%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC007+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 : n009.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 08:53:54 AM UTC 2026
% Result : Theorem 30.25s 4.29s
% Output : CNFRefutation 30.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 73 ( 37 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 88 ( 40 ~; 30 |; 8 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn 10 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,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)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| X0 != X2
| X1 != X3
| nil != X2 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X4,X6) = X0
& app(app(X4,X5),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssList(X4) )
| X0 != X2
| X1 != X3
| nil != X2 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
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 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( ~ ssList(X2)
| app(app(X1,X0),X2) != sK254
| app(X1,X2) != sK253
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
ssList(nil),
inference(demodulation,[status(thm)],[c210,c212]) ).
cnf(d1,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[c111,d0]) ).
cnf(d2,plain,
sK253 = nil,
inference(demodulation,[status(thm)],[c214,c212]) ).
cnf(d3,plain,
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X2),X1) != sK254
| app(X0,X1) != nil ),
inference(demodulation,[status(thm)],[c215,d2]) ).
cnf(d4,plain,
app(nil,sK254) = sK254,
inference(resolution,[status(thm)],[c111,c209]) ).
cnf(d5,plain,
( ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK254)
| app(nil,X0) != nil
| app(sK254,X0) != sK254 ),
inference(superposition,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ ssList(nil)
| ~ ssList(X0)
| app(sK254,X0) != sK254
| app(nil,X0) != nil ),
inference(resolution,[status(thm)],[c209,d5]) ).
cnf(d7,plain,
( ~ ssList(X0)
| app(sK254,X0) != sK254
| app(nil,X0) != nil ),
inference(resolution,[status(thm)],[d0,d6]) ).
cnf(d8,plain,
app(sK254,nil) = sK254,
inference(resolution,[status(thm)],[c194,c209]) ).
cnf(d9,plain,
( ~ ssList(nil)
| app(nil,nil) != nil
| sK254 != sK254 ),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ ssList(nil)
| sK254 != sK254
| nil != nil ),
inference(demodulation,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
( sK254 != sK254
| nil != nil ),
inference(resolution,[status(thm)],[d0,d10]) ).
cnf(d12,plain,
nil != nil,
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
$false,
inference(equality_resolution,[status(thm)],[d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC007+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 12:03:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.25/4.29 % SZS status Theorem for theBenchmark.p
% 30.25/4.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------