%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL536+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 : n016.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 07:59:07 AM UTC 2026
% Result : Theorem 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 49 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 16 ~; 13 |; 3 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn 8 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('theBenchmark.p',necessitation) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_m10,axiom,
( axiom_m10
<=> ! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) ),
file('theBenchmark.p',axiom_m10) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('theBenchmark.p',op_strict_implies) ).
fof(s1_0_m10_axiom_m10,conjecture,
axiom_m10,
file('theBenchmark.p',s1_0_m10_axiom_m10) ).
fof(s1_0_m10_axiom_m10_neg,negated_conjecture,
~ axiom_m10,
inference(assume_negation,[status(cth)],[s1_0_m10_axiom_m10]) ).
cnf(c_141,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A)
| ~ necessitation ),
inference(clausify,[status(thm)],[necessitation]) ).
cnf(c_163,plain,
( is_a_theorem(implies(possibly(A),necessarily(possibly(A))))
| ~ axiom_5 ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(nnf_54,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))
| axiom_m10 )
& ( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_m10 ) ),
inference(fof_nnf,[status(thm)],[axiom_m10]) ).
fof(sk_axiom_m10_sk,plain,
( ( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_m10 )
& ( ! [X0] : is_a_theorem(strict_implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_m10 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_54]) ).
fof(sk_axiom_m10,plain,
( ( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_m10 )
& ! [VAR_0] :
( is_a_theorem(strict_implies(possibly(VAR_0),necessarily(possibly(VAR_0))))
| ~ axiom_m10 ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_m10_sk]) ).
cnf(c_192,plain,
( ~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_m10 ),
inference(split_conjunct,[status(thm)],[sk_axiom_m10]) ).
cnf(c_197,plain,
( strict_implies(A,B) = necessarily(implies(A,B))
| ~ op_strict_implies ),
inference(clausify,[status(thm)],[op_strict_implies]) ).
cnf(c_198,plain,
( necessarily(implies(A,B)) = strict_implies(A,B)
| ~ op_strict_implies ),
inference(copy,[status(thm)],[c_197]) ).
fof(km5_necessitation,axiom,
necessitation,
file('theBenchmark.p',km5_necessitation) ).
cnf(c_201,plain,
necessitation,
inference(clausify,[status(thm)],[km5_necessitation]) ).
fof(km5_axiom_5,axiom,
axiom_5,
file('theBenchmark.p',km5_axiom_5) ).
cnf(c_204,plain,
axiom_5,
inference(clausify,[status(thm)],[km5_axiom_5]) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('theBenchmark.p',s1_0_op_strict_implies) ).
cnf(c_206,plain,
op_strict_implies,
inference(clausify,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_208,negated_conjecture,
~ axiom_m10,
inference(clausify,[status(thm)],[s1_0_m10_axiom_m10_neg]) ).
cnf(c_226,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_201,c_141]) ).
cnf(c_229,plain,
is_a_theorem(implies(possibly(A),necessarily(possibly(A)))),
inference(resolve,[status(thm)],[c_204,c_163]) ).
cnf(c_230,plain,
necessarily(implies(A,B)) = strict_implies(A,B),
inference(resolve,[status(thm)],[c_206,c_198]) ).
cnf(c_232,negated_conjecture,
~ is_a_theorem(strict_implies(possibly(sK0),necessarily(possibly(sK0)))),
inference(resolve,[status(thm)],[c_208,c_192]) ).
cnf(c_318,plain,
is_a_theorem(necessarily(implies(possibly(A),necessarily(possibly(A))))),
inference(resolve,[status(thm)],[c_229,c_226]) ).
cnf(c_316,plain,
is_a_theorem(strict_implies(possibly(A),necessarily(possibly(A)))),
inference(paramod,[status(thm)],[c_230,c_318]) ).
cnf(c_317,plain,
$false,
inference(resolve,[status(thm)],[c_316,c_232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL536+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 22:47:46 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3491775 was started by sandbox2 on n016,
% 0.08/0.36 % Fri Sep 25 22:47:46 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.42
% 0.13/0.42 % SZS status Theorem for theBenchmark
% 0.13/0.42
% 0.13/0.42 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.13/0.42 % Length of proof is 20.
% 0.13/0.42 % Level of proof is 5.
% 0.13/0.42 % Maximum clause weight is 9.000.
% 0.13/0.42 % Given clauses 102.
% 0.13/0.42
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------