%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC052+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 : n014.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 01:02:12 PM UTC 2026
% Result : Theorem 3.26s 1.08s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 20
% Syntax : Number of formulae : 143 ( 17 unt; 14 def)
% Number of atoms : 526 ( 68 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 684 ( 301 ~; 293 |; 59 &)
% ( 18 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn 73 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ax7) ).
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(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X2,X4) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X1,X5)
& segmentP(X0,X5) ) ) ) ) ) ) ),
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
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ frontsegP(X3,X4)
| ~ frontsegP(X2,X4) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X5] :
( ssList(X5)
& neq(X5,nil)
& segmentP(X1,X5)
& segmentP(X0,X5) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
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(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f134,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ssList(X4)
& neq(X4,nil)
& frontsegP(X3,X4)
& frontsegP(X2,X4) )
| ~ neq(X3,nil) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(X1,X5)
| ~ segmentP(X0,X5) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f239,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,[],[f101]) ).
fof(f240,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,[],[f239]) ).
fof(f241,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ( ssList(sK11(X0,X1))
& app(X1,sK11(X0,X1)) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f240]) ).
fof(f245,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(f246,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,[],[f245]) ).
fof(f247,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))],[f246]) ).
fof(f295,plain,
( ssList(sK56)
& sK54 = sK56
& sK53 = sK55
& ( nil = sK55
| nil != sK56 )
& ( ( ssList(sK57)
& neq(sK57,nil)
& frontsegP(sK56,sK57)
& frontsegP(sK55,sK57) )
| ~ neq(sK56,nil) )
& ( ( nil = sK54
& nil != sK53 )
| ( neq(sK54,nil)
& ! [X5] :
( ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(sK54,X5)
| ~ segmentP(sK53,X5) ) ) )
& 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)],[f221]) ).
fof(f308,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f309,plain,
! [X0,X1] :
( ssList(sK11(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f241]) ).
fof(f317,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,[],[f247]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f400,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f402,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f496,plain,
ssList(sK54),
inference(cnf_transformation,[],[f295]) ).
fof(f498,plain,
! [X5] :
( nil != sK53
| ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(sK54,X5)
| ~ segmentP(sK53,X5) ),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
( nil != sK53
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f500,plain,
! [X5] :
( nil = sK54
| ~ ssList(X5)
| ~ neq(X5,nil)
| ~ segmentP(sK54,X5)
| ~ segmentP(sK53,X5) ),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
( nil = sK54
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
( frontsegP(sK55,sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
( frontsegP(sK56,sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
( neq(sK57,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
( ssList(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
( nil = sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f515,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,[],[f317]) ).
fof(f545,definition,
( spl58_1
<=> ! [X5] :
( ~ ssList(X5)
| ~ segmentP(sK53,X5)
| ~ segmentP(sK54,X5)
| ~ neq(X5,nil) ) ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f546,plain,
( ! [X5] :
( ~ segmentP(sK54,X5)
| ~ segmentP(sK53,X5)
| ~ ssList(X5)
| ~ neq(X5,nil) )
| ~ spl58_1 ),
inference(avatar_component_clause,[],[f545]) ).
fof(f548,definition,
( spl58_2
<=> nil = sK53 ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f550,plain,
( nil != sK53
| spl58_2 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f551,plain,
( spl58_1
| ~ spl58_2 ),
inference(avatar_split_clause,[],[f498,f548,f545]) ).
fof(f553,definition,
( spl58_3
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl58_3])],[avatar_definition]) ).
fof(f556,plain,
( spl58_3
| ~ spl58_2 ),
inference(avatar_split_clause,[],[f499,f548,f553]) ).
fof(f558,definition,
( spl58_4
<=> nil = sK54 ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f561,plain,
( spl58_1
| spl58_4 ),
inference(avatar_split_clause,[],[f500,f558,f545]) ).
fof(f562,plain,
( spl58_3
| spl58_4 ),
inference(avatar_split_clause,[],[f501,f558,f553]) ).
fof(f564,definition,
( spl58_5
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl58_5])],[avatar_definition]) ).
fof(f566,plain,
( ~ neq(sK56,nil)
| spl58_5 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f568,definition,
( spl58_6
<=> frontsegP(sK55,sK57) ),
introduced(definition,[new_symbols(definition,[spl58_6])],[avatar_definition]) ).
fof(f570,plain,
( frontsegP(sK55,sK57)
| ~ spl58_6 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f571,plain,
( ~ spl58_5
| spl58_6 ),
inference(avatar_split_clause,[],[f502,f568,f564]) ).
fof(f573,definition,
( spl58_7
<=> frontsegP(sK56,sK57) ),
introduced(definition,[new_symbols(definition,[spl58_7])],[avatar_definition]) ).
fof(f575,plain,
( frontsegP(sK56,sK57)
| ~ spl58_7 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f576,plain,
( ~ spl58_5
| spl58_7 ),
inference(avatar_split_clause,[],[f503,f573,f564]) ).
fof(f578,definition,
( spl58_8
<=> neq(sK57,nil) ),
introduced(definition,[new_symbols(definition,[spl58_8])],[avatar_definition]) ).
fof(f580,plain,
( neq(sK57,nil)
| ~ spl58_8 ),
inference(avatar_component_clause,[],[f578]) ).
fof(f581,plain,
( ~ spl58_5
| spl58_8 ),
inference(avatar_split_clause,[],[f504,f578,f564]) ).
fof(f583,definition,
( spl58_9
<=> ssList(sK57) ),
introduced(definition,[new_symbols(definition,[spl58_9])],[avatar_definition]) ).
fof(f585,plain,
( ssList(sK57)
| ~ spl58_9 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f586,plain,
( ~ spl58_5
| spl58_9 ),
inference(avatar_split_clause,[],[f505,f583,f564]) ).
fof(f588,definition,
( spl58_10
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_10])],[avatar_definition]) ).
fof(f590,plain,
( nil != sK56
| spl58_10 ),
inference(avatar_component_clause,[],[f588]) ).
fof(f592,definition,
( spl58_11
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl58_11])],[avatar_definition]) ).
fof(f594,plain,
( nil = sK55
| ~ spl58_11 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f595,plain,
( ~ spl58_10
| spl58_11 ),
inference(avatar_split_clause,[],[f506,f592,f588]) ).
fof(f597,definition,
( spl58_12
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl58_12])],[avatar_definition]) ).
fof(f598,plain,
( ssList(nil)
| ~ spl58_12 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f630,plain,
spl58_12,
inference(avatar_split_clause,[],[f388,f597]) ).
fof(f635,plain,
( ~ neq(sK54,nil)
| spl58_5 ),
inference(forward_demodulation,[],[f566,f508]) ).
fof(f637,plain,
( nil != sK54
| spl58_10 ),
inference(forward_demodulation,[],[f590,f508]) ).
fof(f644,plain,
( nil = sK53
| ~ spl58_11 ),
inference(superposition,[],[f594,f507]) ).
fof(f650,plain,
( $false
| spl58_2
| ~ spl58_11 ),
inference(forward_subsumption_resolution,[],[f644,f550]) ).
fof(f651,plain,
( spl58_2
| ~ spl58_11 ),
inference(avatar_contradiction_clause,[],[f650]) ).
fof(f653,plain,
( ~ spl58_4
| spl58_10 ),
inference(avatar_split_clause,[],[f637,f588,f558]) ).
fof(f655,plain,
( ~ spl58_3
| spl58_5 ),
inference(avatar_split_clause,[],[f635,f564,f553]) ).
fof(f657,plain,
( frontsegP(sK53,sK57)
| ~ spl58_6 ),
inference(forward_demodulation,[],[f570,f507]) ).
fof(f658,plain,
( frontsegP(sK54,sK57)
| ~ spl58_7 ),
inference(forward_demodulation,[],[f575,f508]) ).
fof(f893,plain,
( sK53 = app(sK57,sK11(sK53,sK57))
| ~ ssList(sK57)
| ~ ssList(sK53)
| ~ spl58_6 ),
inference(resolution,[],[f308,f657]) ).
fof(f894,plain,
( sK54 = app(sK57,sK11(sK54,sK57))
| ~ ssList(sK57)
| ~ ssList(sK54)
| ~ spl58_7 ),
inference(resolution,[],[f308,f658]) ).
fof(f906,plain,
( sK54 = app(sK57,sK11(sK54,sK57))
| ~ ssList(sK54)
| ~ spl58_7
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f894,f585]) ).
fof(f907,plain,
( sK53 = app(sK57,sK11(sK53,sK57))
| ~ ssList(sK53)
| ~ spl58_6
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f893,f585]) ).
fof(f908,plain,
( sK54 = app(sK57,sK11(sK54,sK57))
| ~ spl58_7
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f906,f496]) ).
fof(f909,plain,
( sK53 = app(sK57,sK11(sK53,sK57))
| ~ spl58_6
| ~ spl58_9 ),
inference(forward_subsumption_resolution,[],[f907,f495]) ).
fof(f917,definition,
( spl58_25
<=> ssList(sK11(sK54,sK57)) ),
introduced(definition,[new_symbols(definition,[spl58_25])],[avatar_definition]) ).
fof(f918,plain,
( ssList(sK11(sK54,sK57))
| ~ spl58_25 ),
inference(avatar_component_clause,[],[f917]) ).
fof(f919,plain,
( ~ ssList(sK11(sK54,sK57))
| spl58_25 ),
inference(avatar_component_clause,[],[f917]) ).
fof(f936,plain,
( ~ frontsegP(sK54,sK57)
| ~ ssList(sK57)
| ~ ssList(sK54)
| spl58_25 ),
inference(resolution,[],[f919,f309]) ).
fof(f937,plain,
( ~ ssList(sK57)
| ~ ssList(sK54)
| ~ spl58_7
| spl58_25 ),
inference(forward_subsumption_resolution,[],[f936,f658]) ).
fof(f938,plain,
( ~ ssList(sK54)
| ~ spl58_7
| ~ spl58_9
| spl58_25 ),
inference(forward_subsumption_resolution,[],[f937,f585]) ).
fof(f939,plain,
( $false
| ~ spl58_7
| ~ spl58_9
| spl58_25 ),
inference(forward_subsumption_resolution,[],[f938,f496]) ).
fof(f940,plain,
( ~ spl58_7
| ~ spl58_9
| spl58_25 ),
inference(avatar_contradiction_clause,[],[f939]) ).
fof(f1006,definition,
( spl58_29
<=> ssList(sK11(sK53,sK57)) ),
introduced(definition,[new_symbols(definition,[spl58_29])],[avatar_definition]) ).
fof(f1007,plain,
( ssList(sK11(sK53,sK57))
| ~ spl58_29 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1008,plain,
( ~ ssList(sK11(sK53,sK57))
| spl58_29 ),
inference(avatar_component_clause,[],[f1006]) ).
fof(f1027,plain,
( ~ frontsegP(sK53,sK57)
| ~ ssList(sK57)
| ~ ssList(sK53)
| spl58_29 ),
inference(resolution,[],[f1008,f309]) ).
fof(f1028,plain,
( ~ ssList(sK57)
| ~ ssList(sK53)
| ~ spl58_6
| spl58_29 ),
inference(forward_subsumption_resolution,[],[f1027,f657]) ).
fof(f1029,plain,
( ~ ssList(sK53)
| ~ spl58_6
| ~ spl58_9
| spl58_29 ),
inference(forward_subsumption_resolution,[],[f1028,f585]) ).
fof(f1030,plain,
( $false
| ~ spl58_6
| ~ spl58_9
| spl58_29 ),
inference(forward_subsumption_resolution,[],[f1029,f495]) ).
fof(f1031,plain,
( ~ spl58_6
| ~ spl58_9
| spl58_29 ),
inference(avatar_contradiction_clause,[],[f1030]) ).
fof(f1797,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(superposition,[],[f515,f402]) ).
fof(f1804,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f1797]) ).
fof(f1814,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f1804,f400]) ).
fof(f1821,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl58_12 ),
inference(forward_subsumption_resolution,[],[f1814,f598]) ).
fof(f2601,plain,
( segmentP(sK54,sK57)
| ~ ssList(sK57)
| ~ ssList(sK11(sK54,sK57))
| ~ spl58_7
| ~ spl58_9
| ~ spl58_12 ),
inference(superposition,[],[f1821,f908]) ).
fof(f2602,plain,
( segmentP(sK53,sK57)
| ~ ssList(sK57)
| ~ ssList(sK11(sK53,sK57))
| ~ spl58_6
| ~ spl58_9
| ~ spl58_12 ),
inference(superposition,[],[f1821,f909]) ).
fof(f2615,plain,
( segmentP(sK53,sK57)
| ~ ssList(sK11(sK53,sK57))
| ~ spl58_6
| ~ spl58_9
| ~ spl58_12 ),
inference(forward_subsumption_resolution,[],[f2602,f585]) ).
fof(f2616,plain,
( segmentP(sK54,sK57)
| ~ ssList(sK11(sK54,sK57))
| ~ spl58_7
| ~ spl58_9
| ~ spl58_12 ),
inference(forward_subsumption_resolution,[],[f2601,f585]) ).
fof(f2625,plain,
( segmentP(sK53,sK57)
| ~ spl58_6
| ~ spl58_9
| ~ spl58_12
| ~ spl58_29 ),
inference(forward_subsumption_resolution,[],[f2615,f1007]) ).
fof(f2626,plain,
( segmentP(sK54,sK57)
| ~ spl58_7
| ~ spl58_9
| ~ spl58_12
| ~ spl58_25 ),
inference(forward_subsumption_resolution,[],[f2616,f918]) ).
fof(f2654,plain,
( ~ segmentP(sK53,sK57)
| ~ ssList(sK57)
| ~ neq(sK57,nil)
| ~ spl58_1
| ~ spl58_7
| ~ spl58_9
| ~ spl58_12
| ~ spl58_25 ),
inference(resolution,[],[f2626,f546]) ).
fof(f2663,plain,
( ~ ssList(sK57)
| ~ neq(sK57,nil)
| ~ spl58_1
| ~ spl58_6
| ~ spl58_7
| ~ spl58_9
| ~ spl58_12
| ~ spl58_25
| ~ spl58_29 ),
inference(forward_subsumption_resolution,[],[f2654,f2625]) ).
fof(f2668,plain,
( ~ neq(sK57,nil)
| ~ spl58_1
| ~ spl58_6
| ~ spl58_7
| ~ spl58_9
| ~ spl58_12
| ~ spl58_25
| ~ spl58_29 ),
inference(forward_subsumption_resolution,[],[f2663,f585]) ).
fof(f2674,plain,
( $false
| ~ spl58_1
| ~ spl58_6
| ~ spl58_7
| ~ spl58_8
| ~ spl58_9
| ~ spl58_12
| ~ spl58_25
| ~ spl58_29 ),
inference(forward_subsumption_resolution,[],[f2668,f580]) ).
fof(f2675,plain,
( ~ spl58_1
| ~ spl58_6
| ~ spl58_7
| ~ spl58_8
| ~ spl58_9
| ~ spl58_12
| ~ spl58_25
| ~ spl58_29 ),
inference(avatar_contradiction_clause,[],[f2674]) ).
cnf(s1,plain,
( spl58_1
| ~ spl58_2 ),
inference(sat_conversion,[],[f551]) ).
cnf(s2,plain,
( ~ spl58_2
| spl58_3 ),
inference(sat_conversion,[],[f556]) ).
cnf(s3,plain,
( spl58_1
| spl58_4 ),
inference(sat_conversion,[],[f561]) ).
cnf(s4,plain,
( spl58_3
| spl58_4 ),
inference(sat_conversion,[],[f562]) ).
cnf(s5,plain,
( ~ spl58_5
| spl58_6 ),
inference(sat_conversion,[],[f571]) ).
cnf(s6,plain,
( ~ spl58_5
| spl58_7 ),
inference(sat_conversion,[],[f576]) ).
cnf(s7,plain,
( ~ spl58_5
| spl58_8 ),
inference(sat_conversion,[],[f581]) ).
cnf(s8,plain,
( ~ spl58_5
| spl58_9 ),
inference(sat_conversion,[],[f586]) ).
cnf(s9,plain,
( ~ spl58_10
| spl58_11 ),
inference(sat_conversion,[],[f595]) ).
cnf(s18,plain,
spl58_12,
inference(sat_conversion,[],[f630]) ).
cnf(s24,plain,
( spl58_2
| ~ spl58_11 ),
inference(sat_conversion,[],[f651]) ).
cnf(s25,plain,
( ~ spl58_4
| spl58_10 ),
inference(sat_conversion,[],[f653]) ).
cnf(s26,plain,
( ~ spl58_3
| spl58_5 ),
inference(sat_conversion,[],[f655]) ).
cnf(s33,plain,
( ~ spl58_7
| ~ spl58_9
| spl58_25 ),
inference(sat_conversion,[],[f940]) ).
cnf(s36,plain,
( ~ spl58_6
| ~ spl58_9
| spl58_29 ),
inference(sat_conversion,[],[f1031]) ).
cnf(s123,plain,
( ~ spl58_1
| ~ spl58_6
| ~ spl58_7
| ~ spl58_8
| ~ spl58_9
| ~ spl58_12
| ~ spl58_25
| ~ spl58_29 ),
inference(sat_conversion,[],[f2675]) ).
cnf(s130,plain,
spl58_1,
inference(rat,[],[s9,s24,s25,s1,s3]) ).
cnf(s131,plain,
( ~ spl58_6
| ~ spl58_7
| ~ spl58_8
| ~ spl58_9
| ~ spl58_25 ),
inference(rat,[],[s36,s123,s18,s130]) ).
cnf(s132,plain,
~ spl58_5,
inference(rat,[],[s131,s33,s5,s6,s7,s8]) ).
cnf(s133,plain,
~ spl58_3,
inference(rat,[],[s26,s132]) ).
cnf(s134,plain,
spl58_4,
inference(rat,[],[s4,s133]) ).
cnf(s135,plain,
~ spl58_2,
inference(rat,[],[s2,s133]) ).
cnf(s136,plain,
spl58_10,
inference(rat,[],[s25,s134]) ).
cnf(s138,plain,
~ spl58_11,
inference(rat,[],[s24,s135]) ).
cnf(s139,plain,
$false,
inference(rat,[],[s9,s138,s136]) ).
fof(f2676,plain,
$false,
inference(avatar_sat_refutation,[],[s139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC052+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n014.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 07:37:46 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.26/1.08 % (1611563)Detected formulas, will run a generic FOF schedule.
% 3.26/1.08 % (1611574)dis-21_1_sil=8000:lcm=predicate:random_seed=50738760:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.26/1.08 % (1611571)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=329036283:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.26/1.08 % (1611569)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=1628153287:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.26/1.08 % (1611573)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1270699232:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.26/1.08 % (1611572)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1279230525:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.26/1.08 % (1611568)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=2410344889:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.26/1.08 % (1611570)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=1856011887:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.26/1.08 % (1611573)First to succeed.
% 3.26/1.08 % (1611573)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1611563"
% 3.26/1.08 % (1611572)Instruction limit reached!
% 3.26/1.08 % (1611572)------------------------------
% 3.26/1.08 % (1611572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.08 % (1611572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.08 % (1611572)CaDiCaL version: 2.1.3
% 3.26/1.08 % (1611572)Termination reason: Instruction limit
% 3.26/1.08 % (1611572)Termination phase: Saturation
% 3.26/1.08 % (1611572)Time elapsed: 0.063 s
% 3.26/1.08 % (1611572)Peak memory usage: 88 MB
% 3.26/1.08 % (1611572)Instructions burned: 119 (million)
% 3.26/1.08 % (1611571)Instruction limit reached!
% 3.26/1.08 % (1611571)------------------------------
% 3.26/1.08 % (1611571)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.08 % (1611571)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.08 % (1611571)CaDiCaL version: 2.1.3
% 3.26/1.08 % (1611571)Termination reason: Instruction limit
% 3.26/1.08 % (1611571)Termination phase: Saturation
% 3.26/1.08 % (1611571)Time elapsed: 0.066 s
% 3.26/1.08 % (1611571)Peak memory usage: 89 MB
% 3.26/1.08 % (1611571)Instructions burned: 109 (million)
% 3.26/1.08 % (1611574)Instruction limit reached!
% 3.26/1.08 % (1611574)------------------------------
% 3.26/1.08 % (1611574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.08 % (1611574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.08 % (1611574)CaDiCaL version: 2.1.3
% 3.26/1.08 % (1611574)Termination reason: Instruction limit
% 3.26/1.08 % (1611574)Termination phase: Saturation
% 3.26/1.08 % (1611574)Time elapsed: 0.074 s
% 3.26/1.08 % (1611574)Peak memory usage: 90 MB
% 3.26/1.08 % (1611574)Instructions burned: 129 (million)
% 3.26/1.08 % (1611583)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1364644314:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.26/1.08 % (1611582)lrs+10_1_sil=8000:sp=occurrence:random_seed=2336965620:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.26/1.08 % (1611583)Instruction limit reached!
% 3.26/1.08 % (1611583)------------------------------
% 3.26/1.08 % (1611583)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.26/1.08 % (1611583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.26/1.08 % (1611583)CaDiCaL version: 2.1.3
% 3.26/1.08 % (1611583)Termination reason: Instruction limit
% 3.26/1.08 % (1611583)Termination phase: Saturation
% 3.26/1.08 % (1611583)Time elapsed: 0.040 s
% 3.26/1.08 % (1611583)Peak memory usage: 92 MB
% 3.26/1.08 % (1611583)Instructions burned: 158 (million)
% 3.26/1.08 % (1611584)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1466757752:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.26/1.08 % (1611573)Refutation found. Thanks to Tanya!
% 3.26/1.08 % SZS status Theorem for theBenchmark
% 3.26/1.08 % SZS output start Proof for theBenchmark
% See solution above
% 3.76/1.21 % (1611573)------------------------------
% 3.76/1.21 % (1611573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.76/1.21 % (1611573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.76/1.21 % (1611573)CaDiCaL version: 2.1.3
% 3.76/1.21 % (1611573)Termination reason: Refutation
% 3.76/1.21 % (1611573)Time elapsed: 0.055 s
% 3.76/1.21 % (1611573)Peak memory usage: 90 MB
% 3.76/1.21 % (1611573)Instructions burned: 81 (million)
% 3.76/1.21 % (1611573)------------------------------
% 3.76/1.21 % (1611573)------------------------------
% 3.76/1.21 % (1611563)Success in time 0.48 s
% 3.76/1.21 % Vampire exiting
%------------------------------------------------------------------------------