%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL526+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 : n026.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 01:07:55 PM UTC 2026
% Result : Theorem 0.14s 5.77s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 52
% Syntax : Number of formulae : 202 ( 32 unt; 30 def)
% Number of atoms : 585 ( 30 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 657 ( 274 ~; 289 |; 42 &)
% ( 45 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 43 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 18 con; 0-2 aty)
% Number of variables : 183 ( 161 !; 22 ?)
% 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(f7,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
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(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(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
and_2,
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(f50,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
( substitution_strict_equiv
<=> ! [X,Y] :
( is_a_theorem(strict_equiv(X,Y))
=> X = Y ) ),
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(f64,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
( op_strict_equiv
=> ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f87,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f88,conjecture,
substitution_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,negated_conjecture,
~ substitution_strict_equiv,
inference(negated_conjecture,[status(cth)],[f88]) ).
fof(f90,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(f91,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)],[f90]) ).
fof(f92,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)],[f91]) ).
fof(f93,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)],[f92]) ).
fof(f94,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f98,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f99,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)],[f98]) ).
fof(f100,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)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f120,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f121,plain,
( ( ~ is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,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(f125,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)],[f124]) ).
fof(f126,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[status(thm)],[f125]) ).
fof(f152,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(f153,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)],[f152]) ).
fof(f154,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[status(thm)],[f153]) ).
fof(f213,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f218,plain,
and_1,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f219,plain,
and_2,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f226,plain,
equivalence_3,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f227,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f228,plain,
( necessitation
<=> ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f229,plain,
( ( ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(NNF_transformation,[status(thm)],[f228]) ).
fof(f230,plain,
( ( ( ~ is_a_theorem(necessarily(sK55_skl))
& is_a_theorem(sK55_skl) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f229]) ).
fof(f231,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f234,plain,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f235,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
| modus_ponens_strict_implies )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens_strict_implies ) ),
inference(NNF_transformation,[status(thm)],[f234]) ).
fof(f236,plain,
( ( ? [Y] :
( ~ is_a_theorem(Y)
& ? [X] :
( is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) ) )
| modus_ponens_strict_implies )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens_strict_implies ) ),
inference(miniscoping,[status(thm)],[f235]) ).
fof(f237,plain,
( ( ( ~ is_a_theorem(sK56_skl)
& is_a_theorem(strict_implies(sK57_skl,sK56_skl))
& is_a_theorem(sK57_skl) )
| modus_ponens_strict_implies )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens_strict_implies ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl,sK57_skl]),skolemize(Y,sK56_skl),skolemize(X,sK57_skl)],[f236]) ).
fof(f238,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens_strict_implies ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f239,plain,
( is_a_theorem(sK57_skl)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f240,plain,
( is_a_theorem(strict_implies(sK57_skl,sK56_skl))
| modus_ponens_strict_implies ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f241,plain,
( ~ is_a_theorem(sK56_skl)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f249,plain,
( substitution_strict_equiv
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f250,plain,
( ( ? [X,Y] :
( X != Y
& is_a_theorem(strict_equiv(X,Y)) )
| substitution_strict_equiv )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) )
| ~ substitution_strict_equiv ) ),
inference(NNF_transformation,[status(thm)],[f249]) ).
fof(f251,plain,
( ( ( sK60_skl != sK61_skl
& is_a_theorem(strict_equiv(sK60_skl,sK61_skl)) )
| substitution_strict_equiv )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) )
| ~ substitution_strict_equiv ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60_skl,sK61_skl]),skolemize(X,sK60_skl),skolemize(Y,sK61_skl)],[f250]) ).
fof(f253,plain,
( is_a_theorem(strict_equiv(sK60_skl,sK61_skl))
| substitution_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f251]) ).
fof(f254,plain,
( sK60_skl != sK61_skl
| substitution_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f251]) ).
fof(f259,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(f260,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)],[f259]) ).
fof(f261,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[status(thm)],[f260]) ).
fof(f295,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f296,plain,
( ( ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl,sK79_skl]),skolemize(X,sK78_skl),skolemize(Y,sK79_skl)],[f295]) ).
fof(f297,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
( ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))
| axiom_m2 ),
inference(cnf_transformation,[status(thm)],[f296]) ).
fof(f335,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f336,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(thm)],[f335]) ).
fof(f337,plain,
( ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X))
| ~ op_strict_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f76]) ).
fof(f338,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f340,plain,
necessitation,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f342,plain,
axiom_M,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f347,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f349,plain,
op_strict_equiv,
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f350,plain,
~ substitution_strict_equiv,
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f351,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,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(f355,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f94,f351,f354]) ).
fof(f370,definition,
( sQ5_spl
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( sQ5_spl
| ~ substitution_of_equivalents ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f374,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f101,f370,f373]) ).
fof(f429,definition,
( sQ21_spl
<=> and_1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ21_spl
| ~ and_1 ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,definition,
! [X0,X1] :
( sQ22_spl
<=> is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f433,plain,
! [X0,X1] :
( ~ sQ22_spl
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f122,f429,f432]) ).
fof(f440,definition,
( sQ24_spl
<=> and_2 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ24_spl
| ~ and_2 ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
! [X0,X1] :
( sQ25_spl
<=> is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f444,plain,
! [X0,X1] :
( ~ sQ25_spl
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f126,f440,f443]) ).
fof(f517,definition,
( sQ45_spl
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ45_spl
| ~ equivalence_3 ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,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(f521,plain,
! [X0,X1] :
( ~ sQ46_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,plain,
( sQ46_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f154,f517,f520]) ).
fof(f675,definition,
( sQ88_spl
<=> necessitation ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( sQ88_spl
| ~ necessitation ),
inference(component_clause,[status(thm)],[f675]) ).
fof(f678,definition,
! [X0] :
( sQ89_spl
<=> ( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f679,plain,
! [X0] :
( ~ sQ89_spl
| is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,plain,
( sQ89_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f231,f675,f678]) ).
fof(f690,definition,
( sQ92_spl
<=> modus_ponens_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f693,definition,
! [X0,X1] :
( sQ93_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f694,plain,
! [X0,X1] :
( ~ sQ93_spl
| is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f696,plain,
( sQ93_spl
| ~ sQ92_spl ),
inference(split_clause,[status(thm)],[f238,f690,f693]) ).
fof(f697,definition,
( sQ94_spl
<=> is_a_theorem(sK57_skl) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f698,plain,
( ~ sQ94_spl
| is_a_theorem(sK57_skl) ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f700,plain,
( sQ94_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f239,f690,f697]) ).
fof(f701,definition,
( sQ95_spl
<=> is_a_theorem(strict_implies(sK57_skl,sK56_skl)) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f702,plain,
( ~ sQ95_spl
| is_a_theorem(strict_implies(sK57_skl,sK56_skl)) ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f704,plain,
( sQ95_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f240,f690,f701]) ).
fof(f705,definition,
( sQ96_spl
<=> is_a_theorem(sK56_skl) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f707,plain,
( sQ96_spl
| ~ is_a_theorem(sK56_skl) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f708,plain,
( ~ sQ96_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f241,f690,f705]) ).
fof(f728,definition,
( sQ102_spl
<=> substitution_strict_equiv ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f729,plain,
( ~ sQ102_spl
| substitution_strict_equiv ),
inference(component_clause,[status(thm)],[f728]) ).
fof(f735,definition,
( sQ104_spl
<=> is_a_theorem(strict_equiv(sK60_skl,sK61_skl)) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f736,plain,
( ~ sQ104_spl
| is_a_theorem(strict_equiv(sK60_skl,sK61_skl)) ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f738,plain,
( sQ104_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f253,f728,f735]) ).
fof(f739,definition,
( sQ105_spl
<=> sK60_skl = sK61_skl ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f742,plain,
( ~ sQ105_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f254,f728,f739]) ).
fof(f754,definition,
( sQ109_spl
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f756,plain,
( sQ109_spl
| ~ axiom_M ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f757,definition,
! [X0] :
( sQ110_spl
<=> is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f758,plain,
! [X0] :
( ~ sQ110_spl
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(component_clause,[status(thm)],[f757]) ).
fof(f760,plain,
( sQ110_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f261,f754,f757]) ).
fof(f853,definition,
( sQ136_spl
<=> axiom_m2 ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f856,definition,
! [X0,X1] :
( sQ137_spl
<=> is_a_theorem(strict_implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f857,plain,
! [X0,X1] :
( ~ sQ137_spl
| is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f856]) ).
fof(f859,plain,
( sQ137_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f297,f853,f856]) ).
fof(f860,definition,
( sQ138_spl
<=> is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl)) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f862,plain,
( sQ138_spl
| ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl)) ),
inference(component_clause,[status(thm)],[f860]) ).
fof(f863,plain,
( ~ sQ138_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f298,f853,f860]) ).
fof(f966,definition,
( sQ167_spl
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f968,plain,
( sQ167_spl
| ~ op_strict_implies ),
inference(component_clause,[status(thm)],[f966]) ).
fof(f969,definition,
! [X0,X1] :
( sQ168_spl
<=> strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f970,plain,
! [X0,X1] :
( ~ sQ168_spl
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f969]) ).
fof(f972,plain,
( sQ168_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f336,f966,f969]) ).
fof(f973,definition,
( sQ169_spl
<=> op_strict_equiv ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f975,plain,
( sQ169_spl
| ~ op_strict_equiv ),
inference(component_clause,[status(thm)],[f973]) ).
fof(f976,definition,
! [X0,X1] :
( sQ170_spl
<=> strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f977,plain,
! [X0,X1] :
( ~ sQ170_spl
| strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f976]) ).
fof(f979,plain,
( sQ170_spl
| ~ sQ169_spl ),
inference(split_clause,[status(thm)],[f338,f973,f976]) ).
fof(f980,plain,
( sQ169_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f975,f349]) ).
fof(f981,plain,
sQ169_spl,
inference(contradiction_clause,[status(thm)],[f980]) ).
fof(f982,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f213]) ).
fof(f983,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f984,plain,
( sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f340]) ).
fof(f985,plain,
sQ88_spl,
inference(contradiction_clause,[status(thm)],[f984]) ).
fof(f986,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f227]) ).
fof(f987,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f986]) ).
fof(f988,plain,
( sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f968,f347]) ).
fof(f989,plain,
sQ167_spl,
inference(contradiction_clause,[status(thm)],[f988]) ).
fof(f1006,plain,
( sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f756,f342]) ).
fof(f1007,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f1006]) ).
fof(f1010,plain,
! [X0,X1] :
( ~ sQ168_spl
| ~ sQ110_spl
| is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))) ),
inference(paramodulation,[status(thm)],[f970,f758]) ).
fof(f1011,plain,
! [X0,X1] :
( ~ sQ168_spl
| ~ sQ89_spl
| is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f970,f679]) ).
fof(f1045,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f218]) ).
fof(f1046,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1045]) ).
fof(f1059,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f219]) ).
fof(f1060,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f1059]) ).
fof(f1067,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)],[f355,f374]) ).
fof(f1069,plain,
! [X0] :
( sQ96_spl
| ~ sQ1_spl
| ~ is_a_theorem(implies(X0,sK56_skl))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f355,f707]) ).
fof(f1074,plain,
! [X0,X1] :
( ~ sQ1_spl
| sQ96_spl
| ~ is_a_theorem(implies(X1,implies(X0,sK56_skl)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1069,f355]) ).
fof(f1096,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ138_spl
| ~ is_a_theorem(implies(and(sK78_skl,sK79_skl),sK78_skl)) ),
inference(resolution,[status(thm)],[f862,f1011]) ).
fof(f1098,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ138_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1096,f433]) ).
fof(f1099,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| sQ138_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1098]) ).
fof(f1164,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X1))) ),
inference(paramodulation,[status(thm)],[f977,f857]) ).
fof(f1226,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f226]) ).
fof(f1227,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f1226]) ).
fof(f1525,plain,
! [X0] :
( ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| sQ96_spl
| ~ is_a_theorem(strict_implies(X0,sK56_skl))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1074,f1010]) ).
fof(f1543,plain,
( ~ sQ95_spl
| ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| sQ96_spl
| ~ is_a_theorem(sK57_skl) ),
inference(resolution,[status(thm)],[f1525,f702]) ).
fof(f1546,plain,
( ~ sQ95_spl
| ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| sQ96_spl
| ~ sQ94_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1543,f698]) ).
fof(f1547,plain,
( ~ sQ95_spl
| ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| sQ96_spl
| ~ sQ94_spl ),
inference(contradiction_clause,[status(thm)],[f1546]) ).
fof(f1663,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ137_spl
| ~ sQ93_spl
| is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[status(thm)],[f694,f1164]) ).
fof(f1794,plain,
! [X0] :
( ~ sQ110_spl
| ~ sQ1_spl
| is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[status(thm)],[f355,f758]) ).
fof(f1824,plain,
! [X0,X1] :
( ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f970,f1794]) ).
fof(f1842,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ25_spl
| is_a_theorem(X1)
| ~ is_a_theorem(and(X0,X1)) ),
inference(resolution,[status(thm)],[f444,f355]) ).
fof(f1862,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ1_spl
| ~ sQ25_spl
| is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(paramodulation,[status(thm)],[f977,f1842]) ).
fof(f2030,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ46_spl
| is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f521,f355]) ).
fof(f2056,plain,
( ~ sQ104_spl
| ~ sQ170_spl
| ~ sQ137_spl
| ~ sQ93_spl
| is_a_theorem(strict_implies(sK60_skl,sK61_skl)) ),
inference(resolution,[status(thm)],[f1663,f736]) ).
fof(f2138,plain,
( ~ sQ104_spl
| ~ sQ170_spl
| ~ sQ137_spl
| ~ sQ93_spl
| ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| is_a_theorem(implies(sK60_skl,sK61_skl)) ),
inference(resolution,[status(thm)],[f1824,f2056]) ).
fof(f2174,plain,
( ~ sQ104_spl
| ~ sQ170_spl
| ~ sQ1_spl
| ~ sQ25_spl
| is_a_theorem(strict_implies(sK61_skl,sK60_skl)) ),
inference(resolution,[status(thm)],[f1862,f736]) ).
fof(f2175,plain,
( ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| ~ sQ104_spl
| ~ sQ170_spl
| ~ sQ25_spl
| is_a_theorem(implies(sK61_skl,sK60_skl)) ),
inference(resolution,[status(thm)],[f2174,f1824]) ).
fof(f5021,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ46_spl
| X0 = X1
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f2030,f1067]) ).
fof(f6390,plain,
( ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| ~ sQ104_spl
| ~ sQ170_spl
| ~ sQ25_spl
| ~ sQ6_spl
| ~ sQ46_spl
| sK60_skl = sK61_skl
| ~ is_a_theorem(implies(sK60_skl,sK61_skl)) ),
inference(resolution,[status(thm)],[f5021,f2175]) ).
fof(f6475,definition,
( sQ242_spl
<=> is_a_theorem(implies(sK60_skl,sK61_skl)) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f6477,plain,
( sQ242_spl
| ~ is_a_theorem(implies(sK60_skl,sK61_skl)) ),
inference(component_clause,[status(thm)],[f6475]) ).
fof(f6478,plain,
( ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| ~ sQ104_spl
| ~ sQ170_spl
| ~ sQ25_spl
| ~ sQ6_spl
| ~ sQ46_spl
| sQ105_spl
| ~ sQ242_spl ),
inference(split_clause,[status(thm)],[f6390,f6475,f739,f520,f373,f443,f976,f735,f354,f757,f969]) ).
fof(f6507,plain,
( sQ242_spl
| ~ sQ104_spl
| ~ sQ170_spl
| ~ sQ137_spl
| ~ sQ93_spl
| ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6477,f2138]) ).
fof(f6508,plain,
( sQ242_spl
| ~ sQ104_spl
| ~ sQ170_spl
| ~ sQ137_spl
| ~ sQ93_spl
| ~ sQ168_spl
| ~ sQ110_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f6507]) ).
fof(f6511,plain,
( ~ sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f729,f350]) ).
fof(f6512,plain,
~ sQ102_spl,
inference(contradiction_clause,[status(thm)],[f6511]) ).
fof(f6513,plain,
$false,
inference(sat_refutation,[status(thm)],[f357,f376,f435,f446,f523,f681,f696,f700,f704,f708,f738,f742,f760,f859,f863,f972,f979,f981,f983,f985,f987,f989,f1007,f1046,f1060,f1099,f1227,f1547,f6478,f6508,f6512]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL526+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n026.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Mon Sep 21 00:39:56 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.40 % Drodi V4.1.1
% 0.14/5.77 % Refutation found
% 0.14/5.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.82 % Elapsed time: 0.419490 seconds
% 0.14/5.82 % CPU time: 3.111471 seconds
% 0.14/5.82 % Total memory used: 140.518 MB
% 0.14/5.82 % Net memory used: 137.672 MB
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