%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWC320+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/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 08:54:58 AM UTC 2026
% Result : Theorem 16.75s 4.68s
% Output : CNFRefutation 16.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 1
% Syntax : Number of formulae : 53 ( 10 unt; 0 def)
% Number of atoms : 165 ( 89 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 204 ( 92 ~; 92 |; 12 &)
% ( 0 <=>; 8 =>; 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 : 26 ( 0 sgn 12 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X1
& app(cons(X6,nil),X7) = X0
& ssList(X7) )
& ssItem(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X1
& app(cons(X6,nil),X7) = X0
& ssList(X7) )
& ssItem(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negate_conjecture,[status(cth)],[co1]) ).
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(c217,plain,
( ~ neq(sK256,nil)
| app(cons(sK257,nil),sK258) = sK255 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c218,plain,
( ~ neq(sK256,nil)
| app(sK258,cons(sK257,nil)) = sK256 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c219,plain,
( neq(sK254,nil)
| nil = sK254 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c220,plain,
( app(cons(X0,nil),X1) != sK253
| nil = sK254
| ~ ssList(X1)
| app(X1,cons(X0,nil)) != sK254
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c221,plain,
( neq(sK254,nil)
| nil != sK253 ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(c222,plain,
( nil != sK253
| app(cons(X0,nil),X1) != sK253
| ~ ssList(X1)
| app(X1,cons(X0,nil)) != sK254
| ~ ssItem(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ neq(sK254,nil)
| ssItem(sK257) ),
inference(demodulation,[status(thm)],[c215,c212]) ).
cnf(d1,plain,
( ssItem(sK257)
| nil = sK254 ),
inference(resolution,[status(thm)],[c219,d0]) ).
cnf(d2,plain,
( ssList(sK258)
| ~ neq(sK254,nil) ),
inference(demodulation,[status(thm)],[c216,c212]) ).
cnf(d3,plain,
( ssList(sK258)
| nil = sK254 ),
inference(resolution,[status(thm)],[c219,d2]) ).
cnf(d4,plain,
( ~ neq(sK256,nil)
| app(cons(sK257,nil),sK258) = sK253 ),
inference(demodulation,[status(thm)],[c217,c213]) ).
cnf(d5,plain,
( ~ neq(sK254,nil)
| app(cons(sK257,nil),sK258) = sK253 ),
inference(demodulation,[status(thm)],[d4,c212]) ).
cnf(d6,plain,
( nil = sK254
| app(cons(sK257,nil),sK258) = sK253 ),
inference(resolution,[status(thm)],[d5,c219]) ).
cnf(d7,plain,
( nil = sK254
| ~ ssList(sK258)
| ~ ssItem(sK257)
| nil = sK254
| app(sK258,cons(sK257,nil)) != sK254
| sK253 != sK253 ),
inference(superposition,[status(thm)],[d6,c220]) ).
cnf(d8,plain,
( ~ neq(sK256,nil)
| app(sK258,cons(sK257,nil)) = sK254 ),
inference(demodulation,[status(thm)],[c218,c212]) ).
cnf(d9,plain,
( ~ neq(sK254,nil)
| app(sK258,cons(sK257,nil)) = sK254 ),
inference(demodulation,[status(thm)],[d8,c212]) ).
cnf(d10,plain,
( nil = sK254
| app(sK258,cons(sK257,nil)) = sK254 ),
inference(resolution,[status(thm)],[d9,c219]) ).
cnf(d11,plain,
( nil = sK254
| ~ ssList(sK258)
| ~ ssItem(sK257)
| sK253 != sK253
| nil = sK254
| sK254 != sK254 ),
inference(superposition,[status(thm)],[d10,d7]) ).
cnf(d12,plain,
( ~ ssList(sK258)
| ~ ssItem(sK257)
| sK253 != sK253
| nil = sK254 ),
inference(equality_resolution,[status(thm)],[d11]) ).
cnf(d13,plain,
( ~ ssList(sK258)
| ~ ssItem(sK257)
| nil = sK254 ),
inference(equality_resolution,[status(thm)],[d12]) ).
cnf(d14,plain,
( nil = sK254
| ~ ssItem(sK257)
| nil = sK254 ),
inference(resolution,[status(thm)],[d13,d3]) ).
cnf(d15,plain,
( nil = sK254
| nil = sK254 ),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
( ~ neq(sK254,nil)
| app(sK258,cons(sK257,nil)) = nil ),
inference(demodulation,[status(thm)],[d9,d15]) ).
cnf(d17,plain,
( ~ neq(nil,nil)
| app(sK258,cons(sK257,nil)) = nil ),
inference(demodulation,[status(thm)],[d16,d15]) ).
cnf(d18,plain,
( nil != sK256
| nil = sK253 ),
inference(demodulation,[status(thm)],[c214,c213]) ).
cnf(d19,plain,
( nil != sK254
| nil = sK253 ),
inference(demodulation,[status(thm)],[d18,c212]) ).
cnf(d20,plain,
nil = sK253,
inference(resolution,[status(thm)],[d15,d19]) ).
cnf(d21,plain,
( neq(nil,nil)
| nil != sK253 ),
inference(demodulation,[status(thm)],[c221,d15]) ).
cnf(d22,plain,
( neq(nil,nil)
| nil != nil ),
inference(demodulation,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
neq(nil,nil),
inference(equality_resolution,[status(thm)],[d22]) ).
cnf(d24,plain,
app(sK258,cons(sK257,nil)) = nil,
inference(resolution,[status(thm)],[d23,d17]) ).
cnf(d25,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != sK253
| app(cons(X1,nil),X0) != sK253
| app(X0,cons(X1,nil)) != nil ),
inference(demodulation,[status(thm)],[c222,d15]) ).
cnf(d26,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != sK253
| app(cons(X1,nil),X0) != nil
| app(X0,cons(X1,nil)) != nil ),
inference(demodulation,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
( ~ ssList(X0)
| ~ ssItem(X1)
| nil != nil
| app(cons(X1,nil),X0) != nil
| app(X0,cons(X1,nil)) != nil ),
inference(demodulation,[status(thm)],[d26,d20]) ).
cnf(d28,plain,
( ~ neq(nil,nil)
| app(cons(sK257,nil),sK258) = sK253 ),
inference(demodulation,[status(thm)],[d5,d15]) ).
cnf(d29,plain,
( ~ neq(nil,nil)
| app(cons(sK257,nil),sK258) = nil ),
inference(demodulation,[status(thm)],[d28,d20]) ).
cnf(d30,plain,
app(cons(sK257,nil),sK258) = nil,
inference(resolution,[status(thm)],[d23,d29]) ).
cnf(d31,plain,
( ~ ssList(sK258)
| ~ ssItem(sK257)
| nil != nil
| app(sK258,cons(sK257,nil)) != nil
| nil != nil ),
inference(superposition,[status(thm)],[d30,d27]) ).
cnf(d32,plain,
( ~ ssList(sK258)
| ~ ssItem(sK257)
| nil != nil
| nil != nil ),
inference(demodulation,[status(thm)],[d31,d24]) ).
cnf(d33,plain,
( ssList(sK258)
| ~ neq(nil,nil) ),
inference(demodulation,[status(thm)],[d2,d15]) ).
cnf(d34,plain,
ssList(sK258),
inference(resolution,[status(thm)],[d23,d33]) ).
cnf(d35,plain,
( ~ ssItem(sK257)
| nil != nil
| nil != nil ),
inference(resolution,[status(thm)],[d34,d32]) ).
cnf(d36,plain,
( ~ neq(nil,nil)
| ssItem(sK257) ),
inference(demodulation,[status(thm)],[d0,d15]) ).
cnf(d37,plain,
ssItem(sK257),
inference(resolution,[status(thm)],[d23,d36]) ).
cnf(d38,plain,
nil != nil,
inference(resolution,[status(thm)],[d37,d35]) ).
cnf(d39,plain,
$false,
inference(equality_resolution,[status(thm)],[d38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC320+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n017.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 12:42:48 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.75/4.68 % SZS status Theorem for theBenchmark.p
% 16.75/4.68 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------