%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC073-1 : 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 01:02:19 PM UTC 2026
% Result : Unsatisfiable 3.10s 1.34s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 40
% Syntax : Number of formulae : 167 ( 22 unt; 15 def)
% Number of atoms : 509 ( 75 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 665 ( 323 ~; 327 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 16 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 91 ( 0 sgn 91 !; 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(f100,axiom,
! [X0,X1] :
( cons(X0,X1) != X1
| ~ ssItem(X0)
| ~ ssList(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause99) ).
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,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk2,X0)
| ~ segmentP(sk1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
( nil = sk3
| nil != sk4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
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,
! [X0] :
( ~ neq(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(definition_unfolding,[],[f206,f204,f205]) ).
fof(f214,plain,
( nil != sk4
| nil != sk3 ),
inference(definition_unfolding,[],[f208,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(f221,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(f224,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f118]) ).
fof(f231,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f224]) ).
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(f281,definition,
( spl0_14
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
fof(f282,plain,
( nil != sk3
| spl0_14 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f284,definition,
( spl0_15
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
fof(f285,plain,
( nil != sk4
| spl0_15 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f286,plain,
( ~ spl0_14
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f214,f284,f281]) ).
fof(f287,plain,
( nil = sk3
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f288,plain,
( ~ spl0_15
| spl0_14 ),
inference(avatar_split_clause,[],[f207,f281,f284]) ).
fof(f306,plain,
( ~ ssList(sk4)
| ~ ssList(nil)
| nil = sk4
| spl0_12 ),
inference(resolution,[],[f102,f274]) ).
fof(f307,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(resolution,[],[f102,f213]) ).
fof(f312,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(duplicate_literal_removal,[],[f307]) ).
fof(f313,plain,
! [X0] :
( ~ segmentP(sk4,X0)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk3,X0) ),
inference(forward_subsumption_resolution,[],[f312,f8]) ).
fof(f314,plain,
( ~ ssList(nil)
| nil = sk4
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f306,f203]) ).
fof(f315,plain,
( nil = sk4
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f314,f8]) ).
fof(f316,plain,
( $false
| spl0_12
| spl0_15 ),
inference(forward_subsumption_resolution,[],[f315,f285]) ).
fof(f317,plain,
( spl0_12
| spl0_15 ),
inference(avatar_contradiction_clause,[],[f316]) ).
fof(f318,plain,
( ~ ssList(nil)
| ~ ssList(sk3)
| nil = sk3
| spl0_6 ),
inference(resolution,[],[f256,f102]) ).
fof(f319,plain,
( ~ ssList(sk3)
| nil = sk3
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f318,f8]) ).
fof(f320,plain,
( nil = sk3
| spl0_6 ),
inference(forward_subsumption_resolution,[],[f319,f202]) ).
fof(f321,plain,
( spl0_14
| spl0_6 ),
inference(avatar_split_clause,[],[f320,f255,f281]) ).
fof(f331,plain,
( neq(nil,nil)
| ~ spl0_13
| ~ spl0_14 ),
inference(superposition,[],[f278,f287]) ).
fof(f369,plain,
( ~ ssList(nil)
| ~ spl0_13
| ~ spl0_14 ),
inference(resolution,[],[f331,f231]) ).
fof(f370,plain,
( $false
| ~ spl0_13
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[],[f369,f8]) ).
fof(f371,plain,
( ~ spl0_13
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[],[f370]) ).
fof(f380,plain,
( ~ ssList(sk3)
| nil = sk3
| spl0_7 ),
inference(resolution,[],[f259,f76]) ).
fof(f381,plain,
( nil = sk3
| spl0_7 ),
inference(forward_subsumption_resolution,[],[f380,f202]) ).
fof(f382,plain,
( spl0_14
| spl0_7 ),
inference(avatar_split_clause,[],[f381,f258,f281]) ).
fof(f383,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| spl0_8 ),
inference(resolution,[],[f262,f86]) ).
fof(f384,plain,
( ~ ssItem(hd(sk3))
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f383,f8]) ).
fof(f385,plain,
( ~ spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f384,f261,f258]) ).
fof(f386,plain,
( ~ ssList(sk3)
| nil = sk3
| spl0_9 ),
inference(resolution,[],[f265,f75]) ).
fof(f387,plain,
( nil = sk3
| spl0_9 ),
inference(forward_subsumption_resolution,[],[f386,f202]) ).
fof(f388,plain,
( $false
| spl0_9
| spl0_14 ),
inference(forward_subsumption_resolution,[],[f387,f282]) ).
fof(f389,plain,
( spl0_9
| spl0_14 ),
inference(avatar_contradiction_clause,[],[f388]) ).
fof(f390,plain,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| spl0_11 ),
inference(resolution,[],[f271,f85]) ).
fof(f391,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_11 ),
inference(avatar_split_clause,[],[f390,f270,f264,f261]) ).
fof(f405,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(f417,plain,
! [X0] :
( app(cons(hd(X0),nil),tl(X0)) = X0
| ~ ssList(X0)
| nil = X0
| ~ ssItem(hd(X0)) ),
inference(forward_subsumption_resolution,[],[f405,f75]) ).
fof(f419,plain,
! [X0] :
( app(cons(hd(X0),nil),tl(X0)) = X0
| ~ ssList(X0)
| nil = X0 ),
inference(forward_subsumption_resolution,[],[f417,f76]) ).
fof(f429,plain,
( ! [X0] :
( ~ segmentP(app(tl(sk3),cons(hd(sk3),nil)),X0)
| nil = X0
| ~ ssList(X0)
| ~ segmentP(sk3,X0) )
| ~ spl0_10 ),
inference(superposition,[],[f313,f268]) ).
fof(f475,definition,
( spl0_22
<=> ! [X1] : ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f476,plain,
( ! [X1] : ~ ssList(X1)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f481,plain,
( $false
| ~ spl0_22 ),
inference(resolution,[],[f476,f8]) ).
fof(f492,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f481]) ).
fof(f930,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,[],[f221,f161]) ).
fof(f931,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,[],[f930,f161]) ).
fof(f946,plain,
! [X0,X1] :
( segmentP(app(X1,X0),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f931,f73]) ).
fof(f947,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(superposition,[],[f931,f74]) ).
fof(f949,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f947]) ).
fof(f950,plain,
! [X0,X1] :
( segmentP(app(X1,X0),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X0))
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f946]) ).
fof(f959,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f949,f8]) ).
fof(f960,plain,
! [X0,X1] :
( segmentP(app(X1,X0),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f950,f8]) ).
fof(f965,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f959,f85]) ).
fof(f966,plain,
! [X0,X1] :
( segmentP(app(X1,X0),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f960,f85]) ).
fof(f1128,plain,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| nil = cons(hd(sk3),nil)
| ~ ssList(cons(hd(sk3),nil))
| ~ segmentP(sk3,cons(hd(sk3),nil))
| ~ spl0_10 ),
inference(resolution,[],[f966,f429]) ).
fof(f1143,plain,
( ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| nil = cons(hd(sk3),nil)
| ~ segmentP(sk3,cons(hd(sk3),nil))
| ~ spl0_10 ),
inference(duplicate_literal_removal,[],[f1128]) ).
fof(f1150,definition,
( spl0_28
<=> segmentP(sk3,cons(hd(sk3),nil)) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
fof(f1151,plain,
( ~ segmentP(sk3,cons(hd(sk3),nil))
| spl0_28 ),
inference(avatar_component_clause,[],[f1150]) ).
fof(f1153,definition,
( spl0_29
<=> nil = cons(hd(sk3),nil) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
fof(f1154,plain,
( nil = cons(hd(sk3),nil)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f1155,plain,
( ~ spl0_28
| spl0_29
| ~ spl0_8
| ~ spl0_9
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f1143,f267,f264,f261,f1153,f1150]) ).
fof(f1239,definition,
( spl0_32
<=> ! [X0] :
( ~ segmentP(X0,cons(hd(sk3),nil))
| ~ segmentP(sk3,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_32])],[avatar_definition]) ).
fof(f1240,plain,
( ! [X0] :
( ~ segmentP(X0,cons(hd(sk3),nil))
| ~ segmentP(sk3,X0)
| ~ ssList(X0) )
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f1261,plain,
( ! [X0] :
( app(nil,X0) = cons(hd(sk3),X0)
| ~ ssList(X0)
| ~ ssItem(hd(sk3)) )
| ~ spl0_29 ),
inference(superposition,[],[f126,f1154]) ).
fof(f1290,plain,
( ! [X0] :
( cons(hd(sk3),X0) = X0
| ~ ssList(X0)
| ~ ssItem(hd(sk3)) )
| ~ spl0_29 ),
inference(forward_subsumption_demodulation,[],[f1261,f74]) ).
fof(f1314,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ ssItem(hd(sk3)) )
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f1290,f100]) ).
fof(f1323,plain,
( ~ spl0_7
| spl0_22
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f1314,f1153,f475,f258]) ).
fof(f1345,plain,
( ! [X0] :
( ~ segmentP(X0,cons(hd(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(X0)
| ~ ssList(sk3)
| ~ segmentP(sk3,X0) )
| spl0_28 ),
inference(resolution,[],[f1151,f164]) ).
fof(f1346,plain,
( ! [X0] :
( ~ segmentP(X0,cons(hd(sk3),nil))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(X0)
| ~ segmentP(sk3,X0) )
| spl0_28 ),
inference(forward_subsumption_resolution,[],[f1345,f202]) ).
fof(f1348,plain,
( ~ spl0_8
| spl0_32
| spl0_28 ),
inference(avatar_split_clause,[],[f1346,f1150,f1239,f261]) ).
fof(f1794,plain,
( ! [X0] :
( ~ segmentP(sk3,app(cons(hd(sk3),nil),X0))
| ~ ssList(app(cons(hd(sk3),nil),X0))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(X0) )
| ~ spl0_32 ),
inference(resolution,[],[f1240,f965]) ).
fof(f1811,plain,
( ! [X0] :
( ~ segmentP(sk3,app(cons(hd(sk3),nil),X0))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(X0) )
| ~ spl0_32 ),
inference(forward_subsumption_resolution,[],[f1794,f85]) ).
fof(f1825,definition,
( spl0_78
<=> ! [X0] :
( ~ segmentP(sk3,app(cons(hd(sk3),nil),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_78])],[avatar_definition]) ).
fof(f1826,plain,
( ! [X0] :
( ~ segmentP(sk3,app(cons(hd(sk3),nil),X0))
| ~ ssList(X0) )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1825]) ).
fof(f1827,plain,
( ~ spl0_8
| spl0_78
| ~ spl0_32 ),
inference(avatar_split_clause,[],[f1811,f1239,f1825,f261]) ).
fof(f1915,plain,
( ~ segmentP(sk3,sk3)
| ~ ssList(tl(sk3))
| ~ ssList(sk3)
| nil = sk3
| ~ spl0_78 ),
inference(superposition,[],[f1826,f419]) ).
fof(f1953,plain,
( ~ segmentP(sk3,sk3)
| ~ ssList(sk3)
| nil = sk3
| ~ spl0_78 ),
inference(forward_subsumption_resolution,[],[f1915,f75]) ).
fof(f1963,plain,
( ~ ssList(sk3)
| nil = sk3
| ~ spl0_78 ),
inference(forward_subsumption_resolution,[],[f1953,f57]) ).
fof(f1971,plain,
( nil = sk3
| ~ spl0_78 ),
inference(forward_subsumption_resolution,[],[f1963,f202]) ).
fof(f1977,plain,
( $false
| spl0_14
| ~ spl0_78 ),
inference(forward_subsumption_resolution,[],[f1971,f282]) ).
fof(f1978,plain,
( spl0_14
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f1977]) ).
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(s7,plain,
( ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f286]) ).
cnf(s8,plain,
( spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f288]) ).
cnf(s12,plain,
( spl0_12
| spl0_15 ),
inference(sat_conversion,[],[f317]) ).
cnf(s13,plain,
( spl0_6
| spl0_14 ),
inference(sat_conversion,[],[f321]) ).
cnf(s18,plain,
( ~ spl0_13
| ~ spl0_14 ),
inference(sat_conversion,[],[f371]) ).
cnf(s20,plain,
( spl0_7
| spl0_14 ),
inference(sat_conversion,[],[f382]) ).
cnf(s21,plain,
( ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f385]) ).
cnf(s22,plain,
( spl0_9
| spl0_14 ),
inference(sat_conversion,[],[f389]) ).
cnf(s23,plain,
( ~ spl0_8
| ~ spl0_9
| spl0_11 ),
inference(sat_conversion,[],[f391]) ).
cnf(s28,plain,
~ spl0_22,
inference(sat_conversion,[],[f492]) ).
cnf(s32,plain,
( ~ spl0_8
| ~ spl0_9
| ~ spl0_10
| ~ spl0_28
| spl0_29 ),
inference(sat_conversion,[],[f1155]) ).
cnf(s46,plain,
( ~ spl0_7
| spl0_22
| ~ spl0_29 ),
inference(sat_conversion,[],[f1323]) ).
cnf(s49,plain,
( ~ spl0_8
| spl0_28
| spl0_32 ),
inference(sat_conversion,[],[f1348]) ).
cnf(s95,plain,
( ~ spl0_8
| ~ spl0_32
| spl0_78 ),
inference(sat_conversion,[],[f1827]) ).
cnf(s98,plain,
( spl0_14
| ~ spl0_78 ),
inference(sat_conversion,[],[f1978]) ).
cnf(s104,plain,
~ spl0_14,
inference(rat,[],[s12,s6,s7,s18]) ).
cnf(s105,plain,
~ spl0_78,
inference(rat,[],[s98,s104]) ).
cnf(s106,plain,
spl0_9,
inference(rat,[],[s22,s104]) ).
cnf(s107,plain,
spl0_7,
inference(rat,[],[s20,s104]) ).
cnf(s108,plain,
spl0_6,
inference(rat,[],[s13,s104]) ).
cnf(s109,plain,
~ spl0_15,
inference(rat,[],[s8,s104]) ).
cnf(s110,plain,
~ spl0_29,
inference(rat,[],[s46,s28,s107]) ).
cnf(s111,plain,
spl0_8,
inference(rat,[],[s21,s107]) ).
cnf(s112,plain,
spl0_12,
inference(rat,[],[s12,s109]) ).
cnf(s113,plain,
~ spl0_32,
inference(rat,[],[s95,s105,s111]) ).
cnf(s114,plain,
spl0_28,
inference(rat,[],[s49,s113,s111]) ).
cnf(s116,plain,
spl0_11,
inference(rat,[],[s23,s106,s111]) ).
cnf(s118,plain,
spl0_10,
inference(rat,[],[s5,s106,s116,s111,s107,s108,s112]) ).
cnf(s119,plain,
$false,
inference(rat,[],[s32,s110,s106,s111,s114,s118]) ).
fof(f1980,plain,
$false,
inference(avatar_sat_refutation,[],[s119]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC073-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 07:43:46 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.10/1.34 % (1613630)Input is clausal, will run a generic CNF schedule.
% 3.10/1.34 % (1613637)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=431559275:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.10/1.34 % (1613641)dis-21_1_sil=8000:lcm=predicate:random_seed=2989853727: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)
% 3.10/1.34 % (1613636)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3635797498:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.10/1.34 % (1613635)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=1557969668:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.10/1.34 % (1613638)lrs+10_1_sil=8000:sp=occurrence:random_seed=2689675161:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.10/1.34 % (1613640)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4161778125:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.10/1.34 % (1613639)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=167945864:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.10/1.34 % (1613639)First to succeed.
% 3.10/1.34 % (1613639)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1613630"
% 3.10/1.34 % (1613641)Instruction limit reached!
% 3.10/1.34 % (1613641)------------------------------
% 3.10/1.34 % (1613641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.34 % (1613641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.34 % (1613641)CaDiCaL version: 2.1.3
% 3.10/1.34 % (1613641)Termination reason: Instruction limit
% 3.10/1.34 % (1613641)Termination phase: Saturation
% 3.10/1.34 % (1613641)Time elapsed: 0.065 s
% 3.10/1.34 % (1613641)Peak memory usage: 90 MB
% 3.10/1.34 % (1613641)Instructions burned: 118 (million)
% 3.10/1.34 % (1613638)Instruction limit reached!
% 3.10/1.34 % (1613638)------------------------------
% 3.10/1.34 % (1613638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.34 % (1613638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.34 % (1613638)CaDiCaL version: 2.1.3
% 3.10/1.34 % (1613638)Termination reason: Instruction limit
% 3.10/1.34 % (1613638)Termination phase: Saturation
% 3.10/1.34 % (1613638)Time elapsed: 0.066 s
% 3.10/1.34 % (1613638)Peak memory usage: 89 MB
% 3.10/1.34 % (1613638)Instructions burned: 108 (million)
% 3.10/1.34 % (1613640)Instruction limit reached!
% 3.10/1.34 % (1613640)------------------------------
% 3.10/1.34 % (1613640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.34 % (1613640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.34 % (1613640)CaDiCaL version: 2.1.3
% 3.10/1.34 % (1613640)Termination reason: Instruction limit
% 3.10/1.34 % (1613640)Termination phase: Saturation
% 3.10/1.34 % (1613640)Time elapsed: 0.122 s
% 3.10/1.34 % (1613640)Peak memory usage: 90 MB
% 3.10/1.34 % (1613640)Instructions burned: 181 (million)
% 3.10/1.34 % (1613649)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=216803646:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.10/1.34 % (1613650)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=561022466: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)
% 3.10/1.34 % (1613651)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=900185327:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 3.10/1.34 % (1613639)Refutation found. Thanks to Tanya!
% 3.10/1.34 % SZS status Unsatisfiable for theBenchmark
% 3.10/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 4.11/1.54 % (1613639)------------------------------
% 4.11/1.54 % (1613639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.54 % (1613639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.54 % (1613639)CaDiCaL version: 2.1.3
% 4.11/1.54 % (1613639)Termination reason: Refutation
% 4.11/1.54 % (1613639)Time elapsed: 0.064 s
% 4.11/1.54 % (1613639)Peak memory usage: 90 MB
% 4.11/1.54 % (1613639)Instructions burned: 104 (million)
% 4.11/1.54 % (1613639)------------------------------
% 4.11/1.54 % (1613639)------------------------------
% 4.11/1.54 % (1613630)Success in time 0.494 s
% 4.11/1.54 % Vampire exiting
%------------------------------------------------------------------------------