%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC213+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 : n012.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 08:54:38 AM UTC 2026
% Result : Theorem 17.08s 3.85s
% Output : CNFRefutation 17.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 12 unt; 0 def)
% Number of atoms : 81 ( 34 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 84 ( 25 ~; 26 |; 18 &)
% ( 1 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 14 !; 12 ?)
% 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)
=> ( ( nil = X2
& nil != X3 )
| neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X5
& ssList(X10) )
& ssItem(X9) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( app(cons(X6,nil),X8) = X2
& ssList(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| ~ 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 )
| neq(X0,nil)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X5
& ssList(X10) )
& ssItem(X9) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( app(cons(X6,nil),X8) = X2
& ssList(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ equalelemsP(X2)
| app(app(X4,X2),X5) != X3 ) ) )
| ~ neq(X1,nil)
| 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(c208,plain,
ssList(sK253),
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(c221,plain,
~ neq(sK253,nil),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c222,plain,
( nil != sK255
| nil = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ssList(sK253)
| ~ ssList(nil)
| sK253 = nil ),
inference(resolution,[status(thm)],[c95,c221]) ).
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,
( nil = sK256
| nil != sK253 ),
inference(demodulation,[status(thm)],[c222,c213]) ).
cnf(d4,plain,
( nil = sK254
| nil != sK253 ),
inference(demodulation,[status(thm)],[d3,c212]) ).
cnf(d5,plain,
( nil = sK254
| nil != nil ),
inference(demodulation,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
nil = sK254,
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
neq(nil,nil),
inference(demodulation,[status(thm)],[c214,d6]) ).
cnf(d8,plain,
~ neq(nil,nil),
inference(demodulation,[status(thm)],[c221,d2]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC213+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
% 0.08/0.36 % Computer : n012.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 12:31:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.08/3.85 % SZS status Theorem for theBenchmark.p
% 17.08/3.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------