%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC153+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 : 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 08:54:28 AM UTC 2026
% Result : Theorem 18.65s 3.19s
% Output : CNFRefutation 18.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 50 ( 16 unt; 0 def)
% Number of atoms : 256 ( 35 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 374 ( 168 ~; 164 |; 22 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 20 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ! [X13] :
( ssList(X13)
=> ! [X14] :
( ssList(X14)
=> ( ( leq(X10,X11)
& ! [X15] :
( ssItem(X15)
=> ( ( leq(X10,X15)
& leq(X15,X11) )
| ~ memberP(X13,X15) ) ) )
| ~ leq(X11,X10)
| app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X0 ) ) ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ( ? [X9] :
( ( ~ leq(X9,X5)
| ~ leq(X4,X9) )
& memberP(X7,X9)
& ssItem(X9) )
| ~ leq(X4,X5) )
& leq(X5,X4)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X2
& ssList(X8) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| X2 != X0
| X3 != X1 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X10] :
( ssItem(X10)
=> ! [X11] :
( ssItem(X11)
=> ! [X12] :
( ssList(X12)
=> ! [X13] :
( ssList(X13)
=> ! [X14] :
( ssList(X14)
=> ( ( leq(X10,X11)
& ! [X15] :
( ssItem(X15)
=> ( ( leq(X10,X15)
& leq(X15,X11) )
| ~ memberP(X13,X15) ) ) )
| ~ leq(X11,X10)
| app(app(app(app(X12,cons(X10,nil)),X13),cons(X11,nil)),X14) != X0 ) ) ) ) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( ( ? [X9] :
( ( ~ leq(X9,X5)
| ~ leq(X4,X9) )
& memberP(X7,X9)
& ssItem(X9) )
| ~ leq(X4,X5) )
& leq(X5,X4)
& app(app(app(app(X6,cons(X4,nil)),X7),cons(X5,nil)),X8) = X2
& ssList(X8) )
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
& ssItem(X4) )
| X2 != X0
| X3 != X1 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c213,plain,
sK255 = sK253,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
( ~ ssList(X4)
| app(app(app(app(X4,cons(X1,nil)),X2),cons(X0,nil)),X3) != sK255
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| leq(X1,X0)
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( leq(X1,X3)
| ~ ssItem(X3)
| ~ ssList(X5)
| app(app(app(app(X5,cons(X1,nil)),X2),cons(X0,nil)),X4) != sK255
| ~ ssList(X4)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ memberP(X2,X3)
| ~ leq(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( ~ ssList(X5)
| app(app(app(app(X5,cons(X2,nil)),X3),cons(X1,nil)),X4) != sK255
| ~ ssList(X4)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssList(X3)
| ~ memberP(X3,X0)
| ~ ssItem(X0)
| ~ leq(X1,X2)
| leq(X0,X1) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
ssItem(sK263),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
ssItem(sK264),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
ssList(sK265),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
ssList(sK266),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
ssList(sK267),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c222,plain,
app(app(app(app(sK265,cons(sK263,nil)),sK266),cons(sK264,nil)),sK267) = sK253,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c223,plain,
leq(sK264,sK263),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c224,plain,
( ~ leq(sK263,sK264)
| ssItem(sK268) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c225,plain,
( ~ leq(sK263,sK264)
| memberP(sK266,sK268) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c226,plain,
( ~ leq(sK263,sK264)
| ~ leq(sK263,sK268)
| ~ leq(sK268,sK264) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
app(app(app(app(sK265,cons(sK263,nil)),sK266),cons(sK264,nil)),sK267) = sK255,
inference(demodulation,[status(thm)],[c222,c213]) ).
cnf(d1,plain,
( ~ leq(sK264,sK263)
| leq(sK263,sK264)
| ~ ssList(sK265)
| ~ ssList(sK266)
| ~ ssList(sK267)
| ~ ssItem(sK264)
| ~ ssItem(sK263)
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d0,c214]) ).
cnf(d2,plain,
( ~ leq(sK264,sK263)
| leq(sK263,sK264)
| ~ ssList(sK266)
| ~ ssList(sK265)
| ~ ssItem(sK264)
| ~ ssItem(sK263)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c221,d1]) ).
cnf(d3,plain,
( ~ leq(sK264,sK263)
| leq(sK263,sK264)
| ~ ssList(sK266)
| ~ ssList(sK265)
| ~ ssItem(sK264)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c217,d2]) ).
cnf(d4,plain,
( ~ leq(sK264,sK263)
| leq(sK263,sK264)
| ~ ssList(sK266)
| ~ ssList(sK265)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c218,d3]) ).
cnf(d5,plain,
( ~ leq(sK264,sK263)
| leq(sK263,sK264)
| ~ ssList(sK266)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c219,d4]) ).
cnf(d6,plain,
( ~ leq(sK264,sK263)
| leq(sK263,sK264)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c220,d5]) ).
cnf(d7,plain,
( leq(sK263,sK264)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c223,d6]) ).
cnf(d8,plain,
leq(sK263,sK264),
inference(equality_resolution,[status(thm)],[d7]) ).
cnf(d9,plain,
memberP(sK266,sK268),
inference(resolution,[status(thm)],[d8,c225]) ).
cnf(d10,plain,
( ~ leq(sK264,sK263)
| leq(X0,sK264)
| ~ ssList(sK265)
| ~ ssList(sK266)
| ~ ssList(sK267)
| ~ memberP(sK266,X0)
| ~ ssItem(sK264)
| ~ ssItem(sK263)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d0,c216]) ).
cnf(d11,plain,
( ~ leq(sK264,sK263)
| leq(X0,sK264)
| ~ ssList(sK266)
| ~ ssList(sK265)
| ~ memberP(sK266,X0)
| ~ ssItem(sK264)
| ~ ssItem(sK263)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c221,d10]) ).
cnf(d12,plain,
( ~ leq(sK264,sK263)
| leq(X0,sK264)
| ~ ssList(sK266)
| ~ ssList(sK265)
| ~ memberP(sK266,X0)
| ~ ssItem(sK264)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c217,d11]) ).
cnf(d13,plain,
( ~ leq(sK264,sK263)
| leq(X0,sK264)
| ~ ssList(sK266)
| ~ ssList(sK265)
| ~ memberP(sK266,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c218,d12]) ).
cnf(d14,plain,
( ~ leq(sK264,sK263)
| leq(X0,sK264)
| ~ ssList(sK266)
| ~ memberP(sK266,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c219,d13]) ).
cnf(d15,plain,
( ~ leq(sK264,sK263)
| leq(X0,sK264)
| ~ memberP(sK266,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c220,d14]) ).
cnf(d16,plain,
( leq(X0,sK264)
| ~ memberP(sK266,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c223,d15]) ).
cnf(d17,plain,
( leq(X0,sK264)
| ~ memberP(sK266,X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( leq(sK268,sK264)
| ~ ssItem(sK268) ),
inference(resolution,[status(thm)],[d17,d9]) ).
cnf(d19,plain,
ssItem(sK268),
inference(resolution,[status(thm)],[d8,c224]) ).
cnf(d20,plain,
leq(sK268,sK264),
inference(resolution,[status(thm)],[d19,d18]) ).
cnf(d21,plain,
( ~ leq(sK268,sK264)
| ~ leq(sK263,sK268) ),
inference(resolution,[status(thm)],[d8,c226]) ).
cnf(d22,plain,
( ~ leq(sK264,sK263)
| leq(sK263,X0)
| ~ ssList(sK265)
| ~ ssList(sK266)
| ~ ssList(sK267)
| ~ memberP(sK266,X0)
| ~ ssItem(sK264)
| ~ ssItem(sK263)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(superposition,[status(thm)],[d0,c215]) ).
cnf(d23,plain,
( ~ leq(sK264,sK263)
| leq(sK263,X0)
| ~ ssList(sK266)
| ~ ssList(sK265)
| ~ memberP(sK266,X0)
| ~ ssItem(sK264)
| ~ ssItem(sK263)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c221,d22]) ).
cnf(d24,plain,
( ~ leq(sK264,sK263)
| leq(sK263,X0)
| ~ ssList(sK266)
| ~ ssList(sK265)
| ~ memberP(sK266,X0)
| ~ ssItem(sK264)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c217,d23]) ).
cnf(d25,plain,
( ~ leq(sK264,sK263)
| leq(sK263,X0)
| ~ ssList(sK266)
| ~ ssList(sK265)
| ~ memberP(sK266,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c218,d24]) ).
cnf(d26,plain,
( ~ leq(sK264,sK263)
| leq(sK263,X0)
| ~ ssList(sK266)
| ~ memberP(sK266,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c219,d25]) ).
cnf(d27,plain,
( ~ leq(sK264,sK263)
| leq(sK263,X0)
| ~ memberP(sK266,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c220,d26]) ).
cnf(d28,plain,
( leq(sK263,X0)
| ~ memberP(sK266,X0)
| ~ ssItem(X0)
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c223,d27]) ).
cnf(d29,plain,
( leq(sK263,X0)
| ~ memberP(sK266,X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d28]) ).
cnf(d30,plain,
( leq(sK263,sK268)
| ~ ssItem(sK268) ),
inference(resolution,[status(thm)],[d29,d9]) ).
cnf(d31,plain,
leq(sK263,sK268),
inference(resolution,[status(thm)],[d19,d30]) ).
cnf(d32,plain,
~ leq(sK268,sK264),
inference(resolution,[status(thm)],[d31,d21]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC153+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 : n009.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 12:21:15 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.65/3.19 % SZS status Theorem for theBenchmark.p
% 18.65/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------