%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL535+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 : n003.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 0.37s 0.92s
% Output : CNFRefutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 67
% Syntax : Number of formulae : 247 ( 50 unt; 35 def)
% Number of atoms : 669 ( 44 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 740 ( 318 ~; 331 |; 34 &)
% ( 49 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 54 ( 52 usr; 52 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 18 con; 0-2 aty)
% Number of variables : 221 ( 201 !; 20 ?)
% 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(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(f31,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
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(f34,axiom,
op_equiv,
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(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(f55,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),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(f71,axiom,
( axiom_m9
<=> ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),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(f75,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
op_possibly,
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(f81,axiom,
axiom_5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f88,conjecture,
axiom_m9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f89,negated_conjecture,
~ axiom_m9,
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(f104,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(f105,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)],[f104]) ).
fof(f106,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f112,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(f113,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)],[f112]) ).
fof(f114,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(thm)],[f113]) ).
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(f128,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(f129,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)],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f132,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(f133,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)],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f200,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f201,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f200]) ).
fof(f204,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f205,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f208,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f209,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(thm)],[f208]) ).
fof(f210,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f211,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f212,plain,
op_equiv,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f213,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f214,plain,
modus_tollens,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f216,plain,
implies_2,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f219,plain,
and_2,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f220,plain,
and_3,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f221,plain,
or_1,
inference(cnf_transformation,[status(thm)],[f43]) ).
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(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(f271,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(f272,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)],[f271]) ).
fof(f273,plain,
! [X0] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[status(thm)],[f272]) ).
fof(f323,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| axiom_m9 )
& ( ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| ~ axiom_m9 ) ),
inference(NNF_transformation,[status(thm)],[f71]) ).
fof(f324,plain,
( ( ~ is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl)))
| axiom_m9 )
& ( ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| ~ axiom_m9 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92_skl]),skolemize(X,sK92_skl)],[f323]) ).
fof(f326,plain,
( ~ is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl)))
| axiom_m9 ),
inference(cnf_transformation,[status(thm)],[f324]) ).
fof(f331,plain,
( ! [X] : possibly(X) = not(necessarily(not(X)))
| ~ op_possibly ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f332,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[status(thm)],[f331]) ).
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(f339,plain,
op_possibly,
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f340,plain,
necessitation,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f342,plain,
axiom_M,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f343,plain,
axiom_5,
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f347,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f350,plain,
~ axiom_m9,
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(f385,definition,
( sQ9_spl
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f387,plain,
( sQ9_spl
| ~ modus_tollens ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,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(f389,plain,
! [X0,X1] :
( ~ sQ10_spl
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f106,f385,f388]) ).
fof(f407,definition,
( sQ15_spl
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( sQ15_spl
| ~ implies_2 ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f410,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(f411,plain,
! [X0,X1] :
( ~ sQ16_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f114,f407,f410]) ).
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(f451,definition,
( sQ27_spl
<=> and_3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( sQ27_spl
| ~ and_3 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,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(f455,plain,
! [X0,X1] :
( ~ sQ28_spl
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f130,f451,f454]) ).
fof(f462,definition,
( sQ30_spl
<=> or_1 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ30_spl
| ~ or_1 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,definition,
! [X0,X1] :
( sQ31_spl
<=> is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f466,plain,
! [X0,X1] :
( ~ sQ31_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f134,f462,f465]) ).
fof(f531,definition,
! [X0] :
( sQ49_spl
<=> is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f532,plain,
! [X0] :
( ~ sQ49_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f640,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f640]) ).
fof(f643,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(f644,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f201,f640,f643]) ).
fof(f654,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f656,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f657,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f658,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f660,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f205,f654,f657]) ).
fof(f668,definition,
( sQ86_spl
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f670,plain,
( sQ86_spl
| ~ op_equiv ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f671,definition,
! [X0,X1] :
( sQ87_spl
<=> equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f672,plain,
! [X0,X1] :
( ~ sQ87_spl
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f674,plain,
( sQ87_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f209,f668,f671]) ).
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(f712,definition,
! [X0,X1] :
( sQ98_spl
<=> ( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f713,plain,
! [X0,X1] :
( ~ sQ98_spl
| is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f712]) ).
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(f787,definition,
( sQ118_spl
<=> axiom_5 ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f789,plain,
( sQ118_spl
| ~ axiom_5 ),
inference(component_clause,[status(thm)],[f787]) ).
fof(f790,definition,
! [X0] :
( sQ119_spl
<=> is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f791,plain,
! [X0] :
( ~ sQ119_spl
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(component_clause,[status(thm)],[f790]) ).
fof(f793,plain,
( sQ119_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f273,f787,f790]) ).
fof(f930,definition,
( sQ157_spl
<=> axiom_m9 ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f931,plain,
( ~ sQ157_spl
| axiom_m9 ),
inference(component_clause,[status(thm)],[f930]) ).
fof(f933,definition,
! [X0] :
( sQ158_spl
<=> is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f934,plain,
! [X0] :
( ~ sQ158_spl
| is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f937,definition,
( sQ159_spl
<=> is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl))) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f939,plain,
( sQ159_spl
| ~ is_a_theorem(strict_implies(possibly(possibly(sK92_skl)),possibly(sK92_skl))) ),
inference(component_clause,[status(thm)],[f937]) ).
fof(f940,plain,
( ~ sQ159_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f326,f930,f937]) ).
fof(f952,definition,
( sQ163_spl
<=> op_possibly ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f954,plain,
( sQ163_spl
| ~ op_possibly ),
inference(component_clause,[status(thm)],[f952]) ).
fof(f955,definition,
! [X0] :
( sQ164_spl
<=> possibly(X0) = not(necessarily(not(X0))) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f956,plain,
! [X0] :
( ~ sQ164_spl
| possibly(X0) = not(necessarily(not(X0))) ),
inference(component_clause,[status(thm)],[f955]) ).
fof(f958,plain,
( sQ164_spl
| ~ sQ163_spl ),
inference(split_clause,[status(thm)],[f332,f952,f955]) ).
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(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(f990,plain,
( sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f954,f339]) ).
fof(f991,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f990]) ).
fof(f992,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f670,f212]) ).
fof(f993,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f992]) ).
fof(f994,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f656,f211]) ).
fof(f995,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f994]) ).
fof(f998,plain,
( sQ159_spl
| ~ sQ158_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f939,f934]) ).
fof(f999,plain,
( sQ159_spl
| ~ sQ158_spl ),
inference(contradiction_clause,[status(thm)],[f998]) ).
fof(f1000,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f642,f210]) ).
fof(f1001,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f1000]) ).
fof(f1016,plain,
( sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f756,f342]) ).
fof(f1017,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f1016]) ).
fof(f1023,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(f1024,plain,
! [X0] :
( ~ sQ164_spl
| possibly(necessarily(not(X0))) = not(necessarily(possibly(X0))) ),
inference(paramodulation,[status(thm)],[f956,f956]) ).
fof(f1055,plain,
( sQ118_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f789,f343]) ).
fof(f1056,plain,
sQ118_spl,
inference(contradiction_clause,[status(thm)],[f1055]) ).
fof(f1080,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f221]) ).
fof(f1081,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1080]) ).
fof(f1084,plain,
( sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f219]) ).
fof(f1085,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f1084]) ).
fof(f1107,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ sQ1_spl
| is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f355,f455]) ).
fof(f1162,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f453,f220]) ).
fof(f1163,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1162]) ).
fof(f1168,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f411,f355]) ).
fof(f1170,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f216]) ).
fof(f1171,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1170]) ).
fof(f1177,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ10_spl
| is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(not(X0),not(X1))) ),
inference(resolution,[status(thm)],[f389,f355]) ).
fof(f1183,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f214]) ).
fof(f1184,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1183]) ).
fof(f1205,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f658,f644]) ).
fof(f1369,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ98_spl
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f672,f713]) ).
fof(f1657,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ31_spl
| is_a_theorem(or(X0,or(not(X0),X1))) ),
inference(paramodulation,[status(thm)],[f1205,f466]) ).
fof(f1778,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ28_spl
| is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1107,f355]) ).
fof(f1782,plain,
( ~ sQ1_spl
| ~ sQ28_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1778,f712,f454,f354]) ).
fof(f2011,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(resolution,[status(thm)],[f1168,f455]) ).
fof(f2019,plain,
( ~ sQ28_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f2011,f531,f410,f354,f454]) ).
fof(f2056,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(forward_demodulation,[status(thm)],[f1205,f1177]) ).
fof(f3027,plain,
! [X0] :
( ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0)))
| ~ is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0))) ),
inference(resolution,[status(thm)],[f1369,f791]) ).
fof(f3028,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| is_a_theorem(equiv(and(X0,X0),X0))
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f1369,f532]) ).
fof(f3063,plain,
! [X0] :
( ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3027,f758]) ).
fof(f3064,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ25_spl
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3028,f444]) ).
fof(f3127,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ25_spl
| and(X0,X0) = X0 ),
inference(resolution,[status(thm)],[f3064,f374]) ).
fof(f3147,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ25_spl
| ~ sQ83_spl
| implies(not(X0),X0) = not(not(X0)) ),
inference(paramodulation,[status(thm)],[f3127,f658]) ).
fof(f3166,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(X0,X0) = not(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f1205,f3147]) ).
fof(f3319,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ31_spl
| is_a_theorem(or(X0,not(not(not(X0))))) ),
inference(paramodulation,[status(thm)],[f3166,f1657]) ).
fof(f3962,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| necessarily(possibly(X0)) = possibly(X0) ),
inference(resolution,[status(thm)],[f3063,f374]) ).
fof(f3974,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| possibly(necessarily(not(X0))) = not(possibly(X0)) ),
inference(backward_demodulation,[status(thm)],[f3962,f1024]) ).
fof(f4040,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| possibly(necessarily(possibly(X0))) = not(possibly(necessarily(not(X0)))) ),
inference(paramodulation,[status(thm)],[f956,f3974]) ).
fof(f4052,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| possibly(possibly(X0)) = not(possibly(necessarily(not(X0)))) ),
inference(forward_demodulation,[status(thm)],[f3962,f4040]) ).
fof(f4053,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| possibly(possibly(X0)) = not(not(possibly(X0))) ),
inference(forward_demodulation,[status(thm)],[f3974,f4052]) ).
fof(f4195,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| ~ sQ49_spl
| ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ31_spl
| is_a_theorem(or(possibly(X0),not(possibly(possibly(X0))))) ),
inference(paramodulation,[status(thm)],[f4053,f3319]) ).
fof(f5115,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| ~ sQ49_spl
| ~ sQ25_spl
| ~ sQ31_spl
| is_a_theorem(implies(possibly(possibly(X0)),possibly(X0))) ),
inference(resolution,[status(thm)],[f4195,f2056]) ).
fof(f5138,plain,
! [X0] :
( ~ sQ168_spl
| ~ sQ89_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| ~ sQ49_spl
| ~ sQ25_spl
| ~ sQ31_spl
| is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(resolution,[status(thm)],[f5115,f1023]) ).
fof(f5147,plain,
( ~ sQ168_spl
| ~ sQ89_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| ~ sQ49_spl
| ~ sQ25_spl
| ~ sQ31_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f5138,f933,f465,f443,f531,f757,f712,f671,f790,f373,f955,f657,f643,f388,f354,f678,f969]) ).
fof(f5162,plain,
( ~ sQ157_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f931,f350]) ).
fof(f5163,plain,
~ sQ157_spl,
inference(contradiction_clause,[status(thm)],[f5162]) ).
fof(f5164,plain,
$false,
inference(sat_refutation,[status(thm)],[f357,f376,f391,f413,f446,f457,f468,f646,f660,f674,f681,f760,f793,f940,f958,f972,f983,f985,f987,f989,f991,f993,f995,f999,f1001,f1017,f1056,f1081,f1085,f1163,f1171,f1184,f1782,f2019,f5147,f5163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL535+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 00:39:01 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.37/0.92 % Refutation found
% 0.37/0.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.37/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.37/0.97 % Elapsed time: 0.518094 seconds
% 0.37/0.97 % CPU time: 3.607077 seconds
% 0.37/0.97 % Total memory used: 137.463 MB
% 0.37/0.97 % Net memory used: 134.558 MB
%------------------------------------------------------------------------------