%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWC040+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 08:56:38 AM UTC 2026
% Result : Theorem 1.05s 0.89s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 98 ( 59 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 112 ( 33 ~; 27 |; 40 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 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 : 18 ( 0 sgn 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W ) ) ) )
| ( nil = X
& nil != W )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| app(cons(Y,nil),Z) != W ) ) ) )
| ( nil = X
& nil != W )
| nil = U
| U != W
| V != X
| nil != V ) ) ) ) ),
inference(assume_negation,[status(cth)],[co1]) ).
fof(nnf_87,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& app(cons(Y,nil),Z) = W
& ssList(Z) )
& ssItem(Y) ) )
& ( nil != X
| nil = W )
& nil != U
& W = U
& X = V
& nil = V
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(fof_nnf,[status(thm)],[co1_neg]) ).
fof(sk_co1_neg_sk,plain,
( ( ~ neq(sK1,nil)
| ( app(sK5,cons(sK4,nil)) = sK1
& app(cons(sK4,nil),sK5) = sK0
& ssList(sK5)
& ssItem(sK4) ) )
& ( nil != sK1
| nil = sK0 )
& nil != sK2
& sK0 = sK2
& sK1 = sK3
& nil = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1,sK4,sK5]),skolemize(U,sK2),skolemize(V,sK3),skolemize(W,sK0),skolemize(X,sK1),skolemize(Y,sK4),skolemize(Z,sK5)],[nnf_87]) ).
fof(sk_co1_neg,plain,
( ( ~ neq(sK1,nil)
| app(sK5,cons(sK4,nil)) = sK1 )
& ( ~ neq(sK1,nil)
| app(cons(sK4,nil),sK5) = sK0 )
& ( ~ neq(sK1,nil)
| ssList(sK5) )
& ( ~ neq(sK1,nil)
| ssItem(sK4) )
& ( nil != sK1
| nil = sK0 )
& nil != sK2
& sK0 = sK2
& sK1 = sK3
& nil = sK3
& ssList(sK1)
& ssList(sK0)
& ssList(sK3)
& ssList(sK2) ),
inference(cnf_transformation,[status(thm)],[sk_co1_neg_sk]) ).
cnf(c_194,negated_conjecture,
( nil != sK1
| nil = sK0 ),
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_551,negated_conjecture,
( nil != sK1
| sK0 = nil ),
inference(copy,[status(thm)],[c_194]) ).
cnf(c_195,negated_conjecture,
( sK1 != nil
| sK0 = nil ),
inference(copy,[status(thm)],[c_551]) ).
cnf(c_196,negated_conjecture,
nil != sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_197,negated_conjecture,
sK2 != nil,
inference(copy,[status(thm)],[c_196]) ).
cnf(c_198,negated_conjecture,
sK0 = sK2,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_199,negated_conjecture,
sK1 = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_200,negated_conjecture,
nil = sK3,
inference(split_conjunct,[status(thm)],[sk_co1_neg]) ).
cnf(c_201,negated_conjecture,
sK3 = nil,
inference(copy,[status(thm)],[c_200]) ).
cnf(c_552,negated_conjecture,
( sK1 != nil
| sK2 = nil ),
inference(paramod,[status(thm)],[c_198,c_195]) ).
cnf(c_553,negated_conjecture,
( sK3 != nil
| sK2 = nil ),
inference(paramod,[status(thm)],[c_199,c_552]) ).
cnf(c_554,negated_conjecture,
( nil != nil
| sK2 = nil ),
inference(paramod,[status(thm)],[c_201,c_553]) ).
cnf(c_555,negated_conjecture,
sK2 = nil,
inference(copy,[status(thm)],[c_554]) ).
cnf(c_550,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_197,c_555]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC040+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % Computer : n005.cluster.edu
% 0.10/0.45 % Model : x86_64 x86_64
% 0.10/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.45 % Memory : 8046.5625MB
% 0.10/0.45 % OS : Linux 6.8.0-71-generic
% 0.10/0.46 % CPULimit : 300
% 0.10/0.46 % WCLimit : 300
% 0.10/0.46 % DateTime : Sat Sep 26 12:06:47 UTC 2026
% 0.10/0.46 % CPUTime :
% 0.10/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.46 % Process 2084841 was started by sandbox on n005,
% 0.10/0.46 % Sat Sep 26 12:06:47 2026
% 0.10/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.49
% 0.17/0.49 % From the command line: assign(max_seconds, 300).
% 1.05/0.89
% 1.05/0.89 % SZS status Theorem for theBenchmark
% 1.05/0.89
% 1.05/0.89 % Proof 1 at 0.13 (+ 0.00) seconds.
% 1.05/0.89 % Length of proof is 10.
% 1.05/0.89 % Level of proof is 3.
% 1.05/0.89 % Maximum clause weight is 11.000.
% 1.05/0.89 % Given clauses 0.
% 1.05/0.89
% 1.05/0.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------