%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC088+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 : 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 01:02:23 PM UTC 2026
% Result : Theorem 4.13s 1.58s
% Output : Refutation 5.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 22
% Syntax : Number of formulae : 212 ( 24 unt; 9 def)
% Number of atoms : 840 ( 135 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1080 ( 452 ~; 506 |; 79 &)
% ( 17 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 10 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 201 ( 0 sgn 165 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
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(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
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(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
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] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X2
& app(cons(X5,nil),X6) = X3 ) )
| ( nil != X2
& nil = X3 ) ) ) ) ) ),
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)
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(X6,cons(X5,nil)) != X2
& app(cons(X5,nil),X6) = X3 ) )
| ( nil != X2
& nil = X3 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,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] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X6,cons(X5,nil)) = X2
| app(cons(X5,nil),X6) != X3 ) )
& ( nil = X2
| nil != X3 )
& 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)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X6,cons(X5,nil)) = X2
| app(cons(X5,nil),X6) != X3 ) )
& ( nil = X2
| nil != X3 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f118,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f119,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(flattening,[],[f118]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f144,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f158,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f159,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f160,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(f161,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f162,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f163,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f167,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f181,plain,
( sK7 = sK9
& sK6 = sK8
& neq(sK7,nil)
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK7,X4)
| ~ segmentP(sK6,X4) )
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(X6,cons(X5,nil)) = sK8
| app(cons(X5,nil),X6) != sK9 ) )
& ( nil = sK8
| nil != sK9 )
& ssList(sK9)
& ssList(sK8)
& ssList(sK7)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9)],[f99]) ).
fof(f191,plain,
! [X0] :
( nil = X0
| ( ssList(sK12(X0))
& ssItem(sK13(X0))
& cons(sK13(X0),sK12(X0)) = X0 )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X1,sK12(X0)),skolemize(X2,sK13(X0))],[f119]) ).
fof(f226,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,[],[f160]) ).
fof(f227,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,[],[f226]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK51(X0,X1))
& ssList(sK52(X0,X1))
& app(app(sK51(X0,X1),X1),sK52(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51,sK52]),skolemize(X4,sK51(X0,X1)),skolemize(X5,sK52(X0,X1))],[f227]) ).
fof(f229,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X2,X1) = X0 )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f230,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X3,X1) = X0 )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f229]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X2,X1) != X0 ) )
& ( ( ssList(sK53(X0,X1))
& app(sK53(X0,X1),X1) = X0 )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(X3,sK53(X0,X1))],[f230]) ).
fof(f232,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X2] :
( ssList(X2)
& app(X1,X2) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f162]) ).
fof(f233,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ? [X3] :
( ssList(X3)
& app(X1,X3) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f232]) ).
fof(f234,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| app(X1,X2) != X0 ) )
& ( ( ssList(sK54(X0,X1))
& app(X1,sK54(X0,X1)) = X0 )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(X3,sK54(X0,X1))],[f233]) ).
fof(f235,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f163]) ).
fof(f238,plain,
ssList(sK6),
inference(cnf_transformation,[],[f181]) ).
fof(f239,plain,
ssList(sK7),
inference(cnf_transformation,[],[f181]) ).
fof(f243,plain,
! [X6,X5] :
( app(cons(X5,nil),X6) != sK9
| ~ ssList(X6)
| app(X6,cons(X5,nil)) = sK8
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f181]) ).
fof(f244,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK7,X4)
| ~ segmentP(sK6,X4) ),
inference(cnf_transformation,[],[f181]) ).
fof(f245,plain,
neq(sK7,nil),
inference(cnf_transformation,[],[f181]) ).
fof(f246,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f181]) ).
fof(f247,plain,
sK7 = sK9,
inference(cnf_transformation,[],[f181]) ).
fof(f251,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f280,plain,
! [X0] :
( cons(sK13(X0),sK12(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f281,plain,
! [X0] :
( ssItem(sK13(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f282,plain,
! [X0] :
( ssList(sK12(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f191]) ).
fof(f286,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f363,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f376,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f377,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f381,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,[],[f228]) ).
fof(f382,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| app(sK53(X0,X1),X1) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f383,plain,
! [X0,X1] :
( ssList(sK53(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f384,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| ~ ssList(X2)
| app(X2,X1) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f385,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK54(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f386,plain,
! [X0,X1] :
( ssList(sK54(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f387,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| ~ ssList(X2)
| app(X1,X2) != X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f388,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f389,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f235]) ).
fof(f392,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f396,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f399,plain,
neq(sK9,nil),
inference(definition_unfolding,[],[f245,f247]) ).
fof(f400,plain,
! [X4] :
( ~ segmentP(sK9,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ segmentP(sK8,X4) ),
inference(definition_unfolding,[],[f244,f247,f246]) ).
fof(f401,plain,
ssList(sK9),
inference(definition_unfolding,[],[f239,f247]) ).
fof(f402,plain,
ssList(sK8),
inference(definition_unfolding,[],[f238,f246]) ).
fof(f421,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,[],[f381]) ).
fof(f422,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f384]) ).
fof(f423,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f387]) ).
fof(f424,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f388]) ).
fof(f428,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f424]) ).
fof(f434,definition,
( spl55_1
<=> nil = sK9 ),
introduced(definition,[new_symbols(definition,[spl55_1])],[avatar_definition]) ).
fof(f435,plain,
( nil = sK9
| ~ spl55_1 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f436,plain,
( nil != sK9
| spl55_1 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f443,plain,
( ~ ssList(sK9)
| ~ neq(sK9,nil)
| ~ ssList(sK9)
| ~ segmentP(sK8,sK9) ),
inference(resolution,[],[f396,f400]) ).
fof(f444,plain,
( ~ ssList(sK9)
| ~ neq(sK9,nil)
| ~ segmentP(sK8,sK9) ),
inference(duplicate_literal_removal,[],[f443]) ).
fof(f445,plain,
( ~ neq(sK9,nil)
| ~ segmentP(sK8,sK9) ),
inference(forward_subsumption_resolution,[],[f444,f401]) ).
fof(f446,plain,
~ segmentP(sK8,sK9),
inference(forward_subsumption_resolution,[],[f445,f399]) ).
fof(f496,plain,
! [X0,X1] :
( cons(X0,X1) != sK9
| ~ ssList(X1)
| sK8 = app(X1,cons(X0,nil))
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(superposition,[],[f243,f251]) ).
fof(f503,plain,
! [X0,X1] :
( cons(X0,X1) != sK9
| ~ ssList(X1)
| sK8 = app(X1,cons(X0,nil))
| ~ ssItem(X0) ),
inference(duplicate_literal_removal,[],[f496]) ).
fof(f505,plain,
! [X0] :
( sK9 != X0
| ~ ssList(sK12(X0))
| sK8 = app(sK12(X0),cons(sK13(X0),nil))
| ~ ssItem(sK13(X0))
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f503,f280]) ).
fof(f506,plain,
! [X0] :
( sK9 != X0
| sK8 = app(sK12(X0),cons(sK13(X0),nil))
| ~ ssItem(sK13(X0))
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f505,f282]) ).
fof(f507,plain,
! [X0] :
( sK9 != X0
| sK8 = app(sK12(X0),cons(sK13(X0),nil))
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f506,f281]) ).
fof(f508,plain,
( sK8 = app(sK12(sK9),cons(sK13(sK9),nil))
| nil = sK9
| ~ ssList(sK9) ),
inference(equality_resolution,[],[f507]) ).
fof(f515,definition,
( spl55_3
<=> ssList(sK12(sK9)) ),
introduced(definition,[new_symbols(definition,[spl55_3])],[avatar_definition]) ).
fof(f516,plain,
( ssList(sK12(sK9))
| ~ spl55_3 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f517,plain,
( ~ ssList(sK12(sK9))
| spl55_3 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f519,definition,
( spl55_4
<=> ssList(cons(sK13(sK9),nil)) ),
introduced(definition,[new_symbols(definition,[spl55_4])],[avatar_definition]) ).
fof(f520,plain,
( ssList(cons(sK13(sK9),nil))
| ~ spl55_4 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f521,plain,
( ~ ssList(cons(sK13(sK9),nil))
| spl55_4 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f523,definition,
( spl55_5
<=> nil = sK12(sK9) ),
introduced(definition,[new_symbols(definition,[spl55_5])],[avatar_definition]) ).
fof(f524,plain,
( nil != sK12(sK9)
| spl55_5 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f525,plain,
( nil = sK12(sK9)
| ~ spl55_5 ),
inference(avatar_component_clause,[],[f523]) ).
fof(f546,plain,
! [X0,X1] :
( rearsegP(cons(X0,X1),X1)
| ~ ssList(cons(X0,nil))
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(superposition,[],[f422,f251]) ).
fof(f550,plain,
! [X0,X1] :
( rearsegP(cons(X0,X1),X1)
| ~ ssList(cons(X0,nil))
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ ssItem(X0) ),
inference(duplicate_literal_removal,[],[f546]) ).
fof(f554,plain,
! [X0,X1] :
( ~ ssList(cons(X0,nil))
| rearsegP(cons(X0,X1),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f550,f286]) ).
fof(f561,plain,
( nil = sK9
| ~ ssList(sK9)
| spl55_3 ),
inference(resolution,[],[f517,f282]) ).
fof(f562,plain,
( ~ ssList(sK9)
| spl55_1
| spl55_3 ),
inference(forward_subsumption_resolution,[],[f561,f436]) ).
fof(f563,plain,
( $false
| spl55_1
| spl55_3 ),
inference(forward_subsumption_resolution,[],[f562,f401]) ).
fof(f564,plain,
( spl55_1
| spl55_3 ),
inference(avatar_contradiction_clause,[],[f563]) ).
fof(f565,plain,
( neq(nil,nil)
| ~ spl55_1 ),
inference(superposition,[],[f399,f435]) ).
fof(f586,plain,
( ~ ssList(nil)
| ~ spl55_1 ),
inference(resolution,[],[f565,f428]) ).
fof(f588,plain,
( $false
| ~ spl55_1 ),
inference(forward_subsumption_resolution,[],[f586,f392]) ).
fof(f589,plain,
~ spl55_1,
inference(avatar_contradiction_clause,[],[f588]) ).
fof(f590,plain,
( sK8 = app(sK12(sK9),cons(sK13(sK9),nil))
| ~ ssList(sK9)
| spl55_1 ),
inference(forward_subsumption_resolution,[],[f508,f436]) ).
fof(f591,plain,
( sK8 = app(sK12(sK9),cons(sK13(sK9),nil))
| spl55_1 ),
inference(forward_subsumption_resolution,[],[f590,f401]) ).
fof(f602,plain,
( ~ ssItem(sK13(sK9))
| ~ ssList(nil)
| spl55_4 ),
inference(resolution,[],[f521,f286]) ).
fof(f603,plain,
( ~ ssItem(sK13(sK9))
| spl55_4 ),
inference(forward_subsumption_resolution,[],[f602,f392]) ).
fof(f607,plain,
( nil = sK9
| ~ ssList(sK9)
| spl55_4 ),
inference(resolution,[],[f603,f281]) ).
fof(f608,plain,
( ~ ssList(sK9)
| spl55_1
| spl55_4 ),
inference(forward_subsumption_resolution,[],[f607,f436]) ).
fof(f609,plain,
( $false
| spl55_1
| spl55_4 ),
inference(forward_subsumption_resolution,[],[f608,f401]) ).
fof(f610,plain,
( spl55_1
| spl55_4 ),
inference(avatar_contradiction_clause,[],[f609]) ).
fof(f630,plain,
( frontsegP(sK8,sK12(sK9))
| ~ ssList(cons(sK13(sK9),nil))
| ~ ssList(sK12(sK9))
| ~ ssList(sK8)
| spl55_1 ),
inference(superposition,[],[f423,f591]) ).
fof(f631,plain,
( frontsegP(sK8,sK12(sK9))
| ~ ssList(sK12(sK9))
| ~ ssList(sK8)
| spl55_1
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f630,f520]) ).
fof(f634,plain,
( frontsegP(sK8,sK12(sK9))
| ~ ssList(sK8)
| spl55_1
| ~ spl55_3
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f631,f516]) ).
fof(f637,plain,
( frontsegP(sK8,sK12(sK9))
| spl55_1
| ~ spl55_3
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f634,f402]) ).
fof(f656,plain,
( sK9 = cons(sK13(sK9),nil)
| nil = sK9
| ~ ssList(sK9)
| ~ spl55_5 ),
inference(superposition,[],[f280,f525]) ).
fof(f658,plain,
( sK9 = cons(sK13(sK9),nil)
| ~ ssList(sK9)
| spl55_1
| ~ spl55_5 ),
inference(forward_subsumption_resolution,[],[f656,f436]) ).
fof(f659,plain,
( sK9 = cons(sK13(sK9),nil)
| spl55_1
| ~ spl55_5 ),
inference(forward_subsumption_resolution,[],[f658,f401]) ).
fof(f673,plain,
( sK8 = app(sK12(sK9),sK54(sK8,sK12(sK9)))
| ~ ssList(sK12(sK9))
| ~ ssList(sK8)
| spl55_1
| ~ spl55_3
| ~ spl55_4 ),
inference(resolution,[],[f385,f637]) ).
fof(f675,plain,
( sK8 = app(sK12(sK9),sK54(sK8,sK12(sK9)))
| ~ ssList(sK8)
| spl55_1
| ~ spl55_3
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f673,f516]) ).
fof(f677,plain,
( sK8 = app(sK12(sK9),sK54(sK8,sK12(sK9)))
| spl55_1
| ~ spl55_3
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f675,f402]) ).
fof(f687,plain,
( sK8 = app(sK12(sK9),sK9)
| spl55_1
| ~ spl55_5 ),
inference(superposition,[],[f591,f659]) ).
fof(f720,definition,
( spl55_9
<=> ssItem(sK13(sK9)) ),
introduced(definition,[new_symbols(definition,[spl55_9])],[avatar_definition]) ).
fof(f721,plain,
( ssItem(sK13(sK9))
| ~ spl55_9 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f722,plain,
( ~ ssItem(sK13(sK9))
| spl55_9 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f724,definition,
( spl55_10
<=> sK8 = app(nil,sK9) ),
introduced(definition,[new_symbols(definition,[spl55_10])],[avatar_definition]) ).
fof(f726,plain,
( sK8 = app(nil,sK9)
| ~ spl55_10 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f772,plain,
( sK8 = app(nil,sK9)
| spl55_1
| ~ spl55_5 ),
inference(forward_demodulation,[],[f687,f525]) ).
fof(f807,plain,
( spl55_10
| spl55_1
| ~ spl55_5 ),
inference(avatar_split_clause,[],[f772,f523,f434,f724]) ).
fof(f918,definition,
( spl55_27
<=> ssList(sK54(sK8,sK12(sK9))) ),
introduced(definition,[new_symbols(definition,[spl55_27])],[avatar_definition]) ).
fof(f919,plain,
( ssList(sK54(sK8,sK12(sK9)))
| ~ spl55_27 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f920,plain,
( ~ ssList(sK54(sK8,sK12(sK9)))
| spl55_27 ),
inference(avatar_component_clause,[],[f918]) ).
fof(f954,plain,
( ~ frontsegP(sK8,sK12(sK9))
| ~ ssList(sK12(sK9))
| ~ ssList(sK8)
| spl55_27 ),
inference(resolution,[],[f920,f386]) ).
fof(f955,plain,
( ~ ssList(sK12(sK9))
| ~ ssList(sK8)
| spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_27 ),
inference(forward_subsumption_resolution,[],[f954,f637]) ).
fof(f956,plain,
( ~ ssList(sK8)
| spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_27 ),
inference(forward_subsumption_resolution,[],[f955,f516]) ).
fof(f957,plain,
( $false
| spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_27 ),
inference(forward_subsumption_resolution,[],[f956,f402]) ).
fof(f958,plain,
( spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_27 ),
inference(avatar_contradiction_clause,[],[f957]) ).
fof(f989,plain,
( nil = sK9
| ~ ssList(sK9)
| spl55_9 ),
inference(resolution,[],[f722,f281]) ).
fof(f990,plain,
( ~ ssList(sK9)
| spl55_1
| spl55_9 ),
inference(forward_subsumption_resolution,[],[f989,f436]) ).
fof(f991,plain,
( $false
| spl55_1
| spl55_9 ),
inference(forward_subsumption_resolution,[],[f990,f401]) ).
fof(f992,plain,
( spl55_1
| spl55_9 ),
inference(avatar_contradiction_clause,[],[f991]) ).
fof(f1202,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(superposition,[],[f421,f376]) ).
fof(f1206,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1)
| ~ ssList(app(X0,X1)) ),
inference(superposition,[],[f421,f363]) ).
fof(f1207,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1) ),
inference(duplicate_literal_removal,[],[f1206]) ).
fof(f1209,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(duplicate_literal_removal,[],[f1202]) ).
fof(f1214,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| segmentP(app(X0,X1),X1) ),
inference(forward_subsumption_resolution,[],[f1207,f392]) ).
fof(f1218,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| segmentP(app(X0,X1),X0) ),
inference(forward_subsumption_resolution,[],[f1209,f392]) ).
fof(f1220,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f1214,f377]) ).
fof(f1223,plain,
! [X0,X1] :
( segmentP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(forward_subsumption_resolution,[],[f1218,f377]) ).
fof(f1238,plain,
( sK8 = sK9
| ~ ssList(sK9)
| ~ spl55_10 ),
inference(superposition,[],[f376,f726]) ).
fof(f1258,plain,
( sK8 = sK9
| ~ spl55_10 ),
inference(forward_subsumption_resolution,[],[f1238,f401]) ).
fof(f1277,plain,
( ~ segmentP(sK8,sK8)
| ~ spl55_10 ),
inference(superposition,[],[f446,f1258]) ).
fof(f1425,plain,
( ~ ssList(sK8)
| ~ spl55_10 ),
inference(resolution,[],[f1277,f396]) ).
fof(f1426,plain,
( $false
| ~ spl55_10 ),
inference(forward_subsumption_resolution,[],[f1425,f402]) ).
fof(f1427,plain,
~ spl55_10,
inference(avatar_contradiction_clause,[],[f1426]) ).
fof(f1503,plain,
( segmentP(sK8,sK12(sK9))
| ~ ssList(sK12(sK9))
| ~ ssList(sK54(sK8,sK12(sK9)))
| spl55_1
| ~ spl55_3
| ~ spl55_4 ),
inference(superposition,[],[f1223,f677]) ).
fof(f1512,plain,
( segmentP(sK8,sK12(sK9))
| ~ ssList(sK54(sK8,sK12(sK9)))
| spl55_1
| ~ spl55_3
| ~ spl55_4 ),
inference(forward_subsumption_resolution,[],[f1503,f516]) ).
fof(f1519,plain,
( segmentP(sK8,sK12(sK9))
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_27 ),
inference(forward_subsumption_resolution,[],[f1512,f919]) ).
fof(f1739,plain,
( ! [X0] :
( rearsegP(cons(sK13(sK9),X0),X0)
| ~ ssList(X0)
| ~ ssItem(sK13(sK9)) )
| ~ spl55_4 ),
inference(resolution,[],[f554,f520]) ).
fof(f1743,plain,
( ! [X0] :
( rearsegP(cons(sK13(sK9),X0),X0)
| ~ ssList(X0) )
| ~ spl55_4
| ~ spl55_9 ),
inference(forward_subsumption_resolution,[],[f1739,f721]) ).
fof(f3416,plain,
( rearsegP(sK9,sK12(sK9))
| ~ ssList(sK12(sK9))
| nil = sK9
| ~ ssList(sK9)
| ~ spl55_4
| ~ spl55_9 ),
inference(superposition,[],[f1743,f280]) ).
fof(f3419,plain,
( rearsegP(sK9,sK12(sK9))
| nil = sK9
| ~ ssList(sK9)
| ~ spl55_4
| ~ spl55_9 ),
inference(forward_subsumption_resolution,[],[f3416,f282]) ).
fof(f3422,plain,
( rearsegP(sK9,sK12(sK9))
| ~ ssList(sK9)
| spl55_1
| ~ spl55_4
| ~ spl55_9 ),
inference(forward_subsumption_resolution,[],[f3419,f436]) ).
fof(f3425,plain,
( rearsegP(sK9,sK12(sK9))
| spl55_1
| ~ spl55_4
| ~ spl55_9 ),
inference(forward_subsumption_resolution,[],[f3422,f401]) ).
fof(f3428,plain,
( sK9 = app(sK53(sK9,sK12(sK9)),sK12(sK9))
| ~ ssList(sK12(sK9))
| ~ ssList(sK9)
| spl55_1
| ~ spl55_4
| ~ spl55_9 ),
inference(resolution,[],[f3425,f382]) ).
fof(f3433,plain,
( sK9 = app(sK53(sK9,sK12(sK9)),sK12(sK9))
| ~ ssList(sK9)
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9 ),
inference(forward_subsumption_resolution,[],[f3428,f516]) ).
fof(f3436,plain,
( sK9 = app(sK53(sK9,sK12(sK9)),sK12(sK9))
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9 ),
inference(forward_subsumption_resolution,[],[f3433,f401]) ).
fof(f4503,plain,
( segmentP(sK9,sK12(sK9))
| ~ ssList(sK12(sK9))
| ~ ssList(sK53(sK9,sK12(sK9)))
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9 ),
inference(superposition,[],[f1220,f3436]) ).
fof(f4506,plain,
( segmentP(sK9,sK12(sK9))
| ~ ssList(sK53(sK9,sK12(sK9)))
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9 ),
inference(forward_subsumption_resolution,[],[f4503,f516]) ).
fof(f4539,definition,
( spl55_99
<=> ssList(sK53(sK9,sK12(sK9))) ),
introduced(definition,[new_symbols(definition,[spl55_99])],[avatar_definition]) ).
fof(f4541,plain,
( ~ ssList(sK53(sK9,sK12(sK9)))
| spl55_99 ),
inference(avatar_component_clause,[],[f4539]) ).
fof(f4548,definition,
( spl55_101
<=> segmentP(sK9,sK12(sK9)) ),
introduced(definition,[new_symbols(definition,[spl55_101])],[avatar_definition]) ).
fof(f4550,plain,
( segmentP(sK9,sK12(sK9))
| ~ spl55_101 ),
inference(avatar_component_clause,[],[f4548]) ).
fof(f4551,plain,
( ~ spl55_99
| spl55_101
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9 ),
inference(avatar_split_clause,[],[f4506,f720,f519,f515,f434,f4548,f4539]) ).
fof(f4704,plain,
( ~ rearsegP(sK9,sK12(sK9))
| ~ ssList(sK12(sK9))
| ~ ssList(sK9)
| spl55_99 ),
inference(resolution,[],[f4541,f383]) ).
fof(f4707,plain,
( ~ ssList(sK12(sK9))
| ~ ssList(sK9)
| spl55_1
| ~ spl55_4
| ~ spl55_9
| spl55_99 ),
inference(forward_subsumption_resolution,[],[f4704,f3425]) ).
fof(f4709,plain,
( ~ ssList(sK9)
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9
| spl55_99 ),
inference(forward_subsumption_resolution,[],[f4707,f516]) ).
fof(f4710,plain,
( $false
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9
| spl55_99 ),
inference(forward_subsumption_resolution,[],[f4709,f401]) ).
fof(f4711,plain,
( spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9
| spl55_99 ),
inference(avatar_contradiction_clause,[],[f4710]) ).
fof(f4773,plain,
( ~ neq(sK12(sK9),nil)
| ~ ssList(sK12(sK9))
| ~ segmentP(sK8,sK12(sK9))
| ~ spl55_101 ),
inference(resolution,[],[f4550,f400]) ).
fof(f4784,plain,
( ~ neq(sK12(sK9),nil)
| ~ segmentP(sK8,sK12(sK9))
| ~ spl55_3
| ~ spl55_101 ),
inference(forward_subsumption_resolution,[],[f4773,f516]) ).
fof(f4790,plain,
( ~ neq(sK12(sK9),nil)
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_27
| ~ spl55_101 ),
inference(forward_subsumption_resolution,[],[f4784,f1519]) ).
fof(f4839,plain,
( nil = sK12(sK9)
| ~ ssList(nil)
| ~ ssList(sK12(sK9))
| spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_27
| ~ spl55_101 ),
inference(resolution,[],[f4790,f389]) ).
fof(f4841,plain,
( ~ ssList(nil)
| ~ ssList(sK12(sK9))
| spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_5
| ~ spl55_27
| ~ spl55_101 ),
inference(forward_subsumption_resolution,[],[f4839,f524]) ).
fof(f4843,plain,
( ~ ssList(sK12(sK9))
| spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_5
| ~ spl55_27
| ~ spl55_101 ),
inference(forward_subsumption_resolution,[],[f4841,f392]) ).
fof(f4853,plain,
( $false
| spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_5
| ~ spl55_27
| ~ spl55_101 ),
inference(forward_subsumption_resolution,[],[f4843,f516]) ).
fof(f4854,plain,
( spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_5
| ~ spl55_27
| ~ spl55_101 ),
inference(avatar_contradiction_clause,[],[f4853]) ).
cnf(s5,plain,
( spl55_1
| spl55_3 ),
inference(sat_conversion,[],[f564]) ).
cnf(s6,plain,
~ spl55_1,
inference(sat_conversion,[],[f589]) ).
cnf(s7,plain,
( spl55_1
| spl55_4 ),
inference(sat_conversion,[],[f610]) ).
cnf(s26,plain,
( spl55_1
| ~ spl55_5
| spl55_10 ),
inference(sat_conversion,[],[f807]) ).
cnf(s34,plain,
( spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_27 ),
inference(sat_conversion,[],[f958]) ).
cnf(s35,plain,
( spl55_1
| spl55_9 ),
inference(sat_conversion,[],[f992]) ).
cnf(s37,plain,
~ spl55_10,
inference(sat_conversion,[],[f1427]) ).
cnf(s114,plain,
( spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9
| ~ spl55_99
| spl55_101 ),
inference(sat_conversion,[],[f4551]) ).
cnf(s146,plain,
( spl55_1
| ~ spl55_3
| ~ spl55_4
| ~ spl55_9
| spl55_99 ),
inference(sat_conversion,[],[f4711]) ).
cnf(s150,plain,
( spl55_1
| ~ spl55_3
| ~ spl55_4
| spl55_5
| ~ spl55_27
| ~ spl55_101 ),
inference(sat_conversion,[],[f4854]) ).
cnf(s151,plain,
( spl55_1
| ~ spl55_5 ),
inference(rat,[],[s26,s37]) ).
cnf(s155,plain,
spl55_9,
inference(rat,[],[s35,s6]) ).
cnf(s156,plain,
~ spl55_5,
inference(rat,[],[s151,s6]) ).
cnf(s157,plain,
spl55_4,
inference(rat,[],[s7,s6]) ).
cnf(s163,plain,
spl55_3,
inference(rat,[],[s5,s6]) ).
cnf(s164,plain,
spl55_99,
inference(rat,[],[s146,s157,s155,s6,s163]) ).
cnf(s170,plain,
spl55_27,
inference(rat,[],[s34,s157,s6,s163]) ).
cnf(s198,plain,
spl55_101,
inference(rat,[],[s114,s163,s157,s155,s6,s164]) ).
cnf(s204,plain,
$false,
inference(rat,[],[s150,s163,s157,s156,s6,s198,s170]) ).
fof(f4855,plain,
$false,
inference(avatar_sat_refutation,[],[s204]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC088+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 07:46:41 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 4.13/1.58 % (2230289)Detected formulas, will run a generic FOF schedule.
% 4.13/1.58 % (2230295)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=3289034173:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.13/1.58 % (2230299)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1079613238:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.13/1.58 % (2230294)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=3843243320:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.13/1.58 % (2230298)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3734259721:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.13/1.58 % (2230297)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3837563557:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.13/1.58 % (2230300)dis-21_1_sil=8000:lcm=predicate:random_seed=900187091: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)
% 4.13/1.58 % (2230296)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=706624201:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.13/1.58 % (2230297)Instruction limit reached!
% 4.13/1.58 % (2230297)------------------------------
% 4.13/1.58 % (2230297)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230297)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230297)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230297)Termination reason: Instruction limit
% 4.13/1.58 % (2230297)Termination phase: Saturation
% 4.13/1.58 % (2230297)Time elapsed: 0.065 s
% 4.13/1.58 % (2230297)Peak memory usage: 89 MB
% 4.13/1.58 % (2230297)Instructions burned: 110 (million)
% 4.13/1.58 % (2230298)Instruction limit reached!
% 4.13/1.58 % (2230298)------------------------------
% 4.13/1.58 % (2230298)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230298)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230298)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230298)Termination reason: Instruction limit
% 4.13/1.58 % (2230298)Termination phase: Saturation
% 4.13/1.58 % (2230298)Time elapsed: 0.069 s
% 4.13/1.58 % (2230298)Peak memory usage: 88 MB
% 4.13/1.58 % (2230298)Instructions burned: 119 (million)
% 4.13/1.58 % (2230300)Instruction limit reached!
% 4.13/1.58 % (2230300)------------------------------
% 4.13/1.58 % (2230300)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230300)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230300)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230300)Termination reason: Instruction limit
% 4.13/1.58 % (2230300)Termination phase: Saturation
% 4.13/1.58 % (2230300)Time elapsed: 0.074 s
% 4.13/1.58 % (2230300)Peak memory usage: 90 MB
% 4.13/1.58 % (2230300)Instructions burned: 129 (million)
% 4.13/1.58 % (2230299)Instruction limit reached!
% 4.13/1.58 % (2230299)------------------------------
% 4.13/1.58 % (2230299)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230299)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230299)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230299)Termination reason: Instruction limit
% 4.13/1.58 % (2230299)Termination phase: Saturation
% 4.13/1.58 % (2230299)Time elapsed: 0.098 s
% 4.13/1.58 % (2230299)Peak memory usage: 90 MB
% 4.13/1.58 % (2230299)Instructions burned: 139 (million)
% 4.13/1.58 % (2230309)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2707039450:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.13/1.58 % (2230308)lrs+10_1_sil=8000:sp=occurrence:random_seed=3976384115:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.13/1.58 % (2230310)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3457674953:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.13/1.58 % (2230311)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=673003775:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.13/1.58 % (2230309)Instruction limit reached!
% 4.13/1.58 % (2230309)------------------------------
% 4.13/1.58 % (2230309)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230309)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230309)Termination reason: Instruction limit
% 4.13/1.58 % (2230309)Termination phase: Saturation
% 4.13/1.58 % (2230309)Time elapsed: 0.074 s
% 4.13/1.58 % (2230309)Peak memory usage: 92 MB
% 4.13/1.58 % (2230309)Instructions burned: 157 (million)
% 4.13/1.58 % (2230310)First to succeed.
% 4.13/1.58 % (2230310)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2230289"
% 4.13/1.58 % (2230311)Instruction limit reached!
% 4.13/1.58 % (2230311)------------------------------
% 4.13/1.58 % (2230311)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230311)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230311)Termination reason: Instruction limit
% 4.13/1.58 % (2230311)Termination phase: Saturation
% 4.13/1.58 % (2230311)Time elapsed: 0.118 s
% 4.13/1.58 % (2230311)Peak memory usage: 94 MB
% 4.13/1.58 % (2230311)Instructions burned: 250 (million)
% 4.13/1.58 % (2230308)Instruction limit reached!
% 4.13/1.58 % (2230308)------------------------------
% 4.13/1.58 % (2230308)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230308)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230308)Termination reason: Instruction limit
% 4.13/1.58 % (2230308)Termination phase: Saturation
% 4.13/1.58 % (2230308)Time elapsed: 0.168 s
% 4.13/1.58 % (2230308)Peak memory usage: 92 MB
% 4.13/1.58 % (2230308)Instructions burned: 286 (million)
% 4.13/1.58 % (2230316)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1643170317:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.13/1.58 % (2230317)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4060319964:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 4.13/1.58 % (2230318)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3510653296:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.13/1.58 % (2230316)Instruction limit reached!
% 4.13/1.58 % (2230316)------------------------------
% 4.13/1.58 % (2230316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230316)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230316)Termination reason: Instruction limit
% 4.13/1.58 % (2230316)Termination phase: Saturation
% 4.13/1.58 % (2230316)Time elapsed: 0.164 s
% 4.13/1.58 % (2230316)Peak memory usage: 89 MB
% 4.13/1.58 % (2230316)Instructions burned: 294 (million)
% 4.13/1.58 % (2230318)Instruction limit reached!
% 4.13/1.58 % (2230318)------------------------------
% 4.13/1.58 % (2230318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.58 % (2230318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.58 % (2230318)CaDiCaL version: 2.1.3
% 4.13/1.58 % (2230318)Termination reason: Instruction limit
% 4.13/1.58 % (2230318)Termination phase: Saturation
% 4.13/1.58 % (2230318)Time elapsed: 0.077 s
% 4.13/1.58 % (2230318)Peak memory usage: 90 MB
% 4.13/1.58 % (2230318)Instructions burned: 113 (million)
% 4.13/1.58 % (2230310)Refutation found. Thanks to Tanya!
% 4.13/1.58 % SZS status Theorem for theBenchmark
% 4.13/1.58 % SZS output start Proof for theBenchmark
% See solution above
% 5.77/1.67 % (2230310)------------------------------
% 5.77/1.67 % (2230310)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.77/1.67 % (2230310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.77/1.67 % (2230310)CaDiCaL version: 2.1.3
% 5.77/1.67 % (2230310)Termination reason: Refutation
% 5.77/1.67 % (2230310)Time elapsed: 0.140 s
% 5.77/1.67 % (2230310)Peak memory usage: 92 MB
% 5.77/1.67 % (2230310)Instructions burned: 228 (million)
% 5.77/1.67 % (2230310)------------------------------
% 5.77/1.67 % (2230310)------------------------------
% 5.77/1.67 % (2230289)Success in time 0.754 s
% 5.77/1.67 % Vampire exiting
%------------------------------------------------------------------------------