%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC200+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 08:54:35 AM UTC 2026
% Result : Theorem 80.10s 22.98s
% Output : CNFRefutation 80.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 20 unt; 0 def)
% Number of atoms : 221 ( 89 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 234 ( 96 ~; 106 |; 4 &)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 24 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ) ).
fof(ax23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ) ).
fof(ax37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ) ).
fof(ax38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ) ).
fof(ax75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ) ).
fof(ax81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ) ).
fof(ax85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(app(X0,X1)) = hd(X0) ) ) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ! [X5] :
( ssItem(X5)
=> ( X4 = X5
| ~ memberP(X0,X5) ) )
& ssItem(X4) )
| ~ singletonP(X2)
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X4] :
( ! [X5] :
( ssItem(X5)
=> ( X4 = X5
| ~ memberP(X0,X5) ) )
& ssItem(X4) )
| ~ singletonP(X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
cnf(c9,plain,
( ssItem(sK11(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c10,plain,
( cons(sK11(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax4]) ).
cnf(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
cnf(c104,plain,
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax21]) ).
cnf(c106,plain,
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax23]) ).
cnf(c124,plain,
( memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| X2 = X0
| ~ memberP(cons(X0,X1),X2) ),
inference(clausification,[status(esa)],[ax37]) ).
cnf(c127,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax38]) ).
cnf(c181,plain,
( ssItem(sK210(X0))
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax75]) ).
cnf(c182,plain,
( hd(X0) = sK210(X0)
| nil = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax75]) ).
cnf(c189,plain,
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax81]) ).
cnf(c195,plain,
( hd(app(X0,X1)) = hd(X0)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax85]) ).
cnf(c208,plain,
ssList(sK253),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c209,plain,
ssList(sK254),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c213,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
singletonP(sK255),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( ssItem(sK258(X0))
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( memberP(sK253,sK258(X0))
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( X0 != sK258(X0)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
singletonP(sK253),
inference(demodulation,[status(thm)],[c214,c213]) ).
cnf(d1,plain,
( ~ ssList(sK253)
| cons(sK11(sK253),nil) = sK253 ),
inference(resolution,[status(thm)],[c10,d0]) ).
cnf(d2,plain,
cons(sK11(sK253),nil) = sK253,
inference(resolution,[status(thm)],[c208,d1]) ).
cnf(d3,plain,
( ~ ssItem(X0)
| hd(cons(X0,nil)) = X0 ),
inference(resolution,[status(thm)],[c106,c97]) ).
cnf(d4,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| hd(cons(sK11(X0),nil)) = sK11(X0) ),
inference(resolution,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
( ~ ssList(sK253)
| hd(cons(sK11(sK253),nil)) = sK11(sK253) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
( ~ ssList(sK253)
| hd(sK253) = sK11(sK253) ),
inference(demodulation,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
hd(sK253) = sK11(sK253),
inference(resolution,[status(thm)],[c208,d6]) ).
cnf(d8,plain,
( ~ singletonP(sK253)
| ~ ssList(sK253)
| ssItem(hd(sK253)) ),
inference(superposition,[status(thm)],[d7,c9]) ).
cnf(d9,plain,
( ~ singletonP(sK253)
| ssItem(hd(sK253)) ),
inference(resolution,[status(thm)],[c208,d8]) ).
cnf(d10,plain,
ssItem(hd(sK253)),
inference(resolution,[status(thm)],[d0,d9]) ).
cnf(d11,plain,
( ~ ssList(nil)
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(sK11(sK253))
| X0 = sK11(sK253)
| ~ memberP(sK253,X0) ),
inference(superposition,[status(thm)],[d2,c124]) ).
cnf(d12,plain,
( ~ memberP(sK253,X0)
| memberP(nil,X0)
| ~ ssItem(sK11(sK253))
| ~ ssItem(X0)
| X0 = sK11(sK253) ),
inference(resolution,[status(thm)],[c97,d11]) ).
cnf(d13,plain,
( ~ ssItem(X0)
| memberP(nil,sK258(X0))
| ~ ssItem(sK11(sK253))
| ~ ssItem(sK258(X0))
| sK258(X0) = sK11(sK253) ),
inference(resolution,[status(thm)],[d12,c216]) ).
cnf(d14,plain,
( memberP(nil,sK258(X0))
| ~ ssItem(sK258(X0))
| ~ ssItem(sK11(sK253))
| ~ ssItem(X0)
| sK258(X0) = hd(sK253) ),
inference(demodulation,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
( memberP(nil,sK258(X0))
| ~ ssItem(sK258(X0))
| ~ ssItem(hd(sK253))
| ~ ssItem(X0)
| sK258(X0) = hd(sK253) ),
inference(demodulation,[status(thm)],[d14,d7]) ).
cnf(d16,plain,
( memberP(nil,sK258(X0))
| ~ ssItem(sK258(X0))
| ~ ssItem(X0)
| sK258(X0) = hd(sK253) ),
inference(resolution,[status(thm)],[d10,d15]) ).
cnf(d17,plain,
( ~ ssItem(sK258(X0))
| ~ ssItem(sK258(X0))
| ~ ssItem(X0)
| sK258(X0) = hd(sK253) ),
inference(resolution,[status(thm)],[d16,c127]) ).
cnf(d18,plain,
( ~ ssItem(X0)
| ~ ssItem(X0)
| sK258(X0) = hd(sK253) ),
inference(resolution,[status(thm)],[d17,c215]) ).
cnf(d19,plain,
sK258(hd(sK253)) = hd(sK253),
inference(resolution,[status(thm)],[d18,d10]) ).
cnf(d20,plain,
( ~ ssItem(hd(sK253))
| hd(sK253) != hd(sK253) ),
inference(superposition,[status(thm)],[d19,c217]) ).
cnf(d21,plain,
hd(sK253) != hd(sK253),
inference(resolution,[status(thm)],[d10,d20]) ).
cnf(d22,plain,
( hd(sK253) = sK210(sK253)
| nil = sK253 ),
inference(resolution,[status(thm)],[c182,c208]) ).
cnf(d23,plain,
( ~ ssList(nil)
| ~ ssItem(sK11(sK253))
| nil != sK253 ),
inference(superposition,[status(thm)],[d2,c104]) ).
cnf(d24,plain,
( ~ ssItem(sK11(sK253))
| nil != sK253 ),
inference(resolution,[status(thm)],[c97,d23]) ).
cnf(d25,plain,
( ~ ssItem(hd(sK253))
| nil != sK253 ),
inference(demodulation,[status(thm)],[d24,d7]) ).
cnf(d26,plain,
nil != sK253,
inference(resolution,[status(thm)],[d10,d25]) ).
cnf(d27,plain,
hd(sK253) = sK210(sK253),
inference(resolution,[status(thm)],[d26,d22]) ).
cnf(d28,plain,
( ~ ssItem(X0)
| hd(cons(X0,sK253)) = X0 ),
inference(resolution,[status(thm)],[c106,c208]) ).
cnf(d29,plain,
( hd(cons(sK210(X0),sK253)) = sK210(X0)
| ~ ssList(X0)
| nil = X0 ),
inference(resolution,[status(thm)],[c181,d28]) ).
cnf(d30,plain,
( hd(cons(sK210(sK253),sK253)) = sK210(sK253)
| nil = sK253 ),
inference(resolution,[status(thm)],[d29,c208]) ).
cnf(d31,plain,
( nil = sK253
| nil = sK253
| hd(cons(hd(sK253),sK253)) = sK210(sK253) ),
inference(superposition,[status(thm)],[d22,d30]) ).
cnf(d32,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| hd(cons(sK11(X0),sK253)) = sK11(X0) ),
inference(resolution,[status(thm)],[d28,c9]) ).
cnf(d33,plain,
( ~ ssList(sK253)
| hd(cons(sK11(sK253),sK253)) = sK11(sK253) ),
inference(resolution,[status(thm)],[d32,d0]) ).
cnf(d34,plain,
hd(cons(sK11(sK253),sK253)) = sK11(sK253),
inference(resolution,[status(thm)],[c208,d33]) ).
cnf(d35,plain,
( ~ ssItem(X0)
| cons(X0,sK254) = app(cons(X0,nil),sK254) ),
inference(resolution,[status(thm)],[c189,c209]) ).
cnf(d36,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| cons(sK11(X0),sK254) = app(cons(sK11(X0),nil),sK254) ),
inference(resolution,[status(thm)],[d35,c9]) ).
cnf(d37,plain,
( ~ ssList(sK253)
| cons(sK11(sK253),sK254) = app(cons(sK11(sK253),nil),sK254) ),
inference(resolution,[status(thm)],[d36,d0]) ).
cnf(d38,plain,
( ~ ssList(sK253)
| cons(sK11(sK253),sK254) = app(sK253,sK254) ),
inference(demodulation,[status(thm)],[d37,d2]) ).
cnf(d39,plain,
cons(sK11(sK253),sK254) = app(sK253,sK254),
inference(resolution,[status(thm)],[c208,d38]) ).
cnf(d40,plain,
( ~ ssItem(X0)
| hd(cons(X0,sK254)) = X0 ),
inference(resolution,[status(thm)],[c106,c209]) ).
cnf(d41,plain,
( ~ singletonP(X0)
| ~ ssList(X0)
| hd(cons(sK11(X0),sK254)) = sK11(X0) ),
inference(resolution,[status(thm)],[d40,c9]) ).
cnf(d42,plain,
( ~ ssList(sK253)
| hd(cons(sK11(sK253),sK254)) = sK11(sK253) ),
inference(resolution,[status(thm)],[d41,d0]) ).
cnf(d43,plain,
hd(cons(sK11(sK253),sK254)) = sK11(sK253),
inference(resolution,[status(thm)],[c208,d42]) ).
cnf(d44,plain,
hd(app(sK253,sK254)) = sK11(sK253),
inference(demodulation,[status(thm)],[d43,d39]) ).
cnf(d45,plain,
( ~ ssList(X0)
| hd(app(sK253,X0)) = hd(sK253)
| nil = sK253 ),
inference(resolution,[status(thm)],[c195,c208]) ).
cnf(d46,plain,
( hd(app(sK253,sK254)) = hd(sK253)
| nil = sK253 ),
inference(resolution,[status(thm)],[d45,c209]) ).
cnf(d47,plain,
( sK11(sK253) = hd(sK253)
| nil = sK253 ),
inference(demodulation,[status(thm)],[d46,d44]) ).
cnf(d48,plain,
( nil = sK253
| hd(cons(hd(sK253),sK253)) = sK11(sK253) ),
inference(superposition,[status(thm)],[d47,d34]) ).
cnf(d49,plain,
( nil = sK253
| nil = sK253
| sK11(sK253) = sK210(sK253) ),
inference(superposition,[status(thm)],[d48,d31]) ).
cnf(d50,plain,
( nil = sK253
| hd(sK253) = sK210(sK253) ),
inference(demodulation,[status(thm)],[d49,d7]) ).
cnf(d51,plain,
( hd(sK253) = hd(sK253)
| nil = sK253 ),
inference(demodulation,[status(thm)],[d50,d27]) ).
cnf(d52,plain,
hd(sK253) = hd(sK253),
inference(resolution,[status(thm)],[d26,d51]) ).
cnf(d53,plain,
$false,
inference(resolution,[status(thm)],[d52,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC200+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
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 12:29:51 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 80.10/22.98 % SZS status Theorem for theBenchmark.p
% 80.10/22.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------