%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL556+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 : n017.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 251.13s 32.44s
% Output : CNFRefutation 251.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 53
% Syntax : Number of formulae : 240 ( 41 unt; 27 def)
% Number of atoms : 1010 ( 56 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1451 ( 681 ~; 691 |; 33 &)
% ( 39 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 43 ( 41 usr; 41 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 19 con; 0-2 aty)
% Number of variables : 317 ( 296 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),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,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,negated_conjecture,
~ and_2,
inference(negated_conjecture,[status(cth)],[f77]) ).
fof(f113,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(f114,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)],[f113]) ).
fof(f116,plain,
( ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl))
| and_2 ),
inference(cnf_transformation,[status(thm)],[f114]) ).
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,
~ and_2,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f418,definition,
( sQ24_spl
<=> and_2 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( ~ sQ24_spl
| and_2 ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,definition,
! [X0,X1] :
( sQ25_spl
<=> is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f422,plain,
! [X0,X1] :
( ~ sQ25_spl
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f425,definition,
( sQ26_spl
<=> is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( sQ26_spl
| ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)) ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f428,plain,
( ~ sQ26_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f116,f418,f425]) ).
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(f991,plain,
( sQ142_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f855,f322]) ).
fof(f992,plain,
sQ142_spl,
inference(contradiction_clause,[status(thm)],[f991]) ).
fof(f999,plain,
( sQ136_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f833,f320]) ).
fof(f1000,plain,
sQ136_spl,
inference(contradiction_clause,[status(thm)],[f999]) ).
fof(f1017,plain,
( sQ145_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f866,f323]) ).
fof(f1018,plain,
sQ145_spl,
inference(contradiction_clause,[status(thm)],[f1017]) ).
fof(f1027,plain,
( sQ139_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f844,f321]) ).
fof(f1028,plain,
sQ139_spl,
inference(contradiction_clause,[status(thm)],[f1027]) ).
fof(f1031,plain,
( sQ133_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f822,f319]) ).
fof(f1032,plain,
sQ133_spl,
inference(contradiction_clause,[status(thm)],[f1031]) ).
fof(f1037,plain,
( sQ26_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f422]) ).
fof(f1038,plain,
( sQ26_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f1037]) ).
fof(f1063,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ134_spl
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(and(X0,X1)) ),
inference(resolution,[status(thm)],[f824,f672]) ).
fof(f1094,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(f1159,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f636,f622]) ).
fof(f1160,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f636,f1159]) ).
fof(f1171,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(not(X0),X1) = necessarily(or(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1159,f948]) ).
fof(f1179,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ143_spl
| is_a_theorem(necessarily(or(X0,and(not(X0),not(X0))))) ),
inference(paramodulation,[status(thm)],[f1171,f857]) ).
fof(f1373,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(f1416,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)],[f1094,f710]) ).
fof(f1428,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| and(X0,X1) = and(X1,X0)
| ~ is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(resolution,[status(thm)],[f1416,f824]) ).
fof(f1429,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)],[f1416,f835]) ).
fof(f1430,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| and(X0,X0) = X0
| ~ is_a_theorem(strict_implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f1416,f857]) ).
fof(f1437,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| and(X0,X1) = and(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1428,f824]) ).
fof(f1438,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| and(X0,X0) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f1430,f835]) ).
fof(f1439,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ143_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| is_a_theorem(necessarily(or(X0,not(X0)))) ),
inference(backward_demodulation,[status(thm)],[f1438,f1179]) ).
fof(f1454,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| implies(not(X0),X0) = not(not(X0)) ),
inference(paramodulation,[status(thm)],[f1438,f636]) ).
fof(f1456,plain,
! [X0,X1] :
( ~ sQ143_spl
| ~ sQ103_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)],[f1438,f846]) ).
fof(f1468,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(X0,X0) = not(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f1159,f1454]) ).
fof(f1571,plain,
! [X0,X1,X2] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(and(not(X0),X1),X2) = implies(implies(X1,X0),X2) ),
inference(paramodulation,[status(thm)],[f1437,f1160]) ).
fof(f1573,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| implies(X0,X1) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1437,f636]) ).
fof(f1582,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(and(X0,X1),X1)) ),
inference(paramodulation,[status(thm)],[f1437,f835]) ).
fof(f1667,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| implies(not(X0),X1) = implies(not(X1),X0) ),
inference(paramodulation,[status(thm)],[f636,f1573]) ).
fof(f1691,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| or(X0,X1) = implies(not(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f1159,f1667]) ).
fof(f1692,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| or(X0,X1) = or(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f1159,f1691]) ).
fof(f1716,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(necessarily(or(not(X0),X0))) ),
inference(paramodulation,[status(thm)],[f1692,f1439]) ).
fof(f1737,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| X0 = and(X0,X1)
| ~ is_a_theorem(strict_implies(X0,and(X1,X0))) ),
inference(paramodulation,[status(thm)],[f1437,f1429]) ).
fof(f1913,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| and(X0,X1) = and(and(X0,X1),X0) ),
inference(resolution,[status(thm)],[f1456,f1737]) ).
fof(f1945,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| and(X0,X1) = and(and(X1,X0),X0) ),
inference(paramodulation,[status(thm)],[f1437,f1913]) ).
fof(f2044,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| implies(and(X0,not(X1)),X1) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f1945,f636]) ).
fof(f2072,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| implies(and(X0,not(X1)),X1) = implies(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f1573,f2044]) ).
fof(f2265,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(and(X0,not(X1)),X1) = necessarily(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2072,f948]) ).
fof(f2294,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| strict_implies(and(X0,not(X1)),X1) = strict_implies(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f948,f2265]) ).
fof(f2435,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,X2))
| ~ is_a_theorem(and(strict_implies(X0,not(X1)),necessarily(or(X1,X2)))) ),
inference(paramodulation,[status(thm)],[f1171,f1373]) ).
fof(f2437,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| is_a_theorem(strict_implies(X2,X1))
| ~ is_a_theorem(and(necessarily(or(X0,X1)),strict_implies(X2,not(X0)))) ),
inference(forward_demodulation,[status(thm)],[f1437,f2435]) ).
fof(f3263,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| or(X0,and(not(X1),X2)) = implies(implies(X2,X1),X0) ),
inference(paramodulation,[status(thm)],[f1692,f1571]) ).
fof(f8531,plain,
! [X0,X1,X2] :
( ~ sQ98_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ137_spl
| is_a_theorem(and(X0,strict_implies(and(X1,X2),X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1582,f691]) ).
fof(f8583,plain,
! [X0,X1] :
( ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(and(X0,necessarily(or(not(X1),X1))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1716,f691]) ).
fof(f8584,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(necessarily(or(not(X0),X0)),X1)) ),
inference(resolution,[status(thm)],[f1716,f672]) ).
fof(f11325,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ98_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(X0,X2))
| ~ is_a_theorem(strict_implies(X0,and(X1,X2))) ),
inference(resolution,[status(thm)],[f8531,f1373]) ).
fof(f11327,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| ~ sQ134_spl
| ~ sQ98_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ137_spl
| is_a_theorem(and(strict_implies(and(X1,X2),X2),X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f8531,f1063]) ).
fof(f11617,plain,
! [X0,X1,X2] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,and(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1945,f11325]) ).
fof(f12100,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ98_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(and(X2,X0),X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f11327,f1373]) ).
fof(f14156,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(strict_implies(not(X0),X0)) ),
inference(paramodulation,[status(thm)],[f2294,f12100]) ).
fof(f14180,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ79_spl
| is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(or(X0,X0))) ),
inference(forward_demodulation,[status(thm)],[f1171,f14156]) ).
fof(f14181,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ79_spl
| is_a_theorem(strict_implies(X1,X0))
| ~ is_a_theorem(necessarily(not(not(X0)))) ),
inference(forward_demodulation,[status(thm)],[f1468,f14180]) ).
fof(f17371,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ134_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(and(necessarily(or(not(X1),X1)),X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f8583,f1063]) ).
fof(f18270,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ143_spl
| ~ sQ137_spl
| is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,not(not(X1)))) ),
inference(resolution,[status(thm)],[f17371,f2437]) ).
fof(f22151,plain,
! [X0,X1] :
( ~ sQ137_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ143_spl
| is_a_theorem(strict_implies(and(not(not(X0)),X1),X0)) ),
inference(resolution,[status(thm)],[f18270,f835]) ).
fof(f22239,plain,
! [X0,X1,X2] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| is_a_theorem(strict_implies(and(not(not(and(X0,X1))),X2),X0)) ),
inference(resolution,[status(thm)],[f22151,f11617]) ).
fof(f23095,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| is_a_theorem(strict_implies(and(not(not(and(not(not(X0)),X1))),X2),X0)) ),
inference(resolution,[status(thm)],[f22239,f18270]) ).
fof(f23139,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| is_a_theorem(strict_implies(and(not(implies(X0,not(X1))),X2),X1)) ),
inference(forward_demodulation,[status(thm)],[f1573,f23095]) ).
fof(f25161,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ79_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(not(implies(X0,not(X1))),X1)) ),
inference(paramodulation,[status(thm)],[f2294,f23139]) ).
fof(f25191,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ83_spl
| ~ sQ168_spl
| ~ sQ79_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(necessarily(or(implies(X0,not(X1)),X1))) ),
inference(forward_demodulation,[status(thm)],[f1171,f25161]) ).
fof(f25223,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(necessarily(or(or(X0,not(X1)),X1))) ),
inference(paramodulation,[status(thm)],[f1159,f25191]) ).
fof(f25455,plain,
! [X0] :
( ~ sQ143_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ134_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(necessarily(or(not(not(not(X0))),X0))) ),
inference(paramodulation,[status(thm)],[f1468,f25223]) ).
fof(f26016,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(necessarily(implies(implies(X0,X1),not(not(not(and(not(X1),X0))))))) ),
inference(paramodulation,[status(thm)],[f3263,f25455]) ).
fof(f26034,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(implies(X0,X1),not(not(not(and(not(X1),X0)))))) ),
inference(forward_demodulation,[status(thm)],[f948,f26016]) ).
fof(f26035,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(implies(X0,X1),not(not(implies(X0,X1))))) ),
inference(forward_demodulation,[status(thm)],[f1573,f26034]) ).
fof(f32543,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| not(not(implies(X0,X1))) = implies(X0,X1)
| ~ is_a_theorem(strict_implies(not(not(implies(X0,X1))),implies(X0,X1))) ),
inference(resolution,[status(thm)],[f26035,f1416]) ).
fof(f32567,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| not(not(implies(X0,X1))) = implies(X0,X1)
| ~ is_a_theorem(necessarily(or(not(implies(X0,X1)),implies(X0,X1)))) ),
inference(forward_demodulation,[status(thm)],[f1171,f32543]) ).
fof(f32568,plain,
! [X0,X1] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| not(not(implies(X0,X1))) = implies(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f32567,f1716]) ).
fof(f32631,plain,
! [X0,X1,X2] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X2,implies(X0,X1)))
| ~ is_a_theorem(necessarily(implies(X0,X1))) ),
inference(paramodulation,[status(thm)],[f32568,f14181]) ).
fof(f32790,plain,
! [X0,X1,X2] :
( ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ79_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ168_spl
| ~ sQ93_spl
| ~ sQ146_spl
| is_a_theorem(strict_implies(X2,implies(X0,X1)))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f948,f32631]) ).
fof(f34139,plain,
! [X0,X1] :
( ~ sQ93_spl
| ~ sQ83_spl
| ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ143_spl
| ~ sQ137_spl
| ~ sQ140_spl
| ~ sQ146_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(strict_implies(X0,X1)) ),
inference(resolution,[status(thm)],[f32790,f8584]) ).
fof(f34310,plain,
! [X0,X1] :
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ93_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ146_spl
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(resolution,[status(thm)],[f34139,f1582]) ).
fof(f34330,plain,
( ~ sQ134_spl
| ~ sQ103_spl
| ~ sQ170_spl
| ~ sQ98_spl
| ~ sQ137_spl
| ~ sQ93_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ168_spl
| ~ sQ143_spl
| ~ sQ140_spl
| ~ sQ146_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f34310,f421,f867,f845,f856,f947,f621,f635,f671,f834,f690,f954,f709,f823]) ).
fof(f34343,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f419,f328]) ).
fof(f34344,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f34343]) ).
fof(f34345,plain,
$false,
inference(sat_refutation,[status(thm)],[f428,f624,f638,f674,f693,f712,f826,f837,f848,f859,f870,f950,f957,f959,f961,f963,f965,f969,f975,f977,f992,f1000,f1018,f1028,f1032,f1038,f34330,f34344]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL556+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n017.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 00:33:41 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 251.13/32.44 % Refutation found
% 251.13/32.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 251.13/32.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 214.02/33.71 % Elapsed time: 33.030824 seconds
% 214.02/33.71 % CPU time: 244.424809 seconds
% 214.02/33.71 % Total memory used: 1.283 GB
% 214.02/33.71 % Net memory used: 1.214 GB
%------------------------------------------------------------------------------