%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL513+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 : n015.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 01:07:53 PM UTC 2026
% Result : Theorem 18.17s 2.78s
% Output : CNFRefutation 13.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 37
% Syntax : Number of formulae : 192 ( 26 unt; 21 def)
% Number of atoms : 752 ( 20 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1066 ( 506 ~; 511 |; 18 &)
% ( 27 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 32 ( 30 usr; 30 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 272 ( 260 !; 12 ?)
% 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(f14,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
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(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(f43,conjecture,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ equivalence_2,
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(f103,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| equivalence_2 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| ~ equivalence_2 ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f104,plain,
( ( ~ is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl)))
| equivalence_2 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| ~ equivalence_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl,sK29_skl]),skolemize(X,sK28_skl),skolemize(Y,sK29_skl)],[f103]) ).
fof(f106,plain,
( ~ is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl)))
| equivalence_2 ),
inference(cnf_transformation,[status(thm)],[f104]) ).
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(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(f176,plain,
~ equivalence_2,
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(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(f302,definition,
! [X0,X1] :
( sQ34_spl
<=> is_a_theorem(implies(X0,or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f303,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(component_clause,[status(thm)],[f302]) ).
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(f332,definition,
( sQ42_spl
<=> equivalence_2 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( ~ sQ42_spl
| equivalence_2 ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
! [X0,X1] :
( sQ43_spl
<=> is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f336,plain,
! [X0,X1] :
( ~ sQ43_spl
| is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f339,definition,
( sQ44_spl
<=> is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl))) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ44_spl
| ~ is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl))) ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,plain,
( ~ sQ44_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f106,f332,f339]) ).
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(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(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(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(f547,plain,
( sQ44_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f336]) ).
fof(f548,plain,
( sQ44_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f564,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(f570,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))) ),
inference(paramodulation,[status(thm)],[f498,f358]) ).
fof(f571,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ22_spl
| is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(paramodulation,[status(thm)],[f498,f259]) ).
fof(f572,plain,
( ~ sQ87_spl
| ~ sQ22_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f571,f324,f258,f497]) ).
fof(f580,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f484,f470]) ).
fof(f581,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f484,f580]) ).
fof(f582,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| is_a_theorem(or(X0,and(not(X0),not(X0)))) ),
inference(paramodulation,[status(thm)],[f580,f358]) ).
fof(f583,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ40_spl
| is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))) ),
inference(paramodulation,[status(thm)],[f580,f325]) ).
fof(f584,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)],[f580,f570]) ).
fof(f588,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)],[f580,f181]) ).
fof(f595,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)],[f583,f181]) ).
fof(f605,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)],[f580,f377]) ).
fof(f606,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)],[f605,f181]) ).
fof(f607,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)],[f580,f605]) ).
fof(f611,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,f607]) ).
fof(f620,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ83_spl
| implies(implies(X0,X1),and(X1,not(X0))) = not(equiv(X0,X1)) ),
inference(paramodulation,[status(thm)],[f498,f564]) ).
fof(f621,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)],[f580,f564]) ).
fof(f699,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)],[f611,f181]) ).
fof(f701,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)],[f581,f611]) ).
fof(f706,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)],[f580,f701]) ).
fof(f727,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)],[f706,f181]) ).
fof(f730,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)],[f580,f706]) ).
fof(f734,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)],[f727,f582]) ).
fof(f754,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)],[f734,f181]) ).
fof(f764,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)],[f754,f259]) ).
fof(f774,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)],[f764,f727]) ).
fof(f778,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)],[f774,f181]) ).
fof(f820,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)],[f778,f727]) ).
fof(f824,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,f778]) ).
fof(f825,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)],[f580,f820]) ).
fof(f854,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)],[f825,f181]) ).
fof(f955,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| is_a_theorem(not(and(not(X0),or(X0,X0)))) ),
inference(paramodulation,[status(thm)],[f621,f358]) ).
fof(f1015,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)],[f955,f588]) ).
fof(f1026,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)],[f1015,f606]) ).
fof(f1123,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,f1026]) ).
fof(f1126,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)],[f580,f1123]) ).
fof(f1131,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(or(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f1126,f778]) ).
fof(f1143,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1131,f181]) ).
fof(f1706,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)],[f824,f259]) ).
fof(f1714,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)],[f1706,f727]) ).
fof(f1715,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)],[f1706,f699]) ).
fof(f1786,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)],[f1714,f181]) ).
fof(f1829,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)],[f1786,f1714]) ).
fof(f1931,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)],[f580,f1829]) ).
fof(f1945,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(or(X0,not(X0)),X1)) ),
inference(resolution,[status(thm)],[f1931,f1143]) ).
fof(f1966,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[status(thm)],[f1945,f730]) ).
fof(f1967,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)],[f1945,f584]) ).
fof(f1978,plain,
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ49_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1966,f436,f357,f258,f180,f376,f483,f469]) ).
fof(f1985,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)],[f1967,f595]) ).
fof(f1998,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ22_spl
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f1985,f1126]) ).
fof(f2005,plain,
( ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ49_spl
| ~ sQ40_spl
| ~ sQ87_spl
| ~ sQ22_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1998,f417,f258,f497,f324,f357,f469,f376,f180,f483]) ).
fof(f2014,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(f2022,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ65_spl
| is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[status(thm)],[f418,f181]) ).
fof(f2037,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)],[f2022,f854]) ).
fof(f2979,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| is_a_theorem(or(and(X1,X2),not(and(X2,not(X0)))))
| ~ is_a_theorem(or(X0,X1)) ),
inference(paramodulation,[status(thm)],[f580,f606]) ).
fof(f2987,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| is_a_theorem(or(and(X1,X2),implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f484,f2979]) ).
fof(f3477,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)],[f2037,f259]) ).
fof(f3980,plain,
! [X0] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f1715,f3477]) ).
fof(f4012,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(or(and(X0,X1),not(and(X1,X0)))) ),
inference(resolution,[status(thm)],[f3980,f606]) ).
fof(f4013,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f3980,f181]) ).
fof(f4054,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(implies(implies(X0,X1),not(and(not(X1),X0)))) ),
inference(paramodulation,[status(thm)],[f581,f4012]) ).
fof(f5056,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)],[f699,f3477]) ).
fof(f6138,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(resolution,[status(thm)],[f5056,f1829]) ).
fof(f6168,plain,
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f6138,f302,f417,f357,f258,f376,f469,f483,f180]) ).
fof(f6230,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ34_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,or(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[f303,f181]) ).
fof(f7838,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f176]) ).
fof(f7839,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f7838]) ).
fof(f9699,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ34_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(or(X0,X1),not(X1))) ),
inference(resolution,[status(thm)],[f774,f6230]) ).
fof(f9723,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ34_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(implies(implies(X0,X1),X2),not(X2))) ),
inference(paramodulation,[status(thm)],[f581,f9699]) ).
fof(f11018,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ34_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(not(equiv(X0,X1)),not(and(X1,not(X0))))) ),
inference(paramodulation,[status(thm)],[f620,f9723]) ).
fof(f11027,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ34_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(not(equiv(X0,X1)),implies(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f484,f11018]) ).
fof(f17870,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(not(and(not(X0),X0))) ),
inference(resolution,[status(thm)],[f4054,f4013]) ).
fof(f17925,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ54_spl
| ~ sQ49_spl
| ~ sQ65_spl
| is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X0),X0),X1)) ),
inference(resolution,[status(thm)],[f17870,f588]) ).
fof(f18017,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f17925,f2987]) ).
fof(f18343,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ70_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ65_spl
| ~ is_a_theorem(or(not(X0),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f18017,f2014]) ).
fof(f18774,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ34_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ70_spl
| ~ sQ65_spl
| is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(resolution,[status(thm)],[f18343,f11027]) ).
fof(f18847,plain,
( ~ sQ87_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ34_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ sQ70_spl
| ~ sQ65_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f18774,f335,f417,f436,f357,f258,f376,f302,f180,f469,f483,f497]) ).
fof(f18857,plain,
$false,
inference(sat_refutation,[status(thm)],[f183,f342,f360,f368,f379,f472,f486,f500,f502,f504,f508,f510,f530,f534,f538,f548,f572,f1978,f2005,f6168,f7839,f18847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL513+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % 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 00:39:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 18.17/2.78 % Refutation found
% 18.17/2.78 % SZS status Theorem for theBenchmark: Theorem is valid
% 18.17/2.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.49/2.88 % Elapsed time: 2.492125 seconds
% 13.49/2.88 % CPU time: 19.291628 seconds
% 13.49/2.88 % Total memory used: 335.486 MB
% 13.49/2.88 % Net memory used: 322.609 MB
%------------------------------------------------------------------------------