%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Sun Sep 27 08:54:12 AM UTC 2026
% Result : Theorem 23.28s 6.28s
% Output : CNFRefutation 23.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 8
% Syntax : Number of formulae : 82 ( 32 unt; 0 def)
% Number of atoms : 233 ( 45 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 281 ( 130 ~; 122 |; 8 &)
% ( 2 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(ax17,axiom,
ssList(nil) ).
fof(ax26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ) ).
fof(ax84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( app(X5,X7) != X3
| app(app(X5,X6),X7) != X2
| ~ ssList(X7) ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( app(X5,X7) != X3
| app(app(X5,X6),X7) != X2
| ~ ssList(X7) ) ) )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
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(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c109,plain,
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax26]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c148,plain,
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax55]) ).
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,
neq(sK254,nil),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( ~ segmentP(sK253,X0)
| ~ segmentP(sK254,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
ssList(sK258),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
ssList(sK259),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
ssList(sK260),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
app(app(sK258,sK259),sK260) = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
app(sK258,sK260) = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
app(sK254,nil) = sK254,
inference(resolution,[status(thm)],[c194,c209]) ).
cnf(d1,plain,
app(sK258,sK260) = sK254,
inference(demodulation,[status(thm)],[c220,c212]) ).
cnf(d2,plain,
( segmentP(X1,sK260)
| ~ ssList(sK258)
| ~ ssList(sK260)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK254,X0) != X1 ),
inference(superposition,[status(thm)],[d1,c21]) ).
cnf(d3,plain,
( segmentP(X1,sK260)
| ~ ssList(sK258)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK254,X0) != X1 ),
inference(resolution,[status(thm)],[c218,d2]) ).
cnf(d4,plain,
( segmentP(X1,sK260)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK254,X0) != X1 ),
inference(resolution,[status(thm)],[c216,d3]) ).
cnf(d5,plain,
( segmentP(app(sK254,X0),sK260)
| ~ ssList(X0)
| ~ ssList(app(sK254,X0)) ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ ssList(app(sK254,nil))
| ~ ssList(nil)
| segmentP(sK254,sK260) ),
inference(superposition,[status(thm)],[d0,d5]) ).
cnf(d7,plain,
( segmentP(sK254,sK260)
| ~ ssList(nil)
| ~ ssList(sK254) ),
inference(demodulation,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( segmentP(sK254,sK260)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c209,d7]) ).
cnf(d9,plain,
segmentP(sK254,sK260),
inference(resolution,[status(thm)],[c97,d8]) ).
cnf(d10,plain,
( ~ segmentP(sK253,sK260)
| ~ ssList(sK260)
| ~ neq(sK260,nil) ),
inference(resolution,[status(thm)],[d9,c215]) ).
cnf(d11,plain,
( ~ segmentP(sK253,sK260)
| ~ neq(sK260,nil) ),
inference(resolution,[status(thm)],[c218,d10]) ).
cnf(d12,plain,
app(app(sK258,sK259),sK260) = sK253,
inference(demodulation,[status(thm)],[c219,c213]) ).
cnf(d13,plain,
( segmentP(X1,sK260)
| ~ ssList(app(sK258,sK259))
| ~ ssList(sK260)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(superposition,[status(thm)],[d12,c21]) ).
cnf(d14,plain,
( segmentP(X1,sK260)
| ~ ssList(app(sK258,sK259))
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(resolution,[status(thm)],[c218,d13]) ).
cnf(d15,plain,
app(sK253,nil) = sK253,
inference(resolution,[status(thm)],[c194,c208]) ).
cnf(d16,plain,
( segmentP(X0,sK260)
| ~ ssList(app(sK258,sK259))
| ~ ssList(nil)
| ~ ssList(X0)
| sK253 != X0 ),
inference(superposition,[status(thm)],[d15,d14]) ).
cnf(d17,plain,
( segmentP(X0,sK260)
| ~ ssList(app(sK258,sK259))
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c97,d16]) ).
cnf(d18,plain,
( segmentP(sK253,sK260)
| ~ ssList(app(sK258,sK259))
| ~ ssList(sK253) ),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( segmentP(sK253,sK260)
| ~ ssList(app(sK258,sK259)) ),
inference(resolution,[status(thm)],[c208,d18]) ).
cnf(d20,plain,
( ~ ssList(sK258)
| ~ ssList(sK259)
| segmentP(sK253,sK260) ),
inference(resolution,[status(thm)],[d19,c109]) ).
cnf(d21,plain,
( segmentP(sK253,sK260)
| ~ ssList(sK259) ),
inference(resolution,[status(thm)],[c216,d20]) ).
cnf(d22,plain,
segmentP(sK253,sK260),
inference(resolution,[status(thm)],[c217,d21]) ).
cnf(d23,plain,
~ neq(sK260,nil),
inference(resolution,[status(thm)],[d22,d11]) ).
cnf(d24,plain,
( ~ ssList(sK260)
| ~ ssList(nil)
| sK260 = nil ),
inference(resolution,[status(thm)],[d23,c95]) ).
cnf(d25,plain,
( ~ ssList(nil)
| sK260 = nil ),
inference(resolution,[status(thm)],[c218,d24]) ).
cnf(d26,plain,
sK260 = nil,
inference(resolution,[status(thm)],[c97,d25]) ).
cnf(d27,plain,
app(sK258,nil) = sK254,
inference(demodulation,[status(thm)],[d1,d26]) ).
cnf(d28,plain,
app(sK258,nil) = sK258,
inference(resolution,[status(thm)],[c194,c216]) ).
cnf(d29,plain,
sK254 = sK258,
inference(demodulation,[status(thm)],[d28,d27]) ).
cnf(d30,plain,
app(app(sK258,sK259),nil) = sK253,
inference(demodulation,[status(thm)],[d12,d26]) ).
cnf(d31,plain,
app(app(sK254,sK259),nil) = sK253,
inference(demodulation,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X0,X1),nil) = app(X0,X1) ),
inference(resolution,[status(thm)],[c194,c109]) ).
cnf(d33,plain,
( ~ ssList(X0)
| app(app(sK254,X0),nil) = app(sK254,X0) ),
inference(resolution,[status(thm)],[d32,c209]) ).
cnf(d34,plain,
app(app(sK254,sK259),nil) = app(sK254,sK259),
inference(resolution,[status(thm)],[d33,c217]) ).
cnf(d35,plain,
sK253 = app(sK254,sK259),
inference(demodulation,[status(thm)],[d34,d31]) ).
cnf(d36,plain,
app(nil,sK254) = sK254,
inference(resolution,[status(thm)],[c111,c209]) ).
cnf(d37,plain,
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(equality_resolution,[status(thm)],[c21]) ).
cnf(d38,plain,
app(nil,sK258) = sK258,
inference(resolution,[status(thm)],[c111,c216]) ).
cnf(d39,plain,
( ~ ssList(app(app(nil,sK258),X0))
| ~ ssList(nil)
| ~ ssList(sK258)
| ~ ssList(X0)
| segmentP(app(sK258,X0),sK258) ),
inference(superposition,[status(thm)],[d38,d37]) ).
cnf(d40,plain,
( segmentP(app(sK258,X0),sK258)
| ~ ssList(sK258)
| ~ ssList(nil)
| ~ ssList(app(app(nil,sK254),X0))
| ~ ssList(X0) ),
inference(demodulation,[status(thm)],[d39,d29]) ).
cnf(d41,plain,
( segmentP(app(sK258,X0),sK258)
| ~ ssList(sK258)
| ~ ssList(nil)
| ~ ssList(app(sK254,X0))
| ~ ssList(X0) ),
inference(demodulation,[status(thm)],[d40,d36]) ).
cnf(d42,plain,
( segmentP(app(sK258,X0),sK258)
| ~ ssList(sK254)
| ~ ssList(nil)
| ~ ssList(app(sK254,X0))
| ~ ssList(X0) ),
inference(demodulation,[status(thm)],[d41,d29]) ).
cnf(d43,plain,
( segmentP(app(sK254,X0),sK258)
| ~ ssList(sK254)
| ~ ssList(nil)
| ~ ssList(app(sK254,X0))
| ~ ssList(X0) ),
inference(demodulation,[status(thm)],[d42,d29]) ).
cnf(d44,plain,
( segmentP(app(sK254,X0),sK254)
| ~ ssList(sK254)
| ~ ssList(nil)
| ~ ssList(app(sK254,X0))
| ~ ssList(X0) ),
inference(demodulation,[status(thm)],[d43,d29]) ).
cnf(d45,plain,
( segmentP(app(sK254,X0),sK254)
| ~ ssList(nil)
| ~ ssList(app(sK254,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c209,d44]) ).
cnf(d46,plain,
( segmentP(app(sK254,X0),sK254)
| ~ ssList(app(sK254,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[c97,d45]) ).
cnf(d47,plain,
( ~ ssList(app(sK254,sK259))
| ~ ssList(sK259)
| segmentP(sK253,sK254) ),
inference(superposition,[status(thm)],[d35,d46]) ).
cnf(d48,plain,
( segmentP(sK253,sK254)
| ~ ssList(sK259)
| ~ ssList(sK253) ),
inference(demodulation,[status(thm)],[d47,d35]) ).
cnf(d49,plain,
( segmentP(sK253,sK254)
| ~ ssList(sK259) ),
inference(resolution,[status(thm)],[c208,d48]) ).
cnf(d50,plain,
segmentP(sK253,sK254),
inference(resolution,[status(thm)],[c217,d49]) ).
cnf(d51,plain,
( ~ segmentP(sK253,sK254)
| ~ ssList(sK254)
| ~ neq(sK254,nil)
| ~ ssList(sK254) ),
inference(resolution,[status(thm)],[c148,c215]) ).
cnf(d52,plain,
( ~ segmentP(sK253,sK254)
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c209,d51]) ).
cnf(d53,plain,
~ segmentP(sK253,sK254),
inference(resolution,[status(thm)],[c214,d52]) ).
cnf(d54,plain,
$false,
inference(resolution,[status(thm)],[d53,d50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n015.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 12:16:00 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.28/6.28 % SZS status Theorem for theBenchmark.p
% 23.28/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------