%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC071+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 : n010.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 01:02:18 PM UTC 2026
% Result : Theorem 2.58s 1.27s
% Output : Refutation 3.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 105 ( 13 unt; 1 def)
% Number of atoms : 494 ( 105 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 673 ( 284 ~; 250 |; 105 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 203 ( 162 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(app(X2,X1),X3) = X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X0,X1)
& segmentP(X1,X2) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ( nil = X1
& nil = X0 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X5,nil) != X2
| app(app(X6,X2),X7) != X3
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X5,X8) )
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X9,X5) ) ) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
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
| ? [X4] :
( ssList(X4)
& neq(X4,nil)
& segmentP(X1,X4)
& segmentP(X0,X4) )
| ( nil = X1
& nil = X0 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( ssList(X7)
=> ( cons(X5,nil) != X2
| app(app(X6,X2),X7) != X3
| ? [X8] :
( ssItem(X8)
& memberP(X6,X8)
& lt(X5,X8) )
| ? [X9] :
( ssItem(X9)
& memberP(X7,X9)
& lt(X9,X5) ) ) ) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ( nil != X1
| nil != X0 )
& ( ? [X5] :
( ? [X6] :
( ? [X7] :
( cons(X5,nil) = X2
& app(app(X6,X2),X7) = X3
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X5,X8) )
& ! [X9] :
( ~ ssItem(X9)
| ~ memberP(X7,X9)
| ~ lt(X9,X5) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ( 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
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ( nil != X1
| nil != X0 )
& ( ? [X5] :
( ? [X6] :
( ? [X7] :
( cons(X5,nil) = X2
& app(app(X6,X2),X7) = X3
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X5,X8) )
& ! [X9] :
( ~ ssItem(X9)
| ~ memberP(X7,X9)
| ~ lt(X9,X5) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f125,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f128,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f131]) ).
fof(f133,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(f149,definition,
! [X2,X3] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( cons(X5,nil) = X2
& app(app(X6,X2),X7) = X3
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X5,X8) )
& ! [X9] :
( ~ ssItem(X9)
| ~ memberP(X7,X9)
| ~ lt(X9,X5) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ~ sP0(X2,X3) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f150,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(X1,X4)
| ~ segmentP(X0,X4) )
& ( nil != X1
| nil != X0 )
& ( sP0(X2,X3)
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f149]) ).
fof(f151,plain,
! [X2,X3] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( cons(X5,nil) = X2
& app(app(X6,X2),X7) = X3
& ! [X8] :
( ~ ssItem(X8)
| ~ memberP(X6,X8)
| ~ lt(X5,X8) )
& ! [X9] :
( ~ ssItem(X9)
| ~ memberP(X7,X9)
| ~ lt(X9,X5) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ~ sP0(X2,X3) ),
inference(nnf_transformation,[],[f149]) ).
fof(f152,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( cons(X2,nil) = X0
& app(app(X3,X0),X4) = X1
& ! [X5] :
( ~ ssItem(X5)
| ~ memberP(X3,X5)
| ~ lt(X2,X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ memberP(X4,X6)
| ~ lt(X6,X2) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ( cons(sK1(X0,X1),nil) = X0
& app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
& ! [X5] :
( ~ ssItem(X5)
| ~ memberP(sK2(X0,X1),X5)
| ~ lt(sK1(X0,X1),X5) )
& ! [X6] :
( ~ ssItem(X6)
| ~ memberP(sK3(X0,X1),X6)
| ~ lt(X6,sK1(X0,X1)) )
& ssList(sK3(X0,X1))
& ssList(sK2(X0,X1))
& ssItem(sK1(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f152]) ).
fof(f154,plain,
( sK5 = sK7
& sK4 = sK6
& ! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK5,X4)
| ~ segmentP(sK4,X4) )
& ( nil != sK5
| nil != sK4 )
& ( sP0(sK6,sK7)
| ( nil = sK7
& nil = sK6 ) )
& ssList(sK7)
& ssList(sK6)
& ssList(sK5)
& ssList(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f150]) ).
fof(f159,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f169,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,[],[f133]) ).
fof(f170,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,[],[f169]) ).
fof(f171,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(app(X2,X1),X3) != X0 ) ) )
& ( ( ssList(sK14(X0,X1))
& ssList(sK15(X0,X1))
& app(app(sK14(X0,X1),X1),sK15(X0,X1)) = X0 )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X4,sK14(X0,X1)),skolemize(X5,sK15(X0,X1))],[f170]) ).
fof(f174,plain,
! [X0,X1] :
( ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f175,plain,
! [X0,X1] :
( ssList(sK2(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f176,plain,
! [X0,X1] :
( ssList(sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f179,plain,
! [X0,X1] :
( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f180,plain,
! [X0,X1] :
( cons(sK1(X0,X1),nil) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f153]) ).
fof(f183,plain,
ssList(sK6),
inference(cnf_transformation,[],[f154]) ).
fof(f184,plain,
ssList(sK7),
inference(cnf_transformation,[],[f154]) ).
fof(f185,plain,
( sP0(sK6,sK7)
| nil = sK6 ),
inference(cnf_transformation,[],[f154]) ).
fof(f186,plain,
( sP0(sK6,sK7)
| nil = sK7 ),
inference(cnf_transformation,[],[f154]) ).
fof(f187,plain,
( nil != sK5
| nil != sK4 ),
inference(cnf_transformation,[],[f154]) ).
fof(f188,plain,
! [X4] :
( ~ ssList(X4)
| ~ neq(X4,nil)
| ~ segmentP(sK5,X4)
| ~ segmentP(sK4,X4) ),
inference(cnf_transformation,[],[f154]) ).
fof(f189,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f154]) ).
fof(f190,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f154]) ).
fof(f194,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f201,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f212,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f214,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f159]) ).
fof(f217,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f231,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f233,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f235,plain,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f239,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,[],[f171]) ).
fof(f251,plain,
! [X4] :
( ~ segmentP(sK7,X4)
| ~ neq(X4,nil)
| ~ ssList(X4)
| ~ segmentP(sK6,X4) ),
inference(definition_unfolding,[],[f188,f190,f189]) ).
fof(f252,plain,
( nil != sK7
| nil != sK6 ),
inference(definition_unfolding,[],[f187,f190,f189]) ).
fof(f262,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,[],[f239]) ).
fof(f287,plain,
! [X0,X1] :
( nil != X0
| ~ ssItem(sK1(X0,X1))
| ~ ssList(nil)
| ~ sP0(X0,X1) ),
inference(superposition,[],[f194,f180]) ).
fof(f288,plain,
! [X0,X1] :
( ssList(X0)
| ~ ssItem(sK1(X0,X1))
| ~ ssList(nil)
| ~ sP0(X0,X1) ),
inference(superposition,[],[f201,f180]) ).
fof(f289,plain,
! [X0,X1] :
( ssList(X0)
| ~ ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f288,f217]) ).
fof(f290,plain,
! [X0,X1] :
( nil != X0
| ~ ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f287,f217]) ).
fof(f293,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(X0) ),
inference(forward_subsumption_resolution,[],[f289,f174]) ).
fof(f294,plain,
! [X0,X1] :
( nil != X0
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f290,f174]) ).
fof(f299,plain,
! [X0] : ~ sP0(nil,X0),
inference(equality_resolution,[],[f294]) ).
fof(f357,plain,
! [X0,X1] :
( ssList(X0)
| ~ ssList(sK3(X1,X0))
| ~ ssList(app(sK2(X1,X0),X1))
| ~ sP0(X1,X0) ),
inference(superposition,[],[f212,f179]) ).
fof(f358,plain,
! [X0,X1] :
( ~ ssList(app(sK2(X1,X0),X1))
| ssList(X0)
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f357,f176]) ).
fof(f361,plain,
! [X0,X1] :
( ssList(X0)
| ~ sP0(X1,X0)
| ~ ssList(X1)
| ~ ssList(sK2(X1,X0)) ),
inference(resolution,[],[f358,f212]) ).
fof(f364,plain,
! [X0,X1] :
( ssList(X0)
| ~ sP0(X1,X0)
| ~ ssList(sK2(X1,X0)) ),
inference(forward_subsumption_resolution,[],[f361,f293]) ).
fof(f365,plain,
! [X0,X1] :
( ~ sP0(X1,X0)
| ssList(X0) ),
inference(forward_subsumption_resolution,[],[f364,f175]) ).
fof(f438,plain,
! [X0,X1] :
( ~ segmentP(sK7,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK7)
| ~ neq(X1,nil)
| ~ ssList(X1)
| ~ segmentP(sK6,X1) ),
inference(resolution,[],[f235,f251]) ).
fof(f439,plain,
! [X0,X1] :
( ~ segmentP(sK7,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK7)
| ~ neq(X1,nil)
| ~ segmentP(sK6,X1) ),
inference(duplicate_literal_removal,[],[f438]) ).
fof(f442,plain,
! [X0,X1] :
( ~ segmentP(sK7,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ neq(X1,nil)
| ~ segmentP(sK6,X1) ),
inference(forward_subsumption_resolution,[],[f439,f184]) ).
fof(f488,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ neq(X0,nil)
| ~ segmentP(sK6,X0)
| ~ ssList(sK7) ),
inference(resolution,[],[f442,f231]) ).
fof(f496,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sK6,X0)
| ~ ssList(sK7) ),
inference(forward_subsumption_resolution,[],[f488,f217]) ).
fof(f497,plain,
! [X0] :
( ~ segmentP(sK6,X0)
| ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[],[f496,f184]) ).
fof(f501,plain,
( ~ ssList(sK6)
| ~ neq(sK6,nil)
| ~ segmentP(nil,sK6)
| ~ ssList(sK6) ),
inference(resolution,[],[f497,f233]) ).
fof(f504,plain,
( ~ ssList(sK6)
| ~ neq(sK6,nil)
| ~ segmentP(nil,sK6) ),
inference(duplicate_literal_removal,[],[f501]) ).
fof(f506,plain,
( ~ segmentP(nil,sK6)
| ~ neq(sK6,nil) ),
inference(forward_subsumption_resolution,[],[f504,f183]) ).
fof(f1089,plain,
! [X0,X1] :
( segmentP(X0,X1)
| ~ ssList(sK2(X1,X0))
| ~ ssList(sK3(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ sP0(X1,X0) ),
inference(superposition,[],[f262,f179]) ).
fof(f1105,plain,
! [X0,X1] :
( segmentP(X0,X1)
| ~ ssList(sK3(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f1089,f175]) ).
fof(f1114,plain,
! [X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f1105,f176]) ).
fof(f1118,plain,
! [X0,X1] :
( segmentP(X0,X1)
| ~ ssList(X0)
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f1114,f293]) ).
fof(f1119,plain,
! [X0,X1] :
( segmentP(X0,X1)
| ~ sP0(X1,X0) ),
inference(forward_subsumption_resolution,[],[f1118,f365]) ).
fof(f1151,plain,
( ~ sP0(sK6,nil)
| ~ neq(sK6,nil) ),
inference(resolution,[],[f1119,f506]) ).
fof(f1163,plain,
! [X0] :
( ~ sP0(X0,sK7)
| ~ neq(X0,nil)
| ~ ssList(X0)
| ~ segmentP(sK6,X0) ),
inference(resolution,[],[f1119,f251]) ).
fof(f1164,plain,
! [X0] :
( ~ sP0(X0,sK7)
| ~ neq(X0,nil)
| ~ segmentP(sK6,X0) ),
inference(forward_subsumption_resolution,[],[f1163,f293]) ).
fof(f1233,plain,
( ~ segmentP(sK6,sK6)
| ~ neq(sK6,nil)
| nil = sK7 ),
inference(resolution,[],[f1164,f186]) ).
fof(f1298,plain,
( ~ neq(sK6,nil)
| nil = sK7
| ~ ssList(sK6) ),
inference(resolution,[],[f1233,f233]) ).
fof(f1305,plain,
( ~ neq(sK6,nil)
| nil = sK7 ),
inference(forward_subsumption_resolution,[],[f1298,f183]) ).
fof(f1307,plain,
( nil = sK7
| nil = sK6
| ~ ssList(nil)
| ~ ssList(sK6) ),
inference(resolution,[],[f1305,f214]) ).
fof(f1308,plain,
( nil = sK7
| nil = sK6
| ~ ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f1307,f217]) ).
fof(f1309,plain,
( nil = sK7
| nil = sK6 ),
inference(forward_subsumption_resolution,[],[f1308,f183]) ).
fof(f1347,plain,
( ~ sP0(sK6,sK7)
| ~ neq(sK6,sK7)
| nil = sK6 ),
inference(superposition,[],[f1151,f1309]) ).
fof(f1349,plain,
( sK6 != sK7
| nil = sK6 ),
inference(equality_factoring,[],[f1309]) ).
fof(f1351,plain,
( ~ neq(sK6,sK7)
| nil = sK6 ),
inference(forward_subsumption_resolution,[],[f1347,f185]) ).
fof(f1373,plain,
( nil = sK6
| sK6 = sK7
| ~ ssList(sK7)
| ~ ssList(sK6) ),
inference(resolution,[],[f1351,f214]) ).
fof(f1374,plain,
( nil = sK6
| ~ ssList(sK7)
| ~ ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f1373,f1349]) ).
fof(f1376,plain,
( nil = sK6
| ~ ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f1374,f184]) ).
fof(f1377,plain,
nil = sK6,
inference(forward_subsumption_resolution,[],[f1376,f183]) ).
fof(f1405,plain,
( sK6 != sK7
| sK6 != sK6 ),
inference(superposition,[],[f252,f1377]) ).
fof(f1409,plain,
! [X0] : ~ sP0(sK6,X0),
inference(superposition,[],[f299,f1377]) ).
fof(f1431,plain,
sK6 != sK7,
inference(trivial_inequality_removal,[],[f1405]) ).
fof(f1437,plain,
nil = sK7,
inference(resolution,[],[f1409,f186]) ).
fof(f1439,plain,
sK6 = sK7,
inference(forward_demodulation,[],[f1437,f1377]) ).
fof(f1454,plain,
$false,
inference(forward_subsumption_resolution,[],[f1439,f1431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC071+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 07:43:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.58/1.27 % (1749056)Detected formulas, will run a generic FOF schedule.
% 2.58/1.27 % (1749063)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=3975218238:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.27 % (1749066)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=554638866:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.27 % (1749064)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=33688057:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.27 % (1749065)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3278605567:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.27 % (1749062)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=1210688064:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.27 % (1749061)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=2047210152:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.27 % (1749067)dis-21_1_sil=8000:lcm=predicate:random_seed=140525864: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)
% 2.58/1.27 % (1749065)First to succeed.
% 2.58/1.27 % (1749065)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1749056"
% 2.58/1.27 % (1749064)Instruction limit reached!
% 2.58/1.27 % (1749064)------------------------------
% 2.58/1.27 % (1749064)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.27 % (1749064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.27 % (1749064)CaDiCaL version: 2.1.3
% 2.58/1.27 % (1749064)Termination reason: Instruction limit
% 2.58/1.27 % (1749064)Termination phase: Saturation
% 2.58/1.27 % (1749064)Time elapsed: 0.065 s
% 2.58/1.27 % (1749064)Peak memory usage: 89 MB
% 2.58/1.27 % (1749064)Instructions burned: 109 (million)
% 2.58/1.27 % (1749067)Instruction limit reached!
% 2.58/1.27 % (1749067)------------------------------
% 2.58/1.27 % (1749067)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.27 % (1749067)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.27 % (1749067)CaDiCaL version: 2.1.3
% 2.58/1.27 % (1749067)Termination reason: Instruction limit
% 2.58/1.27 % (1749067)Termination phase: Saturation
% 2.58/1.27 % (1749067)Time elapsed: 0.075 s
% 2.58/1.27 % (1749067)Peak memory usage: 90 MB
% 2.58/1.27 % (1749067)Instructions burned: 130 (million)
% 2.58/1.27 % (1749066)Instruction limit reached!
% 2.58/1.27 % (1749066)------------------------------
% 2.58/1.27 % (1749066)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.27 % (1749066)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.27 % (1749066)CaDiCaL version: 2.1.3
% 2.58/1.27 % (1749066)Termination reason: Instruction limit
% 2.58/1.27 % (1749066)Termination phase: Saturation
% 2.58/1.27 % (1749066)Time elapsed: 0.099 s
% 2.58/1.27 % (1749066)Peak memory usage: 90 MB
% 2.58/1.27 % (1749066)Instructions burned: 140 (million)
% 2.58/1.27 % (1749075)lrs+10_1_sil=8000:sp=occurrence:random_seed=357339787:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.58/1.27 % (1749077)lrs+1011_1_sil=32000:sp=occurrence:random_seed=433235970:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.58/1.27 % (1749076)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3197160620:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.58/1.27 % (1749077)Also succeeded, but the first one will report.
% 2.58/1.27 % (1749065)Refutation found. Thanks to Tanya!
% 2.58/1.27 % SZS status Theorem for theBenchmark
% 2.58/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.52/1.37 % (1749065)------------------------------
% 3.52/1.37 % (1749065)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.52/1.37 % (1749065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.52/1.37 % (1749065)CaDiCaL version: 2.1.3
% 3.52/1.37 % (1749065)Termination reason: Refutation
% 3.52/1.37 % (1749065)Time elapsed: 0.025 s
% 3.52/1.37 % (1749065)Peak memory usage: 88 MB
% 3.52/1.37 % (1749065)Instructions burned: 40 (million)
% 3.52/1.37 % (1749065)------------------------------
% 3.52/1.37 % (1749065)------------------------------
% 3.52/1.37 % (1749056)Success in time 0.435 s
% 3.52/1.37 % Vampire exiting
%------------------------------------------------------------------------------