%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC199+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 : n015.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 01:02:54 PM UTC 2026
% Result : Theorem 3.00s 1.35s
% Output : Refutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 12
% Syntax : Number of formulae : 110 ( 8 unt; 0 def)
% Number of atoms : 625 ( 166 equ)
% Maximal formula atoms : 17 ( 5 avg)
% Number of connectives : 900 ( 385 ~; 413 |; 70 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 265 ( 227 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [X0] :
( ssItem(X0)
& ? [X1] :
( ssItem(X1)
& X0 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
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(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(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(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(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X0,X5)
| X4 = X5 ) ) )
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X6 != X7
& app(app(app(app(X8,cons(X6,nil)),X10),cons(X7,nil)),X9) = X2 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X0,X5)
| X4 = X5 ) ) )
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& ? [X10] :
( ssList(X10)
& X6 != X7
& app(app(app(app(X8,cons(X6,nil)),X10),cons(X7,nil)),X9) = X2 ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ? [X5] :
( memberP(X0,X5)
& X4 != X5
& ssItem(X5) ) )
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| X6 = X7
| app(app(app(app(X8,cons(X6,nil)),X10),cons(X7,nil)),X9) != 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] :
( ~ ssItem(X4)
| ? [X5] :
( memberP(X0,X5)
& X4 != X5
& ssItem(X5) ) )
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| X6 = X7
| app(app(app(app(X8,cons(X6,nil)),X10),cons(X7,nil)),X9) != X2 ) ) ) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f101,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f102,plain,
! [X0] :
( nil = X0
| ? [X1] :
( ssList(X1)
& ? [X2] :
( ssItem(X2)
& cons(X2,X1) = X0 ) )
| ~ ssList(X0) ),
inference(flattening,[],[f101]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f109,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(f110,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f115,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f116,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(f118,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f119,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] :
( ( memberP(X0,X1)
<=> ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& app(X2,cons(X1,X3)) = X0 ) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f122,plain,
( sK1 = sK3
& sK0 = sK2
& ! [X4] :
( ~ ssItem(X4)
| ( memberP(sK0,sK4(X4))
& sK4(X4) != X4
& ssItem(sK4(X4)) ) )
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| ! [X10] :
( ~ ssList(X10)
| X6 = X7
| app(app(app(app(X8,cons(X6,nil)),X10),cons(X7,nil)),X9) != sK2 ) ) ) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X5,sK4(X4))],[f99]) ).
fof(f123,plain,
( ssItem(sK5)
& ssItem(sK6)
& sK5 != sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X0,sK5),skolemize(X1,sK6)],[f2]) ).
fof(f124,plain,
! [X0] :
( nil = X0
| ( ssList(sK7(X0))
& ssItem(sK8(X0))
& cons(sK8(X0),sK7(X0)) = X0 )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f102]) ).
fof(f127,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,[],[f119]) ).
fof(f128,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,[],[f127]) ).
fof(f131,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,[],[f121]) ).
fof(f132,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,[],[f131]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK9(X0,X1))
& ssList(sK10(X0,X1))
& app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f132]) ).
fof(f136,plain,
ssList(sK2),
inference(cnf_transformation,[],[f122]) ).
fof(f138,plain,
! [X10,X8,X6,X9,X7] :
( app(app(app(app(X8,cons(X6,nil)),X10),cons(X7,nil)),X9) != sK2
| ~ ssItem(X7)
| ~ ssList(X8)
| ~ ssList(X9)
| ~ ssList(X10)
| X6 = X7
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f122]) ).
fof(f139,plain,
! [X4] :
( ssItem(sK4(X4))
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f122]) ).
fof(f140,plain,
! [X4] :
( sK4(X4) != X4
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f122]) ).
fof(f141,plain,
! [X4] :
( ~ ssItem(X4)
| memberP(sK0,sK4(X4)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f142,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f122]) ).
fof(f145,plain,
ssItem(sK6),
inference(cnf_transformation,[],[f123]) ).
fof(f148,plain,
! [X0] :
( cons(sK8(X0),sK7(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f149,plain,
! [X0] :
( ssItem(sK8(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f150,plain,
! [X0] :
( ssList(sK7(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f154,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f159,plain,
! [X2,X0,X1] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f160,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f163,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f164,plain,
! [X2,X0,X1] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f166,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f167,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f170,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f174,plain,
! [X0,X1] :
( app(sK9(X0,X1),cons(X1,sK10(X0,X1))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f175,plain,
! [X0,X1] :
( ssList(sK10(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f176,plain,
! [X0,X1] :
( ssList(sK9(X0,X1))
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f178,plain,
! [X4] :
( memberP(sK2,sK4(X4))
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f141,f142]) ).
fof(f183,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f170]) ).
fof(f185,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f183]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( sK2 != app(app(app(cons(X0,nil),X1),cons(X2,nil)),X3)
| ~ ssItem(X2)
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(superposition,[],[f138,f163]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( sK2 != app(app(app(cons(X0,nil),X1),cons(X2,nil)),X3)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(forward_subsumption_resolution,[],[f197,f166]) ).
fof(f216,plain,
! [X0] :
( memberP(X0,sK8(X0))
| ~ ssList(sK7(X0))
| ~ ssItem(sK8(X0))
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f185,f148]) ).
fof(f221,plain,
! [X0] :
( memberP(X0,sK8(X0))
| ~ ssItem(sK8(X0))
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f216,f150]) ).
fof(f223,plain,
! [X0] :
( memberP(X0,sK8(X0))
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f221,f149]) ).
fof(f232,plain,
! [X2,X3,X0,X1] :
( sK2 != app(app(cons(X0,X1),cons(X2,nil)),X3)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(superposition,[],[f199,f160]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( sK2 != app(app(cons(X0,X1),cons(X2,nil)),X3)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(duplicate_literal_removal,[],[f232]) ).
fof(f329,plain,
! [X2,X3,X0,X1] :
( sK2 != app(cons(X0,X1),app(cons(X2,nil),X3))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssList(X3)
| ~ ssList(cons(X2,nil))
| ~ ssList(cons(X0,X1)) ),
inference(superposition,[],[f243,f159]) ).
fof(f369,plain,
! [X2,X3,X0,X1] :
( sK2 != app(cons(X0,X1),app(cons(X2,nil),X3))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssList(cons(X2,nil))
| ~ ssList(cons(X0,X1)) ),
inference(duplicate_literal_removal,[],[f329]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( sK2 != app(cons(X0,X1),app(cons(X2,nil),X3))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssList(cons(X2,nil)) ),
inference(forward_subsumption_resolution,[],[f369,f154]) ).
fof(f509,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| memberP(sK7(X0),X1)
| sK8(X0) = X1
| ~ ssList(sK7(X0))
| ~ ssItem(sK8(X0))
| ~ ssItem(X1)
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f168,f148]) ).
fof(f512,plain,
! [X0,X1] :
( ~ memberP(X0,X1)
| memberP(sK7(X0),X1)
| sK8(X0) = X1
| ~ ssItem(sK8(X0))
| ~ ssItem(X1)
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f509,f150]) ).
fof(f514,plain,
! [X0,X1] :
( memberP(sK7(X0),X1)
| ~ memberP(X0,X1)
| sK8(X0) = X1
| ~ ssItem(X1)
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f512,f149]) ).
fof(f1342,plain,
! [X2,X3,X0,X1] :
( sK2 != app(cons(X2,X3),cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| ~ ssItem(X2)
| ~ ssList(cons(X2,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(X1) ),
inference(superposition,[],[f398,f160]) ).
fof(f1357,plain,
! [X2,X3,X0,X1] :
( sK2 != app(cons(X2,X3),cons(X0,X1))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| X0 = X2
| ~ ssItem(X2)
| ~ ssList(cons(X2,nil))
| ~ ssList(cons(X0,nil)) ),
inference(duplicate_literal_removal,[],[f1342]) ).
fof(f1480,plain,
! [X2,X3,X0,X1] :
( sK2 != cons(X0,app(X1,cons(X2,X3)))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssList(cons(X2,nil))
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(cons(X2,X3)) ),
inference(superposition,[],[f1357,f164]) ).
fof(f1481,plain,
! [X2,X3,X0,X1] :
( sK2 != cons(X0,app(X1,cons(X2,X3)))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssList(cons(X2,nil))
| ~ ssList(cons(X2,X3)) ),
inference(duplicate_literal_removal,[],[f1480]) ).
fof(f1487,plain,
! [X2,X3,X0,X1] :
( sK2 != cons(X0,app(X1,cons(X2,X3)))
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| X0 = X2
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ ssList(cons(X2,nil)) ),
inference(forward_subsumption_resolution,[],[f1481,f154]) ).
fof(f1523,plain,
! [X2,X0,X1] :
( cons(X1,X0) != sK2
| ~ ssItem(X2)
| ~ ssList(sK10(X0,X2))
| ~ ssList(sK9(X0,X2))
| X1 = X2
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(cons(X2,nil))
| ~ memberP(X0,X2)
| ~ ssItem(X2)
| ~ ssList(X0) ),
inference(superposition,[],[f1487,f174]) ).
fof(f1526,plain,
! [X2,X0,X1] :
( cons(X1,X0) != sK2
| ~ ssItem(X2)
| ~ ssList(sK10(X0,X2))
| ~ ssList(sK9(X0,X2))
| X1 = X2
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(cons(X2,nil))
| ~ memberP(X0,X2)
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f1523]) ).
fof(f1529,plain,
! [X2,X0,X1] :
( cons(X1,X0) != sK2
| ~ ssItem(X2)
| ~ ssList(sK9(X0,X2))
| X1 = X2
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(cons(X2,nil))
| ~ memberP(X0,X2)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f1526,f175]) ).
fof(f1535,plain,
! [X2,X0,X1] :
( cons(X1,X0) != sK2
| ~ ssItem(X2)
| X1 = X2
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(cons(X2,nil))
| ~ memberP(X0,X2)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f1529,f176]) ).
fof(f1540,plain,
! [X0,X1] :
( sK2 != X0
| ~ ssItem(X1)
| sK8(X0) = X1
| ~ ssItem(sK8(X0))
| ~ ssList(cons(sK8(X0),nil))
| ~ ssList(cons(X1,nil))
| ~ memberP(sK7(X0),X1)
| ~ ssList(sK7(X0))
| nil = X0
| ~ ssList(X0) ),
inference(superposition,[],[f1535,f148]) ).
fof(f1546,plain,
! [X0,X1] :
( sK2 != X0
| ~ ssItem(X1)
| sK8(X0) = X1
| ~ ssList(cons(sK8(X0),nil))
| ~ ssList(cons(X1,nil))
| ~ memberP(sK7(X0),X1)
| ~ ssList(sK7(X0))
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f1540,f149]) ).
fof(f1548,plain,
! [X0,X1] :
( sK2 != X0
| ~ ssItem(X1)
| sK8(X0) = X1
| ~ ssList(cons(sK8(X0),nil))
| ~ ssList(cons(X1,nil))
| ~ memberP(sK7(X0),X1)
| nil = X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[],[f1546,f150]) ).
fof(f1621,plain,
! [X0] :
( ~ ssItem(X0)
| sK8(sK2) = X0
| ~ ssList(cons(sK8(sK2),nil))
| ~ ssList(cons(X0,nil))
| ~ memberP(sK7(sK2),X0)
| nil = sK2
| ~ ssList(sK2) ),
inference(equality_resolution,[],[f1548]) ).
fof(f1622,plain,
! [X0] :
( ~ ssList(cons(sK8(sK2),nil))
| sK8(sK2) = X0
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ memberP(sK7(sK2),X0)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f1621,f136]) ).
fof(f1623,plain,
! [X0] :
( sK8(sK2) = X0
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| ~ memberP(sK7(sK2),X0)
| nil = sK2
| ~ ssItem(sK8(sK2))
| ~ ssList(nil) ),
inference(resolution,[],[f1622,f154]) ).
fof(f1625,plain,
! [X0] :
( ~ memberP(sK7(sK2),X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| sK8(sK2) = X0
| nil = sK2
| ~ ssItem(sK8(sK2)) ),
inference(forward_subsumption_resolution,[],[f1623,f166]) ).
fof(f2074,plain,
! [X0] :
( ~ memberP(sK2,X0)
| sK8(sK2) = X0
| ~ ssItem(X0)
| nil = sK2
| ~ ssList(sK2)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| sK8(sK2) = X0
| nil = sK2
| ~ ssItem(sK8(sK2)) ),
inference(resolution,[],[f514,f1625]) ).
fof(f2077,plain,
! [X0] :
( ~ memberP(sK2,X0)
| sK8(sK2) = X0
| ~ ssItem(X0)
| nil = sK2
| ~ ssList(sK2)
| ~ ssList(cons(X0,nil))
| ~ ssItem(sK8(sK2)) ),
inference(duplicate_literal_removal,[],[f2074]) ).
fof(f2079,plain,
! [X0] :
( ~ memberP(sK2,X0)
| sK8(sK2) = X0
| ~ ssItem(X0)
| nil = sK2
| ~ ssList(sK2)
| ~ ssList(cons(X0,nil)) ),
inference(forward_subsumption_resolution,[],[f2077,f149]) ).
fof(f2080,plain,
! [X0] :
( ~ ssList(cons(X0,nil))
| sK8(sK2) = X0
| ~ ssItem(X0)
| nil = sK2
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f2079,f136]) ).
fof(f2081,plain,
! [X0] :
( sK8(sK2) = X0
| ~ ssItem(X0)
| nil = sK2
| ~ memberP(sK2,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[],[f2080,f154]) ).
fof(f2082,plain,
! [X0] :
( sK8(sK2) = X0
| ~ ssItem(X0)
| nil = sK2
| ~ memberP(sK2,X0)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f2081]) ).
fof(f2083,plain,
! [X0] :
( sK8(sK2) = X0
| ~ ssItem(X0)
| nil = sK2
| ~ memberP(sK2,X0) ),
inference(forward_subsumption_resolution,[],[f2082,f166]) ).
fof(f2084,plain,
! [X0,X1] :
( X0 = X1
| ~ ssItem(X1)
| nil = sK2
| ~ memberP(sK2,X1)
| ~ ssItem(X0)
| nil = sK2
| ~ memberP(sK2,X0) ),
inference(superposition,[],[f2083,f2083]) ).
fof(f2127,plain,
! [X0,X1] :
( ~ memberP(sK2,X1)
| ~ ssItem(X1)
| nil = sK2
| X0 = X1
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(duplicate_literal_removal,[],[f2084]) ).
fof(f2216,plain,
! [X0,X1] :
( ~ ssItem(sK4(X0))
| nil = sK2
| sK4(X0) = X1
| ~ ssItem(X1)
| ~ memberP(sK2,X1)
| ~ ssItem(X0) ),
inference(resolution,[],[f2127,f178]) ).
fof(f2222,plain,
! [X0,X1] :
( sK4(X0) = X1
| nil = sK2
| ~ ssItem(X1)
| ~ memberP(sK2,X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[],[f2216,f139]) ).
fof(f2244,plain,
! [X0,X1] :
( X0 != X1
| ~ ssItem(X1)
| nil = sK2
| ~ ssItem(X0)
| ~ memberP(sK2,X0)
| ~ ssItem(X1) ),
inference(superposition,[],[f140,f2222]) ).
fof(f2247,plain,
! [X0,X1] :
( X0 != X1
| ~ ssItem(X1)
| nil = sK2
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(duplicate_literal_removal,[],[f2244]) ).
fof(f2250,plain,
! [X0] :
( ~ ssItem(X0)
| nil = sK2
| ~ ssItem(X0)
| ~ memberP(sK2,X0) ),
inference(equality_resolution,[],[f2247]) ).
fof(f2251,plain,
! [X0] :
( ~ memberP(sK2,X0)
| nil = sK2
| ~ ssItem(X0) ),
inference(duplicate_literal_removal,[],[f2250]) ).
fof(f2253,plain,
( nil = sK2
| ~ ssItem(sK8(sK2))
| nil = sK2
| ~ ssList(sK2) ),
inference(resolution,[],[f2251,f223]) ).
fof(f2254,plain,
( nil = sK2
| ~ ssItem(sK8(sK2))
| ~ ssList(sK2) ),
inference(duplicate_literal_removal,[],[f2253]) ).
fof(f2255,plain,
( nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f2254,f149]) ).
fof(f2257,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f2255,f136]) ).
fof(f2284,plain,
! [X0] :
( ~ memberP(sK2,X0)
| ~ ssItem(X0) ),
inference(superposition,[],[f167,f2257]) ).
fof(f2386,plain,
! [X0] :
( ~ ssItem(sK4(X0))
| ~ ssItem(X0) ),
inference(resolution,[],[f2284,f178]) ).
fof(f2389,plain,
! [X0] : ~ ssItem(X0),
inference(forward_subsumption_resolution,[],[f2386,f139]) ).
fof(f2432,plain,
$false,
inference(resolution,[],[f2389,f145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC199+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n015.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 08:28:32 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.00/1.35 % (2470090)Detected formulas, will run a generic FOF schedule.
% 3.00/1.35 % (2470097)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=2104352835:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.00/1.35 % (2470098)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2832045657:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.00/1.35 % (2470096)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=2433793692:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.00/1.35 % (2470095)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=2567236197:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.00/1.35 % (2470099)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3899552233:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.00/1.35 % (2470101)dis-21_1_sil=8000:lcm=predicate:random_seed=1159442163: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)
% 3.00/1.35 % (2470100)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2694703033:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.00/1.35 % (2470099)First to succeed.
% 3.00/1.35 % (2470098)Instruction limit reached!
% 3.00/1.35 % (2470098)------------------------------
% 3.00/1.35 % (2470098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.35 % (2470098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.35 % (2470098)CaDiCaL version: 2.1.3
% 3.00/1.35 % (2470098)Termination reason: Instruction limit
% 3.00/1.35 % (2470098)Termination phase: Saturation
% 3.00/1.35 % (2470098)Time elapsed: 0.068 s
% 3.00/1.35 % (2470098)Peak memory usage: 89 MB
% 3.00/1.35 % (2470098)Instructions burned: 111 (million)
% 3.00/1.35 % (2470099)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2470090"
% 3.00/1.35 % (2470101)Instruction limit reached!
% 3.00/1.35 % (2470101)------------------------------
% 3.00/1.35 % (2470101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.35 % (2470101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.35 % (2470101)CaDiCaL version: 2.1.3
% 3.00/1.35 % (2470101)Termination reason: Instruction limit
% 3.00/1.35 % (2470101)Termination phase: Saturation
% 3.00/1.35 % (2470101)Time elapsed: 0.074 s
% 3.00/1.35 % (2470101)Peak memory usage: 89 MB
% 3.00/1.35 % (2470101)Instructions burned: 130 (million)
% 3.00/1.35 % (2470100)Instruction limit reached!
% 3.00/1.35 % (2470100)------------------------------
% 3.00/1.35 % (2470100)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.35 % (2470100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.35 % (2470100)CaDiCaL version: 2.1.3
% 3.00/1.35 % (2470100)Termination reason: Instruction limit
% 3.00/1.35 % (2470100)Termination phase: Saturation
% 3.00/1.35 % (2470100)Time elapsed: 0.087 s
% 3.00/1.35 % (2470100)Peak memory usage: 90 MB
% 3.00/1.35 % (2470100)Instructions burned: 140 (million)
% 3.00/1.35 % (2470109)lrs+10_1_sil=8000:sp=occurrence:random_seed=1728830846:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.00/1.35 % (2470110)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1401507968:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.00/1.35 % (2470111)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1792936911:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.00/1.35 % (2470110)Instruction limit reached!
% 3.00/1.35 % (2470110)------------------------------
% 3.00/1.35 % (2470110)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.00/1.35 % (2470110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.00/1.35 % (2470110)CaDiCaL version: 2.1.3
% 3.00/1.35 % (2470110)Termination reason: Instruction limit
% 3.00/1.35 % (2470110)Termination phase: Saturation
% 3.00/1.35 % (2470110)Time elapsed: 0.069 s
% 3.00/1.35 % (2470110)Peak memory usage: 90 MB
% 3.00/1.35 % (2470110)Instructions burned: 158 (million)
% 3.00/1.35 % (2470099)Refutation found. Thanks to Tanya!
% 3.00/1.35 % SZS status Theorem for theBenchmark
% 3.00/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.11/1.55 % (2470099)------------------------------
% 4.11/1.55 % (2470099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.11/1.55 % (2470099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.11/1.55 % (2470099)CaDiCaL version: 2.1.3
% 4.11/1.55 % (2470099)Termination reason: Refutation
% 4.11/1.55 % (2470099)Time elapsed: 0.069 s
% 4.11/1.55 % (2470099)Peak memory usage: 89 MB
% 4.11/1.55 % (2470099)Instructions burned: 121 (million)
% 4.11/1.55 % (2470099)------------------------------
% 4.11/1.55 % (2470099)------------------------------
% 4.11/1.55 % (2470090)Success in time 0.501 s
% 4.11/1.55 % Vampire exiting
%------------------------------------------------------------------------------