%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC356+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 01:03:36 PM UTC 2026
% Result : Theorem 4.79s 1.44s
% Output : Refutation 6.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 14
% Syntax : Number of formulae : 118 ( 17 unt; 5 def)
% Number of atoms : 508 ( 75 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 692 ( 302 ~; 282 |; 72 &)
% ( 11 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 6 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 123 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X0,X1)
& segmentP(X1,X2) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| segmentP(X1,X0)
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| segmentP(X1,X0)
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ segmentP(X1,X0)
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X5,X4) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ segmentP(X1,X0)
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ! [X5] :
( ~ ssItem(X5)
| X4 = X5
| ~ memberP(X3,X5)
| ~ leq(X5,X4) )
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f126,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f130,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f133]) ).
fof(f135,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(f205,plain,
( sK7 = sK9
& sK6 = sK8
& neq(sK7,nil)
& ~ segmentP(sK7,sK6)
& ( ( sK8 = cons(sK10,nil)
& memberP(sK9,sK10)
& ! [X5] :
( ~ ssItem(X5)
| sK10 = X5
| ~ memberP(sK9,X5)
| ~ leq(X5,sK10) )
& ssItem(sK10) )
| ( nil = sK9
& nil = sK8 ) )
& ssList(sK9)
& ssList(sK8)
& ssList(sK7)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9),skolemize(X4,sK10)],[f99]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,cons(X1,X5)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f218]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK15(X0,X1))
& ssList(sK16(X0,X1))
& app(sK15(X0,X1),cons(X1,sK16(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X4,sK15(X0,X1)),skolemize(X5,sK16(X0,X1))],[f219]) ).
fof(f221,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f126]) ).
fof(f222,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,[],[f135]) ).
fof(f223,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,[],[f222]) ).
fof(f224,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK17(X0,X1))
& ssList(sK18(X0,X1))
& app(app(sK17(X0,X1),X1),sK18(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X4,sK17(X0,X1)),skolemize(X5,sK18(X0,X1))],[f223]) ).
fof(f259,plain,
ssList(sK6),
inference(cnf_transformation,[],[f205]) ).
fof(f260,plain,
ssList(sK7),
inference(cnf_transformation,[],[f205]) ).
fof(f263,plain,
( ssItem(sK10)
| nil = sK8 ),
inference(cnf_transformation,[],[f205]) ).
fof(f264,plain,
( ssItem(sK10)
| nil = sK9 ),
inference(cnf_transformation,[],[f205]) ).
fof(f267,plain,
( memberP(sK9,sK10)
| nil = sK8 ),
inference(cnf_transformation,[],[f205]) ).
fof(f268,plain,
( memberP(sK9,sK10)
| nil = sK9 ),
inference(cnf_transformation,[],[f205]) ).
fof(f269,plain,
( sK8 = cons(sK10,nil)
| nil = sK8 ),
inference(cnf_transformation,[],[f205]) ).
fof(f270,plain,
( sK8 = cons(sK10,nil)
| nil = sK9 ),
inference(cnf_transformation,[],[f205]) ).
fof(f271,plain,
~ segmentP(sK7,sK6),
inference(cnf_transformation,[],[f205]) ).
fof(f273,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f205]) ).
fof(f274,plain,
sK7 = sK9,
inference(cnf_transformation,[],[f205]) ).
fof(f279,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f280,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f304,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f313,plain,
! [X0,X1] :
( app(sK15(X0,X1),cons(X1,sK16(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f314,plain,
! [X0,X1] :
( ssList(sK16(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f315,plain,
! [X0,X1] :
( ssList(sK15(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f318,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f321,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f323,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f327,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,[],[f224]) ).
fof(f435,plain,
~ segmentP(sK9,sK8),
inference(definition_unfolding,[],[f271,f274,f273]) ).
fof(f436,plain,
ssList(sK9),
inference(definition_unfolding,[],[f260,f274]) ).
fof(f437,plain,
ssList(sK8),
inference(definition_unfolding,[],[f259,f273]) ).
fof(f445,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f318]) ).
fof(f446,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f327]) ).
fof(f467,definition,
( spl47_1
<=> nil = sK8 ),
introduced(definition,[new_symbols(definition,[spl47_1])],[avatar_definition]) ).
fof(f469,plain,
( nil = sK8
| ~ spl47_1 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f471,definition,
( spl47_2
<=> ssItem(sK10) ),
introduced(definition,[new_symbols(definition,[spl47_2])],[avatar_definition]) ).
fof(f473,plain,
( ssItem(sK10)
| ~ spl47_2 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f474,plain,
( spl47_1
| spl47_2 ),
inference(avatar_split_clause,[],[f263,f471,f467]) ).
fof(f476,definition,
( spl47_3
<=> nil = sK9 ),
introduced(definition,[new_symbols(definition,[spl47_3])],[avatar_definition]) ).
fof(f478,plain,
( nil = sK9
| ~ spl47_3 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f479,plain,
( spl47_3
| spl47_2 ),
inference(avatar_split_clause,[],[f264,f471,f476]) ).
fof(f486,definition,
( spl47_5
<=> memberP(sK9,sK10) ),
introduced(definition,[new_symbols(definition,[spl47_5])],[avatar_definition]) ).
fof(f488,plain,
( memberP(sK9,sK10)
| ~ spl47_5 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f489,plain,
( spl47_1
| spl47_5 ),
inference(avatar_split_clause,[],[f267,f486,f467]) ).
fof(f490,plain,
( spl47_3
| spl47_5 ),
inference(avatar_split_clause,[],[f268,f486,f476]) ).
fof(f492,definition,
( spl47_6
<=> sK8 = cons(sK10,nil) ),
introduced(definition,[new_symbols(definition,[spl47_6])],[avatar_definition]) ).
fof(f494,plain,
( sK8 = cons(sK10,nil)
| ~ spl47_6 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f495,plain,
( spl47_1
| spl47_6 ),
inference(avatar_split_clause,[],[f269,f492,f467]) ).
fof(f496,plain,
( spl47_3
| spl47_6 ),
inference(avatar_split_clause,[],[f270,f492,f476]) ).
fof(f497,plain,
! [X0] :
( ~ segmentP(sK9,X0)
| ~ segmentP(X0,sK8)
| ~ ssList(sK8)
| ~ ssList(X0)
| ~ ssList(sK9) ),
inference(resolution,[],[f435,f323]) ).
fof(f498,plain,
! [X0] :
( ~ segmentP(sK9,X0)
| ~ segmentP(X0,sK8)
| ~ ssList(X0)
| ~ ssList(sK9) ),
inference(forward_subsumption_resolution,[],[f497,f437]) ).
fof(f499,plain,
! [X0] :
( ~ segmentP(sK9,X0)
| ~ segmentP(X0,sK8)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f498,f436]) ).
fof(f500,plain,
( ! [X0] :
( ~ segmentP(X0,cons(sK10,nil))
| ~ segmentP(sK9,X0)
| ~ ssList(X0) )
| ~ spl47_6 ),
inference(forward_demodulation,[],[f499,f494]) ).
fof(f503,plain,
( ssList(cons(sK10,nil))
| ~ spl47_6 ),
inference(superposition,[],[f437,f494]) ).
fof(f512,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(app(X0,cons(sK10,nil)),X1))
| ~ ssList(app(app(X0,cons(sK10,nil)),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(cons(sK10,nil))
| ~ ssList(app(app(X0,cons(sK10,nil)),X1)) )
| ~ spl47_6 ),
inference(resolution,[],[f500,f446]) ).
fof(f514,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(app(X0,cons(sK10,nil)),X1))
| ~ ssList(app(app(X0,cons(sK10,nil)),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(cons(sK10,nil)) )
| ~ spl47_6 ),
inference(duplicate_literal_removal,[],[f512]) ).
fof(f518,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(app(X0,cons(sK10,nil)),X1))
| ~ ssList(app(app(X0,cons(sK10,nil)),X1))
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl47_6 ),
inference(forward_subsumption_resolution,[],[f514,f503]) ).
fof(f551,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(X0,app(cons(sK10,nil),X1)))
| ~ ssList(app(X0,app(cons(sK10,nil),X1)))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X1)
| ~ ssList(cons(sK10,nil))
| ~ ssList(X0) )
| ~ spl47_6 ),
inference(superposition,[],[f518,f279]) ).
fof(f558,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(X0,app(cons(sK10,nil),X1)))
| ~ ssList(app(X0,app(cons(sK10,nil),X1)))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(cons(sK10,nil)) )
| ~ spl47_6 ),
inference(duplicate_literal_removal,[],[f551]) ).
fof(f562,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(X0,app(cons(sK10,nil),X1)))
| ~ ssList(app(X0,app(cons(sK10,nil),X1)))
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl47_6 ),
inference(forward_subsumption_resolution,[],[f558,f503]) ).
fof(f879,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(X1,cons(sK10,X0)))
| ~ ssList(app(X1,cons(sK10,X0)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK10)
| ~ ssList(X0) )
| ~ spl47_6 ),
inference(superposition,[],[f562,f280]) ).
fof(f891,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(X1,cons(sK10,X0)))
| ~ ssList(app(X1,cons(sK10,X0)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK10) )
| ~ spl47_6 ),
inference(duplicate_literal_removal,[],[f879]) ).
fof(f899,plain,
( ! [X0,X1] :
( ~ segmentP(sK9,app(X1,cons(sK10,X0)))
| ~ ssList(app(X1,cons(sK10,X0)))
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl47_2
| ~ spl47_6 ),
inference(forward_subsumption_resolution,[],[f891,f473]) ).
fof(f1601,plain,
( ! [X0] :
( ~ segmentP(sK9,X0)
| ~ ssList(X0)
| ~ ssList(sK15(X0,sK10))
| ~ ssList(sK16(X0,sK10))
| ~ memberP(X0,sK10)
| ~ ssItem(sK10)
| ~ ssList(X0) )
| ~ spl47_2
| ~ spl47_6 ),
inference(superposition,[],[f899,f313]) ).
fof(f1609,plain,
( ! [X0] :
( ~ segmentP(sK9,X0)
| ~ ssList(X0)
| ~ ssList(sK15(X0,sK10))
| ~ ssList(sK16(X0,sK10))
| ~ memberP(X0,sK10)
| ~ ssItem(sK10) )
| ~ spl47_2
| ~ spl47_6 ),
inference(duplicate_literal_removal,[],[f1601]) ).
fof(f1615,plain,
( ! [X0] :
( ~ ssList(sK16(X0,sK10))
| ~ ssList(X0)
| ~ ssList(sK15(X0,sK10))
| ~ segmentP(sK9,X0)
| ~ memberP(X0,sK10) )
| ~ spl47_2
| ~ spl47_6 ),
inference(forward_subsumption_resolution,[],[f1609,f473]) ).
fof(f1630,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ ssList(sK15(X0,sK10))
| ~ segmentP(sK9,X0)
| ~ memberP(X0,sK10)
| ~ memberP(X0,sK10)
| ~ ssItem(sK10)
| ~ ssList(X0) )
| ~ spl47_2
| ~ spl47_6 ),
inference(resolution,[],[f1615,f314]) ).
fof(f1631,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ ssList(sK15(X0,sK10))
| ~ segmentP(sK9,X0)
| ~ memberP(X0,sK10)
| ~ ssItem(sK10) )
| ~ spl47_2
| ~ spl47_6 ),
inference(duplicate_literal_removal,[],[f1630]) ).
fof(f1632,plain,
( ! [X0] :
( ~ ssList(sK15(X0,sK10))
| ~ ssList(X0)
| ~ segmentP(sK9,X0)
| ~ memberP(X0,sK10) )
| ~ spl47_2
| ~ spl47_6 ),
inference(forward_subsumption_resolution,[],[f1631,f473]) ).
fof(f1665,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ segmentP(sK9,X0)
| ~ memberP(X0,sK10)
| ~ memberP(X0,sK10)
| ~ ssItem(sK10)
| ~ ssList(X0) )
| ~ spl47_2
| ~ spl47_6 ),
inference(resolution,[],[f1632,f315]) ).
fof(f1666,plain,
( ! [X0] :
( ~ ssList(X0)
| ~ segmentP(sK9,X0)
| ~ memberP(X0,sK10)
| ~ ssItem(sK10) )
| ~ spl47_2
| ~ spl47_6 ),
inference(duplicate_literal_removal,[],[f1665]) ).
fof(f1667,plain,
( ! [X0] :
( ~ segmentP(sK9,X0)
| ~ ssList(X0)
| ~ memberP(X0,sK10) )
| ~ spl47_2
| ~ spl47_6 ),
inference(forward_subsumption_resolution,[],[f1666,f473]) ).
fof(f1708,plain,
( ~ ssList(sK9)
| ~ memberP(sK9,sK10)
| ~ ssList(sK9)
| ~ spl47_2
| ~ spl47_6 ),
inference(resolution,[],[f1667,f321]) ).
fof(f1712,plain,
( ~ ssList(sK9)
| ~ memberP(sK9,sK10)
| ~ spl47_2
| ~ spl47_6 ),
inference(duplicate_literal_removal,[],[f1708]) ).
fof(f1715,plain,
( ~ memberP(sK9,sK10)
| ~ spl47_2
| ~ spl47_6 ),
inference(forward_subsumption_resolution,[],[f1712,f436]) ).
fof(f1717,plain,
( $false
| ~ spl47_2
| ~ spl47_5
| ~ spl47_6 ),
inference(forward_subsumption_resolution,[],[f1715,f488]) ).
fof(f1718,plain,
( ~ spl47_2
| ~ spl47_5
| ~ spl47_6 ),
inference(avatar_contradiction_clause,[],[f1717]) ).
fof(f1754,plain,
( ~ segmentP(sK9,nil)
| ~ spl47_1 ),
inference(superposition,[],[f435,f469]) ).
fof(f1756,plain,
( ~ segmentP(nil,nil)
| ~ spl47_1
| ~ spl47_3 ),
inference(forward_demodulation,[],[f1754,f478]) ).
fof(f1762,plain,
( ~ ssList(nil)
| ~ spl47_1
| ~ spl47_3 ),
inference(resolution,[],[f1756,f445]) ).
fof(f1771,plain,
( $false
| ~ spl47_1
| ~ spl47_3 ),
inference(forward_subsumption_resolution,[],[f1762,f304]) ).
fof(f1772,plain,
( ~ spl47_1
| ~ spl47_3 ),
inference(avatar_contradiction_clause,[],[f1771]) ).
cnf(s1,plain,
( spl47_1
| spl47_2 ),
inference(sat_conversion,[],[f474]) ).
cnf(s2,plain,
( spl47_2
| spl47_3 ),
inference(sat_conversion,[],[f479]) ).
cnf(s5,plain,
( spl47_1
| spl47_5 ),
inference(sat_conversion,[],[f489]) ).
cnf(s6,plain,
( spl47_3
| spl47_5 ),
inference(sat_conversion,[],[f490]) ).
cnf(s7,plain,
( spl47_1
| spl47_6 ),
inference(sat_conversion,[],[f495]) ).
cnf(s8,plain,
( spl47_3
| spl47_6 ),
inference(sat_conversion,[],[f496]) ).
cnf(s13,plain,
( ~ spl47_2
| ~ spl47_5
| ~ spl47_6 ),
inference(sat_conversion,[],[f1718]) ).
cnf(s22,plain,
( ~ spl47_1
| ~ spl47_3 ),
inference(sat_conversion,[],[f1772]) ).
cnf(s23,plain,
spl47_1,
inference(rat,[],[s13,s1,s5,s7]) ).
cnf(s24,plain,
~ spl47_3,
inference(rat,[],[s22,s23]) ).
cnf(s25,plain,
spl47_6,
inference(rat,[],[s8,s24]) ).
cnf(s26,plain,
spl47_5,
inference(rat,[],[s6,s24]) ).
cnf(s28,plain,
spl47_2,
inference(rat,[],[s2,s24]) ).
cnf(s29,plain,
$false,
inference(rat,[],[s13,s25,s26,s28]) ).
fof(f1773,plain,
$false,
inference(avatar_sat_refutation,[],[s29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC356+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:15:40 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running first-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.79/1.44 % (3831927)Detected formulas, will run a generic FOF schedule.
% 4.79/1.44 % (3831981)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1404923075:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.79/1.44 % (3831981)Refutation not found, incomplete strategy
% 4.79/1.44 % (3831981)------------------------------
% 4.79/1.44 % (3831981)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.44 % (3831981)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.44 % (3831981)CaDiCaL version: 2.1.3
% 4.79/1.44 % (3831981)Termination reason: Refutation not found, incomplete strategy
% 4.79/1.44 % (3831981)Time elapsed: 0.002 s
% 4.79/1.44 % (3831981)Peak memory usage: 88 MB
% 4.79/1.44 % (3831981)Instructions burned: 4 (million)
% 4.79/1.44 % (3831980)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=1418010127:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.79/1.44 % (3831978)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=933601993:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.79/1.44 % (3831979)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=1428027540:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.79/1.44 % (3831982)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2307650924:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.79/1.44 % (3831983)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=723512492:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.79/1.44 % (3831984)dis-21_1_sil=8000:lcm=predicate:random_seed=1523046139: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)
% 4.79/1.44 % (3831982)Instruction limit reached!
% 4.79/1.44 % (3831982)------------------------------
% 4.79/1.44 % (3831982)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.44 % (3831982)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.44 % (3831982)CaDiCaL version: 2.1.3
% 4.79/1.44 % (3831982)Termination reason: Instruction limit
% 4.79/1.44 % (3831982)Termination phase: Saturation
% 4.79/1.44 % (3831982)Time elapsed: 0.070 s
% 4.79/1.44 % (3831982)Peak memory usage: 88 MB
% 4.79/1.44 % (3831982)Instructions burned: 120 (million)
% 4.79/1.44 % (3831984)Instruction limit reached!
% 4.79/1.44 % (3831984)------------------------------
% 4.79/1.44 % (3831984)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.44 % (3831984)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.44 % (3831984)CaDiCaL version: 2.1.3
% 4.79/1.44 % (3831984)Termination reason: Instruction limit
% 4.79/1.44 % (3831984)Termination phase: Saturation
% 4.79/1.44 % (3831984)Time elapsed: 0.073 s
% 4.79/1.44 % (3831984)Peak memory usage: 90 MB
% 4.79/1.44 % (3831984)Instructions burned: 130 (million)
% 4.79/1.44 % (3831983)Instruction limit reached!
% 4.79/1.44 % (3831983)------------------------------
% 4.79/1.44 % (3831983)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.44 % (3831983)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.44 % (3831983)CaDiCaL version: 2.1.3
% 4.79/1.44 % (3831983)Termination reason: Instruction limit
% 4.79/1.44 % (3831983)Termination phase: Saturation
% 4.79/1.44 % (3831983)Time elapsed: 0.094 s
% 4.79/1.44 % (3831983)Peak memory usage: 90 MB
% 4.79/1.44 % (3831983)Instructions burned: 140 (million)
% 4.79/1.44 % (3831981)------------------------------
% 4.79/1.44 % (3831981)------------------------------
% 4.79/1.44 % (3831995)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=3239665982:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.79/1.44 % (3831993)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2111421753:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.79/1.44 % (3831992)lrs+10_1_sil=8000:sp=occurrence:random_seed=2311318860:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.79/1.44 % (3831994)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3466482481:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.79/1.44 % (3831995)Instruction limit reached!
% 4.79/1.44 % (3831995)------------------------------
% 4.79/1.44 % (3831995)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.44 % (3831995)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.44 % (3831995)CaDiCaL version: 2.1.3
% 4.79/1.44 % (3831995)Termination reason: Instruction limit
% 4.79/1.44 % (3831995)Termination phase: Saturation
% 4.79/1.44 % (3831995)Time elapsed: 0.063 s
% 4.79/1.44 % (3831995)Peak memory usage: 93 MB
% 4.79/1.44 % (3831995)Instructions burned: 248 (million)
% 4.79/1.44 % (3831993)Instruction limit reached!
% 4.79/1.44 % (3831993)------------------------------
% 4.79/1.44 % (3831993)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.44 % (3831993)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.44 % (3831993)CaDiCaL version: 2.1.3
% 4.79/1.44 % (3831993)Termination reason: Instruction limit
% 4.79/1.44 % (3831993)Termination phase: Saturation
% 4.79/1.44 % (3831993)Time elapsed: 0.076 s
% 4.79/1.44 % (3831993)Peak memory usage: 91 MB
% 4.79/1.44 % (3831993)Instructions burned: 158 (million)
% 4.79/1.44 % (3831992)Instruction limit reached!
% 4.79/1.44 % (3831992)------------------------------
% 4.79/1.44 % (3831992)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.44 % (3831992)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.44 % (3831992)CaDiCaL version: 2.1.3
% 4.79/1.44 % (3831992)Termination reason: Instruction limit
% 4.79/1.44 % (3831992)Termination phase: Saturation
% 4.79/1.44 % (3831992)Time elapsed: 0.174 s
% 4.79/1.44 % (3831992)Peak memory usage: 93 MB
% 4.79/1.44 % (3831992)Instructions burned: 285 (million)
% 4.79/1.44 % (3832000)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3061561032:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.79/1.44 % (3832000)First to succeed.
% 4.79/1.44 % (3832000)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3831927"
% 4.79/1.44 % (3832001)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1472563361:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.79/1.44 % (3831994)Instruction limit reached!
% 4.79/1.44 % (3831994)------------------------------
% 4.79/1.44 % (3831994)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.79/1.44 % (3831994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.79/1.44 % (3831994)CaDiCaL version: 2.1.3
% 4.79/1.44 % (3831994)Termination reason: Instruction limit
% 4.79/1.44 % (3831994)Termination phase: Saturation
% 4.79/1.44 % (3831994)Time elapsed: 0.211 s
% 4.79/1.44 % (3831994)Peak memory usage: 92 MB
% 4.79/1.44 % (3831994)Instructions burned: 325 (million)
% 4.79/1.44 % (3832003)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3995942660:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.79/1.44 % (3832000)Refutation found. Thanks to Tanya!
% 4.79/1.44 % SZS status Theorem for theBenchmark
% 4.79/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 6.00/1.63 % (3832000)------------------------------
% 6.00/1.63 % (3832000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.00/1.63 % (3832000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.00/1.63 % (3832000)CaDiCaL version: 2.1.3
% 6.00/1.63 % (3832000)Termination reason: Refutation
% 6.00/1.63 % (3832000)Time elapsed: 0.037 s
% 6.00/1.63 % (3832000)Peak memory usage: 90 MB
% 6.00/1.63 % (3832000)Instructions burned: 123 (million)
% 6.00/1.63 % (3832000)------------------------------
% 6.00/1.63 % (3832000)------------------------------
% 6.00/1.63 % (3831927)Success in time 0.764 s
% 6.00/1.63 % Vampire exiting
%------------------------------------------------------------------------------