%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL537+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /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 : Thu Sep 24 01:07:56 PM UTC 2026
% Result : Theorem 3.43s 1.03s
% Output : CNFRefutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 69
% Syntax : Number of formulae : 258 ( 47 unt; 37 def)
% Number of atoms : 743 ( 41 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 860 ( 375 ~; 389 |; 38 &)
% ( 53 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 57 ( 55 usr; 55 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 22 con; 0-2 aty)
% Number of variables : 219 ( 195 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
axiom_B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,conjecture,
axiom_5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,negated_conjecture,
~ axiom_5,
inference(negated_conjecture,[status(cth)],[f83]) ).
fof(f85,plain,
( modus_ponens
<=> ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f86,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(NNF_transformation,[status(thm)],[f85]) ).
fof(f87,plain,
( ( ? [Y] :
( ~ is_a_theorem(Y)
& ? [X] :
( is_a_theorem(implies(X,Y))
& is_a_theorem(X) ) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(miniscoping,[status(thm)],[f86]) ).
fof(f88,plain,
( ( ( ~ is_a_theorem(sK0_skl)
& is_a_theorem(implies(sK1_skl,sK0_skl))
& is_a_theorem(sK1_skl) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f87]) ).
fof(f89,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f93,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f94,plain,
( ( ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(NNF_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
( ( ( sK2_skl != sK3_skl
& is_a_theorem(equiv(sK2_skl,sK3_skl)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f99,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f100,plain,
( ( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f107,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f108,plain,
( ( ~ is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f119,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y))
| and_2 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
| ~ and_2 ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f120,plain,
( ( ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl))
| and_2 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f119]) ).
fof(f121,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f123,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f124,plain,
( ( ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f124]) ).
fof(f127,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f128,plain,
( ( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X,sK19_skl),skolemize(Y,sK20_skl)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f147,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| equivalence_3 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f148,plain,
( ( ~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl))))
| equivalence_3 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f151,plain,
( ( ? [P] : ~ is_a_theorem(implies(P,and(P,P)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f152,plain,
( ( ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f151]) ).
fof(f153,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
( ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))
| kn1 ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f171,plain,
( ( ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P))
| cn3 )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f172,plain,
( ( ~ is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))
| cn3 )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f171]) ).
fof(f173,plain,
! [X0] :
( is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f174,plain,
( ~ is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))
| cn3 ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f195,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f196,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f199,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f200,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f205,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f206,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f208,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f209,plain,
modus_tollens,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f211,plain,
implies_2,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f214,plain,
and_2,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f215,plain,
and_3,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f216,plain,
or_1,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f221,plain,
equivalence_3,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f222,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f254,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),X))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f255,plain,
( ( ~ is_a_theorem(implies(necessarily(sK64_skl),sK64_skl))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f254]) ).
fof(f256,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[status(thm)],[f255]) ).
fof(f258,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| axiom_4 )
& ( ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_4 ) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f259,plain,
( ( ~ is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl))))
| axiom_4 )
& ( ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(X,sK65_skl)],[f258]) ).
fof(f260,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f262,plain,
( ( ? [X] : ~ is_a_theorem(implies(X,necessarily(possibly(X))))
| axiom_B )
& ( ! [X] : is_a_theorem(implies(X,necessarily(possibly(X))))
| ~ axiom_B ) ),
inference(NNF_transformation,[status(thm)],[f57]) ).
fof(f263,plain,
( ( ~ is_a_theorem(implies(sK66_skl,necessarily(possibly(sK66_skl))))
| axiom_B )
& ( ! [X] : is_a_theorem(implies(X,necessarily(possibly(X))))
| ~ axiom_B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66_skl]),skolemize(X,sK66_skl)],[f262]) ).
fof(f264,plain,
! [X0] :
( is_a_theorem(implies(X0,necessarily(possibly(X0))))
| ~ axiom_B ),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f266,plain,
( ( ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| axiom_5 )
& ( ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| ~ axiom_5 ) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f267,plain,
( ( ~ is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl))))
| axiom_5 )
& ( ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| ~ axiom_5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl]),skolemize(X,sK67_skl)],[f266]) ).
fof(f269,plain,
( ~ is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl))))
| axiom_5 ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f326,plain,
( ! [X] : possibly(X) = not(necessarily(not(X)))
| ~ op_possibly ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f327,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[status(thm)],[f326]) ).
fof(f334,plain,
op_possibly,
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f337,plain,
axiom_M,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f338,plain,
axiom_4,
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f339,plain,
axiom_B,
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f340,plain,
~ axiom_5,
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f341,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,definition,
! [X0,X1] :
( sQ1_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f345,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f89,f341,f344]) ).
fof(f360,definition,
( sQ5_spl
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( sQ5_spl
| ~ substitution_of_equivalents ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f364,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f96,f360,f363]) ).
fof(f375,definition,
( sQ9_spl
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ9_spl
| ~ modus_tollens ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
! [X0,X1] :
( sQ10_spl
<=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f379,plain,
! [X0,X1] :
( ~ sQ10_spl
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f101,f375,f378]) ).
fof(f397,definition,
( sQ15_spl
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( sQ15_spl
| ~ implies_2 ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,definition,
! [X0,X1] :
( sQ16_spl
<=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f401,plain,
! [X0,X1] :
( ~ sQ16_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f109,f397,f400]) ).
fof(f430,definition,
( sQ24_spl
<=> and_2 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( sQ24_spl
| ~ and_2 ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,definition,
! [X0,X1] :
( sQ25_spl
<=> is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f434,plain,
! [X0,X1] :
( ~ sQ25_spl
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(component_clause,[status(thm)],[f433]) ).
fof(f436,plain,
( sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f121,f430,f433]) ).
fof(f441,definition,
( sQ27_spl
<=> and_3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ27_spl
| ~ and_3 ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
! [X0,X1] :
( sQ28_spl
<=> is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f445,plain,
! [X0,X1] :
( ~ sQ28_spl
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f125,f441,f444]) ).
fof(f452,definition,
( sQ30_spl
<=> or_1 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( sQ30_spl
| ~ or_1 ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,definition,
! [X0,X1] :
( sQ31_spl
<=> is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f456,plain,
! [X0,X1] :
( ~ sQ31_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f129,f452,f455]) ).
fof(f507,definition,
( sQ45_spl
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ45_spl
| ~ equivalence_3 ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,definition,
! [X0,X1] :
( sQ46_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sQ46_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,plain,
( sQ46_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f149,f507,f510]) ).
fof(f518,definition,
( sQ48_spl
<=> kn1 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f521,definition,
! [X0] :
( sQ49_spl
<=> is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f522,plain,
! [X0] :
( ~ sQ49_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,plain,
( sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f153,f518,f521]) ).
fof(f525,definition,
( sQ50_spl
<=> is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ50_spl
| ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,plain,
( ~ sQ50_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f154,f518,f525]) ).
fof(f567,definition,
( sQ61_spl
<=> cn3 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f570,definition,
! [X0] :
( sQ62_spl
<=> is_a_theorem(implies(implies(not(X0),X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f571,plain,
! [X0] :
( ~ sQ62_spl
| is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(component_clause,[status(thm)],[f570]) ).
fof(f573,plain,
( sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f173,f567,f570]) ).
fof(f574,definition,
( sQ63_spl
<=> is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( sQ63_spl
| ~ is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)) ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f577,plain,
( ~ sQ63_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f174,f567,f574]) ).
fof(f630,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f632,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,definition,
! [X0,X1] :
( sQ79_spl
<=> or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f634,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f636,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f196,f630,f633]) ).
fof(f644,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f644]) ).
fof(f647,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f648,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f647]) ).
fof(f650,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f200,f644,f647]) ).
fof(f744,definition,
( sQ109_spl
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f746,plain,
( sQ109_spl
| ~ axiom_M ),
inference(component_clause,[status(thm)],[f744]) ).
fof(f747,definition,
! [X0] :
( sQ110_spl
<=> is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f748,plain,
! [X0] :
( ~ sQ110_spl
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(component_clause,[status(thm)],[f747]) ).
fof(f750,plain,
( sQ110_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f256,f744,f747]) ).
fof(f755,definition,
( sQ112_spl
<=> axiom_4 ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f757,plain,
( sQ112_spl
| ~ axiom_4 ),
inference(component_clause,[status(thm)],[f755]) ).
fof(f758,definition,
! [X0] :
( sQ113_spl
<=> is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f759,plain,
! [X0] :
( ~ sQ113_spl
| is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))) ),
inference(component_clause,[status(thm)],[f758]) ).
fof(f761,plain,
( sQ113_spl
| ~ sQ112_spl ),
inference(split_clause,[status(thm)],[f260,f755,f758]) ).
fof(f766,definition,
( sQ115_spl
<=> axiom_B ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f768,plain,
( sQ115_spl
| ~ axiom_B ),
inference(component_clause,[status(thm)],[f766]) ).
fof(f769,definition,
! [X0] :
( sQ116_spl
<=> is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f770,plain,
! [X0] :
( ~ sQ116_spl
| is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(component_clause,[status(thm)],[f769]) ).
fof(f772,plain,
( sQ116_spl
| ~ sQ115_spl ),
inference(split_clause,[status(thm)],[f264,f766,f769]) ).
fof(f777,definition,
( sQ118_spl
<=> axiom_5 ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f778,plain,
( ~ sQ118_spl
| axiom_5 ),
inference(component_clause,[status(thm)],[f777]) ).
fof(f780,definition,
! [X0] :
( sQ119_spl
<=> is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f781,plain,
! [X0] :
( ~ sQ119_spl
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(component_clause,[status(thm)],[f780]) ).
fof(f784,definition,
( sQ120_spl
<=> is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f786,plain,
( sQ120_spl
| ~ is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl)))) ),
inference(component_clause,[status(thm)],[f784]) ).
fof(f787,plain,
( ~ sQ120_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f269,f777,f784]) ).
fof(f942,definition,
( sQ163_spl
<=> op_possibly ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f944,plain,
( sQ163_spl
| ~ op_possibly ),
inference(component_clause,[status(thm)],[f942]) ).
fof(f945,definition,
! [X0] :
( sQ164_spl
<=> possibly(X0) = not(necessarily(not(X0))) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f946,plain,
! [X0] :
( ~ sQ164_spl
| possibly(X0) = not(necessarily(not(X0))) ),
inference(component_clause,[status(thm)],[f945]) ).
fof(f948,plain,
( sQ164_spl
| ~ sQ163_spl ),
inference(split_clause,[status(thm)],[f327,f942,f945]) ).
fof(f970,plain,
( sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f944,f334]) ).
fof(f971,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f970]) ).
fof(f972,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f208]) ).
fof(f973,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f972]) ).
fof(f976,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f362,f222]) ).
fof(f977,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f976]) ).
fof(f980,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f646,f206]) ).
fof(f981,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f980]) ).
fof(f982,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f632,f205]) ).
fof(f983,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f996,plain,
( sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f746,f337]) ).
fof(f997,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f996]) ).
fof(f1013,plain,
( sQ115_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f768,f339]) ).
fof(f1014,plain,
sQ115_spl,
inference(contradiction_clause,[status(thm)],[f1013]) ).
fof(f1031,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f216]) ).
fof(f1032,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1031]) ).
fof(f1039,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f214]) ).
fof(f1040,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f1039]) ).
fof(f1047,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ sQ1_spl
| X1 = X2
| ~ is_a_theorem(implies(X0,equiv(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f345,f364]) ).
fof(f1061,plain,
( sQ120_spl
| ~ sQ119_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f786,f781]) ).
fof(f1062,plain,
( sQ120_spl
| ~ sQ119_spl ),
inference(contradiction_clause,[status(thm)],[f1061]) ).
fof(f1072,plain,
! [X0] :
( ~ sQ1_spl
| sQ50_spl
| ~ is_a_theorem(implies(X0,implies(sK32_skl,and(sK32_skl,sK32_skl))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f527,f345]) ).
fof(f1075,plain,
( sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f757,f338]) ).
fof(f1076,plain,
sQ112_spl,
inference(contradiction_clause,[status(thm)],[f1075]) ).
fof(f1120,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f648,f634]) ).
fof(f1178,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ6_spl
| ~ is_a_theorem(implies(X3,implies(X0,equiv(X1,X2))))
| ~ is_a_theorem(X3)
| X1 = X2
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1047,f345]) ).
fof(f1214,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f221]) ).
fof(f1215,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f1214]) ).
fof(f1231,plain,
( sQ63_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl)) ),
inference(forward_demodulation,[status(thm)],[f1120,f576]) ).
fof(f1232,plain,
! [X0] :
( ~ sQ1_spl
| sQ63_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ is_a_theorem(implies(X0,implies(or(sK43_skl,sK43_skl),sK43_skl)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1231,f345]) ).
fof(f1286,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f215]) ).
fof(f1287,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1286]) ).
fof(f1330,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f399,f211]) ).
fof(f1331,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1330]) ).
fof(f1335,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f1120,f379]) ).
fof(f1342,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f209]) ).
fof(f1343,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1342]) ).
fof(f1898,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| sQ50_spl
| ~ is_a_theorem(implies(sK32_skl,implies(sK32_skl,and(sK32_skl,sK32_skl)))) ),
inference(resolution,[status(thm)],[f1072,f401]) ).
fof(f1909,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| sQ50_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1898,f445]) ).
fof(f1910,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| sQ50_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f1909]) ).
fof(f2336,plain,
( ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| sQ63_spl
| ~ is_a_theorem(or(sK43_skl,not(or(sK43_skl,sK43_skl)))) ),
inference(resolution,[status(thm)],[f1232,f1335]) ).
fof(f3132,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ is_a_theorem(implies(X1,X0))
| X1 = X0
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1178,f511]) ).
fof(f3438,plain,
! [X0] :
( ~ sQ113_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| necessarily(X0) = necessarily(necessarily(X0))
| ~ is_a_theorem(implies(necessarily(necessarily(X0)),necessarily(X0))) ),
inference(resolution,[status(thm)],[f3132,f759]) ).
fof(f3443,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| X0 = and(X0,X0)
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f3132,f522]) ).
fof(f3455,plain,
! [X0] :
( ~ sQ113_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ110_spl
| necessarily(X0) = necessarily(necessarily(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3438,f748]) ).
fof(f3456,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| X0 = and(X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3443,f434]) ).
fof(f3736,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| implies(not(X0),X0) = not(not(X0)) ),
inference(paramodulation,[status(thm)],[f3456,f648]) ).
fof(f3770,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(X0,X0) = not(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f1120,f3736]) ).
fof(f4464,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ31_spl
| is_a_theorem(implies(X0,not(not(X0)))) ),
inference(paramodulation,[status(thm)],[f3770,f456]) ).
fof(f4619,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ31_spl
| is_a_theorem(implies(not(X0),not(or(X0,X0)))) ),
inference(paramodulation,[status(thm)],[f3770,f4464]) ).
fof(f4623,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ31_spl
| is_a_theorem(or(X0,not(or(X0,X0)))) ),
inference(forward_demodulation,[status(thm)],[f1120,f4619]) ).
fof(f5119,plain,
( ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| sQ63_spl
| ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ31_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f2336,f4623]) ).
fof(f5127,plain,
( ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| sQ63_spl
| ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f5119]) ).
fof(f5134,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(forward_demodulation,[status(thm)],[f1120,f571]) ).
fof(f5202,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ62_spl
| ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X0) = X0
| ~ is_a_theorem(implies(X0,or(X0,X0))) ),
inference(resolution,[status(thm)],[f5134,f3132]) ).
fof(f5206,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ62_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ31_spl
| or(X0,X0) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f5202,f456]) ).
fof(f5214,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ31_spl
| X0 = not(not(X0)) ),
inference(backward_demodulation,[status(thm)],[f5206,f3770]) ).
fof(f5325,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ31_spl
| necessarily(not(X0)) = not(possibly(X0)) ),
inference(paramodulation,[status(thm)],[f946,f5214]) ).
fof(f5693,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ31_spl
| possibly(possibly(X0)) = not(necessarily(necessarily(not(X0)))) ),
inference(paramodulation,[status(thm)],[f5325,f946]) ).
fof(f5732,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ31_spl
| ~ sQ113_spl
| ~ sQ110_spl
| possibly(possibly(X0)) = not(necessarily(not(X0))) ),
inference(forward_demodulation,[status(thm)],[f3455,f5693]) ).
fof(f5733,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ31_spl
| ~ sQ113_spl
| ~ sQ110_spl
| possibly(possibly(X0)) = possibly(X0) ),
inference(forward_demodulation,[status(thm)],[f946,f5732]) ).
fof(f5759,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ31_spl
| ~ sQ113_spl
| ~ sQ110_spl
| ~ sQ116_spl
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(paramodulation,[status(thm)],[f5733,f770]) ).
fof(f5774,plain,
( ~ sQ164_spl
| ~ sQ49_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ31_spl
| ~ sQ113_spl
| ~ sQ110_spl
| ~ sQ116_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f5759,f780,f769,f747,f758,f455,f570,f633,f647,f433,f363,f344,f510,f521,f945]) ).
fof(f5775,plain,
( ~ sQ118_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f778,f340]) ).
fof(f5776,plain,
~ sQ118_spl,
inference(contradiction_clause,[status(thm)],[f5775]) ).
fof(f5777,plain,
$false,
inference(sat_refutation,[status(thm)],[f347,f366,f381,f403,f436,f447,f458,f513,f524,f528,f573,f577,f636,f650,f750,f761,f772,f787,f948,f971,f973,f977,f981,f983,f997,f1014,f1032,f1040,f1062,f1076,f1215,f1287,f1331,f1343,f1910,f5127,f5774,f5776]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL537+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 00:37:36 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.42 % Drodi V4.1.1
% 3.43/1.03 % Refutation found
% 3.43/1.03 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.43/1.03 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.43/1.08 % Elapsed time: 0.678391 seconds
% 3.43/1.08 % CPU time: 4.934357 seconds
% 3.43/1.08 % Total memory used: 149.975 MB
% 3.43/1.08 % Net memory used: 144.436 MB
%------------------------------------------------------------------------------