%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC397+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 : n001.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 08:55:14 AM UTC 2026
% Result : Theorem 53.96s 13.59s
% Output : CNFRefutation 53.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 9
% Syntax : Number of formulae : 88 ( 15 unt; 0 def)
% Number of atoms : 303 ( 81 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 352 ( 137 ~; 175 |; 6 &)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 30 !; 2 ?)
% 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(ax15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ) ).
fof(ax16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ) ).
fof(ax17,axiom,
ssList(nil) ).
fof(ax27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ) ).
fof(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ) ).
fof(ax37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X2 ) ) ) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(X6,cons(X5,nil)) != X3
| app(cons(X5,nil),X6) != X2 ) ) ) )
| ( nil = X3
& nil != X2 )
| ! [X4] :
( ssItem(X4)
=> ( memberP(X1,X4)
| ~ memberP(X0,X4) ) )
| 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(c95,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax15]) ).
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(c110,plain,
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax27]) ).
cnf(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c122,plain,
( ~ memberP(X2,X0)
| memberP(app(X2,X1),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[ax36]) ).
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(c211,plain,
ssList(sK256),
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(c214,plain,
ssItem(sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
memberP(sK253,sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
~ memberP(sK254,sK257),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( nil != sK256
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( ~ neq(sK256,nil)
| ssItem(sK258) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( ~ neq(sK256,nil)
| ssList(sK259) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( ~ neq(sK256,nil)
| app(cons(sK258,nil),sK259) = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( ~ neq(sK256,nil)
| app(sK259,cons(sK258,nil)) = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ neq(sK256,nil)
| ~ ssList(sK259)
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(X0,sK258)
| ~ ssItem(sK258)
| sK256 != X0 ),
inference(superposition,[status(thm)],[c221,c8]) ).
cnf(d1,plain,
( ~ ssList(sK259)
| ~ ssList(X0)
| memberP(X0,sK258)
| ~ neq(sK256,nil)
| ~ ssItem(sK258)
| sK256 != X0 ),
inference(resolution,[status(thm)],[c97,d0]) ).
cnf(d2,plain,
( ~ ssList(sK259)
| ~ ssList(sK256)
| memberP(sK256,sK258)
| ~ neq(sK256,nil)
| ~ ssItem(sK258) ),
inference(equality_resolution,[status(thm)],[d1]) ).
cnf(d3,plain,
( ~ ssList(sK259)
| memberP(sK256,sK258)
| ~ neq(sK256,nil)
| ~ ssItem(sK258) ),
inference(resolution,[status(thm)],[c211,d2]) ).
cnf(d4,plain,
~ memberP(sK256,sK257),
inference(demodulation,[status(thm)],[c216,c212]) ).
cnf(d5,plain,
( ssItem(sK258)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c218]) ).
cnf(d6,plain,
( ~ ssList(nil)
| ssItem(sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d5]) ).
cnf(d7,plain,
( ssItem(sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d6]) ).
cnf(d8,plain,
( ssItem(sK258)
| ~ memberP(nil,sK257) ),
inference(superposition,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
memberP(sK255,sK257),
inference(demodulation,[status(thm)],[c215,c213]) ).
cnf(d10,plain,
( ssItem(sK258)
| nil = sK255
| nil != nil ),
inference(superposition,[status(thm)],[d7,c217]) ).
cnf(d11,plain,
( ssItem(sK258)
| nil = sK255 ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ssItem(sK258)
| memberP(nil,sK257) ),
inference(superposition,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
( ssItem(sK258)
| ssItem(sK258) ),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
( ~ ssList(sK259)
| memberP(sK256,sK258)
| ~ neq(sK256,nil) ),
inference(resolution,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
( ssList(sK259)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c219]) ).
cnf(d16,plain,
( ssList(sK259)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d15]) ).
cnf(d17,plain,
( ssList(sK259)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d16]) ).
cnf(d18,plain,
( ssList(sK259)
| ~ memberP(nil,sK257) ),
inference(superposition,[status(thm)],[d17,d4]) ).
cnf(d19,plain,
( ssList(sK259)
| nil = sK255
| nil != nil ),
inference(superposition,[status(thm)],[d17,c217]) ).
cnf(d20,plain,
( ssList(sK259)
| nil = sK255 ),
inference(equality_resolution,[status(thm)],[d19]) ).
cnf(d21,plain,
( ssList(sK259)
| memberP(nil,sK257) ),
inference(superposition,[status(thm)],[d20,d9]) ).
cnf(d22,plain,
( ssList(sK259)
| ssList(sK259) ),
inference(resolution,[status(thm)],[d21,d18]) ).
cnf(d23,plain,
( memberP(sK256,sK258)
| ~ neq(sK256,nil) ),
inference(resolution,[status(thm)],[d22,d14]) ).
cnf(d24,plain,
( ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil
| memberP(sK256,sK258) ),
inference(resolution,[status(thm)],[d23,c95]) ).
cnf(d25,plain,
( ~ ssList(nil)
| memberP(sK256,sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d24]) ).
cnf(d26,plain,
( memberP(sK256,sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d25]) ).
cnf(d27,plain,
( ~ neq(sK256,nil)
| ~ ssList(cons(sK258,nil))
| ~ ssList(sK259)
| ~ memberP(sK259,X0)
| ~ ssItem(X0)
| memberP(sK256,X0) ),
inference(superposition,[status(thm)],[c221,c122]) ).
cnf(d28,plain,
( ~ ssList(cons(sK258,nil))
| ~ memberP(sK259,X0)
| memberP(sK256,X0)
| ~ neq(sK256,nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d22,d27]) ).
cnf(d29,plain,
( ~ ssList(nil)
| ~ ssItem(sK258)
| ~ memberP(sK259,X0)
| memberP(sK256,X0)
| ~ neq(sK256,nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d28,c96]) ).
cnf(d30,plain,
( ~ memberP(sK259,X0)
| memberP(sK256,X0)
| ~ neq(sK256,nil)
| ~ ssItem(sK258)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[c97,d29]) ).
cnf(d31,plain,
( ~ memberP(sK259,X0)
| memberP(sK256,X0)
| ~ neq(sK256,nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[d13,d30]) ).
cnf(d32,plain,
( ~ ssList(sK259)
| ~ ssList(nil)
| ~ ssItem(sK258)
| ~ neq(sK256,nil)
| cons(sK258,app(nil,sK259)) = sK255 ),
inference(superposition,[status(thm)],[c110,c220]) ).
cnf(d33,plain,
( ~ ssList(sK259)
| ~ neq(sK256,nil)
| ~ ssItem(sK258)
| cons(sK258,app(nil,sK259)) = sK255 ),
inference(resolution,[status(thm)],[c97,d32]) ).
cnf(d34,plain,
( ~ ssList(sK259)
| ~ neq(sK256,nil)
| cons(sK258,app(nil,sK259)) = sK255 ),
inference(resolution,[status(thm)],[d13,d33]) ).
cnf(d35,plain,
( ~ neq(sK256,nil)
| cons(sK258,app(nil,sK259)) = sK255 ),
inference(resolution,[status(thm)],[d22,d34]) ).
cnf(d36,plain,
( ~ ssList(sK259)
| ~ neq(sK256,nil)
| cons(sK258,sK259) = sK255 ),
inference(superposition,[status(thm)],[c111,d35]) ).
cnf(d37,plain,
( ~ neq(sK256,nil)
| cons(sK258,sK259) = sK255 ),
inference(resolution,[status(thm)],[d22,d36]) ).
cnf(d38,plain,
( ~ neq(sK256,nil)
| ~ ssList(sK259)
| memberP(sK259,X0)
| ~ ssItem(X0)
| ~ ssItem(sK258)
| X0 = sK258
| ~ memberP(sK255,X0) ),
inference(superposition,[status(thm)],[d37,c124]) ).
cnf(d39,plain,
( ~ ssList(sK259)
| memberP(sK259,X0)
| ~ memberP(sK255,X0)
| ~ neq(sK256,nil)
| ~ ssItem(X0)
| X0 = sK258 ),
inference(resolution,[status(thm)],[d13,d38]) ).
cnf(d40,plain,
( memberP(sK259,X0)
| ~ memberP(sK255,X0)
| ~ neq(sK256,nil)
| ~ ssItem(X0)
| X0 = sK258 ),
inference(resolution,[status(thm)],[d22,d39]) ).
cnf(d41,plain,
( memberP(sK259,sK257)
| ~ neq(sK256,nil)
| ~ ssItem(sK257)
| sK257 = sK258 ),
inference(resolution,[status(thm)],[d40,d9]) ).
cnf(d42,plain,
( memberP(sK259,sK257)
| ~ neq(sK256,nil)
| sK257 = sK258 ),
inference(resolution,[status(thm)],[c214,d41]) ).
cnf(d43,plain,
( ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil
| memberP(sK259,sK257)
| sK257 = sK258 ),
inference(resolution,[status(thm)],[d42,c95]) ).
cnf(d44,plain,
( ~ ssList(nil)
| memberP(sK259,sK257)
| sK257 = sK258
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d43]) ).
cnf(d45,plain,
( memberP(sK259,sK257)
| sK257 = sK258
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d44]) ).
cnf(d46,plain,
( memberP(sK256,sK257)
| ~ neq(sK256,nil)
| ~ ssItem(sK257)
| sK257 = sK258
| sK256 = nil ),
inference(resolution,[status(thm)],[d45,d31]) ).
cnf(d47,plain,
( memberP(sK256,sK257)
| ~ neq(sK256,nil)
| sK257 = sK258
| sK256 = nil ),
inference(resolution,[status(thm)],[c214,d46]) ).
cnf(d48,plain,
( ~ neq(sK256,nil)
| sK257 = sK258
| sK256 = nil ),
inference(resolution,[status(thm)],[d4,d47]) ).
cnf(d49,plain,
( ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil
| sK257 = sK258
| sK256 = nil ),
inference(resolution,[status(thm)],[d48,c95]) ).
cnf(d50,plain,
( ~ ssList(nil)
| sK257 = sK258
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d49]) ).
cnf(d51,plain,
( sK257 = sK258
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d50]) ).
cnf(d52,plain,
( sK256 = nil
| sK256 = nil
| memberP(sK256,sK257) ),
inference(superposition,[status(thm)],[d51,d26]) ).
cnf(d53,plain,
sK256 = nil,
inference(resolution,[status(thm)],[d4,d52]) ).
cnf(d54,plain,
( nil != nil
| nil = sK255 ),
inference(demodulation,[status(thm)],[c217,d53]) ).
cnf(d55,plain,
nil = sK255,
inference(equality_resolution,[status(thm)],[d54]) ).
cnf(d56,plain,
memberP(nil,sK257),
inference(demodulation,[status(thm)],[d9,d55]) ).
cnf(d57,plain,
~ memberP(nil,sK257),
inference(demodulation,[status(thm)],[d4,d53]) ).
cnf(d58,plain,
$false,
inference(resolution,[status(thm)],[d57,d56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC397+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.39 % Computer : n001.cluster.edu
% 0.07/0.39 % Model : x86_64 x86_64
% 0.07/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.39 % Memory : 8046.5625MB
% 0.07/0.39 % OS : Linux 6.8.0-71-generic
% 0.07/0.39 % CPULimit : 300
% 0.07/0.39 % WCLimit : 300
% 0.07/0.39 % DateTime : Sat Sep 26 13:03:27 UTC 2026
% 0.07/0.39 % CPUTime :
% 0.07/0.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 53.96/13.59 % SZS status Theorem for theBenchmark.p
% 53.96/13.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------