%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL502+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 01:07:52 PM UTC 2026
% Result : Theorem 44.35s 6.10s
% Output : CNFRefutation 39.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 43
% Syntax : Number of formulae : 233 ( 29 unt; 24 def)
% Number of atoms : 1025 ( 31 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1515 ( 723 ~; 730 |; 24 &)
% ( 33 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 37 ( 35 usr; 35 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 13 con; 0-2 aty)
% Number of variables : 322 ( 307 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ modus_tollens,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
( modus_ponens
<=> ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f46,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(NNF_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
( ( ? [Y] :
( ~ is_a_theorem(Y)
& ? [X] :
( is_a_theorem(implies(X,Y))
& is_a_theorem(X) ) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f48,plain,
( ( ( ~ is_a_theorem(sK0_skl)
& is_a_theorem(implies(sK1_skl,sK0_skl))
& is_a_theorem(sK1_skl) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f53,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f54,plain,
( ( ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(NNF_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
( ( ( sK2_skl != sK3_skl
& is_a_theorem(equiv(sK2_skl,sK3_skl)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f59,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f60,plain,
( ( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f59]) ).
fof(f62,plain,
( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f111,plain,
( ( ? [P] : ~ is_a_theorem(implies(P,and(P,P)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f112,plain,
( ( ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f111]) ).
fof(f113,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[status(thm)],[f112]) ).
fof(f115,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P))
| kn2 )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f116,plain,
( ( ~ is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl))
| kn2 )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f115]) ).
fof(f117,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f119,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| kn3 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| ~ kn3 ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f120,plain,
( ( ~ is_a_theorem(implies(implies(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl)))))
| kn3 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl,sK37_skl]),skolemize(P,sK35_skl),skolemize(Q,sK36_skl),skolemize(R,sK37_skl)],[f119]) ).
fof(f121,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f135,plain,
( ( ? [P] : ~ is_a_theorem(implies(or(P,P),P))
| r1 )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f136,plain,
( ( ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))
| r1 )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f135]) ).
fof(f137,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f138,plain,
( ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))
| r1 ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f155,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f156,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f159,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f160,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f163,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f164,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f165,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f166,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f167,plain,
op_equiv,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f168,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f169,plain,
kn1,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f170,plain,
kn2,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f171,plain,
kn3,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f172,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f176,plain,
~ modus_tollens,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f177,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,definition,
! [X0,X1] :
( sQ1_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f181,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f177,f180]) ).
fof(f196,definition,
( sQ5_spl
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ5_spl
| ~ substitution_of_equivalents ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f56,f196,f199]) ).
fof(f211,definition,
( sQ9_spl
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ9_spl
| modus_tollens ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f218,definition,
( sQ11_spl
<=> is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ11_spl
| ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))) ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( ~ sQ11_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f211,f218]) ).
fof(f258,definition,
! [X0,X1] :
( sQ22_spl
<=> is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f259,plain,
! [X0,X1] :
( ~ sQ22_spl
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f324,definition,
! [X0,X1] :
( sQ40_spl
<=> is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f325,plain,
! [X0,X1] :
( ~ sQ40_spl
| is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f354,definition,
( sQ48_spl
<=> kn1 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ48_spl
| ~ kn1 ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,definition,
! [X0] :
( sQ49_spl
<=> is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f358,plain,
! [X0] :
( ~ sQ49_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,plain,
( sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f113,f354,f357]) ).
fof(f365,definition,
( sQ51_spl
<=> kn2 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( sQ51_spl
| ~ kn2 ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( sQ22_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f117,f365,f258]) ).
fof(f373,definition,
( sQ53_spl
<=> kn3 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( sQ53_spl
| ~ kn3 ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,definition,
! [X0,X1,X2] :
( sQ54_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f377,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f379,plain,
( sQ54_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f121,f373,f376]) ).
fof(f395,definition,
! [X0,X1] :
( sQ59_spl
<=> is_a_theorem(implies(X0,implies(not(X0),X1))) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f396,plain,
! [X0,X1] :
( ~ sQ59_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f414,definition,
( sQ64_spl
<=> r1 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f417,definition,
! [X0] :
( sQ65_spl
<=> is_a_theorem(implies(or(X0,X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f418,plain,
! [X0] :
( ~ sQ65_spl
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,plain,
( sQ65_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f137,f414,f417]) ).
fof(f421,definition,
( sQ66_spl
<=> is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( sQ66_spl
| ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)) ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f424,plain,
( ~ sQ66_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f138,f414,f421]) ).
fof(f436,definition,
! [X0,X1] :
( sQ70_spl
<=> is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f437,plain,
! [X0,X1] :
( ~ sQ70_spl
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f466,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,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(f470,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f469]) ).
fof(f472,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f156,f466,f469]) ).
fof(f480,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f483,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f484,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f160,f480,f483]) ).
fof(f494,definition,
( sQ86_spl
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ86_spl
| ~ op_equiv ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f497,definition,
! [X0,X1] :
( sQ87_spl
<=> equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f498,plain,
! [X0,X1] :
( ~ sQ87_spl
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,plain,
( sQ87_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f164,f494,f497]) ).
fof(f501,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f496,f167]) ).
fof(f502,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f503,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f168]) ).
fof(f504,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f172]) ).
fof(f506,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f507,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f166]) ).
fof(f508,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f468,f165]) ).
fof(f510,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f529,plain,
( sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f170]) ).
fof(f530,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f533,plain,
( sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f169]) ).
fof(f534,plain,
sQ48_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f537,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f171]) ).
fof(f538,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f563,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))) ),
inference(paramodulation,[status(thm)],[f484,f484]) ).
fof(f602,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))) ),
inference(paramodulation,[status(thm)],[f498,f358]) ).
fof(f603,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ22_spl
| is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(paramodulation,[status(thm)],[f498,f259]) ).
fof(f604,plain,
( ~ sQ87_spl
| ~ sQ22_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f603,f324,f258,f497]) ).
fof(f613,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f484,f470]) ).
fof(f614,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f484,f613]) ).
fof(f615,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| is_a_theorem(or(X0,and(not(X0),not(X0)))) ),
inference(paramodulation,[status(thm)],[f613,f358]) ).
fof(f616,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ87_spl
| ~ sQ49_spl
| is_a_theorem(implies(or(X0,not(X0)),equiv(not(X0),not(X0)))) ),
inference(paramodulation,[status(thm)],[f613,f602]) ).
fof(f617,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ87_spl
| equiv(X0,not(X1)) = and(implies(X0,not(X1)),or(X1,X0)) ),
inference(paramodulation,[status(thm)],[f613,f498]) ).
fof(f619,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(paramodulation,[status(thm)],[f613,f181]) ).
fof(f621,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ40_spl
| is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))) ),
inference(paramodulation,[status(thm)],[f613,f325]) ).
fof(f629,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ40_spl
| is_a_theorem(or(X0,X1))
| ~ is_a_theorem(equiv(not(X0),X1)) ),
inference(resolution,[status(thm)],[f621,f181]) ).
fof(f646,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| implies(X0,and(not(X1),not(X2))) = not(and(X0,or(X1,X2))) ),
inference(paramodulation,[status(thm)],[f613,f563]) ).
fof(f695,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))) ),
inference(forward_demodulation,[status(thm)],[f613,f377]) ).
fof(f696,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f695,f181]) ).
fof(f697,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))) ),
inference(paramodulation,[status(thm)],[f613,f695]) ).
fof(f698,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),not(and(not(X2),X0))))) ),
inference(paramodulation,[status(thm)],[f614,f695]) ).
fof(f705,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))) ),
inference(forward_demodulation,[status(thm)],[f484,f697]) ).
fof(f748,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| is_a_theorem(or(and(X1,X2),implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f705,f181]) ).
fof(f750,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0)))) ),
inference(paramodulation,[status(thm)],[f614,f705]) ).
fof(f756,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))) ),
inference(forward_demodulation,[status(thm)],[f613,f750]) ).
fof(f761,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f756,f181]) ).
fof(f764,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| is_a_theorem(implies(or(X0,not(X1)),implies(or(X1,X2),or(X2,X0)))) ),
inference(paramodulation,[status(thm)],[f613,f756]) ).
fof(f768,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ1_spl
| ~ sQ54_spl
| is_a_theorem(implies(implies(and(not(X0),not(X0)),X1),or(X1,X0))) ),
inference(resolution,[status(thm)],[f761,f615]) ).
fof(f770,plain,
( sQ11_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ is_a_theorem(implies(or(sK5_skl,not(sK4_skl)),implies(sK4_skl,sK5_skl))) ),
inference(forward_demodulation,[status(thm)],[f613,f220]) ).
fof(f788,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| is_a_theorem(or(X1,X0))
| ~ is_a_theorem(implies(and(not(X0),not(X0)),X1)) ),
inference(resolution,[status(thm)],[f768,f181]) ).
fof(f798,plain,
! [X0] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| is_a_theorem(or(not(X0),X0)) ),
inference(resolution,[status(thm)],[f788,f259]) ).
fof(f808,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))) ),
inference(resolution,[status(thm)],[f798,f761]) ).
fof(f809,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(and(X0,X1),implies(X1,not(X0)))) ),
inference(resolution,[status(thm)],[f798,f748]) ).
fof(f812,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f808,f181]) ).
fof(f854,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(not(X0),X2),or(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f812,f761]) ).
fof(f855,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(and(not(X0),X2),implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f812,f748]) ).
fof(f858,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(X2,implies(X0,X1)))
| ~ is_a_theorem(implies(and(X0,not(X1)),X2)) ),
inference(paramodulation,[status(thm)],[f484,f812]) ).
fof(f859,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(or(X0,X2),or(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f613,f854]) ).
fof(f900,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(X2,X1))
| ~ is_a_theorem(or(X0,X2))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f859,f181]) ).
fof(f936,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| is_a_theorem(not(and(not(X0),or(X0,X0)))) ),
inference(paramodulation,[status(thm)],[f646,f358]) ).
fof(f987,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ49_spl
| is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X0),or(X0,X0)),X1)) ),
inference(resolution,[status(thm)],[f936,f619]) ).
fof(f998,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ is_a_theorem(implies(X1,not(X0)))
| is_a_theorem(not(and(or(X0,X0),X1))) ),
inference(resolution,[status(thm)],[f987,f696]) ).
fof(f1186,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ49_spl
| ~ is_a_theorem(implies(not(X1),not(X0)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(paramodulation,[status(thm)],[f484,f998]) ).
fof(f1190,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ49_spl
| ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(forward_demodulation,[status(thm)],[f613,f1186]) ).
fof(f1195,plain,
( sQ66_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ49_spl
| ~ is_a_theorem(or(sK44_skl,not(sK44_skl))) ),
inference(resolution,[status(thm)],[f1190,f423]) ).
fof(f1608,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f855,f987]) ).
fof(f1633,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1608,f181]) ).
fof(f1724,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| is_a_theorem(or(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f858,f259]) ).
fof(f1732,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),or(X2,X0))) ),
inference(resolution,[status(thm)],[f1724,f761]) ).
fof(f1733,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0))) ),
inference(resolution,[status(thm)],[f1724,f748]) ).
fof(f1770,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f1732,f181]) ).
fof(f1904,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(or(X0,X1),implies(X1,X2))) ),
inference(resolution,[status(thm)],[f1770,f1732]) ).
fof(f1905,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| is_a_theorem(or(or(X0,X1),and(not(X1),not(X1)))) ),
inference(resolution,[status(thm)],[f1770,f768]) ).
fof(f2073,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(or(X0,not(X1)),or(X1,X2))) ),
inference(paramodulation,[status(thm)],[f613,f1904]) ).
fof(f2090,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(or(X0,not(X0)),X1)) ),
inference(resolution,[status(thm)],[f2073,f1633]) ).
fof(f2179,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ22_spl
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[status(thm)],[f2090,f764]) ).
fof(f2180,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ87_spl
| ~ sQ49_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| is_a_theorem(equiv(not(X0),not(X0))) ),
inference(resolution,[status(thm)],[f2090,f616]) ).
fof(f2192,plain,
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ22_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f2179,f436,f258,f357,f180,f376,f483,f469]) ).
fof(f2199,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| is_a_theorem(or(X0,not(X0))) ),
inference(resolution,[status(thm)],[f2180,f629]) ).
fof(f2211,plain,
( sQ66_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ22_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1195,f2199]) ).
fof(f2217,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| is_a_theorem(implies(implies(X0,X1),not(and(X0,not(X1))))) ),
inference(paramodulation,[status(thm)],[f614,f2199]) ).
fof(f2220,plain,
( sQ66_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f2211]) ).
fof(f2225,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| is_a_theorem(implies(implies(X0,X1),implies(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f484,f2217]) ).
fof(f2231,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ65_spl
| is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[status(thm)],[f418,f181]) ).
fof(f2241,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ70_spl
| is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f437,f181]) ).
fof(f2249,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| ~ is_a_theorem(or(X1,X0))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f2231,f900]) ).
fof(f2274,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(or(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f2225,f1770]) ).
fof(f2303,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(implies(implies(X0,X1),or(X1,implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f2274,f761]) ).
fof(f2304,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(or(and(X0,X1),implies(X1,implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f2274,f748]) ).
fof(f2318,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ70_spl
| is_a_theorem(implies(implies(X1,X2),X0))
| ~ is_a_theorem(or(X0,and(X1,not(X2)))) ),
inference(paramodulation,[status(thm)],[f614,f2241]) ).
fof(f2693,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| ~ sQ65_spl
| ~ is_a_theorem(or(and(X0,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f2249,f259]) ).
fof(f2724,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f2693,f1733]) ).
fof(f2876,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(or(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f2303,f181]) ).
fof(f3074,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ65_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f2876,f2231]) ).
fof(f3243,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ1_spl
| ~ sQ65_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(implies(implies(X0,X0),not(and(not(X0),X0)))) ),
inference(resolution,[status(thm)],[f3074,f698]) ).
fof(f3853,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ70_spl
| is_a_theorem(implies(implies(not(X0),X0),or(X1,X0))) ),
inference(resolution,[status(thm)],[f2318,f1905]) ).
fof(f3880,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ70_spl
| is_a_theorem(implies(or(X0,X0),or(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f613,f3853]) ).
fof(f3900,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ70_spl
| is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[status(thm)],[f3880,f181]) ).
fof(f5019,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(not(and(not(X0),X0)))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f3243,f181]) ).
fof(f5028,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(not(and(not(X0),X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f5019,f2724]) ).
fof(f5042,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X0),X0),X1)) ),
inference(resolution,[status(thm)],[f5028,f619]) ).
fof(f5091,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ65_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(resolution,[status(thm)],[f5042,f2304]) ).
fof(f5093,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| ~ sQ40_spl
| ~ sQ87_spl
| is_a_theorem(implies(X0,not(not(X0)))) ),
inference(resolution,[status(thm)],[f5042,f809]) ).
fof(f5118,plain,
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ65_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f5091,f395,f417,f497,f324,f357,f258,f376,f483,f469,f180]) ).
fof(f5121,plain,
! [X0,X1] :
( ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f613,f396]) ).
fof(f5128,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f5121,f181]) ).
fof(f5147,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ70_spl
| ~ sQ59_spl
| is_a_theorem(or(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f5128,f3900]) ).
fof(f5210,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(or(not(X0),X0),X1)) ),
inference(resolution,[status(thm)],[f181,f798]) ).
fof(f5251,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ70_spl
| ~ sQ59_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(or(X1,X0),X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f5147,f181]) ).
fof(f5940,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f176]) ).
fof(f5941,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f5940]) ).
fof(f10074,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(resolution,[status(thm)],[f748,f2693]) ).
fof(f15638,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ22_spl
| ~ sQ70_spl
| ~ sQ59_spl
| is_a_theorem(or(and(X0,X1),implies(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f5251,f705]) ).
fof(f25612,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f15638,f10074]) ).
fof(f25748,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| is_a_theorem(and(X0,or(not(X1),X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f25612,f5210]) ).
fof(f26886,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ87_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| is_a_theorem(equiv(X0,not(not(X0))))
| ~ is_a_theorem(implies(X0,not(not(X0)))) ),
inference(paramodulation,[status(thm)],[f617,f25748]) ).
fof(f26890,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ87_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| ~ sQ40_spl
| is_a_theorem(equiv(X0,not(not(X0)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f26886,f5093]) ).
fof(f26895,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ87_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| ~ sQ40_spl
| X0 = not(not(X0)) ),
inference(resolution,[status(thm)],[f26890,f200]) ).
fof(f27228,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ87_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| ~ sQ40_spl
| or(not(X0),X1) = implies(X0,X1) ),
inference(paramodulation,[status(thm)],[f26895,f613]) ).
fof(f27855,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ87_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| ~ sQ40_spl
| is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))) ),
inference(paramodulation,[status(thm)],[f27228,f437]) ).
fof(f34881,plain,
( sQ11_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ6_spl
| ~ sQ87_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| ~ sQ40_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f770,f27855]) ).
fof(f34903,plain,
( sQ11_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ6_spl
| ~ sQ87_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| ~ sQ65_spl
| ~ sQ70_spl
| ~ sQ59_spl
| ~ sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f34881]) ).
fof(f34904,plain,
$false,
inference(sat_refutation,[status(thm)],[f183,f202,f221,f360,f368,f379,f420,f424,f472,f486,f500,f502,f504,f506,f508,f510,f530,f534,f538,f604,f2192,f2220,f5118,f5941,f34903]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL502+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 00:35:57 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 44.35/6.10 % Refutation found
% 44.35/6.10 % SZS status Theorem for theBenchmark: Theorem is valid
% 44.35/6.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 24.79/6.90 % Elapsed time: 6.519348 seconds
% 24.79/6.90 % CPU time: 46.545475 seconds
% 24.79/6.90 % Total memory used: 722.416 MB
% 24.79/6.90 % Net memory used: 681.535 MB
%------------------------------------------------------------------------------