%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC014+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 : n009.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 01:02:02 PM UTC 2026
% Result : Theorem 4.11s 1.26s
% Output : Refutation 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 156 ( 22 unt; 13 def)
% Number of atoms : 545 ( 142 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 658 ( 269 ~; 270 |; 77 &)
% ( 16 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn 128 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
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(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
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)
& X1 = X4
& ? [X5] :
( ssList(X5)
& tl(X1) = X5
& app(X0,X5) = X4
& neq(nil,X1) ) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X6,nil) != X2
| app(cons(X6,nil),X7) != 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)
& X1 = X4
& ? [X5] :
( ssList(X5)
& tl(X1) = X5
& app(X0,X5) = X4
& neq(nil,X1) ) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X6,nil) != X2
| app(cons(X6,nil),X7) != X3 ) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X1 != X4
| ! [X5] :
( ~ ssList(X5)
| tl(X1) != X5
| app(X0,X5) != X4
| ~ neq(nil,X1) ) )
& ? [X6] :
( ? [X7] :
( cons(X6,nil) = X2
& app(cons(X6,nil),X7) = X3
& ssList(X7) )
& ssItem(X6) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& 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)
| X1 != X4
| ! [X5] :
( ~ ssList(X5)
| tl(X1) != X5
| app(X0,X5) != X4
| ~ neq(nil,X1) ) )
& ? [X6] :
( ? [X7] :
( cons(X6,nil) = X2
& app(cons(X6,nil),X7) = X3
& ssList(X7) )
& ssItem(X6) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f141,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f140]) ).
fof(f145,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f158,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f163,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f169,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f170,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f169]) ).
fof(f171,definition,
! [X1,X0,X2,X3] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X1 != X4
| ! [X5] :
( ~ ssList(X5)
| tl(X1) != X5
| app(X0,X5) != X4
| ~ neq(nil,X1) ) )
& ? [X6] :
( ? [X7] :
( cons(X6,nil) = X2
& app(cons(X6,nil),X7) = X3
& ssList(X7) )
& ssItem(X6) ) )
| ~ sP0(X1,X0,X2,X3) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f172,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( sP0(X1,X0,X2,X3)
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f171]) ).
fof(f182,plain,
! [X1,X0,X2,X3] :
( ( neq(X1,nil)
& ! [X4] :
( ~ ssList(X4)
| X1 != X4
| ! [X5] :
( ~ ssList(X5)
| tl(X1) != X5
| app(X0,X5) != X4
| ~ neq(nil,X1) ) )
& ? [X6] :
( ? [X7] :
( cons(X6,nil) = X2
& app(cons(X6,nil),X7) = X3
& ssList(X7) )
& ssItem(X6) ) )
| ~ sP0(X1,X0,X2,X3) ),
inference(nnf_transformation,[],[f171]) ).
fof(f183,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssList(X4)
| X0 != X4
| ! [X5] :
( ~ ssList(X5)
| tl(X0) != X5
| app(X1,X5) != X4
| ~ neq(nil,X0) ) )
& ? [X6] :
( ? [X7] :
( cons(X6,nil) = X2
& app(cons(X6,nil),X7) = X3
& ssList(X7) )
& ssItem(X6) ) )
| ~ sP0(X0,X1,X2,X3) ),
inference(rectify,[],[f182]) ).
fof(f184,plain,
! [X0,X1,X2,X3] :
( ( neq(X0,nil)
& ! [X4] :
( ~ ssList(X4)
| X0 != X4
| ! [X5] :
( ~ ssList(X5)
| tl(X0) != X5
| app(X1,X5) != X4
| ~ neq(nil,X0) ) )
& cons(sK7(X2,X3),nil) = X2
& app(cons(sK7(X2,X3),nil),sK8(X2,X3)) = X3
& ssList(sK8(X2,X3))
& ssItem(sK7(X2,X3)) )
| ~ sP0(X0,X1,X2,X3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X6,sK7(X2,X3)),skolemize(X7,sK8(X2,X3))],[f183]) ).
fof(f185,plain,
( sK10 = sK12
& sK9 = sK11
& ( sP0(sK10,sK9,sK11,sK12)
| ( neq(sK10,nil)
& ~ neq(sK12,nil) ) )
& ssList(sK12)
& ssList(sK11)
& ssList(sK10)
& ssList(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X3,sK12)],[f172]) ).
fof(f226,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f145]) ).
fof(f227,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f226]) ).
fof(f239,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f163]) ).
fof(f242,plain,
! [X2,X3,X0,X1] :
( ssItem(sK7(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f184]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ssList(sK8(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f184]) ).
fof(f244,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(cons(sK7(X2,X3),nil),sK8(X2,X3)) = X3 ),
inference(cnf_transformation,[],[f184]) ).
fof(f245,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| cons(sK7(X2,X3),nil) = X2 ),
inference(cnf_transformation,[],[f184]) ).
fof(f246,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ ssList(X4)
| X0 != X4
| ~ ssList(X5)
| tl(X0) != X5
| app(X1,X5) != X4
| ~ neq(nil,X0)
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f184]) ).
fof(f247,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| neq(X0,nil) ),
inference(cnf_transformation,[],[f184]) ).
fof(f248,plain,
ssList(sK9),
inference(cnf_transformation,[],[f185]) ).
fof(f249,plain,
ssList(sK10),
inference(cnf_transformation,[],[f185]) ).
fof(f252,plain,
( sP0(sK10,sK9,sK11,sK12)
| ~ neq(sK12,nil) ),
inference(cnf_transformation,[],[f185]) ).
fof(f253,plain,
( sP0(sK10,sK9,sK11,sK12)
| neq(sK10,nil) ),
inference(cnf_transformation,[],[f185]) ).
fof(f254,plain,
sK9 = sK11,
inference(cnf_transformation,[],[f185]) ).
fof(f255,plain,
sK10 = sK12,
inference(cnf_transformation,[],[f185]) ).
fof(f285,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f293,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f369,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f372,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f384,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f397,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f400,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f404,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f405,plain,
( sP0(sK12,sK11,sK11,sK12)
| neq(sK12,nil) ),
inference(definition_unfolding,[],[f253,f255,f254,f255]) ).
fof(f406,plain,
( sP0(sK12,sK11,sK11,sK12)
| ~ neq(sK12,nil) ),
inference(definition_unfolding,[],[f252,f255,f254]) ).
fof(f407,plain,
ssList(sK12),
inference(definition_unfolding,[],[f249,f255]) ).
fof(f408,plain,
ssList(sK11),
inference(definition_unfolding,[],[f248,f254]) ).
fof(f409,plain,
! [X2,X3,X1,X4,X5] :
( ~ ssList(X4)
| ~ ssList(X5)
| tl(X4) != X5
| app(X1,X5) != X4
| ~ neq(nil,X4)
| ~ sP0(X4,X1,X2,X3) ),
inference(equality_resolution,[],[f246]) ).
fof(f410,plain,
! [X2,X3,X1,X4] :
( ~ sP0(X4,X1,X2,X3)
| ~ ssList(tl(X4))
| app(X1,tl(X4)) != X4
| ~ neq(nil,X4)
| ~ ssList(X4) ),
inference(equality_resolution,[],[f409]) ).
fof(f441,definition,
( spl59_1
<=> neq(sK12,nil) ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f445,definition,
( spl59_2
<=> sP0(sK12,sK11,sK11,sK12) ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f447,plain,
( sP0(sK12,sK11,sK11,sK12)
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f448,plain,
( ~ spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f406,f445,f441]) ).
fof(f449,plain,
( spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f405,f445,f441]) ).
fof(f450,plain,
( neq(sK12,nil)
| ~ spl59_2 ),
inference(resolution,[],[f247,f447]) ).
fof(f451,plain,
( spl59_1
| ~ spl59_2 ),
inference(avatar_split_clause,[],[f450,f445,f441]) ).
fof(f469,plain,
( sK11 = cons(sK7(sK11,sK12),nil)
| ~ spl59_2 ),
inference(resolution,[],[f245,f447]) ).
fof(f491,plain,
( nil = tl(sK11)
| ~ ssItem(sK7(sK11,sK12))
| ~ ssList(nil)
| ~ spl59_2 ),
inference(superposition,[],[f285,f469]) ).
fof(f493,plain,
( nil != sK11
| ~ ssItem(sK7(sK11,sK12))
| ~ ssList(nil)
| ~ spl59_2 ),
inference(superposition,[],[f293,f469]) ).
fof(f497,plain,
( nil != sK11
| ~ ssItem(sK7(sK11,sK12))
| ~ spl59_2 ),
inference(forward_subsumption_resolution,[],[f493,f400]) ).
fof(f499,plain,
( nil = tl(sK11)
| ~ ssItem(sK7(sK11,sK12))
| ~ spl59_2 ),
inference(forward_subsumption_resolution,[],[f491,f400]) ).
fof(f503,definition,
( spl59_3
<=> ssItem(sK7(sK11,sK12)) ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
fof(f505,plain,
( ~ ssItem(sK7(sK11,sK12))
| spl59_3 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f542,definition,
( spl59_11
<=> nil = sK11 ),
introduced(definition,[new_symbols(definition,[spl59_11])],[avatar_definition]) ).
fof(f544,plain,
( nil != sK11
| spl59_11 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f546,plain,
( ~ spl59_3
| ~ spl59_11
| ~ spl59_2 ),
inference(avatar_split_clause,[],[f497,f445,f542,f503]) ).
fof(f553,definition,
( spl59_13
<=> nil = tl(sK11) ),
introduced(definition,[new_symbols(definition,[spl59_13])],[avatar_definition]) ).
fof(f555,plain,
( nil = tl(sK11)
| ~ spl59_13 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f556,plain,
( ~ spl59_3
| spl59_13
| ~ spl59_2 ),
inference(avatar_split_clause,[],[f499,f445,f553,f503]) ).
fof(f581,plain,
( ! [X0,X1] : ~ sP0(X0,X1,sK11,sK12)
| spl59_3 ),
inference(resolution,[],[f505,f242]) ).
fof(f584,plain,
( $false
| ~ spl59_2
| spl59_3 ),
inference(resolution,[],[f581,f447]) ).
fof(f585,plain,
( ~ spl59_2
| spl59_3 ),
inference(avatar_contradiction_clause,[],[f584]) ).
fof(f661,definition,
( spl59_16
<=> ! [X0,X1] : ~ sP0(X0,X1,sK11,sK12) ),
introduced(definition,[new_symbols(definition,[spl59_16])],[avatar_definition]) ).
fof(f662,plain,
( ! [X0,X1] : ~ sP0(X0,X1,sK11,sK12)
| ~ spl59_16 ),
inference(avatar_component_clause,[],[f661]) ).
fof(f722,plain,
( sK12 = app(cons(sK7(sK11,sK12),nil),sK8(sK11,sK12))
| ~ spl59_2 ),
inference(resolution,[],[f244,f447]) ).
fof(f723,plain,
( sK12 = app(sK11,sK8(sK11,sK12))
| ~ spl59_2 ),
inference(forward_demodulation,[],[f722,f469]) ).
fof(f814,plain,
( app(tl(sK11),sK8(sK11,sK12)) = tl(sK12)
| nil = sK11
| ~ ssList(sK8(sK11,sK12))
| ~ ssList(sK11)
| ~ spl59_2 ),
inference(superposition,[],[f369,f723]) ).
fof(f816,plain,
( nil != sK12
| nil = sK11
| ~ ssList(sK8(sK11,sK12))
| ~ ssList(sK11)
| ~ spl59_2 ),
inference(superposition,[],[f372,f723]) ).
fof(f832,plain,
( nil != sK12
| ~ ssList(sK8(sK11,sK12))
| ~ ssList(sK11)
| ~ spl59_2
| spl59_11 ),
inference(forward_subsumption_resolution,[],[f816,f544]) ).
fof(f834,plain,
( app(tl(sK11),sK8(sK11,sK12)) = tl(sK12)
| ~ ssList(sK8(sK11,sK12))
| ~ ssList(sK11)
| ~ spl59_2
| spl59_11 ),
inference(forward_subsumption_resolution,[],[f814,f544]) ).
fof(f838,definition,
( spl59_22
<=> ssList(sK8(sK11,sK12)) ),
introduced(definition,[new_symbols(definition,[spl59_22])],[avatar_definition]) ).
fof(f839,plain,
( ssList(sK8(sK11,sK12))
| ~ spl59_22 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f840,plain,
( ~ ssList(sK8(sK11,sK12))
| spl59_22 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f856,definition,
( spl59_26
<=> nil = sK12 ),
introduced(definition,[new_symbols(definition,[spl59_26])],[avatar_definition]) ).
fof(f858,plain,
( nil != sK12
| spl59_26 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f860,plain,
( nil != sK12
| ~ ssList(sK8(sK11,sK12))
| ~ spl59_2
| spl59_11 ),
inference(forward_subsumption_resolution,[],[f832,f408]) ).
fof(f862,plain,
( app(tl(sK11),sK8(sK11,sK12)) = tl(sK12)
| ~ ssList(sK8(sK11,sK12))
| ~ spl59_2
| spl59_11 ),
inference(forward_subsumption_resolution,[],[f834,f408]) ).
fof(f873,plain,
( ~ spl59_22
| ~ spl59_26
| ~ spl59_2
| spl59_11 ),
inference(avatar_split_clause,[],[f860,f542,f445,f856,f838]) ).
fof(f879,plain,
( tl(sK12) = app(nil,sK8(sK11,sK12))
| ~ ssList(sK8(sK11,sK12))
| ~ spl59_2
| spl59_11
| ~ spl59_13 ),
inference(forward_demodulation,[],[f862,f555]) ).
fof(f881,definition,
( spl59_30
<=> tl(sK12) = app(nil,sK8(sK11,sK12)) ),
introduced(definition,[new_symbols(definition,[spl59_30])],[avatar_definition]) ).
fof(f883,plain,
( tl(sK12) = app(nil,sK8(sK11,sK12))
| ~ spl59_30 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f884,plain,
( ~ spl59_22
| spl59_30
| ~ spl59_2
| spl59_11
| ~ spl59_13 ),
inference(avatar_split_clause,[],[f879,f553,f542,f445,f881,f838]) ).
fof(f891,plain,
( ! [X0,X1] : ~ sP0(X0,X1,sK11,sK12)
| spl59_22 ),
inference(resolution,[],[f840,f243]) ).
fof(f892,plain,
( spl59_16
| spl59_22 ),
inference(avatar_split_clause,[],[f891,f838,f661]) ).
fof(f899,plain,
( $false
| ~ spl59_2
| ~ spl59_16 ),
inference(resolution,[],[f662,f447]) ).
fof(f900,plain,
( ~ spl59_2
| ~ spl59_16 ),
inference(avatar_contradiction_clause,[],[f899]) ).
fof(f1246,definition,
( spl59_37
<=> ssList(tl(sK12)) ),
introduced(definition,[new_symbols(definition,[spl59_37])],[avatar_definition]) ).
fof(f1247,plain,
( ssList(tl(sK12))
| ~ spl59_37 ),
inference(avatar_component_clause,[],[f1246]) ).
fof(f1248,plain,
( ~ ssList(tl(sK12))
| spl59_37 ),
inference(avatar_component_clause,[],[f1246]) ).
fof(f1299,plain,
( nil = sK12
| ~ ssList(sK12)
| spl59_37 ),
inference(resolution,[],[f1248,f404]) ).
fof(f1300,plain,
( ~ ssList(sK12)
| spl59_26
| spl59_37 ),
inference(forward_subsumption_resolution,[],[f1299,f858]) ).
fof(f1301,plain,
( $false
| spl59_26
| spl59_37 ),
inference(forward_subsumption_resolution,[],[f1300,f407]) ).
fof(f1302,plain,
( spl59_26
| spl59_37 ),
inference(avatar_contradiction_clause,[],[f1301]) ).
fof(f1315,plain,
( ~ ssList(tl(sK12))
| sK12 != app(sK11,tl(sK12))
| ~ neq(nil,sK12)
| ~ ssList(sK12)
| ~ spl59_2 ),
inference(resolution,[],[f410,f447]) ).
fof(f1316,plain,
( sK12 != app(sK11,tl(sK12))
| ~ neq(nil,sK12)
| ~ ssList(sK12)
| ~ spl59_2
| ~ spl59_37 ),
inference(forward_subsumption_resolution,[],[f1315,f1247]) ).
fof(f1317,plain,
( sK12 != app(sK11,tl(sK12))
| ~ neq(nil,sK12)
| ~ spl59_2
| ~ spl59_37 ),
inference(forward_subsumption_resolution,[],[f1316,f407]) ).
fof(f1319,definition,
( spl59_45
<=> neq(nil,sK12) ),
introduced(definition,[new_symbols(definition,[spl59_45])],[avatar_definition]) ).
fof(f1321,plain,
( ~ neq(nil,sK12)
| spl59_45 ),
inference(avatar_component_clause,[],[f1319]) ).
fof(f1323,definition,
( spl59_46
<=> sK12 = app(sK11,tl(sK12)) ),
introduced(definition,[new_symbols(definition,[spl59_46])],[avatar_definition]) ).
fof(f1325,plain,
( sK12 != app(sK11,tl(sK12))
| spl59_46 ),
inference(avatar_component_clause,[],[f1323]) ).
fof(f1326,plain,
( ~ spl59_45
| ~ spl59_46
| ~ spl59_2
| ~ spl59_37 ),
inference(avatar_split_clause,[],[f1317,f1246,f445,f1323,f1319]) ).
fof(f1328,plain,
( nil = sK12
| ~ ssList(sK12)
| ~ ssList(nil)
| spl59_45 ),
inference(resolution,[],[f1321,f397]) ).
fof(f1329,plain,
( ~ ssList(sK12)
| ~ ssList(nil)
| spl59_26
| spl59_45 ),
inference(forward_subsumption_resolution,[],[f1328,f858]) ).
fof(f1331,plain,
( ~ ssList(nil)
| spl59_26
| spl59_45 ),
inference(forward_subsumption_resolution,[],[f1329,f407]) ).
fof(f1341,plain,
( $false
| spl59_26
| spl59_45 ),
inference(forward_subsumption_resolution,[],[f1331,f400]) ).
fof(f1342,plain,
( spl59_26
| spl59_45 ),
inference(avatar_contradiction_clause,[],[f1341]) ).
fof(f1408,plain,
( sK8(sK11,sK12) = tl(sK12)
| ~ ssList(sK8(sK11,sK12))
| ~ spl59_30 ),
inference(superposition,[],[f384,f883]) ).
fof(f1427,plain,
( sK8(sK11,sK12) = tl(sK12)
| ~ spl59_22
| ~ spl59_30 ),
inference(forward_subsumption_resolution,[],[f1408,f839]) ).
fof(f1477,plain,
( sK12 = app(sK11,tl(sK12))
| ~ spl59_2
| ~ spl59_22
| ~ spl59_30 ),
inference(superposition,[],[f723,f1427]) ).
fof(f1479,plain,
( $false
| ~ spl59_2
| ~ spl59_22
| ~ spl59_30
| spl59_46 ),
inference(forward_subsumption_resolution,[],[f1477,f1325]) ).
fof(f1480,plain,
( ~ spl59_2
| ~ spl59_22
| ~ spl59_30
| spl59_46 ),
inference(avatar_contradiction_clause,[],[f1479]) ).
cnf(s1,plain,
( ~ spl59_1
| spl59_2 ),
inference(sat_conversion,[],[f448]) ).
cnf(s2,plain,
( spl59_1
| spl59_2 ),
inference(sat_conversion,[],[f449]) ).
cnf(s3,plain,
( spl59_1
| ~ spl59_2 ),
inference(sat_conversion,[],[f451]) ).
cnf(s12,plain,
( ~ spl59_2
| ~ spl59_3
| ~ spl59_11 ),
inference(sat_conversion,[],[f546]) ).
cnf(s14,plain,
( ~ spl59_2
| ~ spl59_3
| spl59_13 ),
inference(sat_conversion,[],[f556]) ).
cnf(s17,plain,
( ~ spl59_2
| spl59_3 ),
inference(sat_conversion,[],[f585]) ).
cnf(s31,plain,
( ~ spl59_2
| spl59_11
| ~ spl59_22
| ~ spl59_26 ),
inference(sat_conversion,[],[f873]) ).
cnf(s33,plain,
( ~ spl59_2
| spl59_11
| ~ spl59_13
| ~ spl59_22
| spl59_30 ),
inference(sat_conversion,[],[f884]) ).
cnf(s34,plain,
( spl59_16
| spl59_22 ),
inference(sat_conversion,[],[f892]) ).
cnf(s35,plain,
( ~ spl59_2
| ~ spl59_16 ),
inference(sat_conversion,[],[f900]) ).
cnf(s53,plain,
( spl59_26
| spl59_37 ),
inference(sat_conversion,[],[f1302]) ).
cnf(s54,plain,
( ~ spl59_2
| ~ spl59_37
| ~ spl59_45
| ~ spl59_46 ),
inference(sat_conversion,[],[f1326]) ).
cnf(s56,plain,
( spl59_26
| spl59_45 ),
inference(sat_conversion,[],[f1342]) ).
cnf(s57,plain,
( ~ spl59_2
| ~ spl59_22
| ~ spl59_30
| spl59_46 ),
inference(sat_conversion,[],[f1480]) ).
cnf(s58,plain,
spl59_1,
inference(rat,[],[s2,s3]) ).
cnf(s59,plain,
spl59_2,
inference(rat,[],[s1,s58]) ).
cnf(s60,plain,
~ spl59_16,
inference(rat,[],[s35,s59]) ).
cnf(s61,plain,
spl59_3,
inference(rat,[],[s17,s59]) ).
cnf(s62,plain,
spl59_22,
inference(rat,[],[s34,s60]) ).
cnf(s65,plain,
spl59_13,
inference(rat,[],[s14,s59,s61]) ).
cnf(s67,plain,
~ spl59_11,
inference(rat,[],[s12,s59,s61]) ).
cnf(s81,plain,
spl59_30,
inference(rat,[],[s33,s65,s62,s59,s67]) ).
cnf(s83,plain,
~ spl59_26,
inference(rat,[],[s31,s62,s59,s67]) ).
cnf(s88,plain,
spl59_46,
inference(rat,[],[s57,s62,s59,s81]) ).
cnf(s89,plain,
spl59_45,
inference(rat,[],[s56,s83]) ).
cnf(s90,plain,
spl59_37,
inference(rat,[],[s53,s83]) ).
cnf(s96,plain,
$false,
inference(rat,[],[s54,s88,s59,s89,s90]) ).
fof(f1481,plain,
$false,
inference(avatar_sat_refutation,[],[s96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC014+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.04/0.36 % CPULimit : 300
% 0.04/0.36 % WCLimit : 300
% 0.04/0.36 % DateTime : Mon Sep 28 07:26:00 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.39 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
% 4.11/1.26 % (2859809)Detected formulas, will run a generic FOF schedule.
% 4.11/1.26 % (2859817)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2122130244:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.11/1.26 % (2859819)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=429004873:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.11/1.26 % (2859816)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=729465563:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.11/1.26 % (2859814)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=2302644169:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.11/1.26 % (2859820)dis-21_1_sil=8000:lcm=predicate:random_seed=1238486790: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)
% 4.11/1.26 % (2859818)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3020665808:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.11/1.26 % (2859815)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=2459778287:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.11/1.26 % (2859818)Instruction limit reached!
% 4.11/1.26 % (2859818)------------------------------
% 4.11/1.26 % (2859818)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.26 % (2859818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.26 % (2859818)CaDiCaL version: 2.1.3
% 4.11/1.26 % (2859818)Termination reason: Instruction limit
% 4.11/1.26 % (2859818)Termination phase: Saturation
% 4.11/1.26 % (2859818)Time elapsed: 0.067 s
% 4.11/1.26 % (2859818)Peak memory usage: 88 MB
% 4.11/1.26 % (2859818)Instructions burned: 121 (million)
% 4.11/1.26 % (2859817)Instruction limit reached!
% 4.11/1.26 % (2859817)------------------------------
% 4.11/1.26 % (2859817)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.26 % (2859817)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.26 % (2859817)CaDiCaL version: 2.1.3
% 4.11/1.26 % (2859817)Termination reason: Instruction limit
% 4.11/1.26 % (2859817)Termination phase: Saturation
% 4.11/1.26 % (2859817)Time elapsed: 0.069 s
% 4.11/1.26 % (2859817)Peak memory usage: 89 MB
% 4.11/1.26 % (2859817)Instructions burned: 110 (million)
% 4.11/1.26 % (2859820)Instruction limit reached!
% 4.11/1.26 % (2859820)------------------------------
% 4.11/1.26 % (2859820)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.26 % (2859820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.26 % (2859820)CaDiCaL version: 2.1.3
% 4.11/1.26 % (2859820)Termination reason: Instruction limit
% 4.11/1.26 % (2859820)Termination phase: Saturation
% 4.11/1.26 % (2859820)Time elapsed: 0.072 s
% 4.11/1.26 % (2859820)Peak memory usage: 90 MB
% 4.11/1.26 % (2859820)Instructions burned: 129 (million)
% 4.11/1.26 % (2859819)Instruction limit reached!
% 4.11/1.26 % (2859819)------------------------------
% 4.11/1.26 % (2859819)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.26 % (2859819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.26 % (2859819)CaDiCaL version: 2.1.3
% 4.11/1.26 % (2859819)Termination reason: Instruction limit
% 4.11/1.26 % (2859819)Termination phase: Saturation
% 4.11/1.26 % (2859819)Time elapsed: 0.091 s
% 4.11/1.26 % (2859819)Peak memory usage: 90 MB
% 4.11/1.26 % (2859819)Instructions burned: 141 (million)
% 4.11/1.26 % (2859830)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1971111058:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.11/1.26 % (2859829)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1345396835:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.11/1.26 % (2859828)lrs+10_1_sil=8000:sp=occurrence:random_seed=238224903:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.11/1.26 % (2859831)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=3817674254:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.11/1.26 % (2859830)First to succeed.
% 4.11/1.26 % (2859830)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2859809"
% 4.11/1.26 % (2859829)Instruction limit reached!
% 4.11/1.26 % (2859829)------------------------------
% 4.11/1.26 % (2859829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.26 % (2859829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.26 % (2859829)CaDiCaL version: 2.1.3
% 4.11/1.26 % (2859829)Termination reason: Instruction limit
% 4.11/1.26 % (2859829)Termination phase: Saturation
% 4.11/1.26 % (2859829)Time elapsed: 0.074 s
% 4.11/1.26 % (2859829)Peak memory usage: 91 MB
% 4.11/1.26 % (2859829)Instructions burned: 160 (million)
% 4.11/1.26 % (2859831)Instruction limit reached!
% 4.11/1.26 % (2859831)------------------------------
% 4.11/1.26 % (2859831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.26 % (2859831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.26 % (2859831)CaDiCaL version: 2.1.3
% 4.11/1.26 % (2859831)Termination reason: Instruction limit
% 4.11/1.26 % (2859831)Termination phase: Saturation
% 4.11/1.26 % (2859831)Time elapsed: 0.068 s
% 4.11/1.26 % (2859831)Peak memory usage: 94 MB
% 4.11/1.26 % (2859831)Instructions burned: 250 (million)
% 4.11/1.26 % (2859828)Instruction limit reached!
% 4.11/1.26 % (2859828)------------------------------
% 4.11/1.26 % (2859828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.26 % (2859828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.26 % (2859828)CaDiCaL version: 2.1.3
% 4.11/1.26 % (2859828)Termination reason: Instruction limit
% 4.11/1.26 % (2859828)Termination phase: Saturation
% 4.11/1.26 % (2859828)Time elapsed: 0.162 s
% 4.11/1.26 % (2859828)Peak memory usage: 92 MB
% 4.11/1.26 % (2859828)Instructions burned: 287 (million)
% 4.11/1.26 % (2859837)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3818409334:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.11/1.26 % (2859836)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1559837908:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.11/1.26 % (2859836)Refutation not found, incomplete strategy
% 4.11/1.26 % (2859836)------------------------------
% 4.11/1.26 % (2859836)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.26 % (2859836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.26 % (2859836)CaDiCaL version: 2.1.3
% 4.11/1.26 % (2859836)Termination reason: Refutation not found, incomplete strategy
% 4.11/1.26 % (2859836)Time elapsed: 0.004 s
% 4.11/1.26 % (2859836)Peak memory usage: 88 MB
% 4.11/1.26 % (2859836)Instructions burned: 5 (million)
% 4.11/1.26 % (2859830)Refutation found. Thanks to Tanya!
% 4.11/1.26 % SZS status Theorem for theBenchmark
% 4.11/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 4.96/1.36 % (2859830)------------------------------
% 4.96/1.36 % (2859830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.96/1.36 % (2859830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.36 % (2859830)CaDiCaL version: 2.1.3
% 4.96/1.36 % (2859830)Termination reason: Refutation
% 4.96/1.36 % (2859830)Time elapsed: 0.034 s
% 4.96/1.36 % (2859830)Peak memory usage: 90 MB
% 4.96/1.36 % (2859830)Instructions burned: 51 (million)
% 4.96/1.36 % (2859830)------------------------------
% 4.96/1.36 % (2859830)------------------------------
% 4.96/1.36 % (2859809)Success in time 0.665 s
% 4.96/1.36 % Vampire exiting
%------------------------------------------------------------------------------