%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC024+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 : n014.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 08:53:59 AM UTC 2026
% Result : Theorem 19.15s 8.08s
% Output : CNFRefutation 19.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 17 unt; 0 def)
% Number of atoms : 120 ( 35 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 135 ( 53 ~; 48 |; 17 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 15 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ) ).
fof(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X2
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(X2,X5) != X3 ) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X5] :
( ssList(X5)
=> ( ? [X6] :
( ? [X7] :
( ? [X8] :
( app(X8,cons(X6,nil)) = X2
& ssList(X8) )
& app(cons(X6,nil),X7) = X5
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(X2,X5) != X3 ) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c14,plain,
( ~ ssList(X2)
| app(X2,X0) != X1
| ~ ssList(X1)
| frontsegP(X1,X2)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax5]) ).
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(c131,plain,
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax42]) ).
cnf(c209,plain,
ssList(sK254),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c210,plain,
ssList(sK255),
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,
( ~ frontsegP(sK253,X0)
| ~ frontsegP(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,
app(sK255,sK258) = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( nil != sK255
| nil = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ frontsegP(sK254,X0)
| ~ frontsegP(sK255,X0)
| ~ ssList(X0)
| ~ neq(X0,nil) ),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d1,plain,
( ~ frontsegP(sK254,sK255)
| ~ ssList(sK255)
| ~ neq(sK255,nil)
| ~ ssList(sK255) ),
inference(resolution,[status(thm)],[c131,d0]) ).
cnf(d2,plain,
( ~ frontsegP(sK254,sK255)
| ~ neq(sK255,nil) ),
inference(resolution,[status(thm)],[c210,d1]) ).
cnf(d3,plain,
app(sK255,sK258) = sK254,
inference(demodulation,[status(thm)],[c217,c212]) ).
cnf(d4,plain,
( frontsegP(X0,sK255)
| ~ ssList(X0)
| ~ ssList(sK258)
| ~ ssList(sK255)
| sK254 != X0 ),
inference(superposition,[status(thm)],[d3,c14]) ).
cnf(d5,plain,
( frontsegP(X0,sK255)
| ~ ssList(sK258)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c210,d4]) ).
cnf(d6,plain,
( frontsegP(X0,sK255)
| ~ ssList(X0)
| sK254 != X0 ),
inference(resolution,[status(thm)],[c216,d5]) ).
cnf(d7,plain,
( frontsegP(sK254,sK255)
| ~ ssList(sK254) ),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
frontsegP(sK254,sK255),
inference(resolution,[status(thm)],[c209,d7]) ).
cnf(d9,plain,
~ neq(sK255,nil),
inference(resolution,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ ssList(sK255)
| ~ ssList(nil)
| sK255 = nil ),
inference(resolution,[status(thm)],[d9,c95]) ).
cnf(d11,plain,
( ~ ssList(nil)
| sK255 = nil ),
inference(resolution,[status(thm)],[c210,d10]) ).
cnf(d12,plain,
sK255 = nil,
inference(resolution,[status(thm)],[c97,d11]) ).
cnf(d13,plain,
( nil = sK254
| nil != sK255 ),
inference(demodulation,[status(thm)],[c220,c212]) ).
cnf(d14,plain,
( nil = sK254
| nil != nil ),
inference(demodulation,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
nil = sK254,
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[c214,d15]) ).
cnf(d17,plain,
~ neq(nil,nil),
inference(demodulation,[status(thm)],[d9,d12]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.22 % Problem : SWC024+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.23 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.72 % Computer : n014.cluster.edu
% 0.08/5.72 % Model : x86_64 x86_64
% 0.08/5.72 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.72 % Memory : 8046.5625MB
% 0.08/5.72 % OS : Linux 6.8.0-71-generic
% 0.08/5.72 % CPULimit : 300
% 0.08/5.72 % WCLimit : 300
% 0.08/5.72 % DateTime : Sat Sep 26 12:05:07 UTC 2026
% 0.08/5.72 % CPUTime :
% 0.08/5.72 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.15/8.08 % SZS status Theorem for theBenchmark.p
% 19.15/8.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------