%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL460+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 07:58:59 AM UTC 2026
% Result : Theorem 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 24 ( 11 ~; 8 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 2 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('theBenchmark.p',and_1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('theBenchmark.p',kn2) ).
fof(rosser_kn2,conjecture,
kn2,
file('theBenchmark.p',rosser_kn2) ).
fof(rosser_kn2_neg,negated_conjecture,
~ kn2,
inference(assume_negation,[status(cth)],[rosser_kn2]) ).
cnf(c_48,plain,
( is_a_theorem(implies(and(A,B),A))
| ~ and_1 ),
inference(clausify,[status(thm)],[and_1]) ).
fof(nnf_17,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P))
| kn2 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ) ),
inference(fof_nnf,[status(thm)],[kn2]) ).
fof(sk_kn2_sk,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| kn2 )
& ( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(P,sK0),skolemize(Q,sK1)],[nnf_17]) ).
fof(sk_kn2,plain,
( ( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| kn2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(implies(and(VAR_0,VAR_1),VAR_0))
| ~ kn2 ) ),
inference(cnf_transformation,[status(thm)],[sk_kn2_sk]) ).
cnf(c_69,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| kn2 ),
inference(split_conjunct,[status(thm)],[sk_kn2]) ).
fof(hilbert_and_1,axiom,
and_1,
file('theBenchmark.p',hilbert_and_1) ).
cnf(c_103,plain,
and_1,
inference(clausify,[status(thm)],[hilbert_and_1]) ).
cnf(c_113,negated_conjecture,
~ kn2,
inference(clausify,[status(thm)],[rosser_kn2_neg]) ).
cnf(c_122,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_103,c_48]) ).
cnf(c_133,negated_conjecture,
~ is_a_theorem(implies(and(sK0,sK1),sK0)),
inference(resolve,[status(thm)],[c_113,c_69]) ).
cnf(c_132,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_122,c_133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL460+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n009.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Fri Sep 25 22:36:30 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.20/0.45 % Process 2742085 was started by sandbox2 on n009,
% 0.20/0.45 % Fri Sep 25 22:36:30 2026
% 0.20/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.20/0.46
% 0.20/0.46 % From the command line: assign(max_seconds, 300).
% 0.20/0.48
% 0.20/0.48 % Assigning unary symbol not kb_weight 0 and highest precedence (93).
% 0.20/0.48
% 0.20/0.48 % SZS status Theorem for theBenchmark
% 0.20/0.48
% 0.20/0.48 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.20/0.48 % Length of proof is 9.
% 0.20/0.48 % Level of proof is 3.
% 0.20/0.48 % Maximum clause weight is 22.000.
% 0.20/0.48 % Given clauses 0.
% 0.20/0.48
% 0.20/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------