%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC421+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 : n016.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 01:03:55 PM UTC 2026
% Result : Theorem 0.66s 0.97s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 11
% Syntax : Number of formulae : 83 ( 13 unt; 0 def)
% Number of atoms : 437 ( 138 equ)
% Maximal formula atoms : 27 ( 5 avg)
% Number of connectives : 633 ( 279 ~; 265 |; 63 &)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 121 ( 99 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
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(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
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(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(app(X6,cons(X4,nil)),X5) = X0 ) ) )
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& X3 != X7
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& tl(X2) = X8
& app(X8,X9) = X7
& ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X9
& hd(X2) = X10
& neq(nil,X2) )
& neq(nil,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
| ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X1
& app(app(X6,cons(X4,nil)),X5) = X0 ) ) )
| ( nil != X2
& nil = X3 )
| ( neq(X3,nil)
& ( ~ neq(X2,nil)
| ? [X7] :
( ssList(X7)
& X3 != X7
& ? [X8] :
( ssList(X8)
& ? [X9] :
( ssList(X9)
& tl(X2) = X8
& app(X8,X9) = X7
& ? [X10] :
( ssItem(X10)
& cons(X10,nil) = X9
& hd(X2) = X10
& neq(nil,X2) )
& neq(nil,X2) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(app(X6,cons(X4,nil)),X5) != X0 ) ) )
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& ! [X7] :
( ~ ssList(X7)
| X3 = X7
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| tl(X2) != X8
| app(X8,X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(X2) != X10
| ~ neq(nil,X2) )
| ~ neq(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
& neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X1
| app(app(X6,cons(X4,nil)),X5) != X0 ) ) )
& ( nil = X2
| nil != X3 )
& ( ~ neq(X3,nil)
| ( neq(X2,nil)
& ! [X7] :
( ~ ssList(X7)
| X3 = X7
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| tl(X2) != X8
| app(X8,X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(X2) != X10
| ~ neq(nil,X2) )
| ~ neq(nil,X2) ) ) ) ) )
& 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(f107,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
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(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] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f126,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f125]) ).
fof(f129,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f130,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f129]) ).
fof(f136,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f137,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f136]) ).
fof(f138,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK1
| app(app(X6,cons(X4,nil)),X5) != sK0 ) ) )
& ( nil = sK2
| nil != sK3 )
& ( ~ neq(sK3,nil)
| ( neq(sK2,nil)
& ! [X7] :
( ~ ssList(X7)
| sK3 = X7
| ! [X8] :
( ~ ssList(X8)
| ! [X9] :
( ~ ssList(X9)
| tl(sK2) != X8
| app(X8,X9) != X7
| ! [X10] :
( ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(sK2) != X10
| ~ neq(nil,sK2) )
| ~ neq(nil,sK2) ) ) ) ) )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f99]) ).
fof(f143,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f149,plain,
ssList(sK2),
inference(cnf_transformation,[],[f138]) ).
fof(f150,plain,
ssList(sK3),
inference(cnf_transformation,[],[f138]) ).
fof(f151,plain,
! [X10,X8,X9,X7] :
( ~ neq(sK3,nil)
| ~ ssList(X7)
| sK3 = X7
| ~ ssList(X8)
| ~ ssList(X9)
| tl(sK2) != X8
| app(X8,X9) != X7
| ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(sK2) != X10
| ~ neq(nil,sK2)
| ~ neq(nil,sK2) ),
inference(cnf_transformation,[],[f138]) ).
fof(f152,plain,
( ~ neq(sK3,nil)
| neq(sK2,nil) ),
inference(cnf_transformation,[],[f138]) ).
fof(f154,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK1
| app(app(X6,cons(X4,nil)),X5) != sK0 ),
inference(cnf_transformation,[],[f138]) ).
fof(f155,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f138]) ).
fof(f156,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f138]) ).
fof(f157,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f138]) ).
fof(f168,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f169,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f174,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f177,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f179,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f180,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f181,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f184,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f189,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f191,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f196,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f137]) ).
fof(f197,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f155,f157]) ).
fof(f198,plain,
! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK2
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK3
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f154,f157,f156]) ).
fof(f201,plain,
! [X10,X9,X7] :
( ~ neq(sK3,nil)
| ~ ssList(X7)
| sK3 = X7
| ~ ssList(tl(sK2))
| ~ ssList(X9)
| app(tl(sK2),X9) != X7
| ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(sK2) != X10
| ~ neq(nil,sK2)
| ~ neq(nil,sK2) ),
inference(equality_resolution,[],[f151]) ).
fof(f202,plain,
! [X10,X9] :
( ~ neq(sK3,nil)
| ~ ssList(app(tl(sK2),X9))
| sK3 = app(tl(sK2),X9)
| ~ ssList(tl(sK2))
| ~ ssList(X9)
| ~ ssItem(X10)
| cons(X10,nil) != X9
| hd(sK2) != X10
| ~ neq(nil,sK2)
| ~ neq(nil,sK2) ),
inference(equality_resolution,[],[f201]) ).
fof(f203,plain,
! [X10] :
( ~ neq(sK3,nil)
| ~ ssList(app(tl(sK2),cons(X10,nil)))
| sK3 = app(tl(sK2),cons(X10,nil))
| ~ ssList(tl(sK2))
| ~ ssList(cons(X10,nil))
| ~ ssItem(X10)
| hd(sK2) != X10
| ~ neq(nil,sK2)
| ~ neq(nil,sK2) ),
inference(equality_resolution,[],[f202]) ).
fof(f204,plain,
( ~ neq(sK3,nil)
| ~ ssList(app(tl(sK2),cons(hd(sK2),nil)))
| sK3 = app(tl(sK2),cons(hd(sK2),nil))
| ~ ssList(tl(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssItem(hd(sK2))
| ~ neq(nil,sK2)
| ~ neq(nil,sK2) ),
inference(equality_resolution,[],[f203]) ).
fof(f207,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f180]) ).
fof(f210,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f207]) ).
fof(f212,plain,
( ~ neq(sK3,nil)
| ~ ssList(app(tl(sK2),cons(hd(sK2),nil)))
| sK3 = app(tl(sK2),cons(hd(sK2),nil))
| ~ ssList(tl(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssItem(hd(sK2))
| ~ neq(nil,sK2) ),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f213,plain,
neq(sK2,nil),
inference(forward_subsumption_resolution,[],[f152,f197]) ).
fof(f214,plain,
( sK3 = app(tl(sK2),cons(hd(sK2),nil))
| ~ ssList(app(tl(sK2),cons(hd(sK2),nil)))
| ~ ssList(tl(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssItem(hd(sK2))
| ~ neq(nil,sK2) ),
inference(forward_subsumption_resolution,[],[f212,f197]) ).
fof(f226,plain,
! [X0,X1] :
( sK2 != app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssList(nil)
| sK3 != app(app(X1,cons(X0,nil)),nil)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(superposition,[],[f198,f177]) ).
fof(f230,plain,
! [X0,X1] :
( sK3 != app(app(X1,cons(X0,nil)),nil)
| ~ ssList(X1)
| sK2 != app(cons(X0,nil),X1)
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(forward_subsumption_resolution,[],[f226,f184]) ).
fof(f235,plain,
! [X0,X1] :
( sK3 != app(X0,cons(X1,nil))
| ~ ssList(X0)
| app(cons(X1,nil),X0) != sK2
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil))
| ~ ssList(app(X0,cons(X1,nil))) ),
inference(superposition,[],[f230,f169]) ).
fof(f246,plain,
( sK3 != sK3
| ~ ssList(tl(sK2))
| sK2 != app(cons(hd(sK2),nil),tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssList(sK3)
| ~ ssList(app(tl(sK2),cons(hd(sK2),nil)))
| ~ ssList(tl(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssItem(hd(sK2))
| ~ neq(nil,sK2) ),
inference(superposition,[],[f235,f214]) ).
fof(f249,plain,
( sK3 != sK3
| ~ ssList(tl(sK2))
| sK2 != app(cons(hd(sK2),nil),tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssList(sK3)
| ~ ssList(app(tl(sK2),cons(hd(sK2),nil)))
| ~ neq(nil,sK2) ),
inference(duplicate_literal_removal,[],[f246]) ).
fof(f250,plain,
( ~ ssList(tl(sK2))
| sK2 != app(cons(hd(sK2),nil),tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssList(sK3)
| ~ ssList(app(tl(sK2),cons(hd(sK2),nil)))
| ~ neq(nil,sK2) ),
inference(trivial_inequality_removal,[],[f249]) ).
fof(f252,plain,
( ~ ssList(tl(sK2))
| sK2 != app(cons(hd(sK2),nil),tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ ssList(app(tl(sK2),cons(hd(sK2),nil)))
| ~ neq(nil,sK2) ),
inference(forward_subsumption_resolution,[],[f250,f150]) ).
fof(f261,plain,
( sK2 != app(cons(hd(sK2),nil),tl(sK2))
| ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ neq(nil,sK2) ),
inference(forward_subsumption_resolution,[],[f252,f179]) ).
fof(f413,plain,
( sK2 != cons(hd(sK2),tl(sK2))
| ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ neq(nil,sK2)
| ~ ssItem(hd(sK2))
| ~ ssList(tl(sK2)) ),
inference(superposition,[],[f261,f174]) ).
fof(f433,plain,
( sK2 != cons(hd(sK2),tl(sK2))
| ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ neq(nil,sK2) ),
inference(duplicate_literal_removal,[],[f413]) ).
fof(f456,plain,
( sK2 != sK2
| ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ neq(nil,sK2)
| nil = sK2
| ~ ssList(sK2) ),
inference(superposition,[],[f433,f191]) ).
fof(f457,plain,
( ~ ssList(tl(sK2))
| ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ neq(nil,sK2)
| nil = sK2
| ~ ssList(sK2) ),
inference(trivial_inequality_removal,[],[f456]) ).
fof(f458,plain,
( ~ ssItem(hd(sK2))
| ~ ssList(cons(hd(sK2),nil))
| ~ neq(nil,sK2)
| nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f457,f196]) ).
fof(f461,plain,
( ~ ssList(cons(hd(sK2),nil))
| ~ neq(nil,sK2)
| nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f458,f189]) ).
fof(f464,plain,
( ~ ssList(cons(hd(sK2),nil))
| ~ neq(nil,sK2)
| nil = sK2 ),
inference(forward_subsumption_resolution,[],[f461,f149]) ).
fof(f488,plain,
( ~ neq(nil,sK2)
| nil = sK2
| ~ ssItem(hd(sK2))
| ~ ssList(nil) ),
inference(resolution,[],[f464,f168]) ).
fof(f492,plain,
( ~ neq(nil,sK2)
| nil = sK2
| ~ ssItem(hd(sK2)) ),
inference(forward_subsumption_resolution,[],[f488,f184]) ).
fof(f528,plain,
( nil = sK2
| ~ ssItem(hd(sK2))
| nil = sK2
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(resolution,[],[f492,f181]) ).
fof(f529,plain,
( nil = sK2
| ~ ssItem(hd(sK2))
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f528]) ).
fof(f531,plain,
( nil = sK2
| ~ ssList(sK2)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f529,f189]) ).
fof(f532,plain,
( nil = sK2
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[],[f531,f149]) ).
fof(f533,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f532,f184]) ).
fof(f540,plain,
neq(sK2,sK2),
inference(superposition,[],[f213,f533]) ).
fof(f608,plain,
~ ssList(sK2),
inference(resolution,[],[f540,f210]) ).
fof(f610,plain,
$false,
inference(forward_subsumption_resolution,[],[f608,f149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC421+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n016.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 09:40:03 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 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
% 0.66/0.97 % (3512220)Detected formulas, will run a generic FOF schedule.
% 0.66/0.97 % (3512229)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1675804188:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.66/0.97 % (3512229)First to succeed.
% 0.66/0.97 % (3512229)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3512220"
% 0.66/0.97 % (3512228)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3399684484:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.66/0.97 % (3512225)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=2448351921:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.66/0.97 % (3512226)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=2555627930:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.66/0.97 % (3512227)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=3846976840:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.66/0.97 % (3512230)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1192654678:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.66/0.97 % (3512231)dis-21_1_sil=8000:lcm=predicate:random_seed=2004270001: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)
% 0.66/0.97 % (3512230)Also succeeded, but the first one will report.
% 0.66/0.97 % (3512228)Instruction limit reached!
% 0.66/0.97 % (3512228)------------------------------
% 0.66/0.97 % (3512228)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.97 % (3512228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.97 % (3512228)CaDiCaL version: 2.1.3
% 0.66/0.97 % (3512228)Termination reason: Instruction limit
% 0.66/0.97 % (3512228)Termination phase: Saturation
% 0.66/0.97 % (3512228)Time elapsed: 0.062 s
% 0.66/0.97 % (3512228)Peak memory usage: 89 MB
% 0.66/0.97 % (3512228)Instructions burned: 110 (million)
% 0.66/0.97 % (3512231)Instruction limit reached!
% 0.66/0.97 % (3512231)------------------------------
% 0.66/0.97 % (3512231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.66/0.97 % (3512231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.66/0.97 % (3512231)CaDiCaL version: 2.1.3
% 0.66/0.97 % (3512231)Termination reason: Instruction limit
% 0.66/0.97 % (3512231)Termination phase: Saturation
% 0.66/0.97 % (3512231)Time elapsed: 0.074 s
% 0.66/0.97 % (3512231)Peak memory usage: 90 MB
% 0.66/0.97 % (3512231)Instructions burned: 131 (million)
% 0.66/0.97 % (3512229)Refutation found. Thanks to Tanya!
% 0.66/0.97 % SZS status Theorem for theBenchmark
% 0.66/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.16 % (3512229)------------------------------
% 2.74/1.16 % (3512229)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.16 % (3512229)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.16 % (3512229)CaDiCaL version: 2.1.3
% 2.74/1.16 % (3512229)Termination reason: Refutation
% 2.74/1.16 % (3512229)Time elapsed: 0.008 s
% 2.74/1.16 % (3512229)Peak memory usage: 88 MB
% 2.74/1.16 % (3512229)Instructions burned: 22 (million)
% 2.74/1.16 % (3512229)------------------------------
% 2.74/1.16 % (3512229)------------------------------
% 2.74/1.16 % (3512220)Success in time 0.294 s
% 2.74/1.16 % Vampire exiting
%------------------------------------------------------------------------------