%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC393+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 : n003.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 01:03:47 PM UTC 2026
% Result : Theorem 6.41s 1.77s
% Output : Refutation 8.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 127 ( 28 unt; 10 def)
% Number of atoms : 428 ( 46 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 517 ( 216 ~; 210 |; 55 &)
% ( 16 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn 75 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
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(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X0,X4)
| memberP(X1,X4) ) )
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) ) ) ) ) ) ),
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)
=> ( ~ memberP(X0,X4)
| memberP(X1,X4) ) )
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f103,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(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f146,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(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( memberP(X0,X4)
& ~ memberP(X1,X4)
& ssItem(X4) )
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( memberP(X0,X4)
& ~ memberP(X1,X4)
& ssItem(X4) )
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f246,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,[],[f103]) ).
fof(f247,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,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK13(X0,X1))
& ssList(sK14(X0,X1))
& app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f277,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,[],[f146]) ).
fof(f278,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,[],[f277]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& memberP(sK53,sK57)
& ~ memberP(sK54,sK57)
& ssItem(sK57)
& ( nil = sK55
| nil != sK56 )
& ( ~ neq(sK56,nil)
| ( neq(sK55,nil)
& segmentP(sK56,sK55) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f315,plain,
! [X0,X1] :
( ~ segmentP(X0,X1)
| app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f316,plain,
! [X0,X1] :
( ssList(sK14(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f317,plain,
! [X0,X1] :
( ssList(sK13(X0,X1))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f401,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f414,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f415,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f419,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| segmentP(sK56,sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( nil = sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
~ memberP(sK54,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
memberP(sK53,sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
memberP(sK55,sK57),
inference(definition_unfolding,[],[f505,f506]) ).
fof(f509,plain,
~ memberP(sK56,sK57),
inference(definition_unfolding,[],[f504,f507]) ).
fof(f510,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
fof(f511,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f547,definition,
( spl58_1
<=> segmentP(sK56,sK55) ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f549,plain,
( segmentP(sK56,sK55)
| ~ spl58_1 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f551,definition,
( spl58_2
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f553,plain,
( ~ neq(sK56,nil)
| spl58_2 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f554,plain,
( spl58_1
| ~ spl58_2 ),
inference(avatar_split_clause,[],[f500,f551,f547]) ).
fof(f561,definition,
( spl58_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f563,plain,
( nil != sK56
| spl58_4 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f565,definition,
( spl58_5
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl58_5])],[avatar_definition]) ).
fof(f567,plain,
( nil = sK55
| ~ spl58_5 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f568,plain,
( ~ spl58_4
| spl58_5 ),
inference(avatar_split_clause,[],[f502,f565,f561]) ).
fof(f570,definition,
( spl58_6
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl58_6])],[avatar_definition]) ).
fof(f571,plain,
( ssList(nil)
| ~ spl58_6 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f598,plain,
spl58_6,
inference(avatar_split_clause,[],[f389,f570]) ).
fof(f601,plain,
( nil = sK56
| ~ ssList(nil)
| ~ ssList(sK56)
| spl58_2 ),
inference(resolution,[],[f387,f553]) ).
fof(f602,plain,
( ~ ssList(nil)
| ~ ssList(sK56)
| spl58_2
| spl58_4 ),
inference(forward_subsumption_resolution,[],[f601,f563]) ).
fof(f603,plain,
( ~ ssList(sK56)
| spl58_2
| spl58_4
| ~ spl58_6 ),
inference(forward_subsumption_resolution,[],[f602,f571]) ).
fof(f604,plain,
( $false
| spl58_2
| spl58_4
| ~ spl58_6 ),
inference(forward_subsumption_resolution,[],[f603,f510]) ).
fof(f605,plain,
( spl58_2
| spl58_4
| ~ spl58_6 ),
inference(avatar_contradiction_clause,[],[f604]) ).
fof(f606,plain,
( memberP(nil,sK57)
| ~ spl58_5 ),
inference(superposition,[],[f508,f567]) ).
fof(f614,plain,
( ~ ssItem(sK57)
| ~ spl58_5 ),
inference(resolution,[],[f419,f606]) ).
fof(f615,plain,
( $false
| ~ spl58_5 ),
inference(forward_subsumption_resolution,[],[f614,f503]) ).
fof(f616,plain,
~ spl58_5,
inference(avatar_contradiction_clause,[],[f615]) ).
fof(f625,plain,
( sK56 = app(app(sK13(sK56,sK55),sK55),sK14(sK56,sK55))
| ~ ssList(sK55)
| ~ ssList(sK56)
| ~ spl58_1 ),
inference(resolution,[],[f315,f549]) ).
fof(f626,plain,
( sK56 = app(app(sK13(sK56,sK55),sK55),sK14(sK56,sK55))
| ~ ssList(sK56)
| ~ spl58_1 ),
inference(forward_subsumption_resolution,[],[f625,f511]) ).
fof(f627,plain,
( sK56 = app(app(sK13(sK56,sK55),sK55),sK14(sK56,sK55))
| ~ spl58_1 ),
inference(forward_subsumption_resolution,[],[f626,f510]) ).
fof(f628,plain,
( ! [X0] :
( memberP(sK56,X0)
| ~ memberP(app(sK13(sK56,sK55),sK55),X0)
| ~ ssList(sK14(sK56,sK55))
| ~ ssList(app(sK13(sK56,sK55),sK55))
| ~ ssItem(X0) )
| ~ spl58_1 ),
inference(superposition,[],[f415,f627]) ).
fof(f631,definition,
( spl58_12
<=> ssList(app(sK13(sK56,sK55),sK55)) ),
introduced(definition,[new_symbols(definition,[spl58_12])],[avatar_definition]) ).
fof(f633,plain,
( ~ ssList(app(sK13(sK56,sK55),sK55))
| spl58_12 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f635,definition,
( spl58_13
<=> ssList(sK14(sK56,sK55)) ),
introduced(definition,[new_symbols(definition,[spl58_13])],[avatar_definition]) ).
fof(f637,plain,
( ~ ssList(sK14(sK56,sK55))
| spl58_13 ),
inference(avatar_component_clause,[],[f635]) ).
fof(f643,definition,
( spl58_15
<=> ! [X0] :
( memberP(sK56,X0)
| ~ ssItem(X0)
| ~ memberP(app(sK13(sK56,sK55),sK55),X0) ) ),
introduced(definition,[new_symbols(definition,[spl58_15])],[avatar_definition]) ).
fof(f644,plain,
( ! [X0] :
( ~ memberP(app(sK13(sK56,sK55),sK55),X0)
| ~ ssItem(X0)
| memberP(sK56,X0) )
| ~ spl58_15 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f645,plain,
( ~ spl58_12
| ~ spl58_13
| spl58_15
| ~ spl58_1 ),
inference(avatar_split_clause,[],[f628,f547,f643,f635,f631]) ).
fof(f648,plain,
( ~ ssList(sK55)
| ~ ssList(sK13(sK56,sK55))
| spl58_12 ),
inference(resolution,[],[f401,f633]) ).
fof(f654,plain,
( ~ ssList(sK13(sK56,sK55))
| spl58_12 ),
inference(forward_subsumption_resolution,[],[f648,f511]) ).
fof(f655,plain,
( ~ segmentP(sK56,sK55)
| ~ ssList(sK55)
| ~ ssList(sK56)
| spl58_12 ),
inference(resolution,[],[f654,f317]) ).
fof(f656,plain,
( ~ ssList(sK55)
| ~ ssList(sK56)
| ~ spl58_1
| spl58_12 ),
inference(forward_subsumption_resolution,[],[f655,f549]) ).
fof(f657,plain,
( ~ ssList(sK56)
| ~ spl58_1
| spl58_12 ),
inference(forward_subsumption_resolution,[],[f656,f511]) ).
fof(f658,plain,
( $false
| ~ spl58_1
| spl58_12 ),
inference(forward_subsumption_resolution,[],[f657,f510]) ).
fof(f659,plain,
( ~ spl58_1
| spl58_12 ),
inference(avatar_contradiction_clause,[],[f658]) ).
fof(f662,plain,
( ~ segmentP(sK56,sK55)
| ~ ssList(sK55)
| ~ ssList(sK56)
| spl58_13 ),
inference(resolution,[],[f316,f637]) ).
fof(f665,plain,
( ~ ssList(sK55)
| ~ ssList(sK56)
| ~ spl58_1
| spl58_13 ),
inference(forward_subsumption_resolution,[],[f662,f549]) ).
fof(f666,plain,
( ~ ssList(sK56)
| ~ spl58_1
| spl58_13 ),
inference(forward_subsumption_resolution,[],[f665,f511]) ).
fof(f667,plain,
( $false
| ~ spl58_1
| spl58_13 ),
inference(forward_subsumption_resolution,[],[f666,f510]) ).
fof(f668,plain,
( ~ spl58_1
| spl58_13 ),
inference(avatar_contradiction_clause,[],[f667]) ).
fof(f670,plain,
( ! [X0] :
( ~ ssItem(X0)
| memberP(sK56,X0)
| ~ memberP(sK55,X0)
| ~ ssList(sK55)
| ~ ssList(sK13(sK56,sK55))
| ~ ssItem(X0) )
| ~ spl58_15 ),
inference(resolution,[],[f644,f414]) ).
fof(f671,plain,
( ! [X0] :
( ~ ssItem(X0)
| memberP(sK56,X0)
| ~ memberP(sK55,X0)
| ~ ssList(sK55)
| ~ ssList(sK13(sK56,sK55)) )
| ~ spl58_15 ),
inference(duplicate_literal_removal,[],[f670]) ).
fof(f673,plain,
( ! [X0] :
( ~ ssItem(X0)
| memberP(sK56,X0)
| ~ memberP(sK55,X0)
| ~ ssList(sK13(sK56,sK55)) )
| ~ spl58_15 ),
inference(forward_subsumption_resolution,[],[f671,f511]) ).
fof(f676,definition,
( spl58_16
<=> ssList(sK13(sK56,sK55)) ),
introduced(definition,[new_symbols(definition,[spl58_16])],[avatar_definition]) ).
fof(f678,plain,
( ~ ssList(sK13(sK56,sK55))
| spl58_16 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f680,definition,
( spl58_17
<=> ! [X0] :
( ~ ssItem(X0)
| ~ memberP(sK55,X0)
| memberP(sK56,X0) ) ),
introduced(definition,[new_symbols(definition,[spl58_17])],[avatar_definition]) ).
fof(f681,plain,
( ! [X0] :
( ~ memberP(sK55,X0)
| ~ ssItem(X0)
| memberP(sK56,X0) )
| ~ spl58_17 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f682,plain,
( ~ spl58_16
| spl58_17
| ~ spl58_15 ),
inference(avatar_split_clause,[],[f673,f643,f680,f676]) ).
fof(f687,plain,
( ~ segmentP(sK56,sK55)
| ~ ssList(sK55)
| ~ ssList(sK56)
| spl58_16 ),
inference(resolution,[],[f678,f317]) ).
fof(f688,plain,
( ~ ssList(sK55)
| ~ ssList(sK56)
| ~ spl58_1
| spl58_16 ),
inference(forward_subsumption_resolution,[],[f687,f549]) ).
fof(f689,plain,
( ~ ssList(sK56)
| ~ spl58_1
| spl58_16 ),
inference(forward_subsumption_resolution,[],[f688,f511]) ).
fof(f690,plain,
( $false
| ~ spl58_1
| spl58_16 ),
inference(forward_subsumption_resolution,[],[f689,f510]) ).
fof(f691,plain,
( ~ spl58_1
| spl58_16 ),
inference(avatar_contradiction_clause,[],[f690]) ).
fof(f692,plain,
( ~ ssItem(sK57)
| memberP(sK56,sK57)
| ~ spl58_17 ),
inference(resolution,[],[f681,f508]) ).
fof(f693,plain,
( memberP(sK56,sK57)
| ~ spl58_17 ),
inference(forward_subsumption_resolution,[],[f692,f503]) ).
fof(f694,plain,
( $false
| ~ spl58_17 ),
inference(forward_subsumption_resolution,[],[f693,f509]) ).
fof(f695,plain,
~ spl58_17,
inference(avatar_contradiction_clause,[],[f694]) ).
cnf(s1,plain,
( spl58_1
| ~ spl58_2 ),
inference(sat_conversion,[],[f554]) ).
cnf(s3,plain,
( ~ spl58_4
| spl58_5 ),
inference(sat_conversion,[],[f568]) ).
cnf(s11,plain,
spl58_6,
inference(sat_conversion,[],[f598]) ).
cnf(s12,plain,
( spl58_2
| spl58_4
| ~ spl58_6 ),
inference(sat_conversion,[],[f605]) ).
cnf(s14,plain,
~ spl58_5,
inference(sat_conversion,[],[f616]) ).
cnf(s16,plain,
( ~ spl58_1
| ~ spl58_12
| ~ spl58_13
| spl58_15 ),
inference(sat_conversion,[],[f645]) ).
cnf(s17,plain,
( ~ spl58_1
| spl58_12 ),
inference(sat_conversion,[],[f659]) ).
cnf(s18,plain,
( ~ spl58_1
| spl58_13 ),
inference(sat_conversion,[],[f668]) ).
cnf(s19,plain,
( ~ spl58_15
| ~ spl58_16
| spl58_17 ),
inference(sat_conversion,[],[f682]) ).
cnf(s21,plain,
( ~ spl58_1
| spl58_16 ),
inference(sat_conversion,[],[f691]) ).
cnf(s22,plain,
~ spl58_17,
inference(sat_conversion,[],[f695]) ).
cnf(s23,plain,
( ~ spl58_15
| ~ spl58_16 ),
inference(rat,[],[s19,s22]) ).
cnf(s27,plain,
~ spl58_4,
inference(rat,[],[s3,s14]) ).
cnf(s28,plain,
spl58_2,
inference(rat,[],[s12,s11,s27]) ).
cnf(s30,plain,
spl58_1,
inference(rat,[],[s1,s28]) ).
cnf(s31,plain,
spl58_16,
inference(rat,[],[s21,s30]) ).
cnf(s32,plain,
spl58_13,
inference(rat,[],[s18,s30]) ).
cnf(s33,plain,
spl58_12,
inference(rat,[],[s17,s30]) ).
cnf(s34,plain,
~ spl58_15,
inference(rat,[],[s23,s31]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s16,s30,s32,s34,s33]) ).
fof(f696,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC393+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:28:12 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 6.41/1.77 % (1457639)Detected formulas, will run a generic FOF schedule.
% 6.41/1.77 % (1457648)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2098240915:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.41/1.77 % (1457648)Instruction limit reached!
% 6.41/1.77 % (1457648)------------------------------
% 6.41/1.77 % (1457648)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457648)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457648)Termination reason: Instruction limit
% 6.41/1.77 % (1457648)Termination phase: Saturation
% 6.41/1.77 % (1457648)Time elapsed: 0.028 s
% 6.41/1.77 % (1457648)Peak memory usage: 88 MB
% 6.41/1.77 % (1457648)Instructions burned: 120 (million)
% 6.41/1.77 % (1457649)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=552734945:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.41/1.77 % (1457647)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1531060752:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.41/1.77 % (1457644)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=3615979699:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.41/1.77 % (1457650)dis-21_1_sil=8000:lcm=predicate:random_seed=3939911579: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)
% 6.41/1.77 % (1457646)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=2484663083:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.41/1.77 % (1457645)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=589971354:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.41/1.77 % (1457647)Instruction limit reached!
% 6.41/1.77 % (1457647)------------------------------
% 6.41/1.77 % (1457647)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457647)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457647)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457647)Termination reason: Instruction limit
% 6.41/1.77 % (1457647)Termination phase: Saturation
% 6.41/1.77 % (1457647)Time elapsed: 0.068 s
% 6.41/1.77 % (1457647)Peak memory usage: 89 MB
% 6.41/1.77 % (1457647)Instructions burned: 111 (million)
% 6.41/1.77 % (1457650)Instruction limit reached!
% 6.41/1.77 % (1457650)------------------------------
% 6.41/1.77 % (1457650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457650)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457650)Termination reason: Instruction limit
% 6.41/1.77 % (1457650)Termination phase: Saturation
% 6.41/1.77 % (1457650)Time elapsed: 0.075 s
% 6.41/1.77 % (1457650)Peak memory usage: 90 MB
% 6.41/1.77 % (1457650)Instructions burned: 129 (million)
% 6.41/1.77 % (1457649)Instruction limit reached!
% 6.41/1.77 % (1457649)------------------------------
% 6.41/1.77 % (1457649)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457649)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457649)Termination reason: Instruction limit
% 6.41/1.77 % (1457649)Termination phase: Saturation
% 6.41/1.77 % (1457649)Time elapsed: 0.083 s
% 6.41/1.77 % (1457649)Peak memory usage: 89 MB
% 6.41/1.77 % (1457649)Instructions burned: 139 (million)
% 6.41/1.77 % (1457652)lrs+10_1_sil=8000:sp=occurrence:random_seed=1764337749:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.41/1.77 % (1457652)Instruction limit reached!
% 6.41/1.77 % (1457652)------------------------------
% 6.41/1.77 % (1457652)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457652)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457652)Termination reason: Instruction limit
% 6.41/1.77 % (1457652)Termination phase: Saturation
% 6.41/1.77 % (1457652)Time elapsed: 0.095 s
% 6.41/1.77 % (1457652)Peak memory usage: 93 MB
% 6.41/1.77 % (1457652)Instructions burned: 286 (million)
% 6.41/1.77 % (1457659)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1535601781:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.41/1.77 % (1457660)lrs+1011_1_sil=32000:sp=occurrence:random_seed=997519172:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.41/1.77 % (1457661)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=3770841852:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.41/1.77 % (1457659)Instruction limit reached!
% 6.41/1.77 % (1457659)------------------------------
% 6.41/1.77 % (1457659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457659)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457659)Termination reason: Instruction limit
% 6.41/1.77 % (1457659)Termination phase: Saturation
% 6.41/1.77 % (1457659)Time elapsed: 0.074 s
% 6.41/1.77 % (1457659)Peak memory usage: 92 MB
% 6.41/1.77 % (1457659)Instructions burned: 159 (million)
% 6.41/1.77 % (1457665)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1253129056:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.41/1.77 % (1457661)Instruction limit reached!
% 6.41/1.77 % (1457661)------------------------------
% 6.41/1.77 % (1457661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457661)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457661)Termination reason: Instruction limit
% 6.41/1.77 % (1457661)Termination phase: Saturation
% 6.41/1.77 % (1457661)Time elapsed: 0.122 s
% 6.41/1.77 % (1457661)Peak memory usage: 93 MB
% 6.41/1.77 % (1457661)Instructions burned: 249 (million)
% 6.41/1.77 % (1457665)Instruction limit reached!
% 6.41/1.77 % (1457665)------------------------------
% 6.41/1.77 % (1457665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457665)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457665)Termination reason: Instruction limit
% 6.41/1.77 % (1457665)Termination phase: Saturation
% 6.41/1.77 % (1457665)Time elapsed: 0.073 s
% 6.41/1.77 % (1457665)Peak memory usage: 88 MB
% 6.41/1.77 % (1457665)Instructions burned: 298 (million)
% 6.41/1.77 % (1457660)Instruction limit reached!
% 6.41/1.77 % (1457660)------------------------------
% 6.41/1.77 % (1457660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457660)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457660)Termination reason: Instruction limit
% 6.41/1.77 % (1457660)Termination phase: Saturation
% 6.41/1.77 % (1457660)Time elapsed: 0.197 s
% 6.41/1.77 % (1457660)Peak memory usage: 92 MB
% 6.41/1.77 % (1457660)Instructions burned: 327 (million)
% 6.41/1.77 % (1457667)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=152318745:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.41/1.77 % (1457669)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=1854512391:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.41/1.77 % (1457670)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3582665462:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 6.41/1.77 % (1457670)Instruction limit reached!
% 6.41/1.77 % (1457670)------------------------------
% 6.41/1.77 % (1457670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457670)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457670)Termination reason: Instruction limit
% 6.41/1.77 % (1457670)Termination phase: Saturation
% 6.41/1.77 % (1457670)Time elapsed: 0.034 s
% 6.41/1.77 % (1457670)Peak memory usage: 89 MB
% 6.41/1.77 % (1457670)Instructions burned: 128 (million)
% 6.41/1.77 % (1457671)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2494296182:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 6.41/1.77 % (1457669)Instruction limit reached!
% 6.41/1.77 % (1457669)------------------------------
% 6.41/1.77 % (1457669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457669)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457669)Termination reason: Instruction limit
% 6.41/1.77 % (1457669)Termination phase: Saturation
% 6.41/1.77 % (1457669)Time elapsed: 0.079 s
% 6.41/1.77 % (1457669)Peak memory usage: 90 MB
% 6.41/1.77 % (1457669)Instructions burned: 114 (million)
% 6.41/1.77 % (1457671)Instruction limit reached!
% 6.41/1.77 % (1457671)------------------------------
% 6.41/1.77 % (1457671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457671)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457671)Termination reason: Instruction limit
% 6.41/1.77 % (1457671)Termination phase: Saturation
% 6.41/1.77 % (1457671)Time elapsed: 0.072 s
% 6.41/1.77 % (1457671)Peak memory usage: 89 MB
% 6.41/1.77 % (1457671)Instructions burned: 116 (million)
% 6.41/1.77 % (1457644)First to succeed.
% 6.41/1.77 % (1457644)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1457639"
% 6.41/1.77 % (1457675)lrs+10_1_sil=8000:sp=occurrence:random_seed=1380907017:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.41/1.77 % (1457677)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1627739916:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 6.41/1.77 % (1457678)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2922997014:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.41/1.77 % (1457675)Also succeeded, but the first one will report.
% 6.41/1.77 % (1457677)Instruction limit reached!
% 6.41/1.77 % (1457677)------------------------------
% 6.41/1.77 % (1457677)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.41/1.77 % (1457677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.41/1.77 % (1457677)CaDiCaL version: 2.1.3
% 6.41/1.77 % (1457677)Termination reason: Instruction limit
% 6.41/1.77 % (1457677)Termination phase: Saturation
% 6.41/1.77 % (1457677)Time elapsed: 0.158 s
% 6.41/1.77 % (1457677)Peak memory usage: 88 MB
% 6.41/1.77 % (1457677)Instructions burned: 440 (million)
% 6.41/1.77 % (1457644)Refutation found. Thanks to Tanya!
% 6.41/1.77 % SZS status Theorem for theBenchmark
% 6.41/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 8.20/1.87 % (1457644)------------------------------
% 8.20/1.87 % (1457644)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.20/1.87 % (1457644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.20/1.87 % (1457644)CaDiCaL version: 2.1.3
% 8.20/1.87 % (1457644)Termination reason: Refutation
% 8.20/1.87 % (1457644)Time elapsed: 0.653 s
% 8.20/1.87 % (1457644)Peak memory usage: 130 MB
% 8.20/1.87 % (1457644)Instructions burned: 990 (million)
% 8.20/1.87 % (1457644)------------------------------
% 8.20/1.87 % (1457644)------------------------------
% 8.20/1.87 % (1457639)Success in time 1.097 s
% 8.20/1.87 % Vampire exiting
%------------------------------------------------------------------------------