ).
cnf(s21,plain,
( ~ spl12_4
| ~ spl12_5
| ~ spl12_6
| ~ spl12_11
| ~ spl12_12 ),
inference(sat_conversion,[],[f357]) ).
cnf(s22,plain,
spl12_6,
inference(rat,[],[s9,s11]) ).
cnf(s23,plain,
spl12_5,
inference(rat,[],[s7,s11]) ).
cnf(s24,plain,
spl12_4,
inference(rat,[],[s5,s11]) ).
cnf(s25,plain,
spl12_3,
inference(rat,[],[s3,s11]) ).
cnf(s26,plain,
spl12_7,
inference(rat,[],[s17,s23,s25]) ).
cnf(s27,plain,
spl12_11,
inference(rat,[],[s18,s25,s23,s26]) ).
cnf(s29,plain,
~ spl12_12,
inference(rat,[],[s21,s24,s23,s22,s27]) ).
cnf(s30,plain,
spl12_2,
inference(rat,[],[s1,s11]) ).
cnf(s31,plain,
~ spl12_9,
inference(rat,[],[s19,s29,s23,s30]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s16,s23,s31,s30]) ).
fof(f358,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC080+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 07:45:15 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 4.61/1.90 % (3234549)Detected formulas, will run a generic FOF schedule.
% 4.61/1.90 % (3234558)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2950711548:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.61/1.90 % (3234558)Instruction limit reached!
% 4.61/1.90 % (3234558)------------------------------
% 4.61/1.90 % (3234558)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234558)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234558)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234558)Termination reason: Instruction limit
% 4.61/1.90 % (3234558)Termination phase: Saturation
% 4.61/1.90 % (3234558)Time elapsed: 0.031 s
% 4.61/1.90 % (3234558)Peak memory usage: 88 MB
% 4.61/1.90 % (3234558)Instructions burned: 119 (million)
% 4.61/1.90 % (3234559)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1025193606:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.61/1.90 % (3234556)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=3701905295:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.61/1.90 % (3234554)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=3771110750:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.61/1.90 % (3234557)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=253895255:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.61/1.90 % (3234560)dis-21_1_sil=8000:lcm=predicate:random_seed=1806100950: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)
% 4.61/1.90 % (3234555)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=546848274:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.61/1.90 % (3234557)Instruction limit reached!
% 4.61/1.90 % (3234557)------------------------------
% 4.61/1.90 % (3234557)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234557)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234557)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234557)Termination reason: Instruction limit
% 4.61/1.90 % (3234557)Termination phase: Saturation
% 4.61/1.90 % (3234557)Time elapsed: 0.054 s
% 4.61/1.90 % (3234557)Peak memory usage: 88 MB
% 4.61/1.90 % (3234557)Instructions burned: 110 (million)
% 4.61/1.90 % (3234560)Instruction limit reached!
% 4.61/1.90 % (3234560)------------------------------
% 4.61/1.90 % (3234560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234560)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234560)Termination reason: Instruction limit
% 4.61/1.90 % (3234560)Termination phase: Saturation
% 4.61/1.90 % (3234560)Time elapsed: 0.075 s
% 4.61/1.90 % (3234560)Peak memory usage: 90 MB
% 4.61/1.90 % (3234560)Instructions burned: 129 (million)
% 4.61/1.90 % (3234559)Instruction limit reached!
% 4.61/1.90 % (3234559)------------------------------
% 4.61/1.90 % (3234559)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234559)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234559)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234559)Termination reason: Instruction limit
% 4.61/1.90 % (3234559)Termination phase: Saturation
% 4.61/1.90 % (3234559)Time elapsed: 0.090 s
% 4.61/1.90 % (3234559)Peak memory usage: 90 MB
% 4.61/1.90 % (3234559)Instructions burned: 139 (million)
% 4.61/1.90 % (3234562)lrs+10_1_sil=8000:sp=occurrence:random_seed=4265539797:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.61/1.90 % (3234569)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3168709900:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.61/1.90 % (3234562)Instruction limit reached!
% 4.61/1.90 % (3234562)------------------------------
% 4.61/1.90 % (3234562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234562)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234562)Termination reason: Instruction limit
% 4.61/1.90 % (3234562)Termination phase: Saturation
% 4.61/1.90 % (3234562)Time elapsed: 0.097 s
% 4.61/1.90 % (3234562)Peak memory usage: 93 MB
% 4.61/1.90 % (3234562)Instructions burned: 285 (million)
% 4.61/1.90 % (3234570)lrs+1011_1_sil=32000:sp=occurrence:random_seed=970126979:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.61/1.90 % (3234571)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=2900321482:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.61/1.90 % (3234569)Instruction limit reached!
% 4.61/1.90 % (3234569)------------------------------
% 4.61/1.90 % (3234569)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234569)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234569)Termination reason: Instruction limit
% 4.61/1.90 % (3234569)Termination phase: Saturation
% 4.61/1.90 % (3234569)Time elapsed: 0.076 s
% 4.61/1.90 % (3234569)Peak memory usage: 92 MB
% 4.61/1.90 % (3234569)Instructions burned: 158 (million)
% 4.61/1.90 % (3234574)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=716224682:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.61/1.90 % (3234571)Instruction limit reached!
% 4.61/1.90 % (3234571)------------------------------
% 4.61/1.90 % (3234571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234571)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234571)Termination reason: Instruction limit
% 4.61/1.90 % (3234571)Termination phase: Saturation
% 4.61/1.90 % (3234571)Time elapsed: 0.124 s
% 4.61/1.90 % (3234571)Peak memory usage: 94 MB
% 4.61/1.90 % (3234571)Instructions burned: 248 (million)
% 4.61/1.90 % (3234574)Instruction limit reached!
% 4.61/1.90 % (3234574)------------------------------
% 4.61/1.90 % (3234574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234574)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234574)Termination reason: Instruction limit
% 4.61/1.90 % (3234574)Termination phase: Saturation
% 4.61/1.90 % (3234574)Time elapsed: 0.074 s
% 4.61/1.90 % (3234574)Peak memory usage: 89 MB
% 4.61/1.90 % (3234574)Instructions burned: 295 (million)
% 4.61/1.90 % (3234570)Instruction limit reached!
% 4.61/1.90 % (3234570)------------------------------
% 4.61/1.90 % (3234570)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234570)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234570)Termination reason: Instruction limit
% 4.61/1.90 % (3234570)Termination phase: Saturation
% 4.61/1.90 % (3234570)Time elapsed: 0.197 s
% 4.61/1.90 % (3234570)Peak memory usage: 93 MB
% 4.61/1.90 % (3234570)Instructions burned: 325 (million)
% 4.61/1.90 % (3234577)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4035402295:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.61/1.90 % (3234579)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2634488082:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.61/1.90 % (3234580)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2299064957:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 4.61/1.90 % (3234580)Instruction limit reached!
% 4.61/1.90 % (3234580)------------------------------
% 4.61/1.90 % (3234580)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234580)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234580)Termination reason: Instruction limit
% 4.61/1.90 % (3234580)Termination phase: Saturation
% 4.61/1.90 % (3234580)Time elapsed: 0.035 s
% 4.61/1.90 % (3234580)Peak memory usage: 89 MB
% 4.61/1.90 % (3234580)Instructions burned: 128 (million)
% 4.61/1.90 % (3234581)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=640780408:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 4.61/1.90 % (3234579)Instruction limit reached!
% 4.61/1.90 % (3234579)------------------------------
% 4.61/1.90 % (3234579)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234579)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234579)Termination reason: Instruction limit
% 4.61/1.90 % (3234579)Termination phase: Saturation
% 4.61/1.90 % (3234579)Time elapsed: 0.080 s
% 4.61/1.90 % (3234579)Peak memory usage: 90 MB
% 4.61/1.90 % (3234579)Instructions burned: 113 (million)
% 4.61/1.90 % (3234555)First to succeed.
% 4.61/1.90 % (3234555)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3234549"
% 4.61/1.90 % (3234581)Instruction limit reached!
% 4.61/1.90 % (3234581)------------------------------
% 4.61/1.90 % (3234581)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.61/1.90 % (3234581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.61/1.90 % (3234581)CaDiCaL version: 2.1.3
% 4.61/1.90 % (3234581)Termination reason: Instruction limit
% 4.61/1.90 % (3234581)Termination phase: Saturation
% 4.61/1.90 % (3234581)Time elapsed: 0.069 s
% 4.61/1.90 % (3234581)Peak memory usage: 89 MB
% 4.61/1.90 % (3234581)Instructions burned: 115 (million)
% 4.61/1.90 % (3234585)lrs+10_1_sil=8000:sp=occurrence:random_seed=1114174324:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 4.61/1.90 % (3234587)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=2869733412:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 4.61/1.90 % (3234588)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=547269797:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 4.61/1.90 % (3234555)Refutation found. Thanks to Tanya!
% 4.61/1.90 % SZS status Theorem for theBenchmark
% 4.61/1.90 % SZS output start Proof for theBenchmark
% See solution above
% 8.05/2.10 % (3234555)------------------------------
% 8.05/2.10 % (3234555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.05/2.10 % (3234555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.05/2.10 % (3234555)CaDiCaL version: 2.1.3
% 8.05/2.10 % (3234555)Termination reason: Refutation
% 8.05/2.10 % (3234555)Time elapsed: 0.629 s
% 8.05/2.10 % (3234555)Peak memory usage: 129 MB
% 8.05/2.10 % (3234555)Instructions burned: 933 (million)
% 8.05/2.10 % (3234555)------------------------------
% 8.05/2.10 % (3234555)------------------------------
% 8.05/2.10 % (3234549)Success in time 1.062 s
% 8.05/2.10 % Vampire exiting
%------------------------------------------------------------------------------