%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL558+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 01:07:59 PM UTC 2026
% Result : Theorem 93.38s 12.44s
% Output : CNFRefutation 7.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 57
% Syntax : Number of formulae : 273 ( 41 unt; 31 def)
% Number of atoms : 1218 ( 76 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 1799 ( 854 ~; 862 |; 33 &)
% ( 43 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 47 ( 45 usr; 45 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 19 con; 0-2 aty)
% Number of variables : 343 ( 322 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(Y)
& is_a_theorem(X) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
( substitution_strict_equiv
<=> ! [X,Y] :
( is_a_theorem(strict_equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
( axiom_m1
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
( axiom_m3
<=> ! [X,Y,Z] : is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
( axiom_m5
<=> ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
( op_strict_equiv
=> ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,axiom,
axiom_m3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,conjecture,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f121,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(f122,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)],[f121]) ).
fof(f124,plain,
( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f189,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f190,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f193,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f194,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f205,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)],[f33]) ).
fof(f206,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)],[f205]) ).
fof(f207,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)],[f206]) ).
fof(f208,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)],[f207]) ).
fof(f209,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)],[f208]) ).
fof(f213,plain,
( adjunction
<=> ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f214,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(Y)
& is_a_theorem(X) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(NNF_transformation,[status(thm)],[f213]) ).
fof(f215,plain,
( ( ( ~ is_a_theorem(and(sK58_skl,sK59_skl))
& is_a_theorem(sK59_skl)
& is_a_theorem(sK58_skl) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58_skl,sK59_skl]),skolemize(X,sK58_skl),skolemize(Y,sK59_skl)],[f214]) ).
fof(f216,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ adjunction ),
inference(cnf_transformation,[status(thm)],[f215]) ).
fof(f220,plain,
( substitution_strict_equiv
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f35]) ).
fof(f221,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)],[f220]) ).
fof(f222,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)],[f221]) ).
fof(f223,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f222]) ).
fof(f262,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| axiom_m1 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| ~ axiom_m1 ) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f263,plain,
( ( ~ is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl)))
| axiom_m1 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| ~ axiom_m1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76_skl,sK77_skl]),skolemize(X,sK76_skl),skolemize(Y,sK77_skl)],[f262]) ).
fof(f264,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[status(thm)],[f263]) ).
fof(f266,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)],[f46]) ).
fof(f267,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)],[f266]) ).
fof(f268,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[status(thm)],[f267]) ).
fof(f270,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))
| axiom_m3 )
& ( ! [X,Y,Z] : is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))
| ~ axiom_m3 ) ),
inference(NNF_transformation,[status(thm)],[f47]) ).
fof(f271,plain,
( ( ~ is_a_theorem(strict_implies(and(and(sK80_skl,sK81_skl),sK82_skl),and(sK80_skl,and(sK81_skl,sK82_skl))))
| axiom_m3 )
& ( ! [X,Y,Z] : is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))
| ~ axiom_m3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80_skl,sK81_skl,sK82_skl]),skolemize(X,sK80_skl),skolemize(Y,sK81_skl),skolemize(Z,sK82_skl)],[f270]) ).
fof(f272,plain,
! [X0,X1,X2] :
( is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))
| ~ axiom_m3 ),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f274,plain,
( ( ? [X] : ~ is_a_theorem(strict_implies(X,and(X,X)))
| axiom_m4 )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(NNF_transformation,[status(thm)],[f48]) ).
fof(f275,plain,
( ( ~ is_a_theorem(strict_implies(sK83_skl,and(sK83_skl,sK83_skl)))
| axiom_m4 )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83_skl]),skolemize(X,sK83_skl)],[f274]) ).
fof(f276,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f278,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))
| axiom_m5 )
& ( ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))
| ~ axiom_m5 ) ),
inference(NNF_transformation,[status(thm)],[f49]) ).
fof(f279,plain,
( ( ~ is_a_theorem(strict_implies(and(strict_implies(sK84_skl,sK85_skl),strict_implies(sK85_skl,sK86_skl)),strict_implies(sK84_skl,sK86_skl)))
| axiom_m5 )
& ( ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))
| ~ axiom_m5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84_skl,sK85_skl,sK86_skl]),skolemize(X,sK84_skl),skolemize(Y,sK85_skl),skolemize(Z,sK86_skl)],[f278]) ).
fof(f280,plain,
! [X0,X1,X2] :
( is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(cnf_transformation,[status(thm)],[f279]) ).
fof(f306,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f307,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f308,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)],[f58]) ).
fof(f309,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f311,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f313,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f315,plain,
op_strict_equiv,
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f316,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f317,plain,
substitution_strict_equiv,
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f318,plain,
adjunction,
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f319,plain,
axiom_m1,
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f320,plain,
axiom_m2,
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f321,plain,
axiom_m3,
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f322,plain,
axiom_m4,
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f323,plain,
axiom_m5,
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f325,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f328,plain,
~ or_1,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f410,definition,
! [X0,X1] :
( sQ22_spl
<=> is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f411,plain,
! [X0,X1] :
( ~ sQ22_spl
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f440,definition,
( sQ30_spl
<=> or_1 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ30_spl
| or_1 ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
! [X0,X1] :
( sQ31_spl
<=> is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f444,plain,
! [X0,X1] :
( ~ sQ31_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f447,definition,
( sQ32_spl
<=> is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( sQ32_spl
| ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( ~ sQ32_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f124,f440,f447]) ).
fof(f454,definition,
! [X0,X1] :
( sQ34_spl
<=> is_a_theorem(implies(X0,or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f455,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f618,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f620,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f618]) ).
fof(f621,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(f622,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f190,f618,f621]) ).
fof(f632,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f632]) ).
fof(f635,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f636,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f638,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f194,f632,f635]) ).
fof(f668,definition,
( sQ92_spl
<=> modus_ponens_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f670,plain,
( sQ92_spl
| ~ modus_ponens_strict_implies ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f671,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(f672,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)],[f671]) ).
fof(f674,plain,
( sQ93_spl
| ~ sQ92_spl ),
inference(split_clause,[status(thm)],[f209,f668,f671]) ).
fof(f687,definition,
( sQ97_spl
<=> adjunction ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( sQ97_spl
| ~ adjunction ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,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(f691,plain,
! [X0,X1] :
( ~ sQ98_spl
| is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f690]) ).
fof(f693,plain,
( sQ98_spl
| ~ sQ97_spl ),
inference(split_clause,[status(thm)],[f216,f687,f690]) ).
fof(f706,definition,
( sQ102_spl
<=> substitution_strict_equiv ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( sQ102_spl
| ~ substitution_strict_equiv ),
inference(component_clause,[status(thm)],[f706]) ).
fof(f709,definition,
! [X0,X1] :
( sQ103_spl
<=> ( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f710,plain,
! [X0,X1] :
( ~ sQ103_spl
| X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f712,plain,
( sQ103_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f223,f706,f709]) ).
fof(f820,definition,
( sQ133_spl
<=> axiom_m1 ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f822,plain,
( sQ133_spl
| ~ axiom_m1 ),
inference(component_clause,[status(thm)],[f820]) ).
fof(f823,definition,
! [X0,X1] :
( sQ134_spl
<=> is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f824,plain,
! [X0,X1] :
( ~ sQ134_spl
| is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(component_clause,[status(thm)],[f823]) ).
fof(f826,plain,
( sQ134_spl
| ~ sQ133_spl ),
inference(split_clause,[status(thm)],[f264,f820,f823]) ).
fof(f831,definition,
( sQ136_spl
<=> axiom_m2 ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f833,plain,
( sQ136_spl
| ~ axiom_m2 ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f834,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(f835,plain,
! [X0,X1] :
( ~ sQ137_spl
| is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f834]) ).
fof(f837,plain,
( sQ137_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f268,f831,f834]) ).
fof(f842,definition,
( sQ139_spl
<=> axiom_m3 ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f844,plain,
( sQ139_spl
| ~ axiom_m3 ),
inference(component_clause,[status(thm)],[f842]) ).
fof(f845,definition,
! [X0,X1,X2] :
( sQ140_spl
<=> is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f846,plain,
! [X0,X1,X2] :
( ~ sQ140_spl
| is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
inference(component_clause,[status(thm)],[f845]) ).
fof(f848,plain,
( sQ140_spl
| ~ sQ139_spl ),
inference(split_clause,[status(thm)],[f272,f842,f845]) ).
fof(f853,definition,
( sQ142_spl
<=> axiom_m4 ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f855,plain,
( sQ142_spl
| ~ axiom_m4 ),
inference(component_clause,[status(thm)],[f853]) ).
fof(f856,definition,
! [X0] :
( sQ143_spl
<=> is_a_theorem(strict_implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f857,plain,
! [X0] :
( ~ sQ143_spl
| is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f856]) ).
fof(f859,plain,
( sQ143_spl
| ~ sQ142_spl ),
inference(split_clause,[status(thm)],[f276,f853,f856]) ).
fof(f864,definition,
( sQ145_spl
<=> axiom_m5 ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f866,plain,
( sQ145_spl
| ~ axiom_m5 ),
inference(component_clause,[status(thm)],[f864]) ).
fof(f867,definition,
! [X0,X1,X2] :
( sQ146_spl
<=> is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f868,plain,
! [X0,X1,X2] :
( ~ sQ146_spl
| is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
inference(component_clause,[status(thm)],[f867]) ).
fof(f870,plain,
( sQ146_spl
| ~ sQ145_spl ),
inference(split_clause,[status(thm)],[f280,f864,f867]) ).
fof(f944,definition,
( sQ167_spl
<=> op_strict_implies ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f946,plain,
( sQ167_spl
| ~ op_strict_implies ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f947,definition,
! [X0,X1] :
( sQ168_spl
<=> strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f948,plain,
! [X0,X1] :
( ~ sQ168_spl
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(component_clause,[status(thm)],[f947]) ).
fof(f950,plain,
( sQ168_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f307,f944,f947]) ).
fof(f951,definition,
( sQ169_spl
<=> op_strict_equiv ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f953,plain,
( sQ169_spl
| ~ op_strict_equiv ),
inference(component_clause,[status(thm)],[f951]) ).
fof(f954,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(f955,plain,
! [X0,X1] :
( ~ sQ170_spl
| strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f954]) ).
fof(f957,plain,
( sQ170_spl
| ~ sQ169_spl ),
inference(split_clause,[status(thm)],[f309,f951,f954]) ).
fof(f958,plain,
( sQ169_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f953,f315]) ).
fof(f959,plain,
sQ169_spl,
inference(contradiction_clause,[status(thm)],[f958]) ).
fof(f960,plain,
( sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f318]) ).
fof(f961,plain,
sQ97_spl,
inference(contradiction_clause,[status(thm)],[f960]) ).
fof(f962,plain,
( sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f670,f316]) ).
fof(f963,plain,
sQ92_spl,
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f964,plain,
( sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f708,f317]) ).
fof(f965,plain,
sQ102_spl,
inference(contradiction_clause,[status(thm)],[f964]) ).
fof(f968,plain,
( sQ167_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f946,f313]) ).
fof(f969,plain,
sQ167_spl,
inference(contradiction_clause,[status(thm)],[f968]) ).
fof(f974,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f634,f325]) ).
fof(f975,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f974]) ).
fof(f976,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f620,f311]) ).
fof(f977,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f976]) ).
fof(f998,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_implies(X0,X0))) ),
inference(paramodulation,[status(thm)],[f955,f868]) ).
fof(f1000,plain,
( sQ145_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f866,f323]) ).
fof(f1001,plain,
sQ145_spl,
inference(contradiction_clause,[status(thm)],[f1000]) ).
fof(f1004,plain,
( sQ142_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f855,f322]) ).
fof(f1005,plain,
sQ142_spl,
inference(contradiction_clause,[status(thm)],[f1004]) ).
fof(f1011,plain,
( sQ136_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f833,f320]) ).
fof(f1012,plain,
sQ136_spl,
inference(contradiction_clause,[status(thm)],[f1011]) ).
fof(f1014,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ134_spl
| is_a_theorem(strict_implies(strict_equiv(X0,X1),and(strict_implies(X1,X0),strict_implies(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f955,f824]) ).
fof(f1016,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ134_spl
| is_a_theorem(strict_implies(strict_equiv(X0,X1),strict_equiv(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f955,f1014]) ).
fof(f1039,plain,
( sQ32_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f449,f444]) ).
fof(f1040,plain,
( sQ32_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1039]) ).
fof(f1045,plain,
( sQ139_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f844,f321]) ).
fof(f1046,plain,
sQ139_spl,
inference(contradiction_clause,[status(thm)],[f1045]) ).
fof(f1049,plain,
( sQ133_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f822,f319]) ).
fof(f1050,plain,
sQ133_spl,
inference(contradiction_clause,[status(thm)],[f1049]) ).
fof(f1086,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ98_spl
| is_a_theorem(strict_equiv(X0,X1))
| ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f955,f691]) ).
fof(f1098,definition,
! [X1] :
( sQ172_spl
<=> ~ is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1099,plain,
! [X0] :
( ~ sQ172_spl
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f1098]) ).
fof(f1110,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ170_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,X0))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[status(thm)],[f998,f672]) ).
fof(f1124,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ170_spl
| ~ sQ134_spl
| is_a_theorem(strict_equiv(X1,X0))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[status(thm)],[f1016,f672]) ).
fof(f1152,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ170_spl
| ~ sQ146_spl
| ~ sQ134_spl
| is_a_theorem(strict_implies(X1,X1))
| ~ is_a_theorem(strict_equiv(X0,X1)) ),
inference(resolution,[status(thm)],[f1124,f1110]) ).
fof(f1180,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f636,f622]) ).
fof(f1181,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f636,f1180]) ).
fof(f1187,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(not(X0),X1) = necessarily(or(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1180,f948]) ).
fof(f1207,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,X2))
| ~ is_a_theorem(and(strict_implies(X0,X1),strict_implies(X1,X2))) ),
inference(resolution,[status(thm)],[f868,f672]) ).
fof(f1272,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0)))
| ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(resolution,[status(thm)],[f1086,f824]) ).
fof(f1274,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| is_a_theorem(strict_equiv(and(X0,X0),X0))
| ~ is_a_theorem(strict_implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f1086,f857]) ).
fof(f1279,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| X0 = X1
| ~ is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1086,f710]) ).
fof(f1284,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| is_a_theorem(strict_equiv(and(X0,X1),and(X1,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1272,f824]) ).
fof(f1285,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| is_a_theorem(strict_equiv(and(X0,X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1274,f835]) ).
fof(f1286,plain,
! [X0] :
( ~ sQ93_spl
| ~ sQ170_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ143_spl
| ~ sQ98_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(X0,X0)) ),
inference(resolution,[status(thm)],[f1285,f1152]) ).
fof(f1290,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| and(X0,X0) = X0 ),
inference(resolution,[status(thm)],[f1285,f710]) ).
fof(f1305,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(not(X0),X1) = implies(implies(not(X0),X0),X1) ),
inference(paramodulation,[status(thm)],[f1290,f1181]) ).
fof(f1307,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| implies(not(X0),X0) = not(not(X0)) ),
inference(paramodulation,[status(thm)],[f1290,f636]) ).
fof(f1309,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ140_spl
| is_a_theorem(strict_implies(and(X0,X1),and(X0,and(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f1290,f846]) ).
fof(f1317,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(not(X0),X1) = implies(or(X0,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f1180,f1305]) ).
fof(f1318,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(X0,X0) = not(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f1180,f1307]) ).
fof(f1376,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| implies(X0,not(X1)) = not(and(X0,or(X1,X1))) ),
inference(paramodulation,[status(thm)],[f1318,f636]) ).
fof(f1481,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| and(X0,X1) = and(X1,X0) ),
inference(resolution,[status(thm)],[f1284,f710]) ).
fof(f1518,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| implies(X0,X1) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1481,f636]) ).
fof(f1529,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(and(X0,X1),X1)) ),
inference(paramodulation,[status(thm)],[f1481,f835]) ).
fof(f1721,plain,
! [X0,X1,X2] :
( ~ sQ98_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(strict_implies(X0,X2))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1207,f691]) ).
fof(f1738,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| implies(not(X0),X1) = implies(not(X1),X0) ),
inference(paramodulation,[status(thm)],[f636,f1518]) ).
fof(f1742,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| implies(X0,not(X1)) = not(and(or(X1,X1),X0)) ),
inference(paramodulation,[status(thm)],[f1318,f1518]) ).
fof(f1765,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| or(X0,X1) = implies(not(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f1180,f1738]) ).
fof(f1766,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| or(X0,X1) = or(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f1180,f1765]) ).
fof(f1795,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| strict_implies(not(X0),X1) = necessarily(or(X1,X0)) ),
inference(paramodulation,[status(thm)],[f1766,f1187]) ).
fof(f1806,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| strict_implies(not(X0),X1) = strict_implies(not(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f1187,f1795]) ).
fof(f1810,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| strict_implies(or(X0,X0),X1) = strict_implies(not(X1),not(X0)) ),
inference(paramodulation,[status(thm)],[f1318,f1806]) ).
fof(f1833,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(not(not(X0)),X0)) ),
inference(paramodulation,[status(thm)],[f1806,f1286]) ).
fof(f1866,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(or(X0,X0),X0)) ),
inference(paramodulation,[status(thm)],[f1318,f1833]) ).
fof(f1867,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(not(or(X0,X0)),not(X0))) ),
inference(paramodulation,[status(thm)],[f1318,f1833]) ).
fof(f1901,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| strict_implies(or(X0,X0),X1) = necessarily(or(not(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1317,f948]) ).
fof(f1904,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| strict_implies(or(X0,X0),X1) = strict_implies(not(not(X0)),X1) ),
inference(forward_demodulation,[status(thm)],[f1187,f1901]) ).
fof(f1994,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| X0 = or(X0,X0)
| ~ is_a_theorem(strict_implies(X0,or(X0,X0))) ),
inference(resolution,[status(thm)],[f1279,f1866]) ).
fof(f2011,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| X0 = and(X1,X0)
| ~ is_a_theorem(strict_implies(X0,and(X1,X0))) ),
inference(resolution,[status(thm)],[f1279,f1529]) ).
fof(f2012,plain,
! [X0,X1] :
( ~ sQ137_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| X0 = and(X0,X1)
| ~ is_a_theorem(strict_implies(X0,and(X0,X1))) ),
inference(resolution,[status(thm)],[f1279,f835]) ).
fof(f2591,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| X0 = and(X0,X1)
| ~ is_a_theorem(strict_implies(X0,and(X1,X0))) ),
inference(paramodulation,[status(thm)],[f1481,f2012]) ).
fof(f2951,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| and(X0,X1) = and(and(X0,X1),X0) ),
inference(resolution,[status(thm)],[f1309,f2591]) ).
fof(f2952,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| and(X0,X1) = and(X0,and(X0,X1)) ),
inference(resolution,[status(thm)],[f1309,f2011]) ).
fof(f3016,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| implies(and(not(X0),X1),X0) = not(and(not(X0),X1)) ),
inference(paramodulation,[status(thm)],[f2951,f636]) ).
fof(f3050,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| implies(and(not(X0),X1),X0) = implies(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f1518,f3016]) ).
fof(f3068,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| and(X0,X1) = and(X0,and(X1,X0)) ),
inference(paramodulation,[status(thm)],[f1481,f2952]) ).
fof(f4144,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(and(not(X0),X1),X0) = necessarily(implies(X1,X0)) ),
inference(paramodulation,[status(thm)],[f3050,f948]) ).
fof(f4161,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(and(not(X0),X1),X0) = strict_implies(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f948,f4144]) ).
fof(f4162,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(and(not(X0),X1),X0) = strict_implies(and(X1,not(X0)),X0) ),
inference(paramodulation,[status(thm)],[f3068,f4161]) ).
fof(f4213,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(X0,X1) = strict_implies(and(X0,not(X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f4161,f4162]) ).
fof(f7026,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(or(X0,X0),not(not(X0)))) ),
inference(paramodulation,[status(thm)],[f1810,f1833]) ).
fof(f7214,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| is_a_theorem(strict_implies(not(not(X0)),or(X0,X0))) ),
inference(paramodulation,[status(thm)],[f1904,f1286]) ).
fof(f7309,plain,
! [X0] :
( ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| is_a_theorem(strict_equiv(or(X0,X0),not(not(X0))))
| ~ is_a_theorem(strict_implies(or(X0,X0),not(not(X0)))) ),
inference(resolution,[status(thm)],[f7214,f1086]) ).
fof(f7340,plain,
! [X0] :
( ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| is_a_theorem(strict_equiv(or(X0,X0),not(not(X0)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f7309,f7026]) ).
fof(f7921,plain,
! [X0,X1,X2] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ is_a_theorem(strict_implies(X1,X2))
| is_a_theorem(strict_implies(and(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f1721,f1529]) ).
fof(f7926,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ is_a_theorem(strict_implies(X0,or(X1,X1)))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1721,f1866]) ).
fof(f8156,plain,
( ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ172_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f7340,f1099]) ).
fof(f8197,plain,
( ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ172_spl ),
inference(contradiction_clause,[status(thm)],[f8156]) ).
fof(f12994,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ is_a_theorem(strict_implies(not(X1),X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f4213,f7921]) ).
fof(f13086,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(not(not(or(X0,X0))),X0)) ),
inference(resolution,[status(thm)],[f7926,f1833]) ).
fof(f13333,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(not(X0),not(or(X0,X0)))) ),
inference(paramodulation,[status(thm)],[f1806,f13086]) ).
fof(f13483,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| not(or(X0,X0)) = not(X0)
| ~ is_a_theorem(strict_implies(not(or(X0,X0)),not(X0))) ),
inference(resolution,[status(thm)],[f13333,f1279]) ).
fof(f13516,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| not(or(X0,X0)) = not(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f13483,f1867]) ).
fof(f13631,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| implies(X0,or(X1,X1)) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f13516,f1518]) ).
fof(f13695,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| implies(X0,or(X1,X1)) = implies(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f1518,f13631]) ).
fof(f13756,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| strict_implies(X0,or(X1,X1)) = necessarily(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f13695,f948]) ).
fof(f13807,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ143_spl
| ~ sQ137_spl
| strict_implies(X0,or(X1,X1)) = strict_implies(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f948,f13756]) ).
fof(f15119,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| X0 = or(X0,X0)
| ~ is_a_theorem(strict_implies(X0,X0)) ),
inference(backward_demodulation,[status(thm)],[f13807,f1994]) ).
fof(f15209,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| X0 = or(X0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f15119,f1286]) ).
fof(f15289,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| implies(X0,not(X1)) = not(and(X1,X0)) ),
inference(backward_demodulation,[status(thm)],[f15209,f1742]) ).
fof(f15290,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| implies(X0,not(X1)) = not(and(X0,X1)) ),
inference(backward_demodulation,[status(thm)],[f15209,f1376]) ).
fof(f15292,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| X0 = not(not(X0)) ),
inference(backward_demodulation,[status(thm)],[f15209,f1318]) ).
fof(f15332,plain,
! [X0] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| strict_implies(not(X0),X0) = necessarily(X0) ),
inference(paramodulation,[status(thm)],[f15209,f1187]) ).
fof(f15536,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ79_spl
| ~ is_a_theorem(necessarily(X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(backward_demodulation,[status(thm)],[f15332,f12994]) ).
fof(f16106,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ146_spl
| ~ sQ79_spl
| is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(necessarily(X0)) ),
inference(resolution,[status(thm)],[f15536,f672]) ).
fof(f16112,definition,
! [X0] :
( sQ183_spl
<=> ( is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f16113,plain,
! [X0] :
( ~ sQ183_spl
| is_a_theorem(X0)
| ~ is_a_theorem(necessarily(X0)) ),
inference(component_clause,[status(thm)],[f16112]) ).
fof(f16115,plain,
( ~ sQ93_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ146_spl
| ~ sQ79_spl
| sQ172_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f16106,f16112,f1098,f621,f867,f947,f635,f845,f856,f834,f690,f954,f823,f709,f671]) ).
fof(f16118,plain,
! [X0,X1] :
( ~ sQ168_spl
| ~ sQ183_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f948,f16113]) ).
fof(f16678,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| implies(X0,not(X1)) = implies(X1,not(X0)) ),
inference(forward_demodulation,[status(thm)],[f15289,f15290]) ).
fof(f19604,plain,
! [X0,X1] :
( ~ sQ137_spl
| ~ sQ168_spl
| ~ sQ183_spl
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f16118,f835]) ).
fof(f19618,plain,
( ~ sQ137_spl
| ~ sQ168_spl
| ~ sQ183_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f19604,f410,f16112,f947,f834]) ).
fof(f19635,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ22_spl
| is_a_theorem(implies(X0,not(and(not(X0),X1)))) ),
inference(paramodulation,[status(thm)],[f16678,f411]) ).
fof(f19674,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ22_spl
| is_a_theorem(implies(X0,implies(X1,not(not(X0))))) ),
inference(forward_demodulation,[status(thm)],[f15289,f19635]) ).
fof(f19675,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ22_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f15292,f19674]) ).
fof(f19839,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ22_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(paramodulation,[status(thm)],[f1180,f19675]) ).
fof(f19849,plain,
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ143_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ134_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ22_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f19839,f454,f410,f867,f671,f947,f823,f834,f690,f954,f856,f709,f635,f621]) ).
fof(f19869,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ34_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(paramodulation,[status(thm)],[f1766,f455]) ).
fof(f19873,plain,
( ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ134_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ34_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f19869,f443,f454,f621,f690,f954,f823,f709,f635]) ).
fof(f19875,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f441,f328]) ).
fof(f19876,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f19875]) ).
fof(f19877,plain,
$false,
inference(sat_refutation,[status(thm)],[f450,f624,f638,f674,f693,f712,f826,f837,f848,f859,f870,f950,f957,f959,f961,f963,f965,f969,f975,f977,f1001,f1005,f1012,f1040,f1046,f1050,f8197,f16115,f19618,f19849,f19873,f19876]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL558+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.47 % Computer : n009.cluster.edu
% 0.18/0.47 % Model : x86_64 x86_64
% 0.18/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.47 % Memory : 8046.5625MB
% 0.18/0.47 % OS : Linux 6.8.0-71-generic
% 0.18/0.47 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 00:38:12 UTC 2026
% 0.18/0.48 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 93.38/12.44 % Refutation found
% 93.38/12.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 93.38/12.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.95/12.89 % Elapsed time: 12.390004 seconds
% 7.95/12.89 % CPU time: 95.582445 seconds
% 7.95/12.89 % Total memory used: 716.211 MB
% 7.95/12.89 % Net memory used: 662.334 MB
%------------------------------------------------------------------------------