%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC068+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 : n016.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 25.26s 4.18s
% Output : CNFRefutation 25.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 22 unt; 0 def)
% Number of atoms : 122 ( 43 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 128 ( 54 ~; 47 |; 10 &)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 15 !; 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(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] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3
| app(X3,X3) != X2 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X0
& nil = X1 )
| ? [X4] :
( segmentP(X0,X4)
& segmentP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| X0 != X2
| X1 != X3
| app(X3,X3) != X2 ) ) ) ) ),
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(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,
app(sK256,sK256) = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c213,plain,
sK254 = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
sK253 = sK255,
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,
( nil != sK253
| nil != sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ segmentP(sK253,sK254)
| ~ ssList(sK254)
| ~ neq(sK254,nil)
| ~ ssList(sK254) ),
inference(resolution,[status(thm)],[c148,c215]) ).
cnf(d1,plain,
( ~ segmentP(sK253,sK254)
| ~ neq(sK254,nil) ),
inference(resolution,[status(thm)],[c209,d0]) ).
cnf(d2,plain,
app(sK253,nil) = sK253,
inference(resolution,[status(thm)],[c194,c208]) ).
cnf(d3,plain,
app(sK254,sK256) = sK255,
inference(demodulation,[status(thm)],[c212,c213]) ).
cnf(d4,plain,
app(sK254,sK254) = sK255,
inference(demodulation,[status(thm)],[d3,c213]) ).
cnf(d5,plain,
app(sK254,sK254) = sK253,
inference(demodulation,[status(thm)],[d4,c214]) ).
cnf(d6,plain,
( segmentP(X1,sK254)
| ~ ssList(sK254)
| ~ ssList(sK254)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(superposition,[status(thm)],[d5,c21]) ).
cnf(d7,plain,
( segmentP(X1,sK254)
| ~ ssList(X0)
| ~ ssList(X1)
| app(sK253,X0) != X1 ),
inference(resolution,[status(thm)],[c209,d6]) ).
cnf(d8,plain,
( segmentP(app(sK253,X0),sK254)
| ~ ssList(X0)
| ~ ssList(app(sK253,X0)) ),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
( ~ ssList(app(sK253,nil))
| ~ ssList(nil)
| segmentP(sK253,sK254) ),
inference(superposition,[status(thm)],[d2,d8]) ).
cnf(d10,plain,
( segmentP(sK253,sK254)
| ~ ssList(nil)
| ~ ssList(sK253) ),
inference(demodulation,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
( segmentP(sK253,sK254)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[c208,d10]) ).
cnf(d12,plain,
segmentP(sK253,sK254),
inference(resolution,[status(thm)],[c97,d11]) ).
cnf(d13,plain,
~ neq(sK254,nil),
inference(resolution,[status(thm)],[d12,d1]) ).
cnf(d14,plain,
( ~ ssList(sK254)
| ~ ssList(nil)
| sK254 = nil ),
inference(resolution,[status(thm)],[d13,c95]) ).
cnf(d15,plain,
( ~ ssList(nil)
| sK254 = nil ),
inference(resolution,[status(thm)],[c209,d14]) ).
cnf(d16,plain,
sK254 = nil,
inference(resolution,[status(thm)],[c97,d15]) ).
cnf(d17,plain,
app(nil,sK254) = sK254,
inference(resolution,[status(thm)],[c111,c209]) ).
cnf(d18,plain,
app(nil,nil) = sK254,
inference(demodulation,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
app(nil,nil) = nil,
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
app(nil,sK254) = sK253,
inference(demodulation,[status(thm)],[d5,d16]) ).
cnf(d21,plain,
app(nil,nil) = sK253,
inference(demodulation,[status(thm)],[d20,d16]) ).
cnf(d22,plain,
nil = sK253,
inference(demodulation,[status(thm)],[d21,d19]) ).
cnf(d23,plain,
( nil != nil
| nil != sK253 ),
inference(demodulation,[status(thm)],[c216,d16]) ).
cnf(d24,plain,
( nil != nil
| nil != nil ),
inference(demodulation,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
nil != nil,
inference(equality_resolution,[status(thm)],[d24]) ).
cnf(d26,plain,
$false,
inference(equality_resolution,[status(thm)],[d25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC068+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n016.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 12:15:30 UTC 2026
% 0.19/0.44 % CPUTime :
% 0.19/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.26/4.18 % SZS status Theorem for theBenchmark.p
% 25.26/4.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------