%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC029+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 : n017.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 08:54:00 AM UTC 2026
% Result : Theorem 32.83s 8.58s
% Output : CNFRefutation 32.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 51 ( 12 unt; 0 def)
% Number of atoms : 157 ( 63 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 178 ( 72 ~; 79 |; 8 &)
% ( 2 <=>; 17 =>; 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 : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 17 !; 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(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 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3 ) ) ) )
| ( nil = X3
& nil != 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 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3 ) ) ) )
| ( nil = X3
& nil != 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(c95,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax15]) ).
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(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,
( nil != sK256
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( ~ neq(sK256,nil)
| ssItem(sK257) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( ~ neq(sK256,nil)
| ssList(sK258) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( ~ neq(sK256,nil)
| app(sK258,cons(sK257,nil)) = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( nil = sK253
| nil = sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c222,plain,
( nil != sK254
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( nil != sK256
| nil = sK253 ),
inference(demodulation,[status(thm)],[c214,c213]) ).
cnf(d1,plain,
( nil = sK256
| nil = sK253 ),
inference(demodulation,[status(thm)],[c219,c212]) ).
cnf(d2,plain,
( nil = sK253
| nil = sK253
| nil != nil ),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
nil = sK253,
inference(equality_resolution,[status(thm)],[d2]) ).
cnf(d4,plain,
nil = sK255,
inference(demodulation,[status(thm)],[c213,d3]) ).
cnf(d5,plain,
( ~ neq(sK256,nil)
| app(sK258,cons(sK257,nil)) = nil ),
inference(demodulation,[status(thm)],[c218,d4]) ).
cnf(d6,plain,
( ~ neq(sK256,nil)
| ~ ssList(sK258)
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(X0,sK257)
| ~ ssItem(sK257)
| nil != X0 ),
inference(superposition,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
( nil = sK253
| ssList(nil) ),
inference(superposition,[status(thm)],[d1,c211]) ).
cnf(d8,plain,
( ssList(nil)
| ssList(nil) ),
inference(superposition,[status(thm)],[d7,c208]) ).
cnf(d9,plain,
( ~ ssList(sK258)
| ~ ssList(X0)
| memberP(X0,sK257)
| ~ neq(sK256,nil)
| ~ ssItem(sK257)
| nil != X0 ),
inference(resolution,[status(thm)],[d8,d6]) ).
cnf(d10,plain,
( ~ ssList(sK258)
| ~ ssList(nil)
| memberP(nil,sK257)
| ~ neq(sK256,nil)
| ~ ssItem(sK257) ),
inference(equality_resolution,[status(thm)],[d9]) ).
cnf(d11,plain,
( ~ ssList(sK258)
| memberP(nil,sK257)
| ~ neq(sK256,nil)
| ~ ssItem(sK257) ),
inference(resolution,[status(thm)],[d8,d10]) ).
cnf(d12,plain,
( nil != sK256
| nil != sK253 ),
inference(demodulation,[status(thm)],[c222,c212]) ).
cnf(d13,plain,
nil != sK256,
inference(resolution,[status(thm)],[d3,d12]) ).
cnf(d14,plain,
( ssList(sK258)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c216]) ).
cnf(d15,plain,
( ssList(sK258)
| ~ ssList(sK256)
| sK256 = nil ),
inference(resolution,[status(thm)],[d8,d14]) ).
cnf(d16,plain,
( ssList(sK258)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d15]) ).
cnf(d17,plain,
( ssList(sK258)
| nil != nil ),
inference(superposition,[status(thm)],[d16,d13]) ).
cnf(d18,plain,
ssList(sK258),
inference(equality_resolution,[status(thm)],[d17]) ).
cnf(d19,plain,
( memberP(nil,sK257)
| ~ neq(sK256,nil)
| ~ ssItem(sK257) ),
inference(resolution,[status(thm)],[d18,d11]) ).
cnf(d20,plain,
( ssItem(sK257)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c215]) ).
cnf(d21,plain,
( ~ ssList(sK256)
| ssItem(sK257)
| sK256 = nil ),
inference(resolution,[status(thm)],[d8,d20]) ).
cnf(d22,plain,
( ssItem(sK257)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d21]) ).
cnf(d23,plain,
( ssItem(sK257)
| nil != nil ),
inference(superposition,[status(thm)],[d22,d13]) ).
cnf(d24,plain,
ssItem(sK257),
inference(equality_resolution,[status(thm)],[d23]) ).
cnf(d25,plain,
( memberP(nil,sK257)
| ~ neq(sK256,nil) ),
inference(resolution,[status(thm)],[d24,d19]) ).
cnf(d26,plain,
( ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil
| memberP(nil,sK257) ),
inference(resolution,[status(thm)],[d25,c95]) ).
cnf(d27,plain,
( ~ ssList(sK256)
| memberP(nil,sK257)
| sK256 = nil ),
inference(resolution,[status(thm)],[d8,d26]) ).
cnf(d28,plain,
( memberP(nil,sK257)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d27]) ).
cnf(d29,plain,
( ~ ssItem(sK257)
| sK256 = nil ),
inference(resolution,[status(thm)],[d28,c127]) ).
cnf(d30,plain,
sK256 = nil,
inference(resolution,[status(thm)],[d24,d29]) ).
cnf(d31,plain,
nil != nil,
inference(demodulation,[status(thm)],[d13,d30]) ).
cnf(d32,plain,
$false,
inference(equality_resolution,[status(thm)],[d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC029+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.45 % Computer : n017.cluster.edu
% 0.09/0.45 % Model : x86_64 x86_64
% 0.09/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.45 % Memory : 8046.5625MB
% 0.09/0.45 % OS : Linux 6.8.0-71-generic
% 0.09/0.45 % CPULimit : 300
% 0.09/0.45 % WCLimit : 300
% 0.09/0.45 % DateTime : Sat Sep 26 12:00:49 UTC 2026
% 0.09/0.45 % CPUTime :
% 0.09/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.83/8.58 % SZS status Theorem for theBenchmark.p
% 32.83/8.58 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------