%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC025+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 : n011.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 08:53:59 AM UTC 2026
% Result : Theorem 38.28s 5.70s
% Output : CNFRefutation 38.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 201 ( 52 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 253 ( 107 ~; 118 |; 12 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 15 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ) ).
fof(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ? [X4] :
( ( ( memberP(X3,X4)
& ~ memberP(X2,X4) )
| ( memberP(X2,X4)
& ~ memberP(X3,X4) ) )
& ssItem(X4) )
| ~ duplicatefreeP(X2)
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ? [X4] :
( ( ( memberP(X3,X4)
& ~ memberP(X2,X4) )
| ( memberP(X2,X4)
& ~ memberP(X3,X4) ) )
& ssItem(X4) )
| ~ duplicatefreeP(X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c8,plain,
( ~ ssList(X3)
| app(X1,cons(X0,X3)) != X2
| ~ ssList(X2)
| memberP(X2,X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax3]) ).
cnf(c96,plain,
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax16]) ).
cnf(c101,plain,
( ssList(sK120(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c102,plain,
( ssItem(sK121(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c103,plain,
( cons(sK121(X0),sK120(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax20]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c127,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax38]) ).
cnf(c208,plain,
ssList(sK253),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c209,plain,
ssList(sK254),
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(c215,plain,
( ~ memberP(sK255,X0)
| memberP(sK256,X0)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( ~ memberP(sK256,X0)
| memberP(sK255,X0)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( nil = sK253
| nil = sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( nil != sK254
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( memberP(sK256,X0)
| ~ memberP(sK253,X0)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d1,plain,
( memberP(sK254,X0)
| ~ memberP(sK253,X0)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[d0,c212]) ).
cnf(d2,plain,
( ~ ssList(cons(X0,X1))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X2)
| memberP(X2,X0)
| ~ ssItem(X0)
| cons(X0,X1) != X2 ),
inference(superposition,[status(thm)],[c111,c8]) ).
cnf(d3,plain,
( nil = sK253
| ssList(nil) ),
inference(superposition,[status(thm)],[c217,c209]) ).
cnf(d4,plain,
( ssList(nil)
| ssList(nil) ),
inference(superposition,[status(thm)],[d3,c208]) ).
cnf(d5,plain,
( ~ ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(X2)
| memberP(X2,X0)
| ~ ssItem(X0)
| cons(X0,X1) != X2 ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| memberP(cons(X0,X1),X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
( ~ ssList(X0)
| nil = X0
| ~ ssList(cons(sK121(X0),sK120(X0)))
| ~ ssList(sK120(X0))
| ~ ssItem(sK121(X0))
| memberP(X0,sK121(X0)) ),
inference(superposition,[status(thm)],[c103,d6]) ).
cnf(d8,plain,
( ~ ssList(sK120(X0))
| ~ ssItem(sK121(X0))
| ~ ssList(sK120(X0))
| ~ ssList(X0)
| memberP(X0,sK121(X0))
| ~ ssItem(sK121(X0))
| nil = X0 ),
inference(resolution,[status(thm)],[d7,c96]) ).
cnf(d9,plain,
( memberP(sK254,sK121(sK253))
| ~ ssItem(sK121(sK253))
| ~ ssList(sK120(sK253))
| ~ ssList(sK253)
| ~ ssItem(sK121(sK253))
| nil = sK253 ),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
( ~ ssList(sK120(sK253))
| memberP(sK254,sK121(sK253))
| ~ ssItem(sK121(sK253))
| nil = sK253 ),
inference(resolution,[status(thm)],[c208,d9]) ).
cnf(d11,plain,
( nil = sK253
| ~ ssList(sK120(sK253))
| ~ ssItem(sK121(sK253))
| nil = sK253
| memberP(nil,sK121(sK253)) ),
inference(superposition,[status(thm)],[c217,d10]) ).
cnf(d12,plain,
( ~ ssItem(sK121(sK253))
| ~ ssList(sK120(sK253))
| ~ ssItem(sK121(sK253))
| nil = sK253 ),
inference(resolution,[status(thm)],[d11,c127]) ).
cnf(d13,plain,
( ~ ssList(sK253)
| nil = sK253
| ~ ssItem(sK121(sK253))
| nil = sK253 ),
inference(resolution,[status(thm)],[d12,c101]) ).
cnf(d14,plain,
( ~ ssItem(sK121(sK253))
| nil = sK253 ),
inference(resolution,[status(thm)],[c208,d13]) ).
cnf(d15,plain,
( ~ ssList(sK253)
| nil = sK253
| nil = sK253 ),
inference(resolution,[status(thm)],[d14,c102]) ).
cnf(d16,plain,
nil = sK253,
inference(resolution,[status(thm)],[c208,d15]) ).
cnf(d17,plain,
( ~ memberP(sK256,X0)
| memberP(sK253,X0)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[c216,c213]) ).
cnf(d18,plain,
( ~ memberP(sK254,X0)
| memberP(sK253,X0)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[d17,c212]) ).
cnf(d19,plain,
( ~ memberP(sK254,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(demodulation,[status(thm)],[d18,d16]) ).
cnf(d20,plain,
( memberP(sK253,sK121(sK254))
| ~ ssItem(sK121(sK254))
| ~ ssList(sK120(sK254))
| ~ ssList(sK254)
| ~ ssItem(sK121(sK254))
| nil = sK254 ),
inference(resolution,[status(thm)],[d8,d18]) ).
cnf(d21,plain,
( ~ ssList(sK120(sK254))
| memberP(sK253,sK121(sK254))
| ~ ssItem(sK121(sK254))
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d20]) ).
cnf(d22,plain,
( memberP(sK254,sK121(sK254))
| ~ ssItem(sK121(sK254))
| ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254))
| nil = sK254 ),
inference(resolution,[status(thm)],[d21,d1]) ).
cnf(d23,plain,
nil != sK254,
inference(resolution,[status(thm)],[d16,c220]) ).
cnf(d24,plain,
( ~ ssList(sK120(sK254))
| memberP(sK254,sK121(sK254))
| ~ ssItem(sK121(sK254)) ),
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
( memberP(nil,sK121(sK254))
| ~ ssItem(sK121(sK254))
| ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254)) ),
inference(resolution,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
( ~ ssItem(sK121(sK254))
| ~ ssList(sK120(sK254))
| ~ ssItem(sK121(sK254)) ),
inference(resolution,[status(thm)],[d25,c127]) ).
cnf(d27,plain,
( ~ ssList(sK254)
| nil = sK254
| ~ ssItem(sK121(sK254)) ),
inference(resolution,[status(thm)],[d26,c101]) ).
cnf(d28,plain,
( ~ ssItem(sK121(sK254))
| nil = sK254 ),
inference(resolution,[status(thm)],[c209,d27]) ).
cnf(d29,plain,
~ ssItem(sK121(sK254)),
inference(resolution,[status(thm)],[d23,d28]) ).
cnf(d30,plain,
( ~ ssList(sK254)
| nil = sK254 ),
inference(resolution,[status(thm)],[d29,c102]) ).
cnf(d31,plain,
nil = sK254,
inference(resolution,[status(thm)],[c209,d30]) ).
cnf(d32,plain,
$false,
inference(resolution,[status(thm)],[d23,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC025+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
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 12:05:15 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 38.28/5.70 % SZS status Theorem for theBenchmark.p
% 38.28/5.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------