%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC218+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 : n007.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 08:54:39 AM UTC 2026
% Result : Theorem 17.89s 3.00s
% Output : CNFRefutation 17.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 116 ( 32 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 133 ( 56 ~; 49 |; 2 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 23 !; 2 ?)
% 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(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ) ).
fof(ax58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssItem(X6)
=> app(app(X4,cons(X6,nil)),X5) != X2 )
| app(X4,X5) != X3 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ! [X6] :
( ssItem(X6)
=> app(app(X4,cons(X6,nil)),X5) != X2 )
| app(X4,X5) != X3 ) ) )
| X0 != X2
| X1 != 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(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(c98,plain,
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax18]) ).
cnf(c151,plain,
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax58]) ).
cnf(c208,plain,
ssList(sK253),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c213,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
ssList(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
ssList(sK258),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
ssItem(sK259),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
app(app(sK257,cons(sK259,nil)),sK258) = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
~ neq(sK253,nil),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ssList(sK253)
| ~ ssList(nil)
| sK253 = nil ),
inference(resolution,[status(thm)],[c95,c219]) ).
cnf(d1,plain,
( ~ ssList(nil)
| sK253 = nil ),
inference(resolution,[status(thm)],[c208,d0]) ).
cnf(d2,plain,
sK253 = nil,
inference(resolution,[status(thm)],[c97,d1]) ).
cnf(d3,plain,
app(app(sK257,cons(sK259,nil)),sK258) = sK253,
inference(demodulation,[status(thm)],[c218,c213]) ).
cnf(d4,plain,
( segmentP(X0,cons(sK259,nil))
| ~ ssList(sK257)
| ~ ssList(cons(sK259,nil))
| ~ ssList(sK258)
| ~ ssList(X0)
| sK253 != X0 ),
inference(superposition,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
( segmentP(X0,cons(sK259,nil))
| ~ ssList(sK258)
| ~ ssList(cons(sK259,nil))
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c214,d4]) ).
cnf(d6,plain,
( segmentP(X0,cons(sK259,nil))
| ~ ssList(cons(sK259,nil))
| ~ ssList(X0)
| sK253 != X0 ),
inference(resolution,[status(thm)],[c215,d5]) ).
cnf(d7,plain,
( segmentP(sK253,cons(sK259,nil))
| ~ ssList(cons(sK259,nil))
| ~ ssList(sK253) ),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
( segmentP(sK253,cons(sK259,nil))
| ~ ssList(cons(sK259,nil)) ),
inference(resolution,[status(thm)],[c208,d7]) ).
cnf(d9,plain,
( segmentP(nil,cons(sK259,nil))
| ~ ssList(cons(sK259,nil)) ),
inference(demodulation,[status(thm)],[d8,d2]) ).
cnf(d10,plain,
( ~ ssList(cons(sK259,nil))
| ~ ssList(cons(sK259,nil))
| nil = cons(sK259,nil) ),
inference(resolution,[status(thm)],[c151,d9]) ).
cnf(d11,plain,
( ~ ssList(nil)
| ~ ssItem(sK259)
| nil = cons(sK259,nil) ),
inference(resolution,[status(thm)],[d10,c96]) ).
cnf(d12,plain,
( ~ ssList(nil)
| nil = cons(sK259,nil) ),
inference(resolution,[status(thm)],[c217,d11]) ).
cnf(d13,plain,
nil = cons(sK259,nil),
inference(resolution,[status(thm)],[c97,d12]) ).
cnf(d14,plain,
( ~ ssList(nil)
| ~ ssItem(sK259)
| nil != nil ),
inference(superposition,[status(thm)],[d13,c98]) ).
cnf(d15,plain,
( ~ ssList(nil)
| nil != nil ),
inference(resolution,[status(thm)],[c217,d14]) ).
cnf(d16,plain,
nil != nil,
inference(resolution,[status(thm)],[c97,d15]) ).
cnf(d17,plain,
$false,
inference(equality_resolution,[status(thm)],[d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC218+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
% 0.09/0.37 % Computer : n007.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 12:30:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.89/3.00 % SZS status Theorem for theBenchmark.p
% 17.89/3.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------