%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC325+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 : 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 08:54:59 AM UTC 2026
% Result : Theorem 20.22s 5.50s
% Output : CNFRefutation 20.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 13 unt; 0 def)
% Number of atoms : 187 ( 78 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 232 ( 106 ~; 97 |; 10 &)
% ( 1 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
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(ax28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ) ).
fof(ax84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ) ).
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X3
| app(cons(X6,nil),X7) != X2 ) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(X5,X4) = X0
& app(X4,X5) = X1
& ssList(X5) )
& ssList(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)
& ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X3
| app(cons(X6,nil),X7) != X2 ) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( app(X5,X4) = X0
& app(X4,X5) = X1
& ssList(X5) )
& ssList(X4) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
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(c111,plain,
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax28]) ).
cnf(c194,plain,
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[ax84]) ).
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,
( app(X1,X0) != sK253
| app(X0,X1) != sK254
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( nil != sK256
| nil = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c216,plain,
( ~ neq(sK256,nil)
| ssItem(sK259) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( ~ neq(sK256,nil)
| ssList(sK260) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( ~ neq(sK256,nil)
| app(cons(sK259,nil),sK260) = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( ~ neq(sK256,nil)
| app(sK260,cons(sK259,nil)) = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ ssList(X1)
| ~ ssList(X0)
| app(X1,X0) != sK253
| app(X0,X1) != sK256 ),
inference(demodulation,[status(thm)],[c214,c212]) ).
cnf(d1,plain,
( ~ ssList(X1)
| ~ ssList(X0)
| app(X1,X0) != sK255
| app(X0,X1) != sK256 ),
inference(demodulation,[status(thm)],[d0,c213]) ).
cnf(d2,plain,
( ~ neq(sK256,nil)
| ~ ssList(cons(sK259,nil))
| ~ ssList(sK260)
| app(cons(sK259,nil),sK260) != sK255
| sK256 != sK256 ),
inference(superposition,[status(thm)],[c219,d1]) ).
cnf(d3,plain,
( ~ neq(sK256,nil)
| ~ ssList(sK260)
| ~ ssList(cons(sK259,nil))
| ~ neq(sK256,nil)
| sK256 != sK256
| sK255 != sK255 ),
inference(superposition,[status(thm)],[c218,d2]) ).
cnf(d4,plain,
( ~ ssList(sK260)
| ~ ssList(cons(sK259,nil))
| ~ neq(sK256,nil)
| sK255 != sK255 ),
inference(equality_resolution,[status(thm)],[d3]) ).
cnf(d5,plain,
( ~ ssList(sK260)
| ~ ssList(cons(sK259,nil))
| ~ neq(sK256,nil) ),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( ~ ssList(sK260)
| ~ neq(sK256,nil)
| ~ ssList(nil)
| ~ ssItem(sK259) ),
inference(resolution,[status(thm)],[c96,d5]) ).
cnf(d7,plain,
( ~ ssList(sK260)
| ~ neq(sK256,nil)
| ~ ssItem(sK259) ),
inference(resolution,[status(thm)],[c97,d6]) ).
cnf(d8,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(nil)
| app(X0,nil) != sK255
| X0 != sK256 ),
inference(superposition,[status(thm)],[c111,d1]) ).
cnf(d9,plain,
( ~ ssList(X0)
| app(X0,nil) != sK255
| X0 != sK256 ),
inference(resolution,[status(thm)],[c97,d8]) ).
cnf(d10,plain,
( ~ ssList(nil)
| ~ ssList(nil)
| nil != sK256
| nil != sK255 ),
inference(superposition,[status(thm)],[c111,d9]) ).
cnf(d11,plain,
( nil != sK256
| nil != sK255 ),
inference(resolution,[status(thm)],[c97,d10]) ).
cnf(d12,plain,
( ssItem(sK259)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c216]) ).
cnf(d13,plain,
( ~ ssList(nil)
| ssItem(sK259)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d12]) ).
cnf(d14,plain,
( ssItem(sK259)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d13]) ).
cnf(d15,plain,
( ssItem(sK259)
| nil != sK255
| nil != nil ),
inference(superposition,[status(thm)],[d14,d11]) ).
cnf(d16,plain,
( ssItem(sK259)
| nil = sK255
| nil != nil ),
inference(superposition,[status(thm)],[d14,c215]) ).
cnf(d17,plain,
( ssItem(sK259)
| nil = sK255 ),
inference(equality_resolution,[status(thm)],[d16]) ).
cnf(d18,plain,
( ssItem(sK259)
| ssItem(sK259)
| nil != nil
| nil != nil ),
inference(superposition,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
ssItem(sK259),
inference(equality_resolution,[status(thm)],[d18]) ).
cnf(d20,plain,
( ~ ssList(sK260)
| ~ neq(sK256,nil) ),
inference(resolution,[status(thm)],[d19,d7]) ).
cnf(d21,plain,
( ssList(sK260)
| ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c95,c217]) ).
cnf(d22,plain,
( ssList(sK260)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d21]) ).
cnf(d23,plain,
( ssList(sK260)
| sK256 = nil ),
inference(resolution,[status(thm)],[c97,d22]) ).
cnf(d24,plain,
( ssList(sK260)
| nil != sK255
| nil != nil ),
inference(superposition,[status(thm)],[d23,d11]) ).
cnf(d25,plain,
( ssList(sK260)
| nil = sK255
| nil != nil ),
inference(superposition,[status(thm)],[d23,c215]) ).
cnf(d26,plain,
( ssList(sK260)
| nil = sK255 ),
inference(equality_resolution,[status(thm)],[d25]) ).
cnf(d27,plain,
( ssList(sK260)
| ssList(sK260)
| nil != nil
| nil != nil ),
inference(superposition,[status(thm)],[d26,d24]) ).
cnf(d28,plain,
ssList(sK260),
inference(equality_resolution,[status(thm)],[d27]) ).
cnf(d29,plain,
~ neq(sK256,nil),
inference(resolution,[status(thm)],[d28,d20]) ).
cnf(d30,plain,
( ~ ssList(sK256)
| ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[d29,c95]) ).
cnf(d31,plain,
( ~ ssList(nil)
| sK256 = nil ),
inference(resolution,[status(thm)],[c211,d30]) ).
cnf(d32,plain,
sK256 = nil,
inference(resolution,[status(thm)],[c97,d31]) ).
cnf(d33,plain,
( nil != nil
| nil = sK255 ),
inference(demodulation,[status(thm)],[c215,d32]) ).
cnf(d34,plain,
( ~ ssList(X0)
| ~ ssList(X0)
| X0 != sK256
| X0 != sK255 ),
inference(superposition,[status(thm)],[c194,d9]) ).
cnf(d35,plain,
( ~ ssList(sK256)
| sK256 != sK255 ),
inference(equality_resolution,[status(thm)],[d34]) ).
cnf(d36,plain,
sK256 != sK255,
inference(resolution,[status(thm)],[c211,d35]) ).
cnf(d37,plain,
nil != sK255,
inference(demodulation,[status(thm)],[d36,d32]) ).
cnf(d38,plain,
nil != nil,
inference(resolution,[status(thm)],[d37,d33]) ).
cnf(d39,plain,
$false,
inference(equality_resolution,[status(thm)],[d38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SWC325+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.08 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.45 % Computer : n004.cluster.edu
% 0.12/0.45 % Model : x86_64 x86_64
% 0.12/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.45 % Memory : 8046.5625MB
% 0.12/0.45 % OS : Linux 6.8.0-71-generic
% 0.12/0.46 % CPULimit : 300
% 0.12/0.46 % WCLimit : 300
% 0.12/0.46 % DateTime : Sat Sep 26 12:48:06 UTC 2026
% 0.12/0.46 % CPUTime :
% 0.12/0.46 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.22/5.50 % SZS status Theorem for theBenchmark.p
% 20.22/5.50 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------