%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC067+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 : n018.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 01:02:17 PM UTC 2026
% Result : Theorem 1.68s 1.12s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of formulae : 113 ( 23 unt; 10 def)
% Number of atoms : 459 ( 96 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 588 ( 242 ~; 221 |; 94 &)
% ( 13 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 8 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 126 ( 0 sgn 88 !; 38 ?)
% 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/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ strictorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& lt(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& lt(X12,X10) ) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X14] :
( ssList(X14)
& neq(X14,nil)
& segmentP(X1,X14)
& segmentP(X0,X14) ) ) ) ) ) ) ) ),
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
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ strictorderedP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssItem(X8)
& ? [X9] :
( ssList(X9)
& app(cons(X8,nil),X9) = X2
& lt(X6,X8) ) ) ) )
| ? [X10] :
( ssItem(X10)
& ? [X11] :
( ssList(X11)
& app(cons(X10,nil),X11) = X5
& ? [X12] :
( ssItem(X12)
& ? [X13] :
( ssList(X13)
& app(X13,cons(X12,nil)) = X2
& lt(X12,X10) ) ) ) ) ) ) )
| ( nil != X3
& nil = X2 )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X14] :
( ssList(X14)
& neq(X14,nil)
& segmentP(X1,X14)
& segmentP(X0,X14) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& strictorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ lt(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(X1,X14)
| ~ segmentP(X0,X14) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& strictorderedP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != X2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != X5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != X2
| ~ lt(X12,X10) ) ) ) )
& ssList(X5) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(X1,X14)
| ~ segmentP(X0,X14) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f124,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f129,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(f144,plain,
( sK1 = sK3
& sK0 = sK2
& sK3 = app(app(sK4,sK2),sK5)
& strictorderedP(sK2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != sK4
| ! [X8] :
( ~ ssItem(X8)
| ! [X9] :
( ~ ssList(X9)
| app(cons(X8,nil),X9) != sK2
| ~ lt(X6,X8) ) ) ) )
& ! [X10] :
( ~ ssItem(X10)
| ! [X11] :
( ~ ssList(X11)
| app(cons(X10,nil),X11) != sK5
| ! [X12] :
( ~ ssItem(X12)
| ! [X13] :
( ~ ssList(X13)
| app(X13,cons(X12,nil)) != sK2
| ~ lt(X12,X10) ) ) ) )
& ssList(sK5)
& ssList(sK4)
& ( nil = sK3
| nil != sK2 )
& ( ( nil = sK1
& nil != sK0 )
| ( neq(sK1,nil)
& ! [X14] :
( ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(sK1,X14)
| ~ segmentP(sK0,X14) ) ) )
& ssList(sK3)
& 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)],[f99]) ).
fof(f149,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f151,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f152,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,[],[f129]) ).
fof(f153,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,[],[f152]) ).
fof(f154,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK10(X0,X1))
& ssList(sK11(X0,X1))
& app(app(sK10(X0,X1),X1),sK11(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X4,sK10(X0,X1)),skolemize(X5,sK11(X0,X1))],[f153]) ).
fof(f162,plain,
ssList(sK0),
inference(cnf_transformation,[],[f144]) ).
fof(f163,plain,
ssList(sK1),
inference(cnf_transformation,[],[f144]) ).
fof(f166,plain,
! [X14] :
( nil != sK0
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(sK1,X14)
| ~ segmentP(sK0,X14) ),
inference(cnf_transformation,[],[f144]) ).
fof(f167,plain,
( nil != sK0
| neq(sK1,nil) ),
inference(cnf_transformation,[],[f144]) ).
fof(f168,plain,
! [X14] :
( nil = sK1
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(sK1,X14)
| ~ segmentP(sK0,X14) ),
inference(cnf_transformation,[],[f144]) ).
fof(f170,plain,
( nil = sK3
| nil != sK2 ),
inference(cnf_transformation,[],[f144]) ).
fof(f171,plain,
ssList(sK4),
inference(cnf_transformation,[],[f144]) ).
fof(f172,plain,
ssList(sK5),
inference(cnf_transformation,[],[f144]) ).
fof(f176,plain,
sK3 = app(app(sK4,sK2),sK5),
inference(cnf_transformation,[],[f144]) ).
fof(f177,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f144]) ).
fof(f178,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f144]) ).
fof(f201,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f202,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f149]) ).
fof(f205,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f206,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f210,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f216,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,[],[f154]) ).
fof(f241,plain,
! [X14] :
( nil = sK3
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(sK3,X14)
| ~ segmentP(sK2,X14) ),
inference(definition_unfolding,[],[f168,f178,f178,f177]) ).
fof(f242,plain,
( nil != sK2
| neq(sK3,nil) ),
inference(definition_unfolding,[],[f167,f177,f178]) ).
fof(f243,plain,
! [X14] :
( nil != sK2
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(sK3,X14)
| ~ segmentP(sK2,X14) ),
inference(definition_unfolding,[],[f166,f177,f178,f177]) ).
fof(f244,plain,
ssList(sK3),
inference(definition_unfolding,[],[f163,f178]) ).
fof(f245,plain,
ssList(sK2),
inference(definition_unfolding,[],[f162,f177]) ).
fof(f252,definition,
~ sP21(nil),
introduced(definition,[new_symbols(definition,[sP21])],[inequality_splitting_name_introduction]) ).
fof(f253,plain,
( nil = sK3
| sP21(sK2) ),
inference(inequality_splitting,[],[f170,f252]) ).
fof(f254,definition,
~ sP22(nil),
introduced(definition,[new_symbols(definition,[sP22])],[inequality_splitting_name_introduction]) ).
fof(f255,plain,
( sP22(sK2)
| neq(sK3,nil) ),
inference(inequality_splitting,[],[f242,f254]) ).
fof(f256,definition,
~ sP23(nil),
introduced(definition,[new_symbols(definition,[sP23])],[inequality_splitting_name_introduction]) ).
fof(f257,plain,
! [X14] :
( sP23(sK2)
| ~ ssList(X14)
| ~ neq(X14,nil)
| ~ segmentP(sK3,X14)
| ~ segmentP(sK2,X14) ),
inference(inequality_splitting,[],[f243,f256]) ).
fof(f275,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f201]) ).
fof(f277,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f216]) ).
fof(f288,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f275]) ).
fof(f292,definition,
( spl37_1
<=> ! [X14] :
( ~ ssList(X14)
| ~ segmentP(sK2,X14)
| ~ segmentP(sK3,X14)
| ~ neq(X14,nil) ) ),
introduced(definition,[new_symbols(definition,[spl37_1])],[avatar_definition]) ).
fof(f293,plain,
( ! [X14] :
( ~ segmentP(sK3,X14)
| ~ segmentP(sK2,X14)
| ~ ssList(X14)
| ~ neq(X14,nil) )
| ~ spl37_1 ),
inference(avatar_component_clause,[],[f292]) ).
fof(f295,definition,
( spl37_2
<=> sP23(sK2) ),
introduced(definition,[new_symbols(definition,[spl37_2])],[avatar_definition]) ).
fof(f297,plain,
( sP23(sK2)
| ~ spl37_2 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f298,plain,
( spl37_1
| spl37_2 ),
inference(avatar_split_clause,[],[f257,f295,f292]) ).
fof(f300,definition,
( spl37_3
<=> neq(sK3,nil) ),
introduced(definition,[new_symbols(definition,[spl37_3])],[avatar_definition]) ).
fof(f302,plain,
( neq(sK3,nil)
| ~ spl37_3 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f304,definition,
( spl37_4
<=> sP22(sK2) ),
introduced(definition,[new_symbols(definition,[spl37_4])],[avatar_definition]) ).
fof(f306,plain,
( sP22(sK2)
| ~ spl37_4 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f307,plain,
( spl37_3
| spl37_4 ),
inference(avatar_split_clause,[],[f255,f304,f300]) ).
fof(f309,definition,
( spl37_5
<=> nil = sK3 ),
introduced(definition,[new_symbols(definition,[spl37_5])],[avatar_definition]) ).
fof(f311,plain,
( nil = sK3
| ~ spl37_5 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f312,plain,
( spl37_1
| spl37_5 ),
inference(avatar_split_clause,[],[f241,f309,f292]) ).
fof(f315,definition,
( spl37_6
<=> sP21(sK2) ),
introduced(definition,[new_symbols(definition,[spl37_6])],[avatar_definition]) ).
fof(f317,plain,
( sP21(sK2)
| ~ spl37_6 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f318,plain,
( spl37_6
| spl37_5 ),
inference(avatar_split_clause,[],[f253,f309,f315]) ).
fof(f319,plain,
( neq(nil,nil)
| ~ spl37_3
| ~ spl37_5 ),
inference(superposition,[],[f302,f311]) ).
fof(f324,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK5)
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(superposition,[],[f277,f176]) ).
fof(f349,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK5)
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f324,f171]) ).
fof(f363,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK2)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f349,f172]) ).
fof(f393,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f363,f245]) ).
fof(f412,plain,
segmentP(sK3,sK2),
inference(forward_subsumption_resolution,[],[f393,f244]) ).
fof(f427,plain,
( segmentP(nil,sK2)
| ~ spl37_5 ),
inference(forward_demodulation,[],[f412,f311]) ).
fof(f533,plain,
( ~ ssList(nil)
| ~ spl37_3
| ~ spl37_5 ),
inference(resolution,[],[f319,f288]) ).
fof(f534,plain,
( $false
| ~ spl37_3
| ~ spl37_5 ),
inference(forward_subsumption_resolution,[],[f533,f205]) ).
fof(f535,plain,
( ~ spl37_3
| ~ spl37_5 ),
inference(avatar_contradiction_clause,[],[f534]) ).
fof(f564,plain,
( ~ segmentP(sK2,sK2)
| ~ ssList(sK2)
| ~ neq(sK2,nil)
| ~ spl37_1 ),
inference(resolution,[],[f293,f412]) ).
fof(f569,plain,
( ~ ssList(sK2)
| ~ neq(sK2,nil)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f564,f210]) ).
fof(f570,plain,
( ~ neq(sK2,nil)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f569,f245]) ).
fof(f580,plain,
( nil = sK2
| ~ ssList(sK2)
| ~ spl37_5 ),
inference(resolution,[],[f427,f206]) ).
fof(f584,plain,
( nil = sK2
| ~ spl37_5 ),
inference(forward_subsumption_resolution,[],[f580,f245]) ).
fof(f598,plain,
( nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ spl37_1 ),
inference(resolution,[],[f570,f202]) ).
fof(f605,plain,
( sP23(nil)
| ~ spl37_2
| ~ spl37_5 ),
inference(superposition,[],[f297,f584]) ).
fof(f619,plain,
( $false
| ~ spl37_2
| ~ spl37_5 ),
inference(forward_subsumption_resolution,[],[f605,f256]) ).
fof(f620,plain,
( ~ spl37_2
| ~ spl37_5 ),
inference(avatar_contradiction_clause,[],[f619]) ).
fof(f631,plain,
( nil = sK2
| ~ ssList(sK2)
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f598,f205]) ).
fof(f641,definition,
( spl37_37
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl37_37])],[avatar_definition]) ).
fof(f643,plain,
( nil = sK2
| ~ spl37_37 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f651,plain,
( nil = sK2
| ~ spl37_1 ),
inference(forward_subsumption_resolution,[],[f631,f245]) ).
fof(f653,plain,
( spl37_37
| ~ spl37_1 ),
inference(avatar_split_clause,[],[f651,f292,f641]) ).
fof(f666,plain,
( sP22(nil)
| ~ spl37_4
| ~ spl37_37 ),
inference(superposition,[],[f306,f643]) ).
fof(f667,plain,
( sP21(nil)
| ~ spl37_6
| ~ spl37_37 ),
inference(superposition,[],[f317,f643]) ).
fof(f672,plain,
( $false
| ~ spl37_6
| ~ spl37_37 ),
inference(forward_subsumption_resolution,[],[f667,f252]) ).
fof(f673,plain,
( ~ spl37_6
| ~ spl37_37 ),
inference(avatar_contradiction_clause,[],[f672]) ).
fof(f674,plain,
( $false
| ~ spl37_4
| ~ spl37_37 ),
inference(forward_subsumption_resolution,[],[f666,f254]) ).
fof(f675,plain,
( ~ spl37_4
| ~ spl37_37 ),
inference(avatar_contradiction_clause,[],[f674]) ).
cnf(s1,plain,
( spl37_1
| spl37_2 ),
inference(sat_conversion,[],[f298]) ).
cnf(s2,plain,
( spl37_3
| spl37_4 ),
inference(sat_conversion,[],[f307]) ).
cnf(s3,plain,
( spl37_1
| spl37_5 ),
inference(sat_conversion,[],[f312]) ).
cnf(s5,plain,
( spl37_5
| spl37_6 ),
inference(sat_conversion,[],[f318]) ).
cnf(s31,plain,
( ~ spl37_3
| ~ spl37_5 ),
inference(sat_conversion,[],[f535]) ).
cnf(s36,plain,
( ~ spl37_2
| ~ spl37_5 ),
inference(sat_conversion,[],[f620]) ).
cnf(s41,plain,
( ~ spl37_1
| spl37_37 ),
inference(sat_conversion,[],[f653]) ).
cnf(s42,plain,
( ~ spl37_6
| ~ spl37_37 ),
inference(sat_conversion,[],[f673]) ).
cnf(s43,plain,
( ~ spl37_4
| ~ spl37_37 ),
inference(sat_conversion,[],[f675]) ).
cnf(s64,plain,
spl37_1,
inference(rat,[],[s36,s1,s3]) ).
cnf(s65,plain,
spl37_37,
inference(rat,[],[s41,s64]) ).
cnf(s68,plain,
~ spl37_4,
inference(rat,[],[s43,s65]) ).
cnf(s69,plain,
~ spl37_6,
inference(rat,[],[s42,s65]) ).
cnf(s70,plain,
spl37_3,
inference(rat,[],[s2,s68]) ).
cnf(s71,plain,
spl37_5,
inference(rat,[],[s5,s69]) ).
cnf(s72,plain,
$false,
inference(rat,[],[s31,s71,s70]) ).
fof(f680,plain,
$false,
inference(avatar_sat_refutation,[],[s72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC067+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 07:44:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 1.68/1.12 % (3211300)Detected formulas, will run a generic FOF schedule.
% 1.68/1.12 % (3211308)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3793243783:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.68/1.12 % (3211308)First to succeed.
% 1.68/1.12 % (3211308)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3211300"
% 1.68/1.12 % (3211310)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3911583815:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.68/1.12 % (3211305)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=3625866053:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.68/1.12 % (3211309)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3045257499:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.68/1.12 % (3211311)dis-21_1_sil=8000:lcm=predicate:random_seed=1480473971: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)
% 1.68/1.12 % (3211306)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=233646109:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.68/1.12 % (3211307)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=3753224176:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.68/1.12 % (3211309)Also succeeded, but the first one will report.
% 1.68/1.12 % (3211310)Also succeeded, but the first one will report.
% 1.68/1.12 % (3211311)Instruction limit reached!
% 1.68/1.12 % (3211311)------------------------------
% 1.68/1.12 % (3211311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.68/1.12 % (3211311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.68/1.12 % (3211311)CaDiCaL version: 2.1.3
% 1.68/1.12 % (3211311)Termination reason: Instruction limit
% 1.68/1.12 % (3211311)Termination phase: Saturation
% 1.68/1.12 % (3211311)Time elapsed: 0.074 s
% 1.68/1.12 % (3211311)Peak memory usage: 90 MB
% 1.68/1.12 % (3211311)Instructions burned: 131 (million)
% 1.68/1.12 % (3211308)Refutation found. Thanks to Tanya!
% 1.68/1.12 % SZS status Theorem for theBenchmark
% 1.68/1.12 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/1.31 % (3211308)------------------------------
% 2.51/1.31 % (3211308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.31 % (3211308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.31 % (3211308)CaDiCaL version: 2.1.3
% 2.51/1.31 % (3211308)Termination reason: Refutation
% 2.51/1.31 % (3211308)Time elapsed: 0.007 s
% 2.51/1.31 % (3211308)Peak memory usage: 90 MB
% 2.51/1.31 % (3211308)Instructions burned: 17 (million)
% 2.51/1.31 % (3211308)------------------------------
% 2.51/1.31 % (3211308)------------------------------
% 2.51/1.31 % (3211300)Success in time 0.273 s
% 2.51/1.31 % Vampire exiting
%------------------------------------------------------------------------------