%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC419+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 : n019.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 08:55:19 AM UTC 2026
% Result : Theorem 29.31s 9.88s
% Output : CNFRefutation 29.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 14 unt; 0 def)
% Number of atoms : 128 ( 49 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 170 ( 81 ~; 65 |; 12 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 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 : 39 ( 0 sgn 16 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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] :
( ( neq(X3,nil)
& ! [X7] :
( ssItem(X7)
=> ! [X8] :
( app(X8,cons(X7,nil)) != X2
| app(cons(X7,nil),X8) != X3
| ~ ssList(X8) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X6,cons(X4,nil)),X5) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( neq(X3,nil)
& ! [X7] :
( ssItem(X7)
=> ! [X8] :
( app(X8,cons(X7,nil)) != X2
| app(cons(X7,nil),X8) != X3
| ~ ssList(X8) ) ) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X6,cons(X4,nil)),X5) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| ~ neq(X1,nil)
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
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(c210,plain,
ssList(sK255),
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,
neq(sK254,nil),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c215,plain,
( app(app(X2,cons(X1,nil)),X0) != sK253
| ~ ssList(X2)
| ~ ssItem(X1)
| app(app(X0,cons(X1,nil)),X2) != sK254
| ~ ssList(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c217,plain,
( ~ neq(sK256,nil)
| ssItem(sK260) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( ~ neq(sK256,nil)
| ssList(sK261) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( ~ neq(sK256,nil)
| app(cons(sK260,nil),sK261) = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( ~ neq(sK256,nil)
| app(sK261,cons(sK260,nil)) = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
neq(sK256,nil),
inference(demodulation,[status(thm)],[c214,c212]) ).
cnf(d1,plain,
app(cons(sK260,nil),sK261) = sK256,
inference(resolution,[status(thm)],[d0,c219]) ).
cnf(d2,plain,
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(app(X2,cons(X1,nil)),X0) != sK253
| app(app(X0,cons(X1,nil)),X2) != sK256 ),
inference(demodulation,[status(thm)],[c215,c212]) ).
cnf(d3,plain,
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| app(app(X2,cons(X1,nil)),X0) != sK255
| app(app(X0,cons(X1,nil)),X2) != sK256 ),
inference(demodulation,[status(thm)],[d2,c213]) ).
cnf(d4,plain,
( ~ ssList(cons(X0,nil))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| app(app(X1,cons(X0,nil)),nil) != sK255
| app(cons(X0,nil),X1) != sK256 ),
inference(superposition,[status(thm)],[c111,d3]) ).
cnf(d5,plain,
( ~ ssList(cons(X1,nil))
| ~ ssList(X0)
| ~ ssItem(X1)
| app(cons(X1,nil),X0) != sK256
| app(app(X0,cons(X1,nil)),nil) != sK255 ),
inference(resolution,[status(thm)],[c97,d4]) ).
cnf(d6,plain,
app(sK261,cons(sK260,nil)) = sK255,
inference(resolution,[status(thm)],[d0,c220]) ).
cnf(d7,plain,
( ~ ssList(cons(sK260,nil))
| ~ ssList(sK261)
| ~ ssItem(sK260)
| app(cons(sK260,nil),sK261) != sK256
| app(sK255,nil) != sK255 ),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
( ~ ssList(sK261)
| ~ ssList(cons(sK260,nil))
| ~ ssItem(sK260)
| app(sK255,nil) != sK255
| sK256 != sK256 ),
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
ssList(sK261),
inference(resolution,[status(thm)],[d0,c218]) ).
cnf(d10,plain,
( ~ ssList(cons(sK260,nil))
| ~ ssItem(sK260)
| app(sK255,nil) != sK255
| sK256 != sK256 ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
ssItem(sK260),
inference(resolution,[status(thm)],[d0,c217]) ).
cnf(d12,plain,
( ~ ssList(cons(sK260,nil))
| sK256 != sK256
| app(sK255,nil) != sK255 ),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
( ~ ssList(sK255)
| ~ ssList(cons(sK260,nil))
| sK256 != sK256
| sK255 != sK255 ),
inference(superposition,[status(thm)],[c194,d12]) ).
cnf(d14,plain,
( ~ ssList(cons(sK260,nil))
| sK256 != sK256
| sK255 != sK255 ),
inference(resolution,[status(thm)],[c210,d13]) ).
cnf(d15,plain,
( ~ ssList(cons(sK260,nil))
| sK255 != sK255 ),
inference(equality_resolution,[status(thm)],[d14]) ).
cnf(d16,plain,
~ ssList(cons(sK260,nil)),
inference(equality_resolution,[status(thm)],[d15]) ).
cnf(d17,plain,
( ~ ssList(nil)
| ~ ssItem(sK260) ),
inference(resolution,[status(thm)],[c96,d16]) ).
cnf(d18,plain,
~ ssList(nil),
inference(resolution,[status(thm)],[d11,d17]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[c97,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC419+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.41 % Computer : n019.cluster.edu
% 0.08/0.41 % Model : x86_64 x86_64
% 0.08/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.41 % Memory : 8046.5625MB
% 0.08/0.41 % OS : Linux 6.8.0-71-generic
% 0.08/0.42 % CPULimit : 300
% 0.08/0.42 % WCLimit : 300
% 0.08/0.42 % DateTime : Sat Sep 26 13:01:03 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.31/9.88 % SZS status Theorem for theBenchmark.p
% 29.31/9.88 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------