%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC190+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 08:54:33 AM UTC 2026
% Result : Theorem 72.59s 18.10s
% Output : CNFRefutation 72.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 6
% Syntax : Number of formulae : 56 ( 14 unt; 0 def)
% Number of atoms : 202 ( 22 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 262 ( 116 ~; 115 |; 6 &)
% ( 2 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 27 !; 4 ?)
% 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(ax17,axiom,
ssList(nil) ).
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] :
( ! [X8] :
( ssItem(X8)
=> ? [X9] :
( memberP(X2,X9)
& X8 != X9
& ssItem(X9) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( X4 = X5
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0
| ~ ssList(X7) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ! [X8] :
( ssItem(X8)
=> ? [X9] :
( memberP(X2,X9)
& X8 != X9
& ssItem(X9) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ! [X7] :
( X4 = X5
| app(app(app(X6,cons(X4,nil)),cons(X5,nil)),X7) != X0
| ~ ssList(X7) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(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(c97,plain,
ssList(nil),
inference(clausification,[status(esa)],[ax17]) ).
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(c213,plain,
sK253 = sK255,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c214,plain,
ssItem(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
ssItem(sK258),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
ssList(sK259),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
ssList(sK260),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
app(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)),sK260) = sK253,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
sK257 != sK258,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( ~ memberP(sK255,X0)
| sK261 = X0
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ memberP(sK253,X0)
| ~ ssItem(X0)
| sK261 = X0 ),
inference(demodulation,[status(thm)],[c221,c213]) ).
cnf(d1,plain,
( ~ ssList(sK260)
| ~ ssList(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)))
| ~ memberP(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)),X0)
| ~ ssItem(X0)
| memberP(sK253,X0) ),
inference(superposition,[status(thm)],[c218,c122]) ).
cnf(d2,plain,
( ~ ssList(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)))
| memberP(sK253,X0)
| ~ memberP(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)),X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c217,d1]) ).
cnf(d3,plain,
( ~ ssList(cons(sK258,nil))
| ~ ssList(app(sK259,cons(sK257,nil)))
| ~ memberP(app(sK259,cons(sK257,nil)),X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)))
| memberP(sK253,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d2,c122]) ).
cnf(d4,plain,
( ~ ssList(app(sK259,cons(sK257,nil)))
| ~ ssList(cons(sK258,nil))
| ~ ssList(cons(sK258,nil))
| ~ ssList(app(sK259,cons(sK257,nil)))
| memberP(sK253,X0)
| ~ memberP(app(sK259,cons(sK257,nil)),X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d3,c109]) ).
cnf(d5,plain,
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(X1,cons(X0,X2)))
| memberP(app(X1,cons(X0,X2)),X0)
| ~ ssItem(X0) ),
inference(equality_resolution,[status(thm)],[c8]) ).
cnf(d6,plain,
( ~ ssList(cons(sK258,nil))
| ~ ssList(app(sK259,cons(sK257,nil)))
| memberP(sK253,sK257)
| ~ ssItem(sK257)
| ~ ssList(app(sK259,cons(sK257,nil)))
| ~ ssList(sK259)
| ~ ssList(nil)
| ~ ssItem(sK257) ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( ~ ssList(sK259)
| ~ ssList(nil)
| ~ ssList(cons(sK258,nil))
| ~ ssList(app(sK259,cons(sK257,nil)))
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[c214,d6]) ).
cnf(d8,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK258,nil))
| ~ ssList(app(sK259,cons(sK257,nil)))
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[c216,d7]) ).
cnf(d9,plain,
( ~ ssList(cons(sK258,nil))
| ~ ssList(app(sK259,cons(sK257,nil)))
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[c97,d8]) ).
cnf(d10,plain,
( ~ ssList(sK259)
| ~ ssList(cons(sK257,nil))
| ~ ssList(cons(sK258,nil))
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[d9,c109]) ).
cnf(d11,plain,
( ~ ssList(cons(sK258,nil))
| ~ ssList(cons(sK257,nil))
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[c216,d10]) ).
cnf(d12,plain,
( ~ ssList(nil)
| ~ ssItem(sK258)
| ~ ssList(cons(sK257,nil))
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[d11,c96]) ).
cnf(d13,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK257,nil))
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[c215,d12]) ).
cnf(d14,plain,
( ~ ssList(cons(sK257,nil))
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[c97,d13]) ).
cnf(d15,plain,
( ~ ssList(nil)
| ~ ssItem(sK257)
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[d14,c96]) ).
cnf(d16,plain,
( ~ ssList(nil)
| memberP(sK253,sK257) ),
inference(resolution,[status(thm)],[c214,d15]) ).
cnf(d17,plain,
memberP(sK253,sK257),
inference(resolution,[status(thm)],[c97,d16]) ).
cnf(d18,plain,
( ~ ssItem(sK257)
| sK261 = sK257 ),
inference(resolution,[status(thm)],[d17,d0]) ).
cnf(d19,plain,
sK261 = sK257,
inference(resolution,[status(thm)],[c214,d18]) ).
cnf(d20,plain,
( ~ memberP(sK253,X0)
| ~ ssItem(X0)
| sK257 = X0 ),
inference(demodulation,[status(thm)],[d0,d19]) ).
cnf(d21,plain,
( ~ ssList(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)))
| memberP(sK253,sK258)
| ~ ssItem(sK258)
| ~ ssList(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)))
| ~ ssList(app(sK259,cons(sK257,nil)))
| ~ ssList(nil)
| ~ ssItem(sK258) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d22,plain,
( ~ ssList(nil)
| ~ ssList(app(sK259,cons(sK257,nil)))
| ~ ssList(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)))
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[c215,d21]) ).
cnf(d23,plain,
( ~ ssList(app(sK259,cons(sK257,nil)))
| ~ ssList(app(app(sK259,cons(sK257,nil)),cons(sK258,nil)))
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[c97,d22]) ).
cnf(d24,plain,
( ~ ssList(app(sK259,cons(sK257,nil)))
| ~ ssList(cons(sK258,nil))
| ~ ssList(app(sK259,cons(sK257,nil)))
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[d23,c109]) ).
cnf(d25,plain,
( ~ ssList(sK259)
| ~ ssList(cons(sK257,nil))
| ~ ssList(cons(sK258,nil))
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[d24,c109]) ).
cnf(d26,plain,
( ~ ssList(cons(sK258,nil))
| ~ ssList(cons(sK257,nil))
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[c216,d25]) ).
cnf(d27,plain,
( ~ ssList(nil)
| ~ ssItem(sK258)
| ~ ssList(cons(sK257,nil))
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[d26,c96]) ).
cnf(d28,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK257,nil))
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[c215,d27]) ).
cnf(d29,plain,
( ~ ssList(cons(sK257,nil))
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[c97,d28]) ).
cnf(d30,plain,
( ~ ssList(nil)
| ~ ssItem(sK257)
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[d29,c96]) ).
cnf(d31,plain,
( ~ ssList(nil)
| memberP(sK253,sK258) ),
inference(resolution,[status(thm)],[c214,d30]) ).
cnf(d32,plain,
memberP(sK253,sK258),
inference(resolution,[status(thm)],[c97,d31]) ).
cnf(d33,plain,
( ~ ssItem(sK258)
| sK257 = sK258 ),
inference(resolution,[status(thm)],[d32,d20]) ).
cnf(d34,plain,
sK257 = sK258,
inference(resolution,[status(thm)],[c215,d33]) ).
cnf(d35,plain,
$false,
inference(resolution,[status(thm)],[c219,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC190+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n006.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 26 12:27:56 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 72.59/18.10 % SZS status Theorem for theBenchmark.p
% 72.59/18.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------