%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL535+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 : n007.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 116.62s 16.39s
% Output : CNFRefutation 116.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 36
% Syntax : Number of formulae : 155 ( 101 unt; 0 def)
% Number of atoms : 224 ( 48 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 118 ( 49 ~; 44 |; 4 &)
% ( 13 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 172 ( 8 sgn 35 !; 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(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('theBenchmark.p',substitution_of_equivalents) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('theBenchmark.p',implies_1) ).
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_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('theBenchmark.p',and_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(or_2,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('theBenchmark.p',or_2) ).
fof(or_3,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('theBenchmark.p',or_3) ).
fof(equivalence_3,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('theBenchmark.p',equivalence_3) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('theBenchmark.p',op_or) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('theBenchmark.p',op_implies_and) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('theBenchmark.p',op_equiv) ).
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_5,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('theBenchmark.p',axiom_5) ).
fof(axiom_m9,axiom,
( axiom_m9
<=> ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) ),
file('theBenchmark.p',axiom_m9) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) ),
file('theBenchmark.p',op_possibly) ).
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_m9,conjecture,
axiom_m9,
file('theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
fof(s1_0_m6s3m9b_axiom_m9_neg,negated_conjecture,
~ axiom_m9,
inference(assume_negation,[status(cth)],[s1_0_m6s3m9b_axiom_m9]) ).
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_64,plain,
( B = A
| ~ is_a_theorem(equiv(A,B))
| ~ substitution_of_equivalents ),
inference(clausify,[status(thm)],[substitution_of_equivalents]) ).
cnf(c_69,plain,
( is_a_theorem(implies(A,implies(B,A)))
| ~ implies_1 ),
inference(clausify,[status(thm)],[implies_1]) ).
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_77,plain,
( is_a_theorem(implies(and(A,B),B))
| ~ and_2 ),
inference(clausify,[status(thm)],[and_2]) ).
cnf(c_79,plain,
( is_a_theorem(implies(A,implies(B,and(A,B))))
| ~ and_3 ),
inference(clausify,[status(thm)],[and_3]) ).
cnf(c_83,plain,
( is_a_theorem(implies(A,or(B,A)))
| ~ or_2 ),
inference(clausify,[status(thm)],[or_2]) ).
cnf(c_85,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B))))
| ~ or_3 ),
inference(clausify,[status(thm)],[or_3]) ).
cnf(c_91,plain,
( is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B))))
| ~ equivalence_3 ),
inference(clausify,[status(thm)],[equivalence_3]) ).
cnf(c_115,plain,
( or(A,B) = not(and(not(A),not(B)))
| ~ op_or ),
inference(clausify,[status(thm)],[op_or]) ).
cnf(c_116,plain,
( not(and(not(A),not(B))) = or(A,B)
| ~ op_or ),
inference(copy,[status(thm)],[c_115]) ).
cnf(c_119,plain,
( not(and(A,not(B))) = implies(A,B)
| ~ op_implies_and ),
inference(clausify,[status(thm)],[op_implies_and]) ).
cnf(c_121,plain,
( and(implies(A,B),implies(B,A)) = equiv(A,B)
| ~ op_equiv ),
inference(clausify,[status(thm)],[op_equiv]) ).
fof(hilbert_op_or,axiom,
op_or,
file('theBenchmark.p',hilbert_op_or) ).
cnf(c_122,plain,
op_or,
inference(clausify,[status(thm)],[hilbert_op_or]) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('theBenchmark.p',hilbert_op_implies_and) ).
cnf(c_123,plain,
op_implies_and,
inference(clausify,[status(thm)],[hilbert_op_implies_and]) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',hilbert_op_equiv) ).
cnf(c_124,plain,
op_equiv,
inference(clausify,[status(thm)],[hilbert_op_equiv]) ).
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_1,axiom,
implies_1,
file('theBenchmark.p',hilbert_implies_1) ).
cnf(c_127,plain,
implies_1,
inference(clausify,[status(thm)],[hilbert_implies_1]) ).
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_2,axiom,
and_2,
file('theBenchmark.p',hilbert_and_2) ).
cnf(c_131,plain,
and_2,
inference(clausify,[status(thm)],[hilbert_and_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]) ).
fof(hilbert_or_2,axiom,
or_2,
file('theBenchmark.p',hilbert_or_2) ).
cnf(c_134,plain,
or_2,
inference(clausify,[status(thm)],[hilbert_or_2]) ).
fof(hilbert_or_3,axiom,
or_3,
file('theBenchmark.p',hilbert_or_3) ).
cnf(c_135,plain,
or_3,
inference(clausify,[status(thm)],[hilbert_or_3]) ).
fof(hilbert_equivalence_3,axiom,
equivalence_3,
file('theBenchmark.p',hilbert_equivalence_3) ).
cnf(c_138,plain,
equivalence_3,
inference(clausify,[status(thm)],[hilbert_equivalence_3]) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('theBenchmark.p',use_substitution_of_equivalents) ).
cnf(c_139,plain,
substitution_of_equivalents,
inference(clausify,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(c_140,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A)
| ~ necessitation ),
inference(clausify,[status(thm)],[necessitation]) ).
cnf(c_156,plain,
( is_a_theorem(implies(necessarily(A),A))
| ~ axiom_M ),
inference(clausify,[status(thm)],[axiom_M]) ).
cnf(c_162,plain,
( is_a_theorem(implies(possibly(A),necessarily(possibly(A))))
| ~ axiom_5 ),
inference(clausify,[status(thm)],[axiom_5]) ).
fof(nnf_53,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| axiom_m9 )
& ( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
| ~ axiom_m9 ) ),
inference(fof_nnf,[status(thm)],[axiom_m9]) ).
fof(sk_axiom_m9_sk,plain,
( ( ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0)))
| axiom_m9 )
& ( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
| ~ axiom_m9 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_53]) ).
fof(sk_axiom_m9,plain,
( ( ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0)))
| axiom_m9 )
& ! [VAR_0] :
( is_a_theorem(strict_implies(possibly(possibly(VAR_0)),possibly(VAR_0)))
| ~ axiom_m9 ) ),
inference(cnf_transformation,[status(thm)],[sk_axiom_m9_sk]) ).
cnf(c_189,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(sK0)),possibly(sK0)))
| axiom_m9 ),
inference(split_conjunct,[status(thm)],[sk_axiom_m9]) ).
cnf(c_192,plain,
( possibly(A) = not(necessarily(not(A)))
| ~ op_possibly ),
inference(clausify,[status(thm)],[op_possibly]) ).
cnf(c_193,plain,
( not(necessarily(not(A))) = possibly(A)
| ~ op_possibly ),
inference(copy,[status(thm)],[c_192]) ).
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_op_possibly,axiom,
op_possibly,
file('theBenchmark.p',km5_op_possibly) ).
cnf(c_200,plain,
op_possibly,
inference(clausify,[status(thm)],[km5_op_possibly]) ).
fof(km5_necessitation,axiom,
necessitation,
file('theBenchmark.p',km5_necessitation) ).
cnf(c_201,plain,
necessitation,
inference(clausify,[status(thm)],[km5_necessitation]) ).
fof(km5_axiom_M,axiom,
axiom_M,
file('theBenchmark.p',km5_axiom_M) ).
cnf(c_203,plain,
axiom_M,
inference(clausify,[status(thm)],[km5_axiom_M]) ).
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_m9,
inference(clausify,[status(thm)],[s1_0_m6s3m9b_axiom_m9_neg]) ).
cnf(c_209,plain,
not(and(not(A),not(B))) = or(A,B),
inference(resolve,[status(thm)],[c_122,c_116]) ).
cnf(c_210,plain,
not(and(A,not(B))) = implies(A,B),
inference(resolve,[status(thm)],[c_123,c_119]) ).
cnf(c_211,plain,
and(implies(A,B),implies(B,A)) = equiv(A,B),
inference(resolve,[status(thm)],[c_124,c_121]) ).
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_214,plain,
is_a_theorem(implies(A,implies(B,A))),
inference(resolve,[status(thm)],[c_127,c_69]) ).
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_218,plain,
is_a_theorem(implies(and(A,B),B)),
inference(resolve,[status(thm)],[c_131,c_77]) ).
cnf(c_219,plain,
is_a_theorem(implies(A,implies(B,and(A,B)))),
inference(resolve,[status(thm)],[c_132,c_79]) ).
cnf(c_221,plain,
is_a_theorem(implies(A,or(B,A))),
inference(resolve,[status(thm)],[c_134,c_83]) ).
cnf(c_222,plain,
is_a_theorem(implies(implies(A,B),implies(implies(C,B),implies(or(A,C),B)))),
inference(resolve,[status(thm)],[c_135,c_85]) ).
cnf(c_225,plain,
is_a_theorem(implies(implies(A,B),implies(implies(B,A),equiv(A,B)))),
inference(resolve,[status(thm)],[c_138,c_91]) ).
cnf(c_226,plain,
( B = A
| ~ is_a_theorem(equiv(A,B)) ),
inference(resolve,[status(thm)],[c_139,c_64]) ).
cnf(c_228,plain,
not(necessarily(not(A))) = possibly(A),
inference(resolve,[status(thm)],[c_200,c_193]) ).
cnf(c_229,plain,
( is_a_theorem(necessarily(A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_201,c_140]) ).
cnf(c_231,plain,
is_a_theorem(implies(necessarily(A),A)),
inference(resolve,[status(thm)],[c_203,c_156]) ).
cnf(c_232,plain,
is_a_theorem(implies(possibly(A),necessarily(possibly(A)))),
inference(resolve,[status(thm)],[c_204,c_162]) ).
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(possibly(possibly(sK0)),possibly(sK0))),
inference(resolve,[status(thm)],[c_208,c_189]) ).
cnf(c_236,plain,
implies(not(A),B) = or(A,B),
inference(paramod,[status(thm)],[c_210,c_209]) ).
cnf(c_256,plain,
( is_a_theorem(implies(B,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_214,c_212]) ).
cnf(c_259,plain,
( is_a_theorem(implies(A,B))
| ~ is_a_theorem(implies(A,implies(A,B))) ),
inference(resolve,[status(thm)],[c_215,c_212]) ).
cnf(c_289,plain,
( is_a_theorem(implies(implies(B,A),equiv(A,B)))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_225,c_212]) ).
cnf(c_307,plain,
not(and(A,possibly(B))) = implies(A,necessarily(not(B))),
inference(paramod,[status(thm)],[c_228,c_210]) ).
cnf(c_309,plain,
not(necessarily(possibly(A))) = possibly(necessarily(not(A))),
inference(paramod,[status(thm)],[c_228,c_228]) ).
cnf(c_30922,plain,
implies(possibly(A),B) = or(necessarily(not(A)),B),
inference(paramod,[status(thm)],[c_228,c_236]) ).
cnf(c_359,plain,
or(necessarily(not(A)),B) = implies(possibly(A),B),
inference(copy,[status(thm)],[c_30922]) ).
cnf(c_623,plain,
is_a_theorem(implies(implies(A,B),implies(or(A,A),B))),
inference(resolve,[status(thm)],[c_259,c_222]) ).
cnf(c_624,plain,
is_a_theorem(implies(A,and(A,A))),
inference(resolve,[status(thm)],[c_259,c_219]) ).
cnf(c_626,plain,
is_a_theorem(implies(A,A)),
inference(resolve,[status(thm)],[c_259,c_214]) ).
cnf(c_2606,plain,
is_a_theorem(implies(implies(necessarily(possibly(A)),possibly(A)),equiv(possibly(A),necessarily(possibly(A))))),
inference(resolve,[status(thm)],[c_289,c_232]) ).
cnf(c_2607,plain,
is_a_theorem(implies(implies(A,necessarily(A)),equiv(necessarily(A),A))),
inference(resolve,[status(thm)],[c_289,c_231]) ).
cnf(c_2612,plain,
is_a_theorem(implies(implies(or(A,B),B),equiv(B,or(A,B)))),
inference(resolve,[status(thm)],[c_289,c_221]) ).
cnf(c_2615,plain,
is_a_theorem(implies(implies(A,and(B,A)),equiv(and(B,A),A))),
inference(resolve,[status(thm)],[c_289,c_218]) ).
cnf(c_3725,plain,
( is_a_theorem(and(A,A))
| ~ is_a_theorem(A) ),
inference(resolve,[status(thm)],[c_624,c_212]) ).
cnf(c_30923,plain,
is_a_theorem(and(implies(A,A),implies(A,A))),
inference(resolve,[status(thm)],[c_3725,c_626]) ).
cnf(c_3809,plain,
is_a_theorem(equiv(A,A)),
inference(paramod,[status(thm)],[c_211,c_30923]) ).
cnf(c_4056,plain,
is_a_theorem(necessarily(equiv(A,A))),
inference(resolve,[status(thm)],[c_3809,c_229]) ).
cnf(c_4696,plain,
is_a_theorem(implies(A,necessarily(equiv(B,B)))),
inference(resolve,[status(thm)],[c_4056,c_256]) ).
cnf(c_12769,plain,
( is_a_theorem(implies(or(A,A),B))
| ~ is_a_theorem(implies(A,B)) ),
inference(resolve,[status(thm)],[c_623,c_212]) ).
cnf(c_12810,plain,
is_a_theorem(implies(or(A,A),A)),
inference(resolve,[status(thm)],[c_12769,c_626]) ).
cnf(c_30924,plain,
( is_a_theorem(equiv(possibly(A),necessarily(possibly(A))))
| ~ is_a_theorem(implies(necessarily(possibly(A)),possibly(A))) ),
inference(resolve,[status(thm)],[c_2606,c_212]) ).
cnf(c_17222,plain,
is_a_theorem(equiv(possibly(A),necessarily(possibly(A)))),
inference(resolve,[status(thm)],[c_231,c_30924]) ).
cnf(c_17240,plain,
necessarily(possibly(A)) = possibly(A),
inference(resolve,[status(thm)],[c_17222,c_226]) ).
cnf(c_30925,plain,
not(possibly(A)) = possibly(necessarily(not(A))),
inference(paramod,[status(thm)],[c_17240,c_309]) ).
cnf(c_17289,plain,
possibly(necessarily(not(A))) = not(possibly(A)),
inference(copy,[status(thm)],[c_30925]) ).
cnf(c_17379,plain,
( is_a_theorem(equiv(necessarily(A),A))
| ~ is_a_theorem(implies(A,necessarily(A))) ),
inference(resolve,[status(thm)],[c_2607,c_212]) ).
cnf(c_17447,plain,
is_a_theorem(equiv(necessarily(equiv(A,A)),equiv(A,A))),
inference(resolve,[status(thm)],[c_17379,c_4696]) ).
cnf(c_17620,plain,
( is_a_theorem(equiv(B,or(A,B)))
| ~ is_a_theorem(implies(or(A,B),B)) ),
inference(resolve,[status(thm)],[c_2612,c_212]) ).
cnf(c_17623,plain,
is_a_theorem(equiv(A,or(A,A))),
inference(resolve,[status(thm)],[c_17620,c_12810]) ).
cnf(c_17669,plain,
or(A,A) = A,
inference(resolve,[status(thm)],[c_17623,c_226]) ).
cnf(c_30926,plain,
necessarily(not(A)) = implies(possibly(A),necessarily(not(A))),
inference(paramod,[status(thm)],[c_17669,c_359]) ).
cnf(c_17683,plain,
implies(possibly(A),necessarily(not(A))) = necessarily(not(A)),
inference(copy,[status(thm)],[c_30926]) ).
cnf(c_17829,plain,
( is_a_theorem(equiv(and(B,A),A))
| ~ is_a_theorem(implies(A,and(B,A))) ),
inference(resolve,[status(thm)],[c_2615,c_212]) ).
cnf(c_18857,plain,
is_a_theorem(equiv(and(A,A),A)),
inference(resolve,[status(thm)],[c_17829,c_624]) ).
cnf(c_30927,plain,
A = and(A,A),
inference(resolve,[status(thm)],[c_18857,c_226]) ).
cnf(c_18875,plain,
and(A,A) = A,
inference(copy,[status(thm)],[c_30927]) ).
cnf(c_30928,plain,
not(not(A)) = implies(not(A),A),
inference(paramod,[status(thm)],[c_18875,c_210]) ).
cnf(c_30929,plain,
not(not(A)) = or(A,A),
inference(paramod,[status(thm)],[c_236,c_30928]) ).
cnf(c_18889,plain,
not(not(A)) = A,
inference(paramod,[status(thm)],[c_17669,c_30929]) ).
cnf(c_30930,plain,
implies(A,A) = equiv(A,A),
inference(paramod,[status(thm)],[c_18875,c_211]) ).
cnf(c_18890,plain,
equiv(A,A) = implies(A,A),
inference(copy,[status(thm)],[c_30930]) ).
cnf(c_30931,plain,
not(possibly(A)) = implies(possibly(A),necessarily(not(A))),
inference(paramod,[status(thm)],[c_18875,c_307]) ).
cnf(c_18894,plain,
not(possibly(A)) = necessarily(not(A)),
inference(paramod,[status(thm)],[c_17683,c_30931]) ).
cnf(c_30932,plain,
is_a_theorem(equiv(necessarily(implies(A,A)),equiv(A,A))),
inference(paramod,[status(thm)],[c_18890,c_17447]) ).
cnf(c_30933,plain,
is_a_theorem(equiv(strict_implies(A,A),equiv(A,A))),
inference(paramod,[status(thm)],[c_233,c_30932]) ).
cnf(c_18963,plain,
is_a_theorem(equiv(strict_implies(A,A),implies(A,A))),
inference(paramod,[status(thm)],[c_18890,c_30933]) ).
cnf(c_19154,plain,
possibly(necessarily(not(A))) = necessarily(not(A)),
inference(paramod,[status(thm)],[c_18894,c_17289]) ).
cnf(c_30934,plain,
implies(A,A) = strict_implies(A,A),
inference(resolve,[status(thm)],[c_18963,c_226]) ).
cnf(c_20768,plain,
strict_implies(A,A) = implies(A,A),
inference(copy,[status(thm)],[c_30934]) ).
cnf(c_30935,plain,
possibly(necessarily(A)) = necessarily(not(not(A))),
inference(paramod,[status(thm)],[c_18889,c_19154]) ).
cnf(c_30888,plain,
possibly(necessarily(A)) = necessarily(A),
inference(paramod,[status(thm)],[c_18889,c_30935]) ).
cnf(c_30936,plain,
possibly(possibly(A)) = necessarily(possibly(A)),
inference(paramod,[status(thm)],[c_17240,c_30888]) ).
cnf(c_30906,plain,
possibly(possibly(A)) = possibly(A),
inference(paramod,[status(thm)],[c_17240,c_30936]) ).
cnf(c_30937,negated_conjecture,
~ is_a_theorem(strict_implies(possibly(sK0),possibly(sK0))),
inference(paramod,[status(thm)],[c_30906,c_235]) ).
cnf(c_30938,negated_conjecture,
~ is_a_theorem(implies(possibly(sK0),possibly(sK0))),
inference(paramod,[status(thm)],[c_20768,c_30937]) ).
cnf(c_30921,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_626,c_30938]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 22:40:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 2101907 was started by sandbox on n007,
% 0.08/0.37 % Fri Sep 25 22:40:54 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 116.62/16.39
% 116.62/16.39 % given #500 (T,wt=1): 12850 r1. [back_unit_del(106),unit_del(b,12810)].
% 116.62/16.39
% 116.62/16.39 % given #1000 (A,wt=39): 4462 is_a_theorem(or(A,implies(strict_implies(B,C),implies(strict_implies(C,B),strict_equiv(B,C))))). [resolve(341,a,277,a)].
% 116.62/16.39
% 116.62/16.39 % SZS status Theorem for theBenchmark
% 116.62/16.39
% 116.62/16.39 % Proof 1 at 6.01 (+ 1.68) seconds.
% 116.62/16.39 % Length of proof is 117.
% 116.62/16.39 % Level of proof is 14.
% 116.62/16.39 % Maximum clause weight is 40.000.
% 116.62/16.39 % Given clauses 1187.
% 116.62/16.39
% 116.62/16.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------