%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC061+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:54:08 AM UTC 2026
% Result : Theorem 69.78s 16.11s
% Output : CNFRefutation 69.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 47
% Number of leaves : 15
% Syntax : Number of formulae : 174 ( 13 unt; 0 def)
% Number of atoms : 643 ( 172 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 859 ( 390 ~; 421 |; 16 &)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 32 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ) ).
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ) ).
fof(ax7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ) ).
fof(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ) ).
fof(ax25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ) ).
fof(ax27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax39,axiom,
~ singletonP(nil) ).
fof(ax42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ) ).
fof(ax57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ) ).
fof(ax84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( segmentP(X0,X6)
& segmentP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( segmentP(X0,X6)
& segmentP(X1,X6)
& neq(X6,nil)
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c9,plain,
( ssItem(sK11(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c10,plain,
( cons(sK11(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c11,plain,
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c12,plain,
( ssList(sK15(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax5]) ).
cnf(c13,plain,
( app(X1,sK15(X0,X1)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax5]) ).
cnf(c21,plain,
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X3)
| app(app(X2,X1),X3) != X0
| ~ ssList(X1)
| segmentP(X0,X1) ),
inference(clausification,[status(esa)],[ax7]) ).
cnf(c95,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax15]) ).
cnf(c96,plain,
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax16]) ).
cnf(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c104,plain,
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax21]) ).
cnf(c108,plain,
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax25]) ).
cnf(c110,plain,
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax27]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c128,plain,
~ singletonP(nil),
inference(clausification,[status(esa)],[ax39]) ).
cnf(c131,plain,
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax42]) ).
cnf(c150,plain,
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax57]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
cnf(c208,plain,
ssList(sK253),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c209,plain,
ssList(sK254),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c212,plain,
sK254 = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c213,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
( nil != sK256
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( ~ neq(sK256,nil)
| ssItem(sK257) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( ~ neq(sK256,nil)
| ssList(sK258) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( ~ neq(sK256,nil)
| app(cons(sK257,nil),sK258) = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( ~ neq(sK256,nil)
| app(sK258,cons(sK257,nil)) = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( neq(sK254,nil)
| nil = sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( nil = sK254
| ~ segmentP(sK253,X0)
| ~ ssList(X0)
| ~ segmentP(sK254,X0)
| ~ neq(X0,nil) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( neq(sK254,nil)
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( nil != sK256
| nil = sK253 ),
inference(demodulation,[status(thm)],[c214,c213]) ).
cnf(d1,plain,
( nil != sK254
| nil = sK253 ),
inference(demodulation,[status(thm)],[d0,c212]) ).
cnf(d2,plain,
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[c11]) ).
cnf(d3,plain,
( ~ ssList(nil)
| ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d2,c96]) ).
cnf(d4,plain,
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c97,d3]) ).
cnf(d5,plain,
( ~ neq(sK256,nil)
| app(cons(sK257,nil),sK258) = sK254 ),
inference(demodulation,[status(thm)],[c217,c212]) ).
cnf(d6,plain,
( ~ neq(sK254,nil)
| app(cons(sK257,nil),sK258) = sK254 ),
inference(demodulation,[status(thm)],[d5,c212]) ).
cnf(d7,plain,
( ~ ssList(sK258)
| ~ ssList(nil)
| ~ ssItem(sK257)
| ~ neq(sK254,nil)
| cons(sK257,app(nil,sK258)) = sK254 ),
inference(superposition,[status(thm)],[c110,d6]) ).
cnf(d8,plain,
( ssList(sK258)
| ~ neq(sK254,nil) ),
inference(demodulation,[status(thm)],[c216,c212]) ).
cnf(d9,plain,
( ssList(sK258)
| nil = sK254 ),
inference(resolution,[status(thm)],[c219,d8]) ).
cnf(d10,plain,
( ssList(sK258)
| nil = sK253
| nil != nil ),
inference(superposition,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( ssList(sK258)
| nil = sK253 ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ssList(sK258)
| neq(sK254,nil)
| nil != nil ),
inference(superposition,[status(thm)],[d11,c221]) ).
cnf(d13,plain,
( ssList(sK258)
| neq(sK254,nil) ),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( ssList(sK258)
| ssList(sK258) ),
inference(resolution,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( ~ ssList(nil)
| ~ neq(sK254,nil)
| ~ ssItem(sK257)
| cons(sK257,app(nil,sK258)) = sK254 ),
inference(resolution,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
( ~ neq(sK254,nil)
| ssItem(sK257) ),
inference(demodulation,[status(thm)],[c215,c212]) ).
cnf(d17,plain,
( ssItem(sK257)
| nil = sK254 ),
inference(resolution,[status(thm)],[c219,d16]) ).
cnf(d18,plain,
( ssItem(sK257)
| nil = sK253
| nil != nil ),
inference(superposition,[status(thm)],[d17,d1]) ).
cnf(d19,plain,
( ssItem(sK257)
| nil = sK253 ),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
( ssItem(sK257)
| neq(sK254,nil)
| nil != nil ),
inference(superposition,[status(thm)],[d19,c221]) ).
cnf(d21,plain,
( neq(sK254,nil)
| ssItem(sK257) ),
inference(equality_resolution,[status(thm)],[d20]) ).
cnf(d22,plain,
( ssItem(sK257)
| ssItem(sK257) ),
inference(resolution,[status(thm)],[d21,d16]) ).
cnf(d23,plain,
( ~ ssList(nil)
| ~ neq(sK254,nil)
| cons(sK257,app(nil,sK258)) = sK254 ),
inference(resolution,[status(thm)],[d22,d15]) ).
cnf(d24,plain,
( ~ neq(sK254,nil)
| cons(sK257,app(nil,sK258)) = sK254 ),
inference(resolution,[status(thm)],[c97,d23]) ).
cnf(d25,plain,
( ~ ssList(sK258)
| ~ neq(sK254,nil)
| cons(sK257,sK258) = sK254 ),
inference(superposition,[status(thm)],[c111,d24]) ).
cnf(d26,plain,
( ~ neq(sK254,nil)
| cons(sK257,sK258) = sK254 ),
inference(resolution,[status(thm)],[d14,d25]) ).
cnf(d27,plain,
( ~ neq(sK254,nil)
| segmentP(X1,sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(sK258)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK254,X0) != X1 ),
inference(superposition,[status(thm)],[d6,c21]) ).
cnf(d28,plain,
( segmentP(X1,sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(sK254,nil)
| app(sK254,X0) != X1 ),
inference(resolution,[status(thm)],[d14,d27]) ).
cnf(d29,plain,
( segmentP(app(sK254,X0),sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ ssList(app(sK254,X0))
| ~ neq(sK254,nil) ),
inference(equality_resolution,[status(thm)],[d28]) ).
cnf(d30,plain,
( ~ ssList(sK254)
| ~ ssList(cons(sK257,nil))
| ~ ssList(app(sK254,nil))
| ~ ssList(nil)
| ~ neq(sK254,nil)
| segmentP(sK254,sK258) ),
inference(superposition,[status(thm)],[c194,d29]) ).
cnf(d31,plain,
( segmentP(sK254,sK258)
| ~ ssList(nil)
| ~ ssList(cons(sK257,nil))
| ~ ssList(app(sK254,nil))
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c209,d30]) ).
cnf(d32,plain,
( segmentP(sK254,sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(app(sK254,nil))
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c97,d31]) ).
cnf(d33,plain,
( ~ ssList(nil)
| ~ ssItem(sK257)
| segmentP(sK254,sK258)
| ~ ssList(app(sK254,nil))
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[d32,c96]) ).
cnf(d34,plain,
( segmentP(sK254,sK258)
| ~ ssList(nil)
| ~ ssList(app(sK254,nil))
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[d22,d33]) ).
cnf(d35,plain,
( segmentP(sK254,sK258)
| ~ ssList(app(sK254,nil))
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c97,d34]) ).
cnf(d36,plain,
( ~ ssList(sK254)
| segmentP(sK254,sK258)
| ~ neq(sK254,nil)
| ~ ssList(sK254) ),
inference(superposition,[status(thm)],[c194,d35]) ).
cnf(d37,plain,
( segmentP(sK254,sK258)
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c209,d36]) ).
cnf(d38,plain,
( nil = sK254
| segmentP(sK254,sK258) ),
inference(resolution,[status(thm)],[d37,c219]) ).
cnf(d39,plain,
( ~ segmentP(sK253,sK258)
| ~ ssList(sK258)
| ~ neq(sK258,nil)
| nil = sK254
| nil = sK254 ),
inference(resolution,[status(thm)],[d38,c220]) ).
cnf(d40,plain,
( ~ segmentP(sK253,sK258)
| ~ neq(sK258,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d14,d39]) ).
cnf(d41,plain,
( ~ ssList(X0)
| segmentP(X2,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X0,X1) != X2 ),
inference(superposition,[status(thm)],[c111,c21]) ).
cnf(d42,plain,
( segmentP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| app(X0,X1) != X2 ),
inference(resolution,[status(thm)],[c97,d41]) ).
cnf(d43,plain,
( ~ neq(sK256,nil)
| app(sK258,cons(sK257,nil)) = sK253 ),
inference(demodulation,[status(thm)],[c218,c213]) ).
cnf(d44,plain,
( ~ neq(sK254,nil)
| app(sK258,cons(sK257,nil)) = sK253 ),
inference(demodulation,[status(thm)],[d43,c212]) ).
cnf(d45,plain,
( ~ neq(sK254,nil)
| segmentP(X0,sK258)
| ~ ssList(sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| sK253 != X0 ),
inference(superposition,[status(thm)],[d44,d42]) ).
cnf(d46,plain,
( segmentP(X0,sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ neq(sK254,nil)
| sK253 != X0 ),
inference(resolution,[status(thm)],[d14,d45]) ).
cnf(d47,plain,
( segmentP(sK253,sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(sK253)
| ~ neq(sK254,nil) ),
inference(equality_resolution,[status(thm)],[d46]) ).
cnf(d48,plain,
( segmentP(sK253,sK258)
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c208,d47]) ).
cnf(d49,plain,
( ~ ssList(nil)
| ~ ssItem(sK257)
| segmentP(sK253,sK258)
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[d48,c96]) ).
cnf(d50,plain,
( segmentP(sK253,sK258)
| ~ ssList(nil)
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[d22,d49]) ).
cnf(d51,plain,
( segmentP(sK253,sK258)
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c97,d50]) ).
cnf(d52,plain,
( nil = sK254
| segmentP(sK253,sK258) ),
inference(resolution,[status(thm)],[d51,c219]) ).
cnf(d53,plain,
( ~ neq(sK258,nil)
| nil = sK254
| nil = sK254 ),
inference(resolution,[status(thm)],[d52,d40]) ).
cnf(d54,plain,
( ~ ssList(sK258)
| ~ ssList(nil)
| sK258 = nil
| nil = sK254 ),
inference(resolution,[status(thm)],[d53,c95]) ).
cnf(d55,plain,
( ~ ssList(nil)
| sK258 = nil
| nil = sK254 ),
inference(resolution,[status(thm)],[d14,d54]) ).
cnf(d56,plain,
( sK258 = nil
| nil = sK254 ),
inference(resolution,[status(thm)],[c97,d55]) ).
cnf(d57,plain,
( nil = sK254
| ~ neq(sK254,nil)
| cons(sK257,nil) = sK254 ),
inference(superposition,[status(thm)],[d56,d26]) ).
cnf(d58,plain,
( ~ neq(sK254,nil)
| nil = sK254
| ~ ssItem(sK257)
| singletonP(sK254) ),
inference(superposition,[status(thm)],[d57,d4]) ).
cnf(d59,plain,
( singletonP(sK254)
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d22,d58]) ).
cnf(d60,plain,
( ~ neq(sK254,nil)
| ~ ssList(sK258)
| ~ ssItem(sK257)
| nil != sK254 ),
inference(superposition,[status(thm)],[d26,c104]) ).
cnf(d61,plain,
( ~ neq(sK254,nil)
| ~ ssItem(sK257)
| nil != sK254 ),
inference(resolution,[status(thm)],[d14,d60]) ).
cnf(d62,plain,
( ~ neq(sK254,nil)
| nil != sK254 ),
inference(resolution,[status(thm)],[d22,d61]) ).
cnf(d63,plain,
( ~ neq(sK254,nil)
| segmentP(X1,cons(sK257,nil))
| ~ ssList(sK258)
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(superposition,[status(thm)],[d44,c21]) ).
cnf(d64,plain,
( segmentP(X1,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(sK254,nil)
| app(sK253,X0) != X1 ),
inference(resolution,[status(thm)],[d14,d63]) ).
cnf(d65,plain,
( ~ ssList(sK253)
| segmentP(X0,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ neq(sK254,nil)
| sK253 != X0 ),
inference(superposition,[status(thm)],[c194,d64]) ).
cnf(d66,plain,
( segmentP(X0,cons(sK257,nil))
| ~ ssList(nil)
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ neq(sK254,nil)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c208,d65]) ).
cnf(d67,plain,
( segmentP(X0,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ neq(sK254,nil)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c97,d66]) ).
cnf(d68,plain,
( segmentP(sK253,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ ssList(sK253)
| ~ neq(sK254,nil) ),
inference(equality_resolution,[status(thm)],[d67]) ).
cnf(d69,plain,
( segmentP(sK253,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c208,d68]) ).
cnf(d70,plain,
( ~ frontsegP(X0,sK253)
| ~ ssList(X0)
| ~ ssList(sK253)
| segmentP(X1,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ ssList(sK15(X0,sK253))
| ~ ssList(X1)
| ~ neq(sK254,nil)
| X0 != X1 ),
inference(superposition,[status(thm)],[c13,d64]) ).
cnf(d71,plain,
( segmentP(X1,cons(sK257,nil))
| ~ frontsegP(X0,sK253)
| ~ ssList(sK15(X0,sK253))
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(sK254,nil)
| X0 != X1 ),
inference(resolution,[status(thm)],[c208,d70]) ).
cnf(d72,plain,
( segmentP(X0,cons(sK257,nil))
| ~ frontsegP(X0,sK253)
| ~ ssList(sK15(X0,sK253))
| ~ ssList(cons(sK257,nil))
| ~ ssList(X0)
| ~ ssList(X0)
| ~ neq(sK254,nil) ),
inference(equality_resolution,[status(thm)],[d71]) ).
cnf(d73,plain,
( ~ segmentP(sK253,cons(sK257,nil))
| ~ ssList(cons(sK257,nil))
| ~ neq(cons(sK257,nil),nil)
| nil = sK254
| ~ frontsegP(sK254,sK253)
| ~ ssList(sK15(sK254,sK253))
| ~ ssList(cons(sK257,nil))
| ~ ssList(sK254)
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[d72,c220]) ).
cnf(d74,plain,
( ~ segmentP(sK253,cons(sK257,nil))
| ~ frontsegP(sK254,sK253)
| ~ ssList(sK15(sK254,sK253))
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| ~ neq(cons(sK257,nil),nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d73]) ).
cnf(d75,plain,
( ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| ~ frontsegP(sK254,sK253)
| ~ ssList(sK15(sK254,sK253))
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| ~ neq(cons(sK257,nil),nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d74,d69]) ).
cnf(d76,plain,
( ~ ssList(cons(sK257,nil))
| ~ ssList(nil)
| cons(sK257,nil) = nil
| ~ frontsegP(sK254,sK253)
| ~ ssList(sK15(sK254,sK253))
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d75,c95]) ).
cnf(d77,plain,
( ~ frontsegP(sK254,sK253)
| ~ ssList(sK15(sK254,sK253))
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| nil = sK254
| cons(sK257,nil) = nil ),
inference(resolution,[status(thm)],[c97,d76]) ).
cnf(d78,plain,
( ~ frontsegP(sK254,sK253)
| ~ ssList(sK15(sK254,sK253))
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| nil = sK254
| ~ ssItem(sK257)
| singletonP(nil) ),
inference(superposition,[status(thm)],[d77,d4]) ).
cnf(d79,plain,
( ~ frontsegP(sK254,sK253)
| singletonP(nil)
| ~ ssList(sK15(sK254,sK253))
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d22,d78]) ).
cnf(d80,plain,
( ~ frontsegP(sK254,sK253)
| ~ ssList(sK15(sK254,sK253))
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c128,d79]) ).
cnf(d81,plain,
( ~ frontsegP(sK254,sK253)
| ~ ssList(sK254)
| ~ ssList(sK253)
| ~ frontsegP(sK254,sK253)
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d80,c12]) ).
cnf(d82,plain,
( ~ frontsegP(sK254,sK253)
| ~ ssList(sK254)
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c208,d81]) ).
cnf(d83,plain,
( ~ frontsegP(sK254,sK253)
| ~ ssList(cons(sK257,nil))
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d82]) ).
cnf(d84,plain,
( ~ ssList(nil)
| ~ ssItem(sK257)
| ~ frontsegP(sK254,sK253)
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d83,c96]) ).
cnf(d85,plain,
( ~ frontsegP(sK254,sK253)
| ~ ssList(nil)
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d22,d84]) ).
cnf(d86,plain,
( ~ frontsegP(sK254,sK253)
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c97,d85]) ).
cnf(d87,plain,
( ~ neq(sK254,nil)
| ~ ssList(sK258)
| ~ ssItem(sK257)
| tl(sK254) = sK258 ),
inference(superposition,[status(thm)],[d26,c108]) ).
cnf(d88,plain,
( ~ neq(sK254,nil)
| ~ ssItem(sK257)
| tl(sK254) = sK258 ),
inference(resolution,[status(thm)],[d14,d87]) ).
cnf(d89,plain,
( ~ neq(sK254,nil)
| tl(sK254) = sK258 ),
inference(resolution,[status(thm)],[d22,d88]) ).
cnf(d90,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK11(X0))
| tl(X0) = nil ),
inference(superposition,[status(thm)],[c10,c108]) ).
cnf(d91,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| ~ ssItem(sK11(X0))
| tl(X0) = nil ),
inference(resolution,[status(thm)],[c97,d90]) ).
cnf(d92,plain,
( ~ singletonP(sK254)
| ~ ssList(sK254)
| ~ ssItem(sK11(sK254))
| ~ neq(sK254,nil)
| nil = sK258 ),
inference(superposition,[status(thm)],[d91,d89]) ).
cnf(d93,plain,
( ~ singletonP(sK254)
| ~ neq(sK254,nil)
| ~ ssItem(sK11(sK254))
| nil = sK258 ),
inference(resolution,[status(thm)],[c209,d92]) ).
cnf(d94,plain,
( nil = sK254
| ~ singletonP(sK254)
| ~ ssItem(sK11(sK254))
| nil = sK258 ),
inference(resolution,[status(thm)],[d93,c219]) ).
cnf(d95,plain,
( ~ singletonP(sK254)
| ~ ssList(sK254)
| ~ singletonP(sK254)
| nil = sK258
| nil = sK254 ),
inference(resolution,[status(thm)],[d94,c9]) ).
cnf(d96,plain,
( ~ singletonP(sK254)
| nil = sK258
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d95]) ).
cnf(d97,plain,
( ~ singletonP(sK254)
| nil = sK254
| ~ neq(sK254,nil)
| cons(sK257,nil) = sK254 ),
inference(superposition,[status(thm)],[d96,d26]) ).
cnf(d98,plain,
( ~ singletonP(sK254)
| ~ neq(sK254,nil)
| nil = sK254
| ~ neq(sK254,nil)
| app(sK258,sK254) = sK253 ),
inference(superposition,[status(thm)],[d97,d44]) ).
cnf(d99,plain,
( ~ singletonP(sK254)
| nil = sK254
| ~ neq(sK258,nil)
| nil = sK254
| ~ segmentP(sK253,nil) ),
inference(superposition,[status(thm)],[d96,d40]) ).
cnf(d100,plain,
( ~ ssList(sK253)
| ~ singletonP(sK254)
| ~ neq(sK258,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d99,c150]) ).
cnf(d101,plain,
( ~ singletonP(sK254)
| ~ neq(sK258,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c208,d100]) ).
cnf(d102,plain,
( ~ ssList(sK258)
| ~ ssList(nil)
| sK258 = nil
| ~ singletonP(sK254)
| nil = sK254 ),
inference(resolution,[status(thm)],[d101,c95]) ).
cnf(d103,plain,
( ~ singletonP(sK254)
| ~ ssList(nil)
| sK258 = nil
| nil = sK254 ),
inference(resolution,[status(thm)],[d14,d102]) ).
cnf(d104,plain,
( ~ singletonP(sK254)
| sK258 = nil
| nil = sK254 ),
inference(resolution,[status(thm)],[c97,d103]) ).
cnf(d105,plain,
( ~ singletonP(sK254)
| nil = sK254
| ~ singletonP(sK254)
| ~ neq(sK254,nil)
| nil = sK254
| app(nil,sK254) = sK253 ),
inference(superposition,[status(thm)],[d104,d98]) ).
cnf(d106,plain,
( ~ singletonP(sK254)
| ~ neq(sK254,nil)
| nil = sK254
| ~ ssList(sK254)
| sK253 = sK254 ),
inference(superposition,[status(thm)],[d105,c111]) ).
cnf(d107,plain,
( ~ singletonP(sK254)
| ~ neq(sK254,nil)
| sK253 = sK254
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d106]) ).
cnf(d108,plain,
( nil = sK254
| ~ singletonP(sK254)
| sK253 = sK254
| nil = sK254 ),
inference(resolution,[status(thm)],[d107,c219]) ).
cnf(d109,plain,
( ~ singletonP(sK254)
| nil = sK254
| ~ neq(sK254,nil)
| nil = sK254
| ~ frontsegP(sK254,sK254) ),
inference(superposition,[status(thm)],[d108,d86]) ).
cnf(d110,plain,
( ~ ssList(sK254)
| ~ singletonP(sK254)
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d109,c131]) ).
cnf(d111,plain,
( ~ singletonP(sK254)
| ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d110]) ).
cnf(d112,plain,
( nil = sK254
| ~ singletonP(sK254)
| nil = sK254 ),
inference(resolution,[status(thm)],[d111,c219]) ).
cnf(d113,plain,
( ~ singletonP(sK254)
| ~ neq(sK254,nil)
| nil != nil ),
inference(superposition,[status(thm)],[d112,d62]) ).
cnf(d114,plain,
( ~ singletonP(sK254)
| ~ neq(sK254,nil) ),
inference(equality_resolution,[status(thm)],[d113]) ).
cnf(d115,plain,
( ~ singletonP(sK254)
| nil = sK253
| nil != nil ),
inference(superposition,[status(thm)],[d112,d1]) ).
cnf(d116,plain,
( ~ singletonP(sK254)
| nil = sK253 ),
inference(equality_resolution,[status(thm)],[d115]) ).
cnf(d117,plain,
( ~ singletonP(sK254)
| neq(sK254,nil)
| nil != nil ),
inference(superposition,[status(thm)],[d116,c221]) ).
cnf(d118,plain,
( ~ singletonP(sK254)
| neq(sK254,nil) ),
inference(equality_resolution,[status(thm)],[d117]) ).
cnf(d119,plain,
( ~ singletonP(sK254)
| ~ singletonP(sK254) ),
inference(resolution,[status(thm)],[d118,d114]) ).
cnf(d120,plain,
( ~ neq(sK254,nil)
| nil = sK254 ),
inference(resolution,[status(thm)],[d119,d59]) ).
cnf(d121,plain,
( nil = sK254
| nil = sK254 ),
inference(resolution,[status(thm)],[d120,c219]) ).
cnf(d122,plain,
nil = sK253,
inference(resolution,[status(thm)],[d121,d1]) ).
cnf(d123,plain,
( neq(nil,nil)
| nil != sK253 ),
inference(demodulation,[status(thm)],[c221,d121]) ).
cnf(d124,plain,
( neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d123,d122]) ).
cnf(d125,plain,
~ neq(sK254,nil),
inference(resolution,[status(thm)],[d121,d62]) ).
cnf(d126,plain,
~ neq(nil,nil),
inference(demodulation,[status(thm)],[d125,d121]) ).
cnf(d127,plain,
nil != nil,
inference(resolution,[status(thm)],[d126,d124]) ).
cnf(d128,plain,
$false,
inference(equality_resolution,[status(thm)],[d127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC061+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n001.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 12:15:57 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 69.78/16.11 % SZS status Theorem for theBenchmark.p
% 69.78/16.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------