%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC284+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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 01:03:17 PM UTC 2026
% Result : Theorem 0.84s 0.96s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 134 ( 18 unt; 0 def)
% Number of atoms : 552 ( 113 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 717 ( 299 ~; 313 |; 62 &)
% ( 8 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 167 ( 150 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
fof(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(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ! [X7] :
( ssItem(X7)
=> ( ( ~ memberP(X5,X7)
| leq(X7,X4) )
& ( ~ memberP(X6,X7)
| leq(X4,X7) ) ) ) ) ) )
| ( nil != X2
& nil = X3 )
| ( ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X2
| ~ memberP(X3,X8) )
& neq(X3,nil) ) ) ) ) ),
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
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X0
| ! [X7] :
( ssItem(X7)
=> ( ( ~ memberP(X5,X7)
| leq(X7,X4) )
& ( ~ memberP(X6,X7)
| leq(X4,X7) ) ) ) ) ) )
| ( nil != X2
& nil = X3 )
| ( ! [X8] :
( ~ ssItem(X8)
| cons(X8,nil) != X2
| ~ memberP(X3,X8) )
& neq(X3,nil) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X0
& ? [X7] :
( ( ( memberP(X5,X7)
& ~ leq(X7,X4) )
| ( memberP(X6,X7)
& ~ leq(X4,X7) ) )
& ssItem(X7) ) )
& ssList(X5) )
& ssItem(X4) )
& ( nil = X2
| nil != X3 )
& ( ? [X8] :
( ssItem(X8)
& cons(X8,nil) = X2
& memberP(X3,X8) )
| ~ neq(X3,nil) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f114,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X1,X0)
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f123,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f128,plain,
( ssList(sK3)
& sK1 = sK3
& sK0 = sK2
& ssList(sK6)
& sK0 = app(app(sK5,cons(sK4,nil)),sK6)
& ( ( memberP(sK5,sK7)
& ~ leq(sK7,sK4) )
| ( memberP(sK6,sK7)
& ~ leq(sK4,sK7) ) )
& ssItem(sK7)
& ssList(sK5)
& ssItem(sK4)
& ( nil = sK2
| nil != sK3 )
& ( ( ssItem(sK8)
& sK2 = cons(sK8,nil)
& memberP(sK3,sK8) )
| ~ neq(sK3,nil) )
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7),skolemize(X8,sK8)],[f98]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f117]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f120]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f135]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f121]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X1,X0)
& ~ memberP(X2,X0) ) )
& ( memberP(X1,X0)
| memberP(X2,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f137]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ? [X4] :
( ssList(X4)
& ? [X5] :
( ssList(X5)
& app(X4,cons(X1,X5)) = X0 ) )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f139]) ).
fof(f141,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK13(X0,X1))
& ssList(sK14(X0,X1))
& app(sK13(X0,X1),cons(X1,sK14(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X4,sK13(X0,X1)),skolemize(X5,sK14(X0,X1))],[f140]) ).
fof(f144,plain,
ssList(sK2),
inference(cnf_transformation,[],[f128]) ).
fof(f146,plain,
( sK2 = cons(sK8,nil)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f128]) ).
fof(f147,plain,
( ~ neq(sK3,nil)
| ssItem(sK8) ),
inference(cnf_transformation,[],[f128]) ).
fof(f148,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f128]) ).
fof(f149,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f128]) ).
fof(f150,plain,
ssList(sK5),
inference(cnf_transformation,[],[f128]) ).
fof(f151,plain,
ssItem(sK7),
inference(cnf_transformation,[],[f128]) ).
fof(f152,plain,
( ~ leq(sK7,sK4)
| ~ leq(sK4,sK7) ),
inference(cnf_transformation,[],[f128]) ).
fof(f155,plain,
( memberP(sK6,sK7)
| memberP(sK5,sK7) ),
inference(cnf_transformation,[],[f128]) ).
fof(f156,plain,
sK0 = app(app(sK5,cons(sK4,nil)),sK6),
inference(cnf_transformation,[],[f128]) ).
fof(f157,plain,
ssList(sK6),
inference(cnf_transformation,[],[f128]) ).
fof(f158,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f128]) ).
fof(f160,plain,
ssList(sK3),
inference(cnf_transformation,[],[f128]) ).
fof(f171,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f176,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f180,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f181,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f182,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f184,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f187,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f188,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f189,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f193,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f194,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f198,plain,
! [X2,X3,X0,X1] :
( memberP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f199,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f202,plain,
sK2 = app(app(sK5,cons(sK4,nil)),sK6),
inference(definition_unfolding,[],[f156,f158]) ).
fof(f210,plain,
! [X2,X3,X1] :
( memberP(app(X2,cons(X1,X3)),X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(app(X2,cons(X1,X3))) ),
inference(equality_resolution,[],[f198]) ).
fof(f230,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3)
| ssItem(sK8) ),
inference(resolution,[],[f184,f147]) ).
fof(f235,plain,
( nil = sK3
| ~ ssList(sK3)
| ssItem(sK8) ),
inference(forward_subsumption_resolution,[],[f230,f187]) ).
fof(f236,plain,
( nil = sK3
| ssItem(sK8) ),
inference(forward_subsumption_resolution,[],[f235,f160]) ).
fof(f239,plain,
( sK3 != sK3
| sK2 = sK3
| ssItem(sK8) ),
inference(superposition,[],[f148,f236]) ).
fof(f243,plain,
! [X0] :
( ~ memberP(sK3,X0)
| ~ ssItem(X0)
| ssItem(sK8) ),
inference(superposition,[],[f188,f236]) ).
fof(f246,plain,
( sK2 = sK3
| ssItem(sK8) ),
inference(trivial_inequality_removal,[],[f239]) ).
fof(f314,plain,
! [X0] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0)
| ssItem(sK8)
| ssItem(sK8) ),
inference(superposition,[],[f243,f246]) ).
fof(f315,plain,
! [X0] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0)
| ssItem(sK8) ),
inference(duplicate_literal_removal,[],[f314]) ).
fof(f352,plain,
! [X0] :
( memberP(sK2,X0)
| ~ memberP(sK6,X0)
| ~ ssList(sK6)
| ~ ssList(app(sK5,cons(sK4,nil)))
| ~ ssItem(X0) ),
inference(superposition,[],[f193,f202]) ).
fof(f358,plain,
! [X0] :
( ~ ssList(app(sK5,cons(sK4,nil)))
| ~ memberP(sK6,X0)
| memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f352,f157]) ).
fof(f393,plain,
! [X0] :
( memberP(sK2,X0)
| ~ memberP(app(sK5,cons(sK4,nil)),X0)
| ~ ssList(sK6)
| ~ ssList(app(sK5,cons(sK4,nil)))
| ~ ssItem(X0) ),
inference(superposition,[],[f194,f202]) ).
fof(f402,plain,
! [X0] :
( ~ memberP(app(sK5,cons(sK4,nil)),X0)
| memberP(sK2,X0)
| ~ ssList(app(sK5,cons(sK4,nil)))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f393,f157]) ).
fof(f529,plain,
( sK2 = app(sK5,app(cons(sK4,nil),sK6))
| ~ ssList(sK6)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5) ),
inference(superposition,[],[f202,f176]) ).
fof(f571,plain,
( sK2 = app(sK5,app(cons(sK4,nil),sK6))
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f529,f157]) ).
fof(f587,plain,
( sK2 = app(sK5,app(cons(sK4,nil),sK6))
| ~ ssList(cons(sK4,nil)) ),
inference(forward_subsumption_resolution,[],[f571,f150]) ).
fof(f720,plain,
! [X0] :
( ~ memberP(sK2,X0)
| memberP(nil,X0)
| sK8 = X0
| ~ ssList(nil)
| ~ ssItem(sK8)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f189,f146]) ).
fof(f725,plain,
! [X0] :
( ~ memberP(sK2,X0)
| memberP(nil,X0)
| sK8 = X0
| ~ ssItem(sK8)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f720,f187]) ).
fof(f727,plain,
! [X0] :
( ~ memberP(sK2,X0)
| memberP(nil,X0)
| sK8 = X0
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f725,f315]) ).
fof(f728,plain,
! [X0] :
( ~ memberP(sK2,X0)
| sK8 = X0
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f727,f188]) ).
fof(f982,plain,
( sK2 = app(sK5,cons(sK4,app(nil,sK6)))
| ~ ssList(cons(sK4,nil))
| ~ ssItem(sK4)
| ~ ssList(nil)
| ~ ssList(sK6) ),
inference(superposition,[],[f587,f181]) ).
fof(f1004,plain,
( sK2 = app(sK5,cons(sK4,app(nil,sK6)))
| ~ ssItem(sK4)
| ~ ssList(nil)
| ~ ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f982,f171]) ).
fof(f1006,plain,
( sK2 = app(sK5,cons(sK4,app(nil,sK6)))
| ~ ssList(nil)
| ~ ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f1004,f149]) ).
fof(f1008,plain,
( sK2 = app(sK5,cons(sK4,app(nil,sK6)))
| ~ ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f1006,f187]) ).
fof(f1009,plain,
sK2 = app(sK5,cons(sK4,app(nil,sK6))),
inference(forward_subsumption_resolution,[],[f1008,f157]) ).
fof(f1022,plain,
! [X0] :
( ~ memberP(sK6,X0)
| memberP(sK2,X0)
| ~ ssItem(X0)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5) ),
inference(resolution,[],[f358,f182]) ).
fof(f1029,plain,
! [X0] :
( ~ ssList(cons(sK4,nil))
| memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(sK6,X0) ),
inference(forward_subsumption_resolution,[],[f1022,f150]) ).
fof(f1111,plain,
! [X0] :
( memberP(sK2,X0)
| ~ ssList(app(sK5,cons(sK4,nil)))
| ~ ssItem(X0)
| ~ memberP(sK5,X0)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5)
| ~ ssItem(X0) ),
inference(resolution,[],[f402,f194]) ).
fof(f1119,plain,
! [X0] :
( memberP(sK2,X0)
| ~ ssList(app(sK5,cons(sK4,nil)))
| ~ ssItem(X0)
| ~ memberP(sK5,X0)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5) ),
inference(duplicate_literal_removal,[],[f1111]) ).
fof(f1125,plain,
! [X0] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(sK5,X0)
| ~ ssList(cons(sK4,nil))
| ~ ssList(sK5) ),
inference(forward_subsumption_resolution,[],[f1119,f182]) ).
fof(f1128,plain,
! [X0] :
( ~ ssList(cons(sK4,nil))
| ~ ssItem(X0)
| ~ memberP(sK5,X0)
| memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f1125,f150]) ).
fof(f1177,plain,
( sK2 = app(sK5,cons(sK4,sK6))
| ~ ssList(sK6) ),
inference(superposition,[],[f1009,f180]) ).
fof(f1201,plain,
sK2 = app(sK5,cons(sK4,sK6)),
inference(forward_subsumption_resolution,[],[f1177,f157]) ).
fof(f1204,plain,
( memberP(sK2,sK4)
| ~ ssList(sK5)
| ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ ssList(sK2) ),
inference(superposition,[],[f210,f1201]) ).
fof(f1226,plain,
( memberP(sK2,sK4)
| ~ ssList(sK6)
| ~ ssItem(sK4)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f1204,f150]) ).
fof(f1227,plain,
( memberP(sK2,sK4)
| ~ ssItem(sK4)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f1226,f157]) ).
fof(f1228,plain,
( memberP(sK2,sK4)
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f1227,f149]) ).
fof(f1229,plain,
memberP(sK2,sK4),
inference(forward_subsumption_resolution,[],[f1228,f144]) ).
fof(f1230,plain,
( sK4 = sK8
| ~ ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(resolution,[],[f1229,f728]) ).
fof(f1234,plain,
( ~ neq(sK3,nil)
| sK4 = sK8 ),
inference(forward_subsumption_resolution,[],[f1230,f149]) ).
fof(f1292,plain,
( sK4 = sK8
| nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolution,[],[f1234,f184]) ).
fof(f1298,plain,
( sK4 = sK8
| nil = sK3
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f1292,f187]) ).
fof(f1299,plain,
( sK4 = sK8
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f1298,f160]) ).
fof(f1301,plain,
( ~ leq(sK8,sK7)
| ~ leq(sK7,sK8)
| nil = sK3 ),
inference(superposition,[],[f152,f1299]) ).
fof(f2716,plain,
! [X0] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(sK6,X0)
| ~ ssItem(sK4)
| ~ ssList(nil) ),
inference(resolution,[],[f1029,f171]) ).
fof(f2721,plain,
! [X0] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(sK6,X0)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f2716,f149]) ).
fof(f2722,plain,
! [X0] :
( memberP(sK2,X0)
| ~ ssItem(X0)
| ~ memberP(sK6,X0) ),
inference(forward_subsumption_resolution,[],[f2721,f187]) ).
fof(f2723,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sK6,X0)
| sK8 = X0
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(resolution,[],[f2722,f728]) ).
fof(f2727,plain,
! [X0] :
( ~ memberP(sK6,X0)
| ~ ssItem(X0)
| sK8 = X0
| ~ neq(sK3,nil) ),
inference(duplicate_literal_removal,[],[f2723]) ).
fof(f2820,plain,
( ~ ssItem(sK7)
| sK7 = sK8
| ~ neq(sK3,nil)
| memberP(sK5,sK7) ),
inference(resolution,[],[f2727,f155]) ).
fof(f2825,plain,
( memberP(sK5,sK7)
| ~ neq(sK3,nil)
| sK7 = sK8 ),
inference(forward_subsumption_resolution,[],[f2820,f151]) ).
fof(f2962,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sK5,X0)
| memberP(sK2,X0)
| ~ ssItem(sK4)
| ~ ssList(nil) ),
inference(resolution,[],[f1128,f171]) ).
fof(f2967,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(sK5,X0)
| memberP(sK2,X0)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f2962,f149]) ).
fof(f2968,plain,
! [X0] :
( memberP(sK2,X0)
| ~ memberP(sK5,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f2967,f187]) ).
fof(f3027,plain,
! [X0] :
( ~ memberP(sK5,X0)
| ~ ssItem(X0)
| sK8 = X0
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(resolution,[],[f2968,f728]) ).
fof(f3031,plain,
! [X0] :
( ~ memberP(sK5,X0)
| ~ ssItem(X0)
| sK8 = X0
| ~ neq(sK3,nil) ),
inference(duplicate_literal_removal,[],[f3027]) ).
fof(f3032,plain,
( ~ ssItem(sK7)
| sK7 = sK8
| ~ neq(sK3,nil)
| ~ neq(sK3,nil)
| sK7 = sK8 ),
inference(resolution,[],[f3031,f2825]) ).
fof(f3036,plain,
( ~ ssItem(sK7)
| sK7 = sK8
| ~ neq(sK3,nil) ),
inference(duplicate_literal_removal,[],[f3032]) ).
fof(f3039,plain,
( ~ neq(sK3,nil)
| sK7 = sK8 ),
inference(forward_subsumption_resolution,[],[f3036,f151]) ).
fof(f3042,plain,
( sK7 = sK8
| nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolution,[],[f3039,f184]) ).
fof(f3048,plain,
( sK7 = sK8
| nil = sK3
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f3042,f187]) ).
fof(f3049,plain,
( sK7 = sK8
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f3048,f160]) ).
fof(f3178,plain,
( ~ leq(sK8,sK8)
| ~ leq(sK8,sK8)
| nil = sK3
| nil = sK3 ),
inference(superposition,[],[f1301,f3049]) ).
fof(f3179,plain,
( ~ leq(sK8,sK8)
| nil = sK3 ),
inference(duplicate_literal_removal,[],[f3178]) ).
fof(f3180,plain,
( nil = sK3
| ~ ssItem(sK8) ),
inference(resolution,[],[f3179,f199]) ).
fof(f3184,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f3180,f236]) ).
fof(f3189,plain,
( sK3 != sK3
| sK2 = sK3 ),
inference(superposition,[],[f148,f3184]) ).
fof(f3194,plain,
! [X0] :
( ~ memberP(sK3,X0)
| ~ ssItem(X0) ),
inference(superposition,[],[f188,f3184]) ).
fof(f3234,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f3189]) ).
fof(f3456,plain,
! [X0] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[],[f3194,f3234]) ).
fof(f3642,plain,
~ ssItem(sK4),
inference(resolution,[],[f3456,f1229]) ).
fof(f3654,plain,
$false,
inference(forward_subsumption_resolution,[],[f3642,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC284+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.17 % Computer : n017.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 08:47:36 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.21 Running first-order theorem proving
% 0.06/0.21 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
% 0.84/0.96 % (3406740)Detected formulas, will run a generic FOF schedule.
% 0.84/0.96 % (3406749)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=850394862:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.84/0.96 % (3406749)First to succeed.
% 0.84/0.96 % (3406749)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3406740"
% 0.84/0.96 % (3406746)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=2217693407:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.84/0.96 % (3406747)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=1917805321:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.84/0.96 % (3406748)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=479678685:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.84/0.96 % (3406745)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=3760219025:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.84/0.96 % (3406751)dis-21_1_sil=8000:lcm=predicate:random_seed=987320643: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)
% 0.84/0.96 % (3406750)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1717408077:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.84/0.96 % (3406748)Also succeeded, but the first one will report.
% 0.84/0.96 % (3406751)Instruction limit reached!
% 0.84/0.96 % (3406751)------------------------------
% 0.84/0.96 % (3406751)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.84/0.96 % (3406751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.96 % (3406751)CaDiCaL version: 2.1.3
% 0.84/0.96 % (3406751)Termination reason: Instruction limit
% 0.84/0.96 % (3406751)Termination phase: Saturation
% 0.84/0.96 % (3406751)Time elapsed: 0.074 s
% 0.84/0.96 % (3406751)Peak memory usage: 90 MB
% 0.84/0.96 % (3406751)Instructions burned: 129 (million)
% 0.84/0.96 % (3406750)Instruction limit reached!
% 0.84/0.96 % (3406750)------------------------------
% 0.84/0.96 % (3406750)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.84/0.96 % (3406750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.84/0.96 % (3406750)CaDiCaL version: 2.1.3
% 0.84/0.96 % (3406750)Termination reason: Instruction limit
% 0.84/0.96 % (3406750)Termination phase: Saturation
% 0.84/0.96 % (3406750)Time elapsed: 0.096 s
% 0.84/0.96 % (3406750)Peak memory usage: 90 MB
% 0.84/0.96 % (3406750)Instructions burned: 139 (million)
% 0.84/0.96 % (3406749)Refutation found. Thanks to Tanya!
% 0.84/0.96 % SZS status Theorem for theBenchmark
% 0.84/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/1.16 % (3406749)------------------------------
% 2.79/1.16 % (3406749)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.16 % (3406749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.16 % (3406749)CaDiCaL version: 2.1.3
% 2.79/1.16 % (3406749)Termination reason: Refutation
% 2.79/1.16 % (3406749)Time elapsed: 0.037 s
% 2.79/1.16 % (3406749)Peak memory usage: 89 MB
% 2.79/1.16 % (3406749)Instructions burned: 113 (million)
% 2.79/1.16 % (3406749)------------------------------
% 2.79/1.16 % (3406749)------------------------------
% 2.79/1.16 % (3406740)Success in time 0.306 s
% 2.79/1.16 % Vampire exiting
%------------------------------------------------------------------------------