%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL531+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 : n020.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 1.00s 0.57s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 40 ( 21 unt; 0 def)
% Number of atoms : 72 ( 4 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 55 ( 23 ~; 20 |; 4 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 13 !; 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_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('theBenchmark.p',implies_2) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('theBenchmark.p',and_3) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('theBenchmark.p',necessitation) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('theBenchmark.p',axiom_m4) ).
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_m4,conjecture,
axiom_m4,
file('theBenchmark.p',s1_0_axiom_m4) ).
fof(s1_0_axiom_m4_neg,negated_conjecture,
~ axiom_m4,
inference(assume_negation,[status(cth)],[s1_0_axiom_m4]) ).
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_71,plain,
( is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B)))
| ~ implies_2 ),
inference(clausify,[status(thm)],[implies_2]) ).
cnf(c_79,plain,
( is_a_theorem(implies(A,implies(B,and(A,B))))
| ~ and_3 ),
inference(clausify,[status(thm)],[and_3]) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('theBenchmark.p',hilbert_modus_ponens) ).
cnf(c_125,plain,
modus_ponens,
inference(clausify,[status(thm)],[hilbert_modus_ponens]) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('theBenchmark.p',hilbert_implies_2) ).
cnf(c_128,plain,
implies_2,
inference(clausify,[status(thm)],[hilbert_implies_2]) ).
fof(hilbert_and_3,axiom,
and_3,
file('theBenchmark.p',hilbert_and_3) ).
cnf(c_132,plain,
and_3,
inference(clausify,[status(thm)],[hilbert_and_3]) ).
cnf(c_140,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A)
| ~ necessitation ),
inference(clausify,[status(thm)],[necessitation]) ).
fof(nnf_48,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,and(X,X)))
| axiom_m4 )
& ( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ) ),
inference(fof_nnf,[status(thm)],[axiom_m4]) ).
fof(sk_axiom_m4_sk,plain,
( ( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| axiom_m4 )
& ( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_48]) ).
fof(sk_axiom_m4,plain,
( ( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| axiom_m4 )
& ! [VAR_0] :
( is_a_theorem(strict_implies(VAR_0,and(VAR_0,VAR_0)))
| ~ axiom_m4 ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_m4_sk]) ).
cnf(c_179,plain,
( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| axiom_m4 ),
inference(split_conjunct,[status(thm)],[sk_axiom_m4]) ).
cnf(c_196,plain,
( strict_implies(A,B) = necessarily(implies(A,B))
| ~ op_strict_implies ),
inference(clausify,[status(thm)],[op_strict_implies]) ).
cnf(c_197,plain,
( necessarily(implies(A,B)) = strict_implies(A,B)
| ~ op_strict_implies ),
inference(copy,[status(thm)],[c_196]) ).
fof(km5_necessitation,axiom,
necessitation,
file('theBenchmark.p',km5_necessitation) ).
cnf(c_201,plain,
necessitation,
inference(clausify,[status(thm)],[km5_necessitation]) ).
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_m4,
inference(clausify,[status(thm)],[s1_0_axiom_m4_neg]) ).
cnf(c_212,plain,
( is_a_theorem(B)
| ~ is_a_theorem(implies(A,B))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_125,c_60]) ).
cnf(c_215,plain,
is_a_theorem(implies(implies(A,implies(A,B)),implies(A,B))),
inference(resolve,[status(thm)],[c_128,c_71]) ).
cnf(c_219,plain,
is_a_theorem(implies(A,implies(B,and(A,B)))),
inference(resolve,[status(thm)],[c_132,c_79]) ).
cnf(c_229,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_201,c_140]) ).
cnf(c_233,plain,
necessarily(implies(A,B)) = strict_implies(A,B),
inference(resolve,[status(thm)],[c_206,c_197]) ).
cnf(c_235,negated_conjecture,
~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))),
inference(resolve,[status(thm)],[c_208,c_179]) ).
cnf(c_958,plain,
( is_a_theorem(C)
| ~ is_a_theorem(implies(implies(A,implies(B,and(A,B))),C)) ),
inference(resolve,[status(thm)],[c_212,c_219]) ).
cnf(c_302,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_958,c_215]) ).
cnf(c_959,plain,
is_a_theorem(necessarily(implies(A,and(A,A)))),
inference(resolve,[status(thm)],[c_302,c_229]) ).
cnf(c_956,plain,
is_a_theorem(strict_implies(A,and(A,A))),
inference(paramod,[status(thm)],[c_233,c_959]) ).
cnf(c_957,plain,
$false,
inference(resolve,[status(thm)],[c_956,c_235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 22:43:33 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 3996854 was started by sandbox on n020,
% 0.09/0.37 % Fri Sep 25 22:43:33 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.39
% 0.15/0.39 % From the command line: assign(max_seconds, 300).
% 1.00/0.57
% 1.00/0.57 % SZS status Theorem for theBenchmark
% 1.00/0.57
% 1.00/0.57 % Proof 1 at 0.14 (+ 0.03) seconds.
% 1.00/0.57 % Length of proof is 29.
% 1.00/0.57 % Level of proof is 5.
% 1.00/0.57 % Maximum clause weight is 46.000.
% 1.00/0.57 % Given clauses 176.
% 1.00/0.57
% 1.00/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------