%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC041+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 08:54:03 AM UTC 2026
% Result : Theorem 7.93s 20.44s
% Output : CNFRefutation 7.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 15 unt; 0 def)
% Number of atoms : 83 ( 35 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 89 ( 32 ~; 31 |; 11 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 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 : 27 ( 0 sgn 13 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ) ).
fof(ax46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| nil = X0
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| nil = X0
| X0 != X2
| X1 != X3
| nil != X1 ) ) ) ) ),
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(c137,plain,
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax46]) ).
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,
nil = sK254,
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,
nil != sK253,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
ssList(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
app(sK255,sK257) = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
nil = sK256,
inference(demodulation,[status(thm)],[c213,c212]) ).
cnf(d1,plain,
app(sK255,sK257) = nil,
inference(demodulation,[status(thm)],[c217,d0]) ).
cnf(d2,plain,
( frontsegP(X0,sK255)
| ~ ssList(X0)
| ~ ssList(sK257)
| ~ ssList(sK255)
| nil != X0 ),
inference(superposition,[status(thm)],[d1,c14]) ).
cnf(d3,plain,
( frontsegP(X0,sK255)
| ~ ssList(sK257)
| ~ ssList(X0)
| nil != X0 ),
inference(resolution,[status(thm)],[c210,d2]) ).
cnf(d4,plain,
( frontsegP(X0,sK255)
| ~ ssList(X0)
| nil != X0 ),
inference(resolution,[status(thm)],[c216,d3]) ).
cnf(d5,plain,
( frontsegP(nil,sK255)
| ~ ssList(nil) ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
ssList(nil),
inference(demodulation,[status(thm)],[c209,c212]) ).
cnf(d7,plain,
frontsegP(nil,sK255),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ ssList(sK255)
| nil = sK255 ),
inference(resolution,[status(thm)],[c137,d7]) ).
cnf(d9,plain,
nil = sK255,
inference(resolution,[status(thm)],[c210,d8]) ).
cnf(d10,plain,
nil != sK255,
inference(demodulation,[status(thm)],[c215,c214]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d10,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC041+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
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.06/15.54 % CPULimit : 300
% 0.06/15.54 % WCLimit : 300
% 0.06/15.54 % DateTime : Sat Sep 26 12:07:31 UTC 2026
% 0.06/15.55 % CPUTime :
% 0.06/15.55 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.93/20.44 % SZS status Theorem for theBenchmark.p
% 7.93/20.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------