%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC089-1 : 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 : n015.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 01:02:23 PM UTC 2026
% Result : Unsatisfiable 1.92s 1.30s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 40
% Syntax : Number of formulae : 179 ( 28 unt; 17 def)
% Number of atoms : 555 ( 66 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 731 ( 355 ~; 359 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 18 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause8) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause74) ).
fof(f75,axiom,
! [X0] :
( ssList(tl(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause75) ).
fof(f76,axiom,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause76) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| neq(X1,X0)
| X1 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause100) ).
fof(f102,plain,
! [X0,X1] :
( neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| X0 = X1 ),
inference(reorient_equations,[],[f101]) ).
fof(f107,axiom,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0)
| nil = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause104) ).
fof(f118,axiom,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause115) ).
fof(f125,axiom,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssList(X1)
| app(cons(X0,nil),X1) = cons(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f161,axiom,
! [X2,X0,X1] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause149) ).
fof(f164,axiom,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause152) ).
fof(f187,axiom,
! [X2,X3,X0,X1] :
( app(app(X0,X1),X2) != X3
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| segmentP(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause173) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f209,negated_conjecture,
( ~ neq(sk4,nil)
| neq(sk3,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
! [X2,X3,X0,X1] :
( ~ neq(sk4,nil)
| ~ ssList(X0)
| sk4 = X0
| ~ ssList(X1)
| ~ ssList(X2)
| tl(sk3) != X1
| app(X1,X2) != X0
| ~ ssItem(X3)
| cons(X3,nil) != X2
| hd(sk3) != X3
| ~ neq(nil,sk3)
| ~ neq(nil,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f213,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f214,plain,
! [X0] :
( ~ neq(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f207,f204,f205]) ).
fof(f215,plain,
! [X2,X3,X0] :
( ~ neq(sk4,nil)
| ~ ssList(X0)
| sk4 = X0
| ~ ssList(tl(sk3))
| ~ ssList(X2)
| app(tl(sk3),X2) != X0
| ~ ssItem(X3)
| cons(X3,nil) != X2
| hd(sk3) != X3
| ~ neq(nil,sk3)
| ~ neq(nil,sk3) ),
inference(equality_resolution,[],[f210]) ).
fof(f216,plain,
! [X2,X3] :
( ~ neq(sk4,nil)
| ~ ssList(app(tl(sk3),X2))
| sk4 = app(tl(sk3),X2)
| ~ ssList(tl(sk3))
| ~ ssList(X2)
| ~ ssItem(X3)
| cons(X3,nil) != X2
| hd(sk3) != X3
| ~ neq(nil,sk3)
| ~ neq(nil,sk3) ),
inference(equality_resolution,[],[f215]) ).
fof(f217,plain,
! [X3] :
( ~ neq(sk4,nil)
| ~ ssList(app(tl(sk3),cons(X3,nil)))
| sk4 = app(tl(sk3),cons(X3,nil))
| ~ ssList(tl(sk3))
| ~ ssList(cons(X3,nil))
| ~ ssItem(X3)
| hd(sk3) != X3
| ~ neq(nil,sk3)
| ~ neq(nil,sk3) ),
inference(equality_resolution,[],[f216]) ).
fof(f218,plain,
( ~ neq(sk4,nil)
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil)))
| sk4 = app(tl(sk3),cons(hd(sk3),nil))
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3)
| ~ neq(nil,sk3) ),
inference(equality_resolution,[],[f217]) ).
fof(f222,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f223,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| segmentP(app(app(X0,X1),X2),X1) ),
inference(equality_resolution,[],[f187]) ).
fof(f231,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f222]) ).
fof(f234,plain,
( ~ neq(sk4,nil)
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil)))
| sk4 = app(tl(sk3),cons(hd(sk3),nil))
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3) ),
inference(duplicate_literal_removal,[],[f218]) ).
fof(f255,definition,
( spl0_6
<=> neq(nil,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f256,plain,
( ~ neq(nil,sk3)
| spl0_6 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f258,definition,
( spl0_7
<=> ssItem(hd(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f259,plain,
( ~ ssItem(hd(sk3))
| spl0_7 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,definition,
( spl0_8
<=> ssList(cons(hd(sk3),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f262,plain,
( ~ ssList(cons(hd(sk3),nil))
| spl0_8 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f264,definition,
( spl0_9
<=> ssList(tl(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f265,plain,
( ~ ssList(tl(sk3))
| spl0_9 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f267,definition,
( spl0_10
<=> sk4 = app(tl(sk3),cons(hd(sk3),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f268,plain,
( sk4 = app(tl(sk3),cons(hd(sk3),nil))
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f270,definition,
( spl0_11
<=> ssList(app(tl(sk3),cons(hd(sk3),nil))) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
fof(f271,plain,
( ~ ssList(app(tl(sk3),cons(hd(sk3),nil)))
| spl0_11 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f273,definition,
( spl0_12
<=> neq(sk4,nil) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f274,plain,
( ~ neq(sk4,nil)
| spl0_12 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f275,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f234,f273,f270,f267,f264,f261,f258,f255]) ).
fof(f277,definition,
( spl0_13
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f278,plain,
( neq(sk3,nil)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f279,plain,
( spl0_13
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f209,f273,f277]) ).
fof(f284,definition,
( spl0_15
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f285,plain,
( nil = sk3
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f287,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f274,f213]) ).
fof(f288,plain,
spl0_12,
inference(avatar_contradiction_clause,[],[f287]) ).
fof(f290,plain,
( ~ ssList(sk3)
| ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3)
| ~ spl0_13 ),
inference(resolution,[],[f214,f278]) ).
fof(f291,plain,
( ~ segmentP(sk4,sk3)
| ~ segmentP(sk3,sk3)
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[],[f290,f202]) ).
fof(f294,definition,
( spl0_16
<=> segmentP(sk3,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
fof(f295,plain,
( ~ segmentP(sk3,sk3)
| spl0_16 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f297,definition,
( spl0_17
<=> segmentP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
fof(f298,plain,
( ~ segmentP(sk4,sk3)
| spl0_17 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f299,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f291,f277,f297,f294]) ).
fof(f309,plain,
( ~ ssList(sk3)
| spl0_16 ),
inference(resolution,[],[f57,f295]) ).
fof(f313,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[],[f309,f202]) ).
fof(f314,plain,
spl0_16,
inference(avatar_contradiction_clause,[],[f313]) ).
fof(f330,plain,
( ~ ssList(nil)
| ~ ssList(sk3)
| nil = sk3
| spl0_6 ),
inference(resolution,[],[f102,f256]) ).
fof(f331,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(resolution,[],[f102,f214]) ).
fof(f336,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(duplicate_literal_removal,[],[f331]) ).
fof(f337,plain,
! [X0] :
( ~ segmentP(sk4,X0)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ),
inference(forward_subsumption_resolution,[],[f336,f8]) ).
fof(f338,plain,
( ~ ssList(sk3)
| nil = sk3
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f330,f8]) ).
fof(f339,plain,
( nil = sk3
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f338,f202]) ).
fof(f340,plain,
( spl0_15
| spl0_6 ),
inference(avatar_split_clause,[],[f339,f255,f284]) ).
fof(f343,plain,
( neq(nil,nil)
| ~ spl0_13
| ~ spl0_15 ),
inference(superposition,[],[f278,f285]) ).
fof(f348,plain,
( ~ ssList(nil)
| ~ spl0_13
| ~ spl0_15 ),
inference(resolution,[],[f343,f231]) ).
fof(f349,plain,
( $false
| ~ spl0_13
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[],[f348,f8]) ).
fof(f350,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(avatar_contradiction_clause,[],[f349]) ).
fof(f359,plain,
( ~ ssList(sk3)
| nil = sk3
| spl0_7 ),
inference(resolution,[],[f259,f76]) ).
fof(f360,plain,
( nil = sk3
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f359,f202]) ).
fof(f361,plain,
( spl0_15
| spl0_7 ),
inference(avatar_split_clause,[],[f360,f258,f284]) ).
fof(f362,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| spl0_8 ),
inference(resolution,[],[f262,f86]) ).
fof(f363,plain,
( ~ ssItem(hd(sk3))
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f362,f8]) ).
fof(f364,plain,
( ~ spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f363,f261,f258]) ).
fof(f365,plain,
( ~ ssList(sk3)
| nil = sk3
| spl0_9 ),
inference(resolution,[],[f265,f75]) ).
fof(f366,plain,
( nil = sk3
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f365,f202]) ).
fof(f367,plain,
( spl0_15
| spl0_9 ),
inference(avatar_split_clause,[],[f366,f264,f284]) ).
fof(f368,plain,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| spl0_11 ),
inference(resolution,[],[f271,f85]) ).
fof(f369,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f368,f270,f264,f261]) ).
fof(f371,plain,
( ~ segmentP(app(tl(sk3),cons(hd(sk3),nil)),sk3)
| ~ spl0_10
| spl0_17 ),
inference(superposition,[],[f298,f268]) ).
fof(f374,plain,
( ssList(app(tl(sk3),cons(hd(sk3),nil)))
| ~ spl0_10 ),
inference(superposition,[],[f203,f268]) ).
fof(f420,plain,
! [X0] :
( app(cons(hd(X0),nil),tl(X0)) = X0
| ~ ssList(X0)
| nil = X0
| ~ ssList(tl(X0))
| ~ ssItem(hd(X0)) ),
inference(superposition,[],[f107,f126]) ).
fof(f432,plain,
! [X0] :
( app(cons(hd(X0),nil),tl(X0)) = X0
| ~ ssList(X0)
| nil = X0
| ~ ssItem(hd(X0)) ),
inference(forward_subsumption_resolution,[],[f420,f75]) ).
fof(f434,plain,
! [X0] :
( app(cons(hd(X0),nil),tl(X0)) = X0
| ~ ssList(X0)
| nil = X0 ),
inference(forward_subsumption_resolution,[],[f432,f76]) ).
fof(f438,plain,
( ! [X0] :
( ~ segmentP(app(tl(sk3),cons(hd(sk3),nil)),X0)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk3,X0) )
| ~ spl0_10 ),
inference(superposition,[],[f337,f268]) ).
fof(f574,plain,
( ! [X0] :
( ~ segmentP(X0,sk3)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil)))
| ~ segmentP(app(tl(sk3),cons(hd(sk3),nil)),X0) )
| ~ spl0_10
| spl0_17 ),
inference(resolution,[],[f164,f371]) ).
fof(f589,plain,
( ! [X0] :
( ~ segmentP(X0,sk3)
| ~ ssList(X0)
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil)))
| ~ segmentP(app(tl(sk3),cons(hd(sk3),nil)),X0) )
| ~ spl0_10
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f574,f202]) ).
fof(f594,plain,
( ! [X0] :
( ~ segmentP(app(tl(sk3),cons(hd(sk3),nil)),X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3) )
| ~ spl0_10
| spl0_17 ),
inference(forward_subsumption_resolution,[],[f589,f374]) ).
fof(f960,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(X0,app(X1,X2)))
| segmentP(app(app(X0,X1),X2),X1) ),
inference(forward_subsumption_demodulation,[],[f223,f161]) ).
fof(f961,plain,
! [X2,X0,X1] :
( segmentP(app(X0,app(X1,X2)),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(X0,app(X1,X2)))
| ~ ssList(X2) ),
inference(forward_subsumption_demodulation,[],[f960,f161]) ).
fof(f976,plain,
! [X0,X1] :
( segmentP(app(X1,X0),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f961,f73]) ).
fof(f977,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(superposition,[],[f961,f74]) ).
fof(f979,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f977]) ).
fof(f980,plain,
! [X0,X1] :
( segmentP(app(X1,X0),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X0))
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f976]) ).
fof(f989,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f979,f8]) ).
fof(f990,plain,
! [X0,X1] :
( segmentP(app(X1,X0),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f980,f8]) ).
fof(f995,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f989,f85]) ).
fof(f996,plain,
! [X0,X1] :
( segmentP(app(X1,X0),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f990,f85]) ).
fof(f1117,plain,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| nil = tl(sk3)
| ~ ssList(tl(sk3))
| ~ segmentP(sk3,tl(sk3))
| ~ spl0_10 ),
inference(resolution,[],[f995,f438]) ).
fof(f1132,plain,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| nil = tl(sk3)
| ~ segmentP(sk3,tl(sk3))
| ~ spl0_10 ),
inference(duplicate_literal_removal,[],[f1117]) ).
fof(f1139,definition,
( spl0_28
<=> segmentP(sk3,tl(sk3)) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f1140,plain,
( ~ segmentP(sk3,tl(sk3))
| spl0_28 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f1142,definition,
( spl0_29
<=> nil = tl(sk3) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f1143,plain,
( nil = tl(sk3)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1144,plain,
( ~ spl0_28
| spl0_29
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f1132,f267,f264,f261,f1142,f1139]) ).
fof(f1154,definition,
( spl0_31
<=> ! [X0] :
( ~ segmentP(X0,tl(sk3))
| ~ segmentP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_31])],[avatar_definition]) ).
fof(f1155,plain,
( ! [X0] :
( ~ segmentP(X0,tl(sk3))
| ~ segmentP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f1157,plain,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ~ segmentP(cons(hd(sk3),nil),sk3)
| ~ spl0_10
| spl0_17 ),
inference(resolution,[],[f996,f594]) ).
fof(f1174,plain,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ segmentP(cons(hd(sk3),nil),sk3)
| ~ spl0_10
| spl0_17 ),
inference(duplicate_literal_removal,[],[f1157]) ).
fof(f1187,definition,
( spl0_34
<=> segmentP(cons(hd(sk3),nil),sk3) ),
introduced(definition,[new_symbols(definition,[spl0_34])],[avatar_definition]) ).
fof(f1188,plain,
( ~ segmentP(cons(hd(sk3),nil),sk3)
| spl0_34 ),
inference(avatar_component_clause,[],[f1187]) ).
fof(f1189,plain,
( ~ spl0_34
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_17 ),
inference(avatar_split_clause,[],[f1174,f297,f267,f264,f261,f1187]) ).
fof(f1207,definition,
( spl0_35
<=> sk3 = cons(hd(sk3),nil) ),
introduced(definition,[new_symbols(definition,[spl0_35])],[avatar_definition]) ).
fof(f1208,plain,
( sk3 = cons(hd(sk3),nil)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1207]) ).
fof(f1373,plain,
( sk3 = cons(hd(sk3),nil)
| ~ ssList(sk3)
| nil = sk3
| ~ spl0_29 ),
inference(superposition,[],[f107,f1143]) ).
fof(f1375,plain,
( sk3 = cons(hd(sk3),nil)
| nil = sk3
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f1373,f202]) ).
fof(f1377,plain,
( spl0_15
| spl0_35
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f1375,f1142,f1207,f284]) ).
fof(f1542,plain,
( ~ segmentP(sk3,sk3)
| spl0_34
| ~ spl0_35 ),
inference(superposition,[],[f1188,f1208]) ).
fof(f1609,plain,
( ~ spl0_16
| spl0_34
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f1542,f1207,f1187,f294]) ).
fof(f1645,plain,
( nil != sk3
| spl0_15 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f1675,plain,
( ! [X0] :
( ~ segmentP(X0,tl(sk3))
| ~ ssList(tl(sk3))
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ segmentP(sk3,X0) )
| spl0_28 ),
inference(resolution,[],[f1140,f164]) ).
fof(f1676,plain,
( ! [X0] :
( ~ segmentP(X0,tl(sk3))
| ~ ssList(tl(sk3))
| ~ ssList(X0)
| ~ segmentP(sk3,X0) )
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f1675,f202]) ).
fof(f1678,plain,
( ~ spl0_9
| spl0_31
| spl0_28 ),
inference(avatar_split_clause,[],[f1676,f1139,f1154,f264]) ).
fof(f1750,plain,
( ! [X0] :
( ~ segmentP(sk3,app(X0,tl(sk3)))
| ~ ssList(app(X0,tl(sk3)))
| ~ ssList(X0)
| ~ ssList(tl(sk3)) )
| ~ spl0_31 ),
inference(resolution,[],[f1155,f996]) ).
fof(f1757,plain,
( ! [X0] :
( ~ segmentP(sk3,app(X0,tl(sk3)))
| ~ ssList(X0)
| ~ ssList(tl(sk3)) )
| ~ spl0_31 ),
inference(forward_subsumption_resolution,[],[f1750,f85]) ).
fof(f1769,definition,
( spl0_70
<=> ! [X0] :
( ~ segmentP(sk3,app(X0,tl(sk3)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_70])],[avatar_definition]) ).
fof(f1770,plain,
( ! [X0] :
( ~ segmentP(sk3,app(X0,tl(sk3)))
| ~ ssList(X0) )
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1769]) ).
fof(f1771,plain,
( ~ spl0_9
| spl0_70
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f1757,f1154,f1769,f264]) ).
fof(f1858,plain,
( ~ segmentP(sk3,sk3)
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(sk3)
| nil = sk3
| ~ spl0_70 ),
inference(superposition,[],[f1770,f434]) ).
fof(f1896,plain,
( ~ ssList(cons(hd(sk3),nil))
| ~ ssList(sk3)
| nil = sk3
| ~ spl0_70 ),
inference(forward_subsumption_resolution,[],[f1858,f57]) ).
fof(f1905,plain,
( ~ ssList(cons(hd(sk3),nil))
| nil = sk3
| ~ spl0_70 ),
inference(forward_subsumption_resolution,[],[f1896,f202]) ).
fof(f1912,plain,
( ~ ssList(cons(hd(sk3),nil))
| spl0_15
| ~ spl0_70 ),
inference(forward_subsumption_resolution,[],[f1905,f1645]) ).
fof(f1917,plain,
( ~ spl0_8
| spl0_15
| ~ spl0_70 ),
inference(avatar_split_clause,[],[f1912,f1769,f284,f261]) ).
cnf(s5,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_8
| ~ spl0_9
| spl0_10
| ~ spl0_11
| ~ spl0_12 ),
inference(sat_conversion,[],[f275]) ).
cnf(s6,plain,
( ~ spl0_12
| spl0_13 ),
inference(sat_conversion,[],[f279]) ).
cnf(s8,plain,
spl0_12,
inference(sat_conversion,[],[f288]) ).
cnf(s9,plain,
( ~ spl0_13
| ~ spl0_16
| ~ spl0_17 ),
inference(sat_conversion,[],[f299]) ).
cnf(s13,plain,
spl0_16,
inference(sat_conversion,[],[f314]) ).
cnf(s16,plain,
( spl0_6
| spl0_15 ),
inference(sat_conversion,[],[f340]) ).
cnf(s17,plain,
( ~ spl0_13
| ~ spl0_15 ),
inference(sat_conversion,[],[f350]) ).
cnf(s19,plain,
( spl0_7
| spl0_15 ),
inference(sat_conversion,[],[f361]) ).
cnf(s20,plain,
( ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f364]) ).
cnf(s21,plain,
( spl0_9
| spl0_15 ),
inference(sat_conversion,[],[f367]) ).
cnf(s22,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f369]) ).
cnf(s31,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f1144]) ).
cnf(s35,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| spl0_17
| ~ spl0_34 ),
inference(sat_conversion,[],[f1189]) ).
cnf(s43,plain,
( spl0_15
| ~ spl0_29
| spl0_35 ),
inference(sat_conversion,[],[f1377]) ).
cnf(s71,plain,
( ~ spl0_16
| spl0_34
| ~ spl0_35 ),
inference(sat_conversion,[],[f1609]) ).
cnf(s85,plain,
( ~ spl0_9
| spl0_28
| spl0_31 ),
inference(sat_conversion,[],[f1678]) ).
cnf(s91,plain,
( ~ spl0_9
| ~ spl0_31
| spl0_70 ),
inference(sat_conversion,[],[f1771]) ).
cnf(s95,plain,
( ~ spl0_8
| spl0_15
| ~ spl0_70 ),
inference(sat_conversion,[],[f1917]) ).
cnf(s98,plain,
( ~ spl0_13
| ~ spl0_17 ),
inference(rat,[],[s9,s13]) ).
cnf(s99,plain,
spl0_13,
inference(rat,[],[s6,s8]) ).
cnf(s100,plain,
~ spl0_15,
inference(rat,[],[s17,s99]) ).
cnf(s101,plain,
~ spl0_17,
inference(rat,[],[s98,s99]) ).
cnf(s102,plain,
spl0_9,
inference(rat,[],[s21,s100]) ).
cnf(s103,plain,
spl0_7,
inference(rat,[],[s19,s100]) ).
cnf(s104,plain,
spl0_6,
inference(rat,[],[s16,s100]) ).
cnf(s107,plain,
spl0_8,
inference(rat,[],[s20,s103]) ).
cnf(s108,plain,
~ spl0_70,
inference(rat,[],[s95,s100,s107]) ).
cnf(s109,plain,
spl0_11,
inference(rat,[],[s22,s102,s107]) ).
cnf(s110,plain,
~ spl0_31,
inference(rat,[],[s91,s102,s108]) ).
cnf(s111,plain,
spl0_28,
inference(rat,[],[s85,s102,s110]) ).
cnf(s112,plain,
spl0_10,
inference(rat,[],[s5,s8,s109,s102,s107,s103,s104]) ).
cnf(s114,plain,
~ spl0_34,
inference(rat,[],[s35,s107,s101,s102,s112]) ).
cnf(s117,plain,
spl0_29,
inference(rat,[],[s31,s111,s107,s102,s112]) ).
cnf(s118,plain,
~ spl0_35,
inference(rat,[],[s71,s13,s114]) ).
cnf(s122,plain,
$false,
inference(rat,[],[s43,s100,s118,s117]) ).
fof(f1918,plain,
$false,
inference(avatar_sat_refutation,[],[s122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC089-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 07:52:16 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 1.92/1.30 % (2457069)Input is clausal, will run a generic CNF schedule.
% 1.92/1.30 % (2457074)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=3050623968:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 1.92/1.30 % (2457078)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1673154353:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 1.92/1.30 % (2457075)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1317924054:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 1.92/1.30 % (2457077)lrs+10_1_sil=8000:sp=occurrence:random_seed=1384125766:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 1.92/1.30 % (2457076)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3260534513:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 1.92/1.30 % (2457079)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=263433527:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 1.92/1.30 % (2457080)dis-21_1_sil=8000:lcm=predicate:random_seed=2077466672:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 1.92/1.30 % (2457078)First to succeed.
% 1.92/1.30 % (2457078)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2457069"
% 1.92/1.30 % (2457077)Instruction limit reached!
% 1.92/1.30 % (2457077)------------------------------
% 1.92/1.30 % (2457077)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.92/1.30 % (2457077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/1.30 % (2457077)CaDiCaL version: 2.1.3
% 1.92/1.30 % (2457077)Termination reason: Instruction limit
% 1.92/1.30 % (2457077)Termination phase: Saturation
% 1.92/1.30 % (2457077)Time elapsed: 0.066 s
% 1.92/1.30 % (2457077)Peak memory usage: 89 MB
% 1.92/1.30 % (2457077)Instructions burned: 108 (million)
% 1.92/1.30 % (2457080)Instruction limit reached!
% 1.92/1.30 % (2457080)------------------------------
% 1.92/1.30 % (2457080)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.92/1.30 % (2457080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/1.30 % (2457080)CaDiCaL version: 2.1.3
% 1.92/1.30 % (2457080)Termination reason: Instruction limit
% 1.92/1.30 % (2457080)Termination phase: Saturation
% 1.92/1.30 % (2457080)Time elapsed: 0.062 s
% 1.92/1.30 % (2457080)Peak memory usage: 90 MB
% 1.92/1.30 % (2457080)Instructions burned: 118 (million)
% 1.92/1.30 % (2457079)Instruction limit reached!
% 1.92/1.30 % (2457079)------------------------------
% 1.92/1.30 % (2457079)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.92/1.30 % (2457079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/1.30 % (2457079)CaDiCaL version: 2.1.3
% 1.92/1.30 % (2457079)Termination reason: Instruction limit
% 1.92/1.30 % (2457079)Termination phase: Saturation
% 1.92/1.30 % (2457079)Time elapsed: 0.122 s
% 1.92/1.30 % (2457079)Peak memory usage: 90 MB
% 1.92/1.30 % (2457079)Instructions burned: 180 (million)
% 1.92/1.30 % (2457089)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3744539731:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 1.92/1.30 % (2457088)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=1318053394:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 1.92/1.30 % (2457090)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3224573297:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 1.92/1.30 % (2457088)Instruction limit reached!
% 1.92/1.30 % (2457088)------------------------------
% 1.92/1.30 % (2457088)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.92/1.30 % (2457088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.92/1.30 % (2457088)CaDiCaL version: 2.1.3
% 1.92/1.30 % (2457088)Termination reason: Instruction limit
% 1.92/1.30 % (2457088)Termination phase: Saturation
% 1.92/1.30 % (2457088)Time elapsed: 0.091 s
% 1.92/1.30 % (2457088)Peak memory usage: 90 MB
% 1.92/1.30 % (2457088)Instructions burned: 143 (million)
% 1.92/1.30 % (2457078)Refutation found. Thanks to Tanya!
% 1.92/1.30 % SZS status Unsatisfiable for theBenchmark
% 1.92/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.49 % (2457078)------------------------------
% 3.77/1.49 % (2457078)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.49 % (2457078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.49 % (2457078)CaDiCaL version: 2.1.3
% 3.77/1.49 % (2457078)Termination reason: Refutation
% 3.77/1.49 % (2457078)Time elapsed: 0.063 s
% 3.77/1.49 % (2457078)Peak memory usage: 90 MB
% 3.77/1.49 % (2457078)Instructions burned: 102 (million)
% 3.77/1.49 % (2457078)------------------------------
% 3.77/1.49 % (2457078)------------------------------
% 3.77/1.49 % (2457069)Success in time 0.459 s
% 3.77/1.49 % Vampire exiting
%------------------------------------------------------------------------------