%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC079+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 : n007.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 01:02:20 PM UTC 2026
% Result : Theorem 3.13s 1.35s
% Output : Refutation 4.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 25
% Syntax : Number of formulae : 165 ( 23 unt; 11 def)
% Number of atoms : 620 ( 96 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 799 ( 344 ~; 352 |; 59 &)
% ( 15 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 110 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
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(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ? [X5] :
( ssList(X5)
& X2 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X3) = X6
& neq(nil,X3) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ? [X5] :
( ssList(X5)
& X2 != X5
& ? [X6] :
( ssItem(X6)
& cons(X6,nil) = X5
& hd(X3) = X6
& neq(nil,X3) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f126,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f126]) ).
fof(f129,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f129]) ).
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(f172,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f175,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f192,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ! [X5] :
( ~ ssList(X5)
| X2 = X5
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X3) != X6
| ~ neq(nil,X3) ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ! [X5] :
( ~ ssList(X5)
| X2 = X5
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(X3) != X6
| ~ neq(nil,X3) ) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f246,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f103]) ).
fof(f247,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(app(X4,X1),X5) = X0 ) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f246]) ).
fof(f248,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK13(X0,X1))
& ssList(sK14(X0,X1))
& app(app(sK13(X0,X1),X1),sK14(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f247]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( ( neq(sK54,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4) )
& ! [X5] :
( ~ ssList(X5)
| sK55 = X5
| ! [X6] :
( ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(sK56) != X6
| ~ neq(nil,sK56) ) ) )
| ( neq(sK54,nil)
& ~ neq(sK56,nil) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f318,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,[],[f248]) ).
fof(f387,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f388,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f390,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f397,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f399,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f401,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f403,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f440,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f172]) ).
fof(f442,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f175]) ).
fof(f474,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f499,plain,
ssList(sK56),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
! [X6,X5] :
( ~ ssList(X5)
| sK55 = X5
| ~ ssItem(X6)
| cons(X6,nil) != X5
| hd(sK56) != X6
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK54,X4)
| ~ segmentP(sK53,X4)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( neq(sK54,nil)
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f513,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,[],[f318]) ).
fof(f537,plain,
! [X6] :
( ~ ssList(cons(X6,nil))
| cons(X6,nil) = sK55
| ~ ssItem(X6)
| hd(sK56) != X6
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f500]) ).
fof(f538,plain,
( ~ ssList(cons(hd(sK56),nil))
| sK55 = cons(hd(sK56),nil)
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ neq(sK56,nil) ),
inference(equality_resolution,[],[f537]) ).
fof(f539,plain,
neq(sK54,nil),
inference(duplicate_literal_removal,[],[f505]) ).
fof(f548,definition,
( spl57_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f549,plain,
( neq(sK56,nil)
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f552,definition,
( spl57_2
<=> neq(nil,sK56) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f554,plain,
( ~ neq(nil,sK56)
| spl57_2 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f556,definition,
( spl57_3
<=> ssItem(hd(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f557,plain,
( ssItem(hd(sK56))
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f558,plain,
( ~ ssItem(hd(sK56))
| spl57_3 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f560,definition,
( spl57_4
<=> sK55 = cons(hd(sK56),nil) ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f562,plain,
( sK55 = cons(hd(sK56),nil)
| ~ spl57_4 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f564,definition,
( spl57_5
<=> ssList(cons(hd(sK56),nil)) ),
introduced(definition,[new_symbols(definition,[spl57_5])],[avatar_definition]) ).
fof(f566,plain,
( ~ ssList(cons(hd(sK56),nil))
| spl57_5 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f567,plain,
( ~ spl57_1
| ~ spl57_2
| ~ spl57_3
| spl57_4
| ~ spl57_5 ),
inference(avatar_split_clause,[],[f538,f564,f560,f556,f552,f548]) ).
fof(f569,definition,
( spl57_6
<=> neq(sK54,nil) ),
introduced(definition,[new_symbols(definition,[spl57_6])],[avatar_definition]) ).
fof(f571,plain,
( neq(sK54,nil)
| ~ spl57_6 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f574,definition,
( spl57_7
<=> ! [X4] :
( ~ ssList(X4)
| ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil) ) ),
introduced(definition,[new_symbols(definition,[spl57_7])],[avatar_definition]) ).
fof(f575,plain,
( ! [X4] :
( ~ ssList(X4)
| ~ segmentP(sK53,X4)
| ~ segmentP(sK54,X4)
| ~ neq(X4,nil) )
| ~ spl57_7 ),
inference(avatar_component_clause,[],[f574]) ).
fof(f576,plain,
( ~ spl57_1
| spl57_7 ),
inference(avatar_split_clause,[],[f502,f574,f548]) ).
fof(f579,plain,
spl57_6,
inference(avatar_split_clause,[],[f539,f569]) ).
fof(f581,definition,
( spl57_8
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl57_8])],[avatar_definition]) ).
fof(f582,plain,
( ssList(nil)
| ~ spl57_8 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f614,plain,
spl57_8,
inference(avatar_split_clause,[],[f389,f581]) ).
fof(f617,plain,
( neq(sK56,nil)
| ~ spl57_6 ),
inference(forward_demodulation,[],[f571,f507]) ).
fof(f620,plain,
( ! [X4] :
( ~ segmentP(sK56,X4)
| ~ ssList(X4)
| ~ segmentP(sK53,X4)
| ~ neq(X4,nil) )
| ~ spl57_7 ),
inference(forward_demodulation,[],[f575,f507]) ).
fof(f621,plain,
( spl57_1
| ~ spl57_6 ),
inference(avatar_split_clause,[],[f617,f569,f548]) ).
fof(f622,plain,
( ~ ssList(sK56)
| ~ ssList(sK56)
| ~ segmentP(sK53,sK56)
| ~ neq(sK56,nil)
| ~ spl57_7 ),
inference(resolution,[],[f440,f620]) ).
fof(f623,plain,
( ~ ssList(sK56)
| ~ segmentP(sK53,sK56)
| ~ neq(sK56,nil)
| ~ spl57_7 ),
inference(duplicate_literal_removal,[],[f622]) ).
fof(f624,plain,
( ~ segmentP(sK53,sK56)
| ~ neq(sK56,nil)
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f623,f499]) ).
fof(f625,plain,
( ~ segmentP(sK53,sK56)
| ~ spl57_1
| ~ spl57_7 ),
inference(forward_subsumption_resolution,[],[f624,f549]) ).
fof(f634,definition,
( spl57_16
<=> segmentP(sK53,nil) ),
introduced(definition,[new_symbols(definition,[spl57_16])],[avatar_definition]) ).
fof(f636,plain,
( ~ segmentP(sK53,nil)
| spl57_16 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f675,definition,
( spl57_19
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_19])],[avatar_definition]) ).
fof(f676,plain,
( nil != sK56
| spl57_19 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f677,plain,
( nil = sK56
| ~ spl57_19 ),
inference(avatar_component_clause,[],[f675]) ).
fof(f679,plain,
( nil = sK56
| ~ ssList(sK56)
| ~ ssList(nil)
| spl57_2 ),
inference(resolution,[],[f387,f554]) ).
fof(f686,plain,
( nil = sK56
| ~ ssList(nil)
| spl57_2 ),
inference(forward_subsumption_resolution,[],[f679,f499]) ).
fof(f687,plain,
( nil = sK56
| spl57_2
| ~ spl57_8 ),
inference(forward_subsumption_resolution,[],[f686,f582]) ).
fof(f688,plain,
( spl57_19
| spl57_2
| ~ spl57_8 ),
inference(avatar_split_clause,[],[f687,f581,f552,f675]) ).
fof(f690,plain,
( ~ segmentP(sK53,nil)
| ~ spl57_1
| ~ spl57_7
| ~ spl57_19 ),
inference(superposition,[],[f625,f677]) ).
fof(f697,plain,
( ~ spl57_16
| ~ spl57_1
| ~ spl57_7
| ~ spl57_19 ),
inference(avatar_split_clause,[],[f690,f675,f574,f548,f634]) ).
fof(f700,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_3 ),
inference(resolution,[],[f558,f397]) ).
fof(f701,plain,
( nil = sK56
| spl57_3 ),
inference(forward_subsumption_resolution,[],[f700,f499]) ).
fof(f702,plain,
( spl57_19
| spl57_3 ),
inference(avatar_split_clause,[],[f701,f556,f675]) ).
fof(f703,plain,
( ~ ssList(sK53)
| spl57_16 ),
inference(resolution,[],[f636,f442]) ).
fof(f704,plain,
( $false
| spl57_16 ),
inference(forward_subsumption_resolution,[],[f703,f496]) ).
fof(f705,plain,
spl57_16,
inference(avatar_contradiction_clause,[],[f704]) ).
fof(f706,plain,
( ~ ssItem(hd(sK56))
| ~ ssList(nil)
| spl57_5 ),
inference(resolution,[],[f566,f388]) ).
fof(f707,plain,
( ~ ssList(nil)
| ~ spl57_3
| spl57_5 ),
inference(forward_subsumption_resolution,[],[f706,f557]) ).
fof(f708,plain,
( $false
| ~ spl57_3
| spl57_5
| ~ spl57_8 ),
inference(forward_subsumption_resolution,[],[f707,f582]) ).
fof(f709,plain,
( ~ spl57_3
| spl57_5
| ~ spl57_8 ),
inference(avatar_contradiction_clause,[],[f708]) ).
fof(f710,plain,
( sK53 = cons(hd(sK56),nil)
| ~ spl57_4 ),
inference(forward_demodulation,[],[f562,f506]) ).
fof(f726,plain,
( nil != sK53
| ~ ssItem(hd(sK56))
| ~ ssList(nil)
| ~ spl57_4 ),
inference(superposition,[],[f390,f710]) ).
fof(f728,plain,
( nil != sK53
| ~ ssList(nil)
| ~ spl57_3
| ~ spl57_4 ),
inference(forward_subsumption_resolution,[],[f726,f557]) ).
fof(f739,plain,
( nil != sK53
| ~ spl57_3
| ~ spl57_4
| ~ spl57_8 ),
inference(forward_subsumption_resolution,[],[f728,f582]) ).
fof(f902,plain,
( ! [X0] :
( cons(hd(sK56),X0) = app(sK53,X0)
| ~ ssItem(hd(sK56))
| ~ ssList(X0) )
| ~ spl57_4 ),
inference(superposition,[],[f477,f710]) ).
fof(f911,plain,
( ! [X0] :
( cons(hd(sK56),X0) = app(sK53,X0)
| ~ ssList(X0) )
| ~ spl57_3
| ~ spl57_4 ),
inference(forward_subsumption_resolution,[],[f902,f557]) ).
fof(f917,plain,
( sK56 = app(sK53,tl(sK56))
| nil = sK56
| ~ ssList(sK56)
| ~ ssList(tl(sK56))
| ~ spl57_3
| ~ spl57_4 ),
inference(superposition,[],[f474,f911]) ).
fof(f954,plain,
( sK56 = app(sK53,tl(sK56))
| nil = sK56
| ~ ssList(sK56)
| ~ spl57_3
| ~ spl57_4 ),
inference(forward_subsumption_resolution,[],[f917,f399]) ).
fof(f968,plain,
( sK56 = app(sK53,tl(sK56))
| ~ ssList(sK56)
| ~ spl57_3
| ~ spl57_4
| spl57_19 ),
inference(forward_subsumption_resolution,[],[f954,f676]) ).
fof(f979,plain,
( sK56 = app(sK53,tl(sK56))
| ~ spl57_3
| ~ spl57_4
| spl57_19 ),
inference(forward_subsumption_resolution,[],[f968,f499]) ).
fof(f1126,definition,
( spl57_25
<=> ssList(tl(sK56)) ),
introduced(definition,[new_symbols(definition,[spl57_25])],[avatar_definition]) ).
fof(f1127,plain,
( ssList(tl(sK56))
| ~ spl57_25 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f1128,plain,
( ~ ssList(tl(sK56))
| spl57_25 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f1157,plain,
( nil = sK56
| ~ ssList(sK56)
| spl57_25 ),
inference(resolution,[],[f1128,f399]) ).
fof(f1158,plain,
( ~ ssList(sK56)
| spl57_19
| spl57_25 ),
inference(forward_subsumption_resolution,[],[f1157,f676]) ).
fof(f1159,plain,
( $false
| spl57_19
| spl57_25 ),
inference(forward_subsumption_resolution,[],[f1158,f499]) ).
fof(f1160,plain,
( spl57_19
| spl57_25 ),
inference(avatar_contradiction_clause,[],[f1159]) ).
fof(f1911,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(superposition,[],[f513,f403]) ).
fof(f1920,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f1911]) ).
fof(f1930,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f1920,f401]) ).
fof(f1937,plain,
( ! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl57_8 ),
inference(forward_subsumption_resolution,[],[f1930,f582]) ).
fof(f3060,plain,
( segmentP(sK56,sK53)
| ~ ssList(sK53)
| ~ ssList(tl(sK56))
| ~ spl57_3
| ~ spl57_4
| ~ spl57_8
| spl57_19 ),
inference(superposition,[],[f1937,f979]) ).
fof(f3074,plain,
( segmentP(sK56,sK53)
| ~ ssList(tl(sK56))
| ~ spl57_3
| ~ spl57_4
| ~ spl57_8
| spl57_19 ),
inference(forward_subsumption_resolution,[],[f3060,f496]) ).
fof(f3084,plain,
( segmentP(sK56,sK53)
| ~ spl57_3
| ~ spl57_4
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(forward_subsumption_resolution,[],[f3074,f1127]) ).
fof(f3113,plain,
( ~ ssList(sK53)
| ~ segmentP(sK53,sK53)
| ~ neq(sK53,nil)
| ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(resolution,[],[f3084,f620]) ).
fof(f3120,plain,
( ~ ssList(sK53)
| ~ neq(sK53,nil)
| ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(forward_subsumption_resolution,[],[f3113,f440]) ).
fof(f3124,plain,
( ~ neq(sK53,nil)
| ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(forward_subsumption_resolution,[],[f3120,f496]) ).
fof(f3156,plain,
( nil = sK53
| ~ ssList(nil)
| ~ ssList(sK53)
| ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(resolution,[],[f3124,f387]) ).
fof(f3158,plain,
( ~ ssList(nil)
| ~ ssList(sK53)
| ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(forward_subsumption_resolution,[],[f3156,f739]) ).
fof(f3159,plain,
( ~ ssList(sK53)
| ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(forward_subsumption_resolution,[],[f3158,f582]) ).
fof(f3160,plain,
( $false
| ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(forward_subsumption_resolution,[],[f3159,f496]) ).
fof(f3161,plain,
( ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(avatar_contradiction_clause,[],[f3160]) ).
cnf(s1,plain,
( ~ spl57_1
| ~ spl57_2
| ~ spl57_3
| spl57_4
| ~ spl57_5 ),
inference(sat_conversion,[],[f567]) ).
cnf(s3,plain,
( ~ spl57_1
| spl57_7 ),
inference(sat_conversion,[],[f576]) ).
cnf(s6,plain,
spl57_6,
inference(sat_conversion,[],[f579]) ).
cnf(s15,plain,
spl57_8,
inference(sat_conversion,[],[f614]) ).
cnf(s17,plain,
( spl57_1
| ~ spl57_6 ),
inference(sat_conversion,[],[f621]) ).
cnf(s20,plain,
( spl57_2
| ~ spl57_8
| spl57_19 ),
inference(sat_conversion,[],[f688]) ).
cnf(s22,plain,
( ~ spl57_1
| ~ spl57_7
| ~ spl57_16
| ~ spl57_19 ),
inference(sat_conversion,[],[f697]) ).
cnf(s25,plain,
( spl57_3
| spl57_19 ),
inference(sat_conversion,[],[f702]) ).
cnf(s26,plain,
spl57_16,
inference(sat_conversion,[],[f705]) ).
cnf(s27,plain,
( ~ spl57_3
| spl57_5
| ~ spl57_8 ),
inference(sat_conversion,[],[f709]) ).
cnf(s37,plain,
( spl57_19
| spl57_25 ),
inference(sat_conversion,[],[f1160]) ).
cnf(s110,plain,
( ~ spl57_3
| ~ spl57_4
| ~ spl57_7
| ~ spl57_8
| spl57_19
| ~ spl57_25 ),
inference(sat_conversion,[],[f3161]) ).
cnf(s118,plain,
( ~ spl57_1
| ~ spl57_7
| ~ spl57_19 ),
inference(rat,[],[s22,s26]) ).
cnf(s124,plain,
spl57_1,
inference(rat,[],[s17,s6]) ).
cnf(s125,plain,
spl57_7,
inference(rat,[],[s3,s124]) ).
cnf(s126,plain,
~ spl57_19,
inference(rat,[],[s118,s124,s125]) ).
cnf(s128,plain,
spl57_25,
inference(rat,[],[s37,s126]) ).
cnf(s129,plain,
spl57_3,
inference(rat,[],[s25,s126]) ).
cnf(s130,plain,
spl57_2,
inference(rat,[],[s20,s15,s126]) ).
cnf(s131,plain,
~ spl57_4,
inference(rat,[],[s110,s128,s126,s15,s125,s129]) ).
cnf(s133,plain,
spl57_5,
inference(rat,[],[s27,s15,s129]) ).
cnf(s134,plain,
$false,
inference(rat,[],[s1,s133,s131,s129,s130,s124]) ).
fof(f3162,plain,
$false,
inference(avatar_sat_refutation,[],[s134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC079+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 07:43:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.13/1.35 % (2229453)Detected formulas, will run a generic FOF schedule.
% 3.13/1.35 % (2229464)dis-21_1_sil=8000:lcm=predicate:random_seed=289672589: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)
% 3.13/1.35 % (2229462)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1302099618:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.13/1.35 % (2229461)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1647881483:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.13/1.35 % (2229459)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=1794683179:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.13/1.35 % (2229460)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=3531601469:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.13/1.35 % (2229458)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=374938844:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.13/1.35 % (2229463)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3490988614:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.13/1.35 % (2229464)Instruction limit reached!
% 3.13/1.35 % (2229464)------------------------------
% 3.13/1.35 % (2229464)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2229464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2229464)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2229464)Termination reason: Instruction limit
% 3.13/1.35 % (2229464)Termination phase: Saturation
% 3.13/1.35 % (2229464)Time elapsed: 0.040 s
% 3.13/1.35 % (2229464)Peak memory usage: 90 MB
% 3.13/1.35 % (2229464)Instructions burned: 130 (million)
% 3.13/1.35 % (2229461)Instruction limit reached!
% 3.13/1.35 % (2229461)------------------------------
% 3.13/1.35 % (2229461)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2229461)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2229461)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2229461)Termination reason: Instruction limit
% 3.13/1.35 % (2229461)Termination phase: Saturation
% 3.13/1.35 % (2229461)Time elapsed: 0.061 s
% 3.13/1.35 % (2229461)Peak memory usage: 89 MB
% 3.13/1.35 % (2229461)Instructions burned: 110 (million)
% 3.13/1.35 % (2229463)First to succeed.
% 3.13/1.35 % (2229463)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2229453"
% 3.13/1.35 % (2229462)Instruction limit reached!
% 3.13/1.35 % (2229462)------------------------------
% 3.13/1.35 % (2229462)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2229462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2229462)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2229462)Termination reason: Instruction limit
% 3.13/1.35 % (2229462)Termination phase: Saturation
% 3.13/1.35 % (2229462)Time elapsed: 0.070 s
% 3.13/1.35 % (2229462)Peak memory usage: 88 MB
% 3.13/1.35 % (2229462)Instructions burned: 120 (million)
% 3.13/1.35 % (2229472)lrs+10_1_sil=8000:sp=occurrence:random_seed=301901160:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.13/1.35 % (2229472)Instruction limit reached!
% 3.13/1.35 % (2229472)------------------------------
% 3.13/1.35 % (2229472)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2229472)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2229472)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2229472)Termination reason: Instruction limit
% 3.13/1.35 % (2229472)Termination phase: Saturation
% 3.13/1.35 % (2229472)Time elapsed: 0.093 s
% 3.13/1.35 % (2229472)Peak memory usage: 93 MB
% 3.13/1.35 % (2229472)Instructions burned: 287 (million)
% 3.13/1.35 % (2229473)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2500966662:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.13/1.35 % (2229474)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4187443844:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.13/1.35 % (2229473)Instruction limit reached!
% 3.13/1.35 % (2229473)------------------------------
% 3.13/1.35 % (2229473)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.13/1.35 % (2229473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.13/1.35 % (2229473)CaDiCaL version: 2.1.3
% 3.13/1.35 % (2229473)Termination reason: Instruction limit
% 3.13/1.35 % (2229473)Termination phase: Saturation
% 3.13/1.35 % (2229473)Time elapsed: 0.076 s
% 3.13/1.35 % (2229473)Peak memory usage: 91 MB
% 3.13/1.35 % (2229473)Instructions burned: 158 (million)
% 3.13/1.35 % (2229463)Refutation found. Thanks to Tanya!
% 3.13/1.35 % SZS status Theorem for theBenchmark
% 3.13/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.03/1.45 % (2229463)------------------------------
% 4.03/1.45 % (2229463)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.03/1.45 % (2229463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.03/1.45 % (2229463)CaDiCaL version: 2.1.3
% 4.03/1.45 % (2229463)Termination reason: Refutation
% 4.03/1.45 % (2229463)Time elapsed: 0.069 s
% 4.03/1.45 % (2229463)Peak memory usage: 91 MB
% 4.03/1.45 % (2229463)Instructions burned: 99 (million)
% 4.03/1.45 % (2229463)------------------------------
% 4.03/1.45 % (2229463)------------------------------
% 4.03/1.45 % (2229453)Success in time 0.499 s
% 4.03/1.45 % Vampire exiting
%------------------------------------------------------------------------------