%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL509+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 : n018.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 8.25s 1.85s
% Output : CNFRefutation 8.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 28
% Syntax : Number of formulae : 151 ( 23 unt; 14 def)
% Number of atoms : 585 ( 13 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 823 ( 389 ~; 393 |; 18 &)
% ( 20 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 24 ( 22 usr; 22 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 212 ( 200 !; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox2/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/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(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ or_1,
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(f87,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f88,plain,
( ( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X,sK19_skl),skolemize(Y,sK20_skl)],[f87]) ).
fof(f90,plain,
( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 ),
inference(cnf_transformation,[status(thm)],[f88]) ).
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(f165,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f166,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
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,
~ or_1,
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(f288,definition,
( sQ30_spl
<=> or_1 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( ~ sQ30_spl
| or_1 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f295,definition,
( sQ32_spl
<=> is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( sQ32_spl
| ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))) ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( ~ sQ32_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f90,f288,f295]) ).
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(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(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(f519,plain,
( sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f367,f170]) ).
fof(f520,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f525,plain,
( sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f169]) ).
fof(f526,plain,
sQ48_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f563,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f171]) ).
fof(f564,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f567,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(f607,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f484,f470]) ).
fof(f608,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f484,f607]) ).
fof(f609,plain,
! [X0] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| is_a_theorem(or(X0,and(not(X0),not(X0)))) ),
inference(paramodulation,[status(thm)],[f607,f358]) ).
fof(f615,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)],[f607,f181]) ).
fof(f730,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ49_spl
| is_a_theorem(not(and(not(X0),implies(not(X0),X0)))) ),
inference(paramodulation,[status(thm)],[f567,f358]) ).
fof(f744,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ79_spl
| is_a_theorem(not(and(not(X0),or(X0,X0)))) ),
inference(forward_demodulation,[status(thm)],[f607,f730]) ).
fof(f746,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)],[f744,f615]) ).
fof(f811,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)],[f607,f377]) ).
fof(f812,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)],[f811,f181]) ).
fof(f814,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)],[f607,f811]) ).
fof(f816,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)],[f608,f811]) ).
fof(f822,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,f814]) ).
fof(f841,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)],[f822,f181]) ).
fof(f844,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)],[f608,f822]) ).
fof(f851,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)],[f607,f844]) ).
fof(f857,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)],[f851,f181]) ).
fof(f867,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)],[f857,f609]) ).
fof(f900,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)],[f867,f181]) ).
fof(f917,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)],[f900,f259]) ).
fof(f925,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)],[f917,f857]) ).
fof(f929,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)],[f925,f181]) ).
fof(f931,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(or(X0,X1),or(X1,not(not(X0))))) ),
inference(paramodulation,[status(thm)],[f607,f925]) ).
fof(f975,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)],[f929,f857]) ).
fof(f980,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)],[f607,f975]) ).
fof(f988,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(X1,not(not(X0))))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f931,f181]) ).
fof(f1023,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)],[f980,f181]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| is_a_theorem(not(and(or(X1,X1),X0)))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(resolution,[status(thm)],[f812,f746]) ).
fof(f1123,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| is_a_theorem(not(and(or(X1,X1),not(X0))))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f607,f1027]) ).
fof(f1125,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ49_spl
| ~ sQ54_spl
| is_a_theorem(implies(or(X1,X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(forward_demodulation,[status(thm)],[f484,f1123]) ).
fof(f1145,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ is_a_theorem(or(X0,X1))
| is_a_theorem(implies(or(not(X0),not(X0)),X1)) ),
inference(resolution,[status(thm)],[f1125,f988]) ).
fof(f1336,plain,
! [X0] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| is_a_theorem(implies(or(not(not(X0)),not(not(X0))),X0)) ),
inference(resolution,[status(thm)],[f1145,f917]) ).
fof(f1354,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ49_spl
| ~ sQ54_spl
| is_a_theorem(X0)
| ~ is_a_theorem(or(not(not(X0)),not(not(X0)))) ),
inference(resolution,[status(thm)],[f1336,f181]) ).
fof(f1365,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ is_a_theorem(or(X0,not(not(X0))))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1354,f988]) ).
fof(f1373,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1365,f988]) ).
fof(f1383,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| ~ is_a_theorem(or(X1,X0))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1373,f1023]) ).
fof(f1721,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| is_a_theorem(or(X0,not(and(X0,X1)))) ),
inference(resolution,[status(thm)],[f929,f259]) ).
fof(f1730,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| is_a_theorem(or(X0,implies(X0,X1))) ),
inference(paramodulation,[status(thm)],[f484,f1721]) ).
fof(f1735,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)],[f1730,f841]) ).
fof(f1803,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| ~ is_a_theorem(or(and(X0,X1),X0))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f1383,f259]) ).
fof(f1864,plain,
! [X0] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f1735,f1803]) ).
fof(f1867,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X2),X0))) ),
inference(paramodulation,[status(thm)],[f608,f1735]) ).
fof(f1874,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),or(X2,X0))) ),
inference(forward_demodulation,[status(thm)],[f607,f1867]) ).
fof(f2042,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)],[f1874,f181]) ).
fof(f2179,plain,
! [X0,X1] :
( ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ49_spl
| is_a_theorem(or(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f2042,f1864]) ).
fof(f2185,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(and(X0,X1),implies(X1,implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f2179,f841]) ).
fof(f2324,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(X1),implies(X0,X2)))) ),
inference(paramodulation,[status(thm)],[f608,f2185]) ).
fof(f2332,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(X0,X1),or(X1,implies(X0,X2)))) ),
inference(forward_demodulation,[status(thm)],[f607,f2324]) ).
fof(f3042,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(or(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f2332,f181]) ).
fof(f3582,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f3042,f1373]) ).
fof(f3816,plain,
! [X0] :
( ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(implies(X0,X0),not(and(not(X0),X0)))) ),
inference(resolution,[status(thm)],[f3582,f816]) ).
fof(f4583,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(not(and(not(X0),X0)))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f3816,f181]) ).
fof(f4591,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(not(and(not(X0),X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f4583,f1864]) ).
fof(f4600,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ1_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(X1)
| ~ is_a_theorem(or(and(not(X0),X0),X1)) ),
inference(resolution,[status(thm)],[f4591,f615]) ).
fof(f4632,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(resolution,[status(thm)],[f4600,f2185]) ).
fof(f4661,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f607,f4632]) ).
fof(f4663,plain,
( sQ32_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f297,f4661]) ).
fof(f4673,plain,
( sQ32_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ54_spl
| ~ sQ22_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f4663]) ).
fof(f4675,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f289,f176]) ).
fof(f4676,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f4675]) ).
fof(f4677,plain,
$false,
inference(sat_refutation,[status(thm)],[f183,f298,f360,f368,f379,f472,f486,f504,f508,f510,f520,f526,f564,f4673,f4676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL509+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.65 % Computer : n018.cluster.edu
% 0.15/0.65 % Model : x86_64 x86_64
% 0.15/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.65 % Memory : 8046.5625MB
% 0.15/0.65 % OS : Linux 6.8.0-71-generic
% 0.15/0.65 % CPULimit : 300
% 0.15/0.65 % WCLimit : 300
% 0.15/0.65 % DateTime : Mon Sep 21 00:38:29 UTC 2026
% 0.15/0.65 % CPUTime :
% 0.19/0.67 % Drodi V4.1.1
% 8.25/1.85 % Refutation found
% 8.25/1.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 8.25/1.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.32/1.91 % Elapsed time: 1.238427 seconds
% 8.32/1.91 % CPU time: 9.449499 seconds
% 8.32/1.91 % Total memory used: 213.309 MB
% 8.32/1.91 % Net memory used: 205.965 MB
%------------------------------------------------------------------------------