%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC377+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 : n001.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 01:03:42 PM UTC 2026
% Result : Theorem 0.66s 1.00s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 9
% Syntax : Number of formulae : 133 ( 13 unt; 0 def)
% Number of atoms : 583 ( 110 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 762 ( 312 ~; 344 |; 69 &)
% ( 8 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 144 ( 122 !; 22 ?)
% 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(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(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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ( ( ~ memberP(X1,X4)
& ~ memberP(X0,X4) )
| ( memberP(X1,X4)
& memberP(X0,X4) ) ) )
| ( nil != X2
& nil = X3 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(cons(X5,nil),X6) != X2
| app(X6,cons(X5,nil)) != X3 ) ) )
& 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)
=> ( ( ~ memberP(X1,X4)
& ~ memberP(X0,X4) )
| ( memberP(X1,X4)
& memberP(X0,X4) ) ) )
| ( nil != X2
& nil = X3 )
| ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(cons(X5,nil),X6) != X2
| app(X6,cons(X5,nil)) != X3 ) ) )
& neq(X3,nil) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( ( memberP(X1,X4)
| memberP(X0,X4) )
& ( ~ memberP(X1,X4)
| ~ memberP(X0,X4) )
& ssItem(X4) )
& ( nil = X2
| nil != X3 )
& ( ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X2
& app(X6,cons(X5,nil)) = X3
& ssList(X6) )
& ssItem(X5) )
| ~ 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
& ? [X4] :
( ( memberP(X1,X4)
| memberP(X0,X4) )
& ( ~ memberP(X1,X4)
| ~ memberP(X0,X4) )
& ssItem(X4) )
& ( nil = X2
| nil != X3 )
& ( ? [X5] :
( ? [X6] :
( app(cons(X5,nil),X6) = X2
& app(X6,cons(X5,nil)) = X3
& ssList(X6) )
& ssItem(X5) )
| ~ neq(X3,nil) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f110,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f121,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(f122,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(f123,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(f124,plain,
( sK1 = sK3
& sK0 = sK2
& ( memberP(sK1,sK4)
| memberP(sK0,sK4) )
& ( ~ memberP(sK1,sK4)
| ~ memberP(sK0,sK4) )
& ssItem(sK4)
& ( nil = sK2
| nil != sK3 )
& ( ( sK2 = app(cons(sK5,nil),sK6)
& sK3 = app(sK6,cons(sK5,nil))
& ssList(sK6)
& ssItem(sK5) )
| ~ neq(sK3,nil) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f99]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f131,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,[],[f121]) ).
fof(f132,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,[],[f131]) ).
fof(f133,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,[],[f122]) ).
fof(f134,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,[],[f133]) ).
fof(f135,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,[],[f123]) ).
fof(f136,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,[],[f135]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ( ( memberP(X0,X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| app(X2,cons(X1,X3)) != X0 ) ) )
& ( ( ssList(sK11(X0,X1))
& ssList(sK12(X0,X1))
& app(sK11(X0,X1),cons(X1,sK12(X0,X1))) = X0 )
| ~ memberP(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X4,sK11(X0,X1)),skolemize(X5,sK12(X0,X1))],[f136]) ).
fof(f141,plain,
ssList(sK3),
inference(cnf_transformation,[],[f124]) ).
fof(f142,plain,
( ~ neq(sK3,nil)
| ssItem(sK5) ),
inference(cnf_transformation,[],[f124]) ).
fof(f143,plain,
( ~ neq(sK3,nil)
| ssList(sK6) ),
inference(cnf_transformation,[],[f124]) ).
fof(f144,plain,
( sK3 = app(sK6,cons(sK5,nil))
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f124]) ).
fof(f145,plain,
( sK2 = app(cons(sK5,nil),sK6)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f124]) ).
fof(f146,plain,
( nil != sK3
| nil = sK2 ),
inference(cnf_transformation,[],[f124]) ).
fof(f147,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f124]) ).
fof(f148,plain,
( ~ memberP(sK1,sK4)
| ~ memberP(sK0,sK4) ),
inference(cnf_transformation,[],[f124]) ).
fof(f149,plain,
( memberP(sK1,sK4)
| memberP(sK0,sK4) ),
inference(cnf_transformation,[],[f124]) ).
fof(f150,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f124]) ).
fof(f151,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f124]) ).
fof(f162,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f168,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f175,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f178,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f179,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f180,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f181,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f182,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ memberP(app(X1,X2),X0)
| memberP(X2,X0)
| memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f185,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f189,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,[],[f137]) ).
fof(f190,plain,
( memberP(sK3,sK4)
| memberP(sK2,sK4) ),
inference(definition_unfolding,[],[f149,f151,f150]) ).
fof(f191,plain,
( ~ memberP(sK3,sK4)
| ~ memberP(sK2,sK4) ),
inference(definition_unfolding,[],[f148,f151,f150]) ).
fof(f198,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f182]) ).
fof(f199,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,[],[f189]) ).
fof(f200,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f198]) ).
fof(f211,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3)
| ssList(sK6) ),
inference(resolution,[],[f175,f143]) ).
fof(f212,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3)
| ssItem(sK5) ),
inference(resolution,[],[f175,f142]) ).
fof(f217,plain,
( nil = sK3
| ~ ssList(sK3)
| ssItem(sK5) ),
inference(forward_subsumption_resolution,[],[f212,f178]) ).
fof(f218,plain,
( nil = sK3
| ~ ssList(sK3)
| ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f211,f178]) ).
fof(f219,plain,
( nil = sK3
| ssItem(sK5) ),
inference(forward_subsumption_resolution,[],[f217,f141]) ).
fof(f220,plain,
( nil = sK3
| ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f218,f141]) ).
fof(f225,plain,
( sK3 != sK3
| sK2 = sK3
| ssItem(sK5) ),
inference(superposition,[],[f146,f219]) ).
fof(f230,plain,
( sK2 = sK3
| ssItem(sK5) ),
inference(trivial_inequality_removal,[],[f225]) ).
fof(f242,plain,
( sK3 != sK3
| sK2 = sK3
| ssList(sK6) ),
inference(superposition,[],[f146,f220]) ).
fof(f247,plain,
( sK2 = sK3
| ssList(sK6) ),
inference(trivial_inequality_removal,[],[f242]) ).
fof(f249,plain,
( ~ memberP(sK2,sK4)
| ~ memberP(sK2,sK4)
| ssItem(sK5) ),
inference(superposition,[],[f191,f230]) ).
fof(f250,plain,
( memberP(sK2,sK4)
| memberP(sK2,sK4)
| ssItem(sK5) ),
inference(superposition,[],[f190,f230]) ).
fof(f255,plain,
( memberP(sK2,sK4)
| ssItem(sK5) ),
inference(duplicate_literal_removal,[],[f250]) ).
fof(f256,plain,
( ~ memberP(sK2,sK4)
| ssItem(sK5) ),
inference(duplicate_literal_removal,[],[f249]) ).
fof(f266,plain,
( memberP(sK2,sK4)
| memberP(sK2,sK4)
| ssList(sK6) ),
inference(superposition,[],[f190,f247]) ).
fof(f267,plain,
( ~ memberP(sK2,sK4)
| ~ memberP(sK2,sK4)
| ssList(sK6) ),
inference(superposition,[],[f191,f247]) ).
fof(f269,plain,
( ~ memberP(sK2,sK4)
| ssList(sK6) ),
inference(duplicate_literal_removal,[],[f267]) ).
fof(f270,plain,
( memberP(sK2,sK4)
| ssList(sK6) ),
inference(duplicate_literal_removal,[],[f266]) ).
fof(f306,plain,
ssItem(sK5),
inference(forward_subsumption_resolution,[],[f256,f255]) ).
fof(f310,plain,
( sK2 = cons(sK5,sK6)
| ~ neq(sK3,nil)
| ~ ssItem(sK5)
| ~ ssList(sK6) ),
inference(superposition,[],[f145,f168]) ).
fof(f317,plain,
( sK2 = cons(sK5,sK6)
| ~ neq(sK3,nil)
| ~ ssList(sK6) ),
inference(forward_subsumption_resolution,[],[f310,f306]) ).
fof(f319,plain,
( sK2 = cons(sK5,sK6)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f317,f143]) ).
fof(f325,plain,
ssList(sK6),
inference(forward_subsumption_resolution,[],[f270,f269]) ).
fof(f340,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(sK6,X0)
| ~ ssList(cons(sK5,nil))
| ~ ssList(sK6)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f185,f144]) ).
fof(f344,plain,
! [X0] :
( ~ ssList(cons(sK5,nil))
| ~ memberP(sK6,X0)
| memberP(sK3,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f340,f325]) ).
fof(f515,plain,
! [X0] :
( ~ memberP(sK3,X0)
| memberP(cons(sK5,nil),X0)
| memberP(sK6,X0)
| ~ ssList(cons(sK5,nil))
| ~ ssList(sK6)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f183,f144]) ).
fof(f523,plain,
! [X0] :
( memberP(cons(sK5,nil),X0)
| ~ memberP(sK3,X0)
| memberP(sK6,X0)
| ~ ssList(cons(sK5,nil))
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f515,f325]) ).
fof(f551,plain,
! [X0] :
( ~ memberP(sK2,X0)
| memberP(sK6,X0)
| sK5 = X0
| ~ ssList(sK6)
| ~ ssItem(sK5)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f180,f319]) ).
fof(f552,plain,
! [X0] :
( memberP(sK2,X0)
| ~ memberP(sK6,X0)
| ~ ssList(sK6)
| ~ ssItem(sK5)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f181,f319]) ).
fof(f553,plain,
( memberP(sK2,sK5)
| ~ ssList(sK6)
| ~ ssItem(sK5)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f200,f319]) ).
fof(f554,plain,
( memberP(sK2,sK5)
| ~ ssItem(sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f553,f325]) ).
fof(f555,plain,
! [X0] :
( memberP(sK2,X0)
| ~ memberP(sK6,X0)
| ~ ssItem(sK5)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f552,f325]) ).
fof(f556,plain,
! [X0] :
( ~ memberP(sK2,X0)
| memberP(sK6,X0)
| sK5 = X0
| ~ ssItem(sK5)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f551,f325]) ).
fof(f564,plain,
( memberP(sK2,sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f554,f306]) ).
fof(f565,plain,
! [X0] :
( memberP(sK2,X0)
| ~ memberP(sK6,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f555,f306]) ).
fof(f566,plain,
! [X0] :
( memberP(sK6,X0)
| ~ memberP(sK2,X0)
| sK5 = X0
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f556,f306]) ).
fof(f602,plain,
( memberP(sK3,sK5)
| ~ ssList(sK6)
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(superposition,[],[f199,f144]) ).
fof(f607,plain,
( memberP(sK3,sK5)
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f602,f325]) ).
fof(f613,plain,
( memberP(sK3,sK5)
| ~ ssItem(sK5)
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f607,f178]) ).
fof(f619,plain,
( memberP(sK3,sK5)
| ~ ssList(sK3)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f613,f306]) ).
fof(f621,plain,
( memberP(sK3,sK5)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f619,f141]) ).
fof(f663,plain,
! [X0] :
( ~ memberP(sK6,X0)
| memberP(sK3,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil)
| ~ ssItem(sK5)
| ~ ssList(nil) ),
inference(resolution,[],[f344,f162]) ).
fof(f666,plain,
! [X0] :
( ~ memberP(sK6,X0)
| memberP(sK3,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f663,f142]) ).
fof(f667,plain,
! [X0] :
( memberP(sK3,X0)
| ~ memberP(sK6,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f666,f178]) ).
fof(f668,plain,
( ~ memberP(sK6,sK4)
| ~ ssItem(sK4)
| ~ neq(sK3,nil)
| ~ memberP(sK2,sK4) ),
inference(resolution,[],[f667,f191]) ).
fof(f671,plain,
( ~ memberP(sK6,sK4)
| ~ ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f668,f565]) ).
fof(f672,plain,
( ~ memberP(sK6,sK4)
| ~ neq(sK3,nil) ),
inference(forward_subsumption_resolution,[],[f671,f147]) ).
fof(f673,plain,
( ~ neq(sK3,nil)
| ~ memberP(sK2,sK4)
| sK4 = sK5
| ~ ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(resolution,[],[f672,f566]) ).
fof(f674,plain,
( ~ neq(sK3,nil)
| ~ memberP(sK2,sK4)
| sK4 = sK5
| ~ ssItem(sK4) ),
inference(duplicate_literal_removal,[],[f673]) ).
fof(f675,plain,
( ~ memberP(sK2,sK4)
| ~ neq(sK3,nil)
| sK4 = sK5 ),
inference(forward_subsumption_resolution,[],[f674,f147]) ).
fof(f986,plain,
! [X0] :
( ~ memberP(sK3,X0)
| memberP(sK6,X0)
| ~ ssList(cons(sK5,nil))
| ~ ssItem(X0)
| ~ neq(sK3,nil)
| memberP(nil,X0)
| sK5 = X0
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssItem(X0) ),
inference(resolution,[],[f523,f180]) ).
fof(f993,plain,
! [X0] :
( ~ memberP(sK3,X0)
| memberP(sK6,X0)
| ~ ssList(cons(sK5,nil))
| ~ ssItem(X0)
| ~ neq(sK3,nil)
| memberP(nil,X0)
| sK5 = X0
| ~ ssList(nil)
| ~ ssItem(sK5) ),
inference(duplicate_literal_removal,[],[f986]) ).
fof(f995,plain,
! [X0] :
( ~ memberP(sK3,X0)
| memberP(sK6,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil)
| memberP(nil,X0)
| sK5 = X0
| ~ ssList(nil)
| ~ ssItem(sK5) ),
inference(forward_subsumption_resolution,[],[f993,f162]) ).
fof(f996,plain,
! [X0] :
( ~ memberP(sK3,X0)
| memberP(sK6,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil)
| memberP(nil,X0)
| sK5 = X0
| ~ ssItem(sK5) ),
inference(forward_subsumption_resolution,[],[f995,f178]) ).
fof(f997,plain,
! [X0] :
( ~ memberP(sK3,X0)
| memberP(sK6,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil)
| memberP(nil,X0)
| sK5 = X0 ),
inference(forward_subsumption_resolution,[],[f996,f142]) ).
fof(f998,plain,
! [X0] :
( memberP(sK6,X0)
| ~ memberP(sK3,X0)
| ~ ssItem(X0)
| ~ neq(sK3,nil)
| sK5 = X0 ),
inference(forward_subsumption_resolution,[],[f997,f179]) ).
fof(f1008,plain,
( ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| ~ neq(sK3,nil)
| sK4 = sK5
| ~ neq(sK3,nil) ),
inference(resolution,[],[f998,f672]) ).
fof(f1009,plain,
( ~ memberP(sK3,sK4)
| ~ ssItem(sK4)
| ~ neq(sK3,nil)
| sK4 = sK5 ),
inference(duplicate_literal_removal,[],[f1008]) ).
fof(f1010,plain,
( ~ memberP(sK3,sK4)
| ~ neq(sK3,nil)
| sK4 = sK5 ),
inference(forward_subsumption_resolution,[],[f1009,f147]) ).
fof(f1011,plain,
( ~ neq(sK3,nil)
| sK4 = sK5
| memberP(sK2,sK4) ),
inference(resolution,[],[f1010,f190]) ).
fof(f1016,plain,
( ~ neq(sK3,nil)
| sK4 = sK5 ),
inference(forward_subsumption_resolution,[],[f1011,f675]) ).
fof(f1018,plain,
( sK4 = sK5
| nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolution,[],[f1016,f175]) ).
fof(f1023,plain,
( sK4 = sK5
| nil = sK3
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f1018,f178]) ).
fof(f1024,plain,
( sK4 = sK5
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f1023,f141]) ).
fof(f1045,plain,
( ~ memberP(sK3,sK5)
| ~ memberP(sK2,sK5)
| nil = sK3 ),
inference(superposition,[],[f191,f1024]) ).
fof(f1087,plain,
( ~ memberP(sK2,sK5)
| nil = sK3
| ~ neq(sK3,nil) ),
inference(resolution,[],[f1045,f621]) ).
fof(f1095,plain,
( ~ neq(sK3,nil)
| nil = sK3 ),
inference(forward_subsumption_resolution,[],[f1087,f564]) ).
fof(f1098,plain,
( nil = sK3
| nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(resolution,[],[f1095,f175]) ).
fof(f1101,plain,
( nil = sK3
| ~ ssList(nil)
| ~ ssList(sK3) ),
inference(duplicate_literal_removal,[],[f1098]) ).
fof(f1103,plain,
( nil = sK3
| ~ ssList(sK3) ),
inference(forward_subsumption_resolution,[],[f1101,f178]) ).
fof(f1104,plain,
nil = sK3,
inference(forward_subsumption_resolution,[],[f1103,f141]) ).
fof(f1109,plain,
( sK3 != sK3
| sK2 = sK3 ),
inference(superposition,[],[f146,f1104]) ).
fof(f1135,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f1109]) ).
fof(f1139,plain,
( memberP(sK2,sK4)
| memberP(sK2,sK4) ),
inference(superposition,[],[f190,f1135]) ).
fof(f1140,plain,
( ~ memberP(sK2,sK4)
| ~ memberP(sK2,sK4) ),
inference(superposition,[],[f191,f1135]) ).
fof(f1154,plain,
~ memberP(sK2,sK4),
inference(duplicate_literal_removal,[],[f1140]) ).
fof(f1155,plain,
memberP(sK2,sK4),
inference(duplicate_literal_removal,[],[f1139]) ).
fof(f1231,plain,
$false,
inference(forward_subsumption_resolution,[],[f1155,f1154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC377+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n001.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 09:27:18 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 0.66/1.00 % (238575)Detected formulas, will run a generic FOF schedule.
% 0.66/1.00 % (238584)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1681316813:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.66/1.00 % (238584)First to succeed.
% 0.66/1.00 % (238584)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-238575"
% 0.66/1.00 % (238585)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=595910361:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.66/1.00 % (238582)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=3583888154:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.66/1.00 % (238580)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=3355394499:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.66/1.00 % (238581)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=2479388913:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.66/1.00 % (238583)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=902545864:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.66/1.00 % (238586)dis-21_1_sil=8000:lcm=predicate:random_seed=3649216329: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)
% 0.66/1.00 % (238583)Also succeeded, but the first one will report.
% 0.66/1.00 % (238586)Instruction limit reached!
% 0.66/1.00 % (238586)------------------------------
% 0.66/1.00 % (238586)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/1.00 % (238586)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/1.00 % (238586)CaDiCaL version: 2.1.3
% 0.66/1.00 % (238586)Termination reason: Instruction limit
% 0.66/1.00 % (238586)Termination phase: Saturation
% 0.66/1.00 % (238586)Time elapsed: 0.075 s
% 0.66/1.00 % (238586)Peak memory usage: 90 MB
% 0.66/1.00 % (238586)Instructions burned: 130 (million)
% 0.66/1.00 % (238585)Instruction limit reached!
% 0.66/1.00 % (238585)------------------------------
% 0.66/1.00 % (238585)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/1.00 % (238585)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/1.00 % (238585)CaDiCaL version: 2.1.3
% 0.66/1.00 % (238585)Termination reason: Instruction limit
% 0.66/1.00 % (238585)Termination phase: Saturation
% 0.66/1.00 % (238585)Time elapsed: 0.096 s
% 0.66/1.00 % (238585)Peak memory usage: 90 MB
% 0.66/1.00 % (238585)Instructions burned: 140 (million)
% 0.66/1.00 % (238584)Refutation found. Thanks to Tanya!
% 0.66/1.00 % SZS status Theorem for theBenchmark
% 0.66/1.00 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.20 % (238584)------------------------------
% 0.20/1.20 % (238584)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.20 % (238584)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.20 % (238584)CaDiCaL version: 2.1.3
% 0.20/1.20 % (238584)Termination reason: Refutation
% 0.20/1.20 % (238584)Time elapsed: 0.013 s
% 0.20/1.20 % (238584)Peak memory usage: 88 MB
% 0.20/1.20 % (238584)Instructions burned: 37 (million)
% 0.20/1.20 % (238584)------------------------------
% 0.20/1.20 % (238584)------------------------------
% 0.20/1.20 % (238575)Success in time 0.309 s
% 0.20/1.20 % Vampire exiting
%------------------------------------------------------------------------------