%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC279+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 : n014.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 08:54:50 AM UTC 2026
% Result : Theorem 8.26s 4.97s
% Output : CNFRefutation 8.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 1
% Syntax : Number of formulae : 37 ( 12 unt; 0 def)
% Number of atoms : 149 ( 21 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 188 ( 76 ~; 80 |; 16 &)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 16 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ! [X11] :
( ssItem(X11)
=> ( ( leq(X8,X11)
| ~ memberP(X10,X11) )
& ( leq(X11,X8)
| ~ memberP(X9,X11) ) ) )
| app(app(X9,cons(X8,nil)),X10) != X0 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ( ( memberP(X5,X7)
& ~ leq(X7,X4) )
| ( memberP(X6,X7)
& ~ leq(X4,X7) ) )
& ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ssList(X10)
=> ( ! [X11] :
( ssItem(X11)
=> ( ( leq(X8,X11)
| ~ memberP(X10,X11) )
& ( leq(X11,X8)
| ~ memberP(X9,X11) ) ) )
| app(app(X9,cons(X8,nil)),X10) != X0 ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ( ( memberP(X5,X7)
& ~ leq(X7,X4) )
| ( memberP(X6,X7)
& ~ leq(X4,X7) ) )
& ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c213,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
( ~ ssList(X0)
| ~ ssItem(X3)
| app(app(X2,cons(X3,nil)),X0) != sK255
| ~ ssItem(X1)
| leq(X3,X1)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( ~ ssList(X3)
| ~ ssItem(X2)
| app(app(X0,cons(X2,nil)),X3) != sK255
| ~ memberP(X0,X1)
| leq(X1,X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
ssItem(sK261),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
ssList(sK262),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
ssList(sK263),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
app(app(sK262,cons(sK261,nil)),sK263) = sK253,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
ssItem(sK264),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( memberP(sK263,sK264)
| memberP(sK262,sK264) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c222,plain,
( ~ leq(sK261,sK264)
| memberP(sK262,sK264) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c223,plain,
( memberP(sK263,sK264)
| ~ leq(sK264,sK261) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c224,plain,
( ~ leq(sK261,sK264)
| ~ leq(sK264,sK261) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
app(app(sK262,cons(sK261,nil)),sK263) = sK255,
inference(demodulation,[status(thm)],[c219,c213]) ).
cnf(d1,plain,
( leq(sK261,X0)
| ~ ssList(sK263)
| ~ ssList(sK262)
| ~ memberP(sK263,X0)
| ~ ssItem(X0)
| ~ ssItem(sK261)
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d0,c214]) ).
cnf(d2,plain,
( leq(sK261,X0)
| ~ ssList(sK263)
| ~ ssList(sK262)
| ~ memberP(sK263,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c216,d1]) ).
cnf(d3,plain,
( leq(sK261,X0)
| ~ ssList(sK263)
| ~ memberP(sK263,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c217,d2]) ).
cnf(d4,plain,
( leq(sK261,X0)
| ~ memberP(sK263,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c218,d3]) ).
cnf(d5,plain,
( leq(sK261,X0)
| ~ memberP(sK263,X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( leq(X0,sK261)
| ~ ssList(sK263)
| ~ ssList(sK262)
| ~ memberP(sK262,X0)
| ~ ssItem(sK261)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d0,c215]) ).
cnf(d7,plain,
( leq(X0,sK261)
| ~ ssList(sK263)
| ~ ssList(sK262)
| ~ memberP(sK262,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c216,d6]) ).
cnf(d8,plain,
( leq(X0,sK261)
| ~ ssList(sK263)
| ~ memberP(sK262,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c217,d7]) ).
cnf(d9,plain,
( leq(X0,sK261)
| ~ memberP(sK262,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c218,d8]) ).
cnf(d10,plain,
( leq(X0,sK261)
| ~ memberP(sK262,X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( memberP(sK262,sK264)
| leq(sK261,sK264)
| ~ ssItem(sK264) ),
inference(resolution,[status(thm)],[d5,c221]) ).
cnf(d12,plain,
( leq(sK261,sK264)
| memberP(sK262,sK264) ),
inference(resolution,[status(thm)],[c220,d11]) ).
cnf(d13,plain,
( leq(sK261,sK264)
| leq(sK264,sK261)
| ~ ssItem(sK264) ),
inference(resolution,[status(thm)],[d10,d12]) ).
cnf(d14,plain,
( leq(sK264,sK261)
| leq(sK261,sK264) ),
inference(resolution,[status(thm)],[c220,d13]) ).
cnf(d15,plain,
( memberP(sK262,sK264)
| leq(sK264,sK261) ),
inference(resolution,[status(thm)],[d14,c222]) ).
cnf(d16,plain,
( leq(sK264,sK261)
| ~ ssItem(sK264)
| leq(sK264,sK261) ),
inference(resolution,[status(thm)],[d15,d10]) ).
cnf(d17,plain,
leq(sK264,sK261),
inference(resolution,[status(thm)],[c220,d16]) ).
cnf(d18,plain,
memberP(sK263,sK264),
inference(resolution,[status(thm)],[d17,c223]) ).
cnf(d19,plain,
( leq(sK261,sK264)
| ~ ssItem(sK264) ),
inference(resolution,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
leq(sK261,sK264),
inference(resolution,[status(thm)],[c220,d19]) ).
cnf(d21,plain,
~ leq(sK261,sK264),
inference(resolution,[status(thm)],[d17,c224]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[d21,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC279+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n014.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 12:40:31 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.26/4.97 % SZS status Theorem for theBenchmark.p
% 8.26/4.97 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------