%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL542+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 07:59:08 AM UTC 2026
% Result : Theorem 0.14s 0.43s
% Output : CNFRefutation 0.14s
% 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 : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 31 ( 4 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('theBenchmark.p',and_1) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('theBenchmark.p',necessitation) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('theBenchmark.p',axiom_m2) ).
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_axiom_m2,conjecture,
axiom_m2,
file('theBenchmark.p',s1_0_axiom_m2) ).
fof(s1_0_axiom_m2_neg,negated_conjecture,
~ axiom_m2,
inference(assume_negation,[status(cth)],[s1_0_axiom_m2]) ).
cnf(c_75,plain,
( is_a_theorem(implies(and(A,B),A))
| ~ and_1 ),
inference(clausify,[status(thm)],[and_1]) ).
fof(hilbert_and_1,axiom,
and_1,
file('theBenchmark.p',hilbert_and_1) ).
cnf(c_131,plain,
and_1,
inference(clausify,[status(thm)],[hilbert_and_1]) ).
cnf(c_141,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A)
| ~ necessitation ),
inference(clausify,[status(thm)],[necessitation]) ).
fof(nnf_46,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X))
| axiom_m2 )
& ( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ) ),
inference(fof_nnf,[status(thm)],[axiom_m2]) ).
fof(sk_axiom_m2_sk,plain,
( ( ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0))
| axiom_m2 )
& ( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_46]) ).
fof(sk_axiom_m2,plain,
( ( ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0))
| axiom_m2 )
& ! [VAR_0,VAR_1] :
( is_a_theorem(strict_implies(and(VAR_0,VAR_1),VAR_0))
| ~ axiom_m2 ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_m2_sk]) ).
cnf(c_176,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0))
| axiom_m2 ),
inference(split_conjunct,[status(thm)],[sk_axiom_m2]) ).
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(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_m2,
inference(clausify,[status(thm)],[s1_0_axiom_m2_neg]) ).
cnf(c_218,plain,
is_a_theorem(implies(and(A,B),A)),
inference(resolve,[status(thm)],[c_131,c_75]) ).
cnf(c_227,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_201,c_141]) ).
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(and(sK0,sK1),sK0)),
inference(resolve,[status(thm)],[c_209,c_176]) ).
cnf(c_305,plain,
is_a_theorem(necessarily(implies(and(A,B),A))),
inference(resolve,[status(thm)],[c_227,c_218]) ).
cnf(c_303,plain,
is_a_theorem(strict_implies(and(A,B),A)),
inference(paramod,[status(thm)],[c_232,c_305]) ).
cnf(c_304,plain,
$false,
inference(resolve,[status(thm)],[c_303,c_234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n019.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 22:43:20 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 3949288 was started by sandbox on n019,
% 0.11/0.36 % Fri Sep 25 22:43:20 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.43
% 0.14/0.43 % SZS status Theorem for theBenchmark
% 0.14/0.43
% 0.14/0.43 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.14/0.43 % Length of proof is 20.
% 0.14/0.43 % Level of proof is 5.
% 0.14/0.43 % Maximum clause weight is 9.000.
% 0.14/0.43 % Given clauses 99.
% 0.14/0.43
% 0.14/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------