%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC402+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:55:16 AM UTC 2026
% Result : Theorem 12.80s 10.02s
% Output : CNFRefutation 12.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 13 unt; 0 def)
% Number of atoms : 132 ( 21 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 164 ( 61 ~; 63 |; 26 &)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 19 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ) ).
fof(ax36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X2
& nil != X3 )
| ! [X14] :
( memberP(X1,X14)
| ~ memberP(X0,X14)
| ~ ssItem(X14) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3
| ~ ssList(X5) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( nil = X2
& nil != X3 )
| ! [X14] :
( memberP(X1,X14)
| ~ memberP(X0,X14)
| ~ ssItem(X14) )
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ? [X10] :
( ? [X11] :
( ? [X12] :
( ? [X13] :
( leq(X12,X10)
& app(X13,cons(X12,nil)) = X2
& ssList(X13) )
& ssItem(X12) )
& app(cons(X10,nil),X11) = X5
& ssList(X11) )
& ssItem(X10) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ? [X9] :
( leq(X6,X8)
& app(cons(X8,nil),X9) = X2
& ssList(X9) )
& ssItem(X8) )
& app(X7,cons(X6,nil)) = X4
& ssList(X7) )
& ssItem(X6) )
| ~ totalorderedP(X2)
| app(app(X4,X2),X5) != X3
| ~ ssList(X5) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c109,plain,
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax26]) ).
cnf(c122,plain,
( ~ memberP(X2,X0)
| memberP(app(X2,X1),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax36]) ).
cnf(c123,plain,
( ~ ssList(X2)
| memberP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
inference(clausification,[status(esa)],[ax36]) ).
cnf(c210,plain,
ssList(sK255),
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,
ssList(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
ssList(sK258),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
app(app(sK257,sK255),sK258) = sK256,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
ssItem(sK267),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
memberP(sK253,sK267),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c222,plain,
~ memberP(sK254,sK267),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
memberP(sK255,sK267),
inference(demodulation,[status(thm)],[c221,c213]) ).
cnf(d1,plain,
( ~ ssList(sK258)
| ~ ssList(app(sK257,sK255))
| ~ memberP(app(sK257,sK255),X0)
| ~ ssItem(X0)
| memberP(sK256,X0) ),
inference(superposition,[status(thm)],[c216,c122]) ).
cnf(d2,plain,
( ~ ssList(app(sK257,sK255))
| memberP(sK256,X0)
| ~ memberP(app(sK257,sK255),X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c215,d1]) ).
cnf(d3,plain,
( ~ ssList(app(sK257,sK255))
| memberP(sK256,X0)
| ~ ssItem(X0)
| ~ ssList(sK255)
| ~ ssList(sK257)
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c123,d2]) ).
cnf(d4,plain,
( ~ ssList(sK257)
| ~ ssList(app(sK257,sK255))
| memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c210,d3]) ).
cnf(d5,plain,
( ~ ssList(app(sK257,sK255))
| memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c214,d4]) ).
cnf(d6,plain,
( ~ ssList(sK257)
| ~ ssList(sK255)
| memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d5,c109]) ).
cnf(d7,plain,
( ~ ssList(sK257)
| memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c210,d6]) ).
cnf(d8,plain,
( memberP(sK256,X0)
| ~ memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c214,d7]) ).
cnf(d9,plain,
( memberP(sK256,sK267)
| ~ ssItem(sK267) ),
inference(resolution,[status(thm)],[d8,d0]) ).
cnf(d10,plain,
memberP(sK256,sK267),
inference(resolution,[status(thm)],[c220,d9]) ).
cnf(d11,plain,
~ memberP(sK256,sK267),
inference(demodulation,[status(thm)],[c222,c212]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC402+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 12:58:51 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.80/10.02 % SZS status Theorem for theBenchmark.p
% 12.80/10.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------