%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL546+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 : n004.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 07:59:08 AM UTC 2026
% Result : Theorem 29.24s 4.65s
% Output : CNFRefutation 29.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of formulae : 47 ( 25 unt; 0 def)
% Number of atoms : 82 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 25 ~; 22 |; 4 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 14 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('theBenchmark.p',modus_ponens) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('theBenchmark.p',implies_3) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('theBenchmark.p',necessitation) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('theBenchmark.p',axiom_M) ).
fof(axiom_B,axiom,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ),
file('theBenchmark.p',axiom_B) ).
fof(axiom_m6,axiom,
( axiom_m6
<=> ! [X] : is_a_theorem(strict_implies(X,possibly(X))) ),
file('theBenchmark.p',axiom_m6) ).
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_m6s3m9b_axiom_m6,conjecture,
axiom_m6,
file('theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
fof(s1_0_m6s3m9b_axiom_m6_neg,negated_conjecture,
~ axiom_m6,
inference(assume_negation,[status(cth)],[s1_0_m6s3m9b_axiom_m6]) ).
cnf(c_60,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A)
| ~ modus_ponens ),
inference(clausify,[status(thm)],[modus_ponens]) ).
cnf(c_73,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C))))
| ~ implies_3 ),
inference(clausify,[status(thm)],[implies_3]) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',hilbert_modus_ponens) ).
cnf(c_126,plain,
modus_ponens,
inference(clausify,[status(thm)],[hilbert_modus_ponens]) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('theBenchmark.p',hilbert_implies_3) ).
cnf(c_130,plain,
implies_3,
inference(clausify,[status(thm)],[hilbert_implies_3]) ).
cnf(c_141,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A)
| ~ necessitation ),
inference(clausify,[status(thm)],[necessitation]) ).
cnf(c_157,plain,
( is_a_theorem(implies(necessarily(A),A))
| ~ axiom_M ),
inference(clausify,[status(thm)],[axiom_M]) ).
cnf(c_161,plain,
( is_a_theorem(implies(A,necessarily(possibly(A))))
| ~ axiom_B ),
inference(clausify,[status(thm)],[axiom_B]) ).
fof(nnf_50,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,possibly(X)))
| axiom_m6 )
& ( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ axiom_m6 ) ),
inference(fof_nnf,[status(thm)],[axiom_m6]) ).
fof(sk_axiom_m6_sk,plain,
( ( ~ is_a_theorem(strict_implies(sK0,possibly(sK0)))
| axiom_m6 )
& ( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ axiom_m6 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_50]) ).
fof(sk_axiom_m6,plain,
( ( ~ is_a_theorem(strict_implies(sK0,possibly(sK0)))
| axiom_m6 )
& ! [VAR_0] :
( is_a_theorem(strict_implies(VAR_0,possibly(VAR_0)))
| ~ axiom_m6 ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_m6_sk]) ).
cnf(c_184,plain,
( ~ is_a_theorem(strict_implies(sK0,possibly(sK0)))
| axiom_m6 ),
inference(split_conjunct,[status(thm)],[sk_axiom_m6]) ).
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(km4b_necessitation,axiom,
necessitation,
file('theBenchmark.p',km4b_necessitation) ).
cnf(c_201,plain,
necessitation,
inference(clausify,[status(thm)],[km4b_necessitation]) ).
fof(km4b_axiom_M,axiom,
axiom_M,
file('theBenchmark.p',km4b_axiom_M) ).
cnf(c_203,plain,
axiom_M,
inference(clausify,[status(thm)],[km4b_axiom_M]) ).
fof(km4b_axiom_B,axiom,
axiom_B,
file('theBenchmark.p',km4b_axiom_B) ).
cnf(c_205,plain,
axiom_B,
inference(clausify,[status(thm)],[km4b_axiom_B]) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('theBenchmark.p',s1_0_op_strict_implies) ).
cnf(c_207,plain,
op_strict_implies,
inference(clausify,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(c_209,negated_conjecture,
~ axiom_m6,
inference(clausify,[status(thm)],[s1_0_m6s3m9b_axiom_m6_neg]) ).
cnf(c_213,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_126,c_60]) ).
cnf(c_217,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,C),implies(A,C)))),
inference(resolve,[status(thm)],[c_130,c_73]) ).
cnf(c_227,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(necessarily(A),A)),
inference(resolve,[status(thm)],[c_203,c_157]) ).
cnf(c_231,plain,
is_a_theorem(implies(A,necessarily(possibly(A)))),
inference(resolve,[status(thm)],[c_205,c_161]) ).
cnf(c_232,plain,
necessarily(implies(A,B)) = strict_implies(A,B),
inference(resolve,[status(thm)],[c_207,c_198]) ).
cnf(c_234,negated_conjecture,
~ is_a_theorem(strict_implies(sK0,possibly(sK0))),
inference(resolve,[status(thm)],[c_209,c_184]) ).
cnf(c_276,plain,
( is_a_theorem(implies(implies(B,C),implies(A,C)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_217,c_213]) ).
cnf(c_333,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(implies(necessarily(A),A),B)) ),
inference(resolve,[status(thm)],[c_229,c_213]) ).
cnf(c_1777,plain,
is_a_theorem(implies(implies(necessarily(possibly(A)),B),implies(A,B))),
inference(resolve,[status(thm)],[c_276,c_231]) ).
cnf(c_16143,plain,
is_a_theorem(implies(A,possibly(A))),
inference(resolve,[status(thm)],[c_1777,c_333]) ).
cnf(c_16201,plain,
is_a_theorem(necessarily(implies(A,possibly(A)))),
inference(resolve,[status(thm)],[c_16143,c_227]) ).
cnf(c_16199,plain,
is_a_theorem(strict_implies(A,possibly(A))),
inference(paramod,[status(thm)],[c_232,c_16201]) ).
cnf(c_16200,plain,
$false,
inference(resolve,[status(thm)],[c_16199,c_234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n004.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 22:43:22 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 189951 was started by sandbox2 on n004,
% 0.09/0.37 % Fri Sep 25 22:43:22 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 29.24/4.65
% 29.24/4.65 % given #500 (A,wt=24): 494 is_a_theorem(implies(A,implies(B,implies(C,and(B,C))))). [resolve(270,a,220,a)].
% 29.24/4.65
% 29.24/4.65 % SZS status Theorem for theBenchmark
% 29.24/4.65
% 29.24/4.65 % Proof 1 at 3.28 (+ 0.89) seconds.
% 29.24/4.65 % Length of proof is 36.
% 29.24/4.65 % Level of proof is 7.
% 29.24/4.65 % Maximum clause weight is 29.000.
% 29.24/4.65 % Given clauses 796.
% 29.24/4.65
% 29.24/4.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------