%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC069+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 : n011.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 08:54:09 AM UTC 2026
% Result : Theorem 17.60s 2.58s
% Output : CNFRefutation 17.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 135 ( 51 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 152 ( 59 ~; 68 |; 12 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 18 ( 0 sgn 12 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssList(X5)
=> ( ~ segmentP(X2,X5)
| ~ segmentP(X3,X5)
| ~ neq(X5,nil) ) ) )
| ( nil = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssList(X5)
=> ( ~ segmentP(X2,X5)
| ~ segmentP(X3,X5)
| ~ neq(X5,nil) ) ) )
| ( nil = X0
& nil = X1 )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
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(c211,plain,
ssList(sK256),
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,
( ~ segmentP(sK253,X0)
| ~ segmentP(sK254,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( nil != sK256
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( nil != sK253
| nil != sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( ~ neq(sK256,nil)
| ssList(sK258) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( ~ neq(sK256,nil)
| neq(sK258,nil) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( ~ neq(sK256,nil)
| segmentP(sK256,sK258) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( ~ neq(sK256,nil)
| segmentP(sK255,sK258) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ssList(sK258)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c217]) ).
cnf(d1,plain,
( ssList(sK258)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d0]) ).
cnf(d2,plain,
( ssList(sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d1]) ).
cnf(d3,plain,
( neq(sK258,nil)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c218]) ).
cnf(d4,plain,
( ~ ssList(nil)
| neq(sK258,nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d3]) ).
cnf(d5,plain,
( neq(sK258,nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d4]) ).
cnf(d6,plain,
( segmentP(sK253,sK258)
| ~ neq(sK256,nil) ),
inference(demodulation,[status(thm)],[c220,c213]) ).
cnf(d7,plain,
( segmentP(sK253,sK258)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,d6]) ).
cnf(d8,plain,
( segmentP(sK253,sK258)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d7]) ).
cnf(d9,plain,
( segmentP(sK253,sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d8]) ).
cnf(d10,plain,
( ~ segmentP(sK256,X0)
| ~ segmentP(sK253,X0)
| ~ ssList(X0)
| ~ neq(X0,nil) ),
inference(demodulation,[status(thm)],[c214,c212]) ).
cnf(d11,plain,
( segmentP(sK256,sK258)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c219]) ).
cnf(d12,plain,
( segmentP(sK256,sK258)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d11]) ).
cnf(d13,plain,
( segmentP(sK256,sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d12]) ).
cnf(d14,plain,
( ~ segmentP(sK253,sK258)
| ~ ssList(sK258)
| ~ neq(sK258,nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[d13,d10]) ).
cnf(d15,plain,
( sK256 = nil
| ~ ssList(sK258)
| ~ neq(sK258,nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[d14,d9]) ).
cnf(d16,plain,
( sK256 = nil
| ~ ssList(sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[d15,d5]) ).
cnf(d17,plain,
( sK256 = nil
| sK256 = nil ),
inference(resolution,[status(thm)],[d16,d2]) ).
cnf(d18,plain,
( nil != sK256
| nil = sK253 ),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d19,plain,
( nil != nil
| nil = sK253 ),
inference(demodulation,[status(thm)],[d18,d17]) ).
cnf(d20,plain,
nil = sK253,
inference(equality_resolution,[status(thm)],[d19]) ).
cnf(d21,plain,
( nil != sK256
| nil != sK253 ),
inference(demodulation,[status(thm)],[c216,c212]) ).
cnf(d22,plain,
( nil != nil
| nil != sK253 ),
inference(demodulation,[status(thm)],[d21,d17]) ).
cnf(d23,plain,
( nil != nil
| nil != nil ),
inference(demodulation,[status(thm)],[d22,d20]) ).
cnf(d24,plain,
nil != nil,
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
$false,
inference(equality_resolution,[status(thm)],[d24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC069+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 12:10:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.60/2.58 % SZS status Theorem for theBenchmark.p
% 17.60/2.58 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------