%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.69s 0.71s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 35 ( 17 unt; 0 def)
% Number of atoms : 80 ( 4 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 72 ( 27 ~; 28 |; 11 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 13 !; 2 ?)
% 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(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('theBenchmark.p',modus_ponens_strict_implies) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('theBenchmark.p',axiom_M) ).
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_modus_ponens_strict_implies,conjecture,
modus_ponens_strict_implies,
file('theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(s1_0_modus_ponens_strict_implies_neg,negated_conjecture,
~ modus_ponens_strict_implies,
inference(assume_negation,[status(cth)],[s1_0_modus_ponens_strict_implies]) ).
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]) ).
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(nnf_33,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
| modus_ponens_strict_implies )
& ( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens_strict_implies ) ),
inference(fof_nnf,[status(thm)],[modus_ponens_strict_implies]) ).
fof(sk_modus_ponens_strict_implies_sk,plain,
( ( ( ~ is_a_theorem(sK1)
& is_a_theorem(strict_implies(sK0,sK1))
& is_a_theorem(sK0) )
| modus_ponens_strict_implies )
& ( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens_strict_implies ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_33]) ).
fof(sk_modus_ponens_strict_implies,plain,
( ( ~ is_a_theorem(sK1)
| modus_ponens_strict_implies )
& ( is_a_theorem(strict_implies(sK0,sK1))
| modus_ponens_strict_implies )
& ( is_a_theorem(sK0)
| modus_ponens_strict_implies )
& ! [VAR_0,VAR_1] :
( is_a_theorem(VAR_1)
| ~ is_a_theorem(strict_implies(VAR_0,VAR_1))
| ~ is_a_theorem(VAR_0)
| ~ modus_ponens_strict_implies ) ),
inference(cnf_transformation,[status(thm)],[sk_modus_ponens_strict_implies_sk]) ).
cnf(c_145,plain,
( is_a_theorem(sK0)
| modus_ponens_strict_implies ),
inference(split_conjunct,[status(thm)],[sk_modus_ponens_strict_implies]) ).
cnf(c_146,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| modus_ponens_strict_implies ),
inference(split_conjunct,[status(thm)],[sk_modus_ponens_strict_implies]) ).
cnf(c_147,plain,
( ~ is_a_theorem(sK1)
| modus_ponens_strict_implies ),
inference(split_conjunct,[status(thm)],[sk_modus_ponens_strict_implies]) ).
cnf(c_157,plain,
( is_a_theorem(implies(necessarily(A),A))
| ~ axiom_M ),
inference(clausify,[status(thm)],[axiom_M]) ).
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_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(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,
~ modus_ponens_strict_implies,
inference(clausify,[status(thm)],[s1_0_modus_ponens_strict_implies_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_232,plain,
is_a_theorem(implies(necessarily(A),A)),
inference(resolve,[status(thm)],[c_203,c_157]) ).
cnf(c_235,plain,
necessarily(implies(A,B)) = strict_implies(A,B),
inference(resolve,[status(thm)],[c_207,c_198]) ).
cnf(c_237,negated_conjecture,
~ is_a_theorem(sK1),
inference(resolve,[status(thm)],[c_209,c_147]) ).
cnf(c_238,negated_conjecture,
is_a_theorem(strict_implies(sK0,sK1)),
inference(resolve,[status(thm)],[c_209,c_146]) ).
cnf(c_239,negated_conjecture,
is_a_theorem(sK0),
inference(resolve,[status(thm)],[c_209,c_145]) ).
cnf(c_341,plain,
( is_a_theorem(A)
| ~ is_a_theorem(necessarily(A)) ),
inference(resolve,[status(thm)],[c_232,c_213]) ).
cnf(c_436,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(strict_implies(A,B)) ),
inference(paramod,[status(thm)],[c_235,c_341]) ).
cnf(c_937,plain,
is_a_theorem(implies(sK0,sK1)),
inference(resolve,[status(thm)],[c_436,c_238]) ).
cnf(c_950,plain,
( is_a_theorem(sK1)
| ~ is_a_theorem(sK0) ),
inference(resolve,[status(thm)],[c_937,c_213]) ).
cnf(c_951,plain,
is_a_theorem(sK1),
inference(resolve,[status(thm)],[c_239,c_950]) ).
cnf(c_949,plain,
$false,
inference(resolve,[status(thm)],[c_237,c_951]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL538+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.44 % Computer : n019.cluster.edu
% 0.11/0.44 % Model : x86_64 x86_64
% 0.11/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.44 % Memory : 8046.5625MB
% 0.11/0.44 % OS : Linux 6.8.0-71-generic
% 0.11/0.44 % CPULimit : 300
% 0.11/0.44 % WCLimit : 300
% 0.11/0.44 % DateTime : Fri Sep 25 22:42:48 UTC 2026
% 0.11/0.44 % CPUTime :
% 0.11/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.45 % Process 3946997 was started by sandbox on n019,
% 0.11/0.45 % Fri Sep 25 22:42:48 2026
% 0.11/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.47
% 0.11/0.47 % From the command line: assign(max_seconds, 300).
% 0.69/0.71
% 0.69/0.71 % SZS status Theorem for theBenchmark
% 0.69/0.71
% 0.69/0.71 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.69/0.71 % Length of proof is 26.
% 0.69/0.71 % Level of proof is 6.
% 0.69/0.71 % Maximum clause weight is 24.000.
% 0.69/0.71 % Given clauses 158.
% 0.69/0.71
% 0.69/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------