%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL458+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 : n002.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 01:07:47 PM UTC 2026
% Result : Theorem 4.37s 0.99s
% Output : CNFRefutation 4.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 40
% Syntax : Number of formulae : 167 ( 32 unt; 20 def)
% Number of atoms : 545 ( 51 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 693 ( 315 ~; 322 |; 22 &)
% ( 28 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 33 ( 31 usr; 31 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 14 con; 0-2 aty)
% Number of variables : 214 ( 198 !; 16 ?)
% 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(f2,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
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(f28,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(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(f30,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),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,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
r5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ r5,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,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(f56,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)],[f55]) ).
fof(f57,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)],[f56]) ).
fof(f58,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)],[f57]) ).
fof(f59,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f63,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f64,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)],[f63]) ).
fof(f65,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)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,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(f70,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)],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f81,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| implies_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f82,plain,
( ( ~ is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl))))
| implies_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(X,sK10_skl),skolemize(Y,sK11_skl),skolemize(Z,sK12_skl)],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f117,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| equivalence_3 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f118,plain,
( ( ~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl))))
| equivalence_3 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[status(thm)],[f118]) ).
fof(f161,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| r5 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f162,plain,
( ( ~ is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl))))
| r5 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl]),skolemize(P,sK52_skl),skolemize(Q,sK53_skl),skolemize(R,sK54_skl)],[f161]) ).
fof(f164,plain,
( ~ is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl))))
| r5 ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f165,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f166,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f167,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f168,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(thm)],[f167]) ).
fof(f169,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f170,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f171,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f172,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f175,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f176,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f178,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f179,plain,
modus_tollens,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f182,plain,
implies_3,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f191,plain,
equivalence_3,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f192,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f193,plain,
op_implies_or,
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f194,plain,
op_and,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f196,plain,
~ r5,
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f197,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,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(f201,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f197,f200]) ).
fof(f216,definition,
( sQ5_spl
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ5_spl
| ~ substitution_of_equivalents ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f220,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f66,f216,f219]) ).
fof(f231,definition,
( sQ9_spl
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ9_spl
| ~ modus_tollens ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,definition,
! [X0,X1] :
( sQ10_spl
<=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f235,plain,
! [X0,X1] :
( ~ sQ10_spl
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f71,f231,f234]) ).
fof(f264,definition,
( sQ18_spl
<=> implies_3 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( sQ18_spl
| ~ implies_3 ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,definition,
! [X0,X1,X2] :
( sQ19_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f268,plain,
! [X0,X1,X2] :
( ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f83,f264,f267]) ).
fof(f363,definition,
( sQ45_spl
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f365,plain,
( sQ45_spl
| ~ equivalence_3 ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,definition,
! [X0,X1] :
( sQ46_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f367,plain,
! [X0,X1] :
( ~ sQ46_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(component_clause,[status(thm)],[f366]) ).
fof(f369,plain,
( sQ46_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f119,f363,f366]) ).
fof(f475,definition,
( sQ75_spl
<=> r5 ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( ~ sQ75_spl
| r5 ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f482,definition,
( sQ77_spl
<=> is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( sQ77_spl
| ~ is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl)))) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( ~ sQ77_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f164,f475,f482]) ).
fof(f486,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,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(f490,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f166,f486,f489]) ).
fof(f493,definition,
( sQ80_spl
<=> op_and ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ80_spl
| ~ op_and ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
! [X0,X1] :
( sQ81_spl
<=> and(X0,X1) = not(or(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f497,plain,
! [X0,X1] :
( ~ sQ81_spl
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( sQ81_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f168,f493,f496]) ).
fof(f500,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f504,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f170,f500,f503]) ).
fof(f507,definition,
( sQ84_spl
<=> op_implies_or ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ84_spl
| ~ op_implies_or ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f510,definition,
! [X0,X1] :
( sQ85_spl
<=> implies(X0,X1) = or(not(X0),X1) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sQ85_spl
| implies(X0,X1) = or(not(X0),X1) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f513,plain,
( sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f172,f507,f510]) ).
fof(f523,plain,
( sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f193]) ).
fof(f524,plain,
sQ84_spl,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f176]) ).
fof(f526,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f194]) ).
fof(f528,plain,
sQ80_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f175]) ).
fof(f530,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f555,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f178]) ).
fof(f556,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f557,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f192]) ).
fof(f558,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f557]) ).
fof(f559,plain,
! [X0,X1] :
( ~ sQ81_spl
| ~ sQ85_spl
| and(X0,X1) = not(implies(X0,not(X1))) ),
inference(forward_demodulation,[status(thm)],[f511,f497]) ).
fof(f561,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))) ),
inference(backward_demodulation,[status(thm)],[f564,f235]) ).
fof(f564,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f504,f490]) ).
fof(f591,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f365,f191]) ).
fof(f592,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f610,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f179]) ).
fof(f611,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f610]) ).
fof(f615,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f182]) ).
fof(f616,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f615]) ).
fof(f628,plain,
! [X0,X1,X2] :
( ~ sQ81_spl
| ~ sQ85_spl
| implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f559,f511]) ).
fof(f630,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ79_spl
| or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f504,f564]) ).
fof(f631,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| and(not(X0),X1) = not(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f564,f559]) ).
fof(f638,plain,
! [X0,X1,X2] :
( ~ sQ6_spl
| ~ sQ1_spl
| X1 = X2
| ~ is_a_theorem(implies(X0,equiv(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f201,f220]) ).
fof(f695,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))) ),
inference(paramodulation,[status(thm)],[f564,f561]) ).
fof(f709,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,not(X1)),implies(or(X1,X2),implies(X0,X2)))) ),
inference(paramodulation,[status(thm)],[f564,f268]) ).
fof(f712,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ19_spl
| ~ sQ81_spl
| ~ sQ85_spl
| is_a_theorem(or(and(X0,X1),implies(or(X1,X2),implies(X0,X2)))) ),
inference(forward_demodulation,[status(thm)],[f628,f709]) ).
fof(f726,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| implies(or(X0,not(X1)),X2) = or(and(not(X0),X1),X2) ),
inference(paramodulation,[status(thm)],[f631,f511]) ).
fof(f729,plain,
! [X0,X1] :
( ~ sQ10_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| is_a_theorem(or(and(not(X0),X1),implies(X1,X0))) ),
inference(backward_demodulation,[status(thm)],[f726,f561]) ).
fof(f730,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| is_a_theorem(or(and(not(X0),not(X1)),or(X1,X0))) ),
inference(backward_demodulation,[status(thm)],[f726,f695]) ).
fof(f734,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| is_a_theorem(implies(implies(not(X0),X1),or(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f630,f730]) ).
fof(f736,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f564,f734]) ).
fof(f753,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))) ),
inference(paramodulation,[status(thm)],[f511,f736]) ).
fof(f765,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ6_spl
| ~ is_a_theorem(implies(X3,implies(X0,equiv(X1,X2))))
| ~ is_a_theorem(X3)
| X1 = X2
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f638,f201]) ).
fof(f2877,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ is_a_theorem(implies(X1,X0))
| X1 = X0
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f765,f367]) ).
fof(f2929,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| or(X1,X0) = or(X0,X1)
| ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[status(thm)],[f2877,f736]) ).
fof(f2936,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| implies(X1,X0) = or(X0,not(X1))
| ~ is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))) ),
inference(resolution,[status(thm)],[f2877,f753]) ).
fof(f2962,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| or(X0,X1) = or(X1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2929,f736]) ).
fof(f2974,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| implies(X1,X0) = or(X0,not(X1))
| ~ is_a_theorem(or(and(not(X0),X1),implies(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f726,f2936]) ).
fof(f2993,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| implies(implies(X0,X1),X2) = or(and(not(X1),X0),X2) ),
inference(backward_demodulation,[status(thm)],[f3265,f726]) ).
fof(f3001,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| and(not(X0),X1) = not(implies(X1,X0)) ),
inference(backward_demodulation,[status(thm)],[f3265,f631]) ).
fof(f3265,plain,
! [X0,X1] :
( ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| implies(X0,X1) = or(X1,not(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2974,f729]) ).
fof(f3321,plain,
! [X0,X1] :
( ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| and(X0,X1) = and(not(not(X1)),X0) ),
inference(backward_demodulation,[status(thm)],[f3001,f559]) ).
fof(f3623,plain,
! [X0,X1] :
( ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| implies(not(not(X0)),X1) = not(and(not(X1),X0)) ),
inference(paramodulation,[status(thm)],[f3321,f504]) ).
fof(f3690,plain,
! [X0,X1] :
( ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| or(not(X0),X1) = not(and(not(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f564,f3623]) ).
fof(f3704,plain,
! [X0,X1] :
( ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| implies(X0,X1) = not(and(not(X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f511,f3690]) ).
fof(f4354,plain,
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| sQ77_spl
| ~ is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK53_skl,sK52_skl),or(sK52_skl,sK54_skl)))) ),
inference(paramodulation,[status(thm)],[f2962,f484]) ).
fof(f4719,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| implies(not(X0),X1) = implies(not(X1),X0) ),
inference(paramodulation,[status(thm)],[f504,f3704]) ).
fof(f4746,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| or(X0,X1) = implies(not(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f564,f4719]) ).
fof(f5008,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ19_spl
| is_a_theorem(or(and(not(X0),X1),implies(or(X1,X2),or(X2,X0)))) ),
inference(paramodulation,[status(thm)],[f4746,f712]) ).
fof(f5045,plain,
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| sQ77_spl
| ~ sQ19_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f4354,f5046]) ).
fof(f5046,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ79_spl
| ~ sQ10_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(or(X0,X2),or(X2,X1)))) ),
inference(forward_demodulation,[status(thm)],[f2993,f5008]) ).
fof(f5066,plain,
( ~ sQ79_spl
| ~ sQ83_spl
| ~ sQ10_spl
| ~ sQ81_spl
| ~ sQ85_spl
| ~ sQ46_spl
| ~ sQ1_spl
| ~ sQ6_spl
| sQ77_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f5045]) ).
fof(f5067,plain,
( ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f476,f196]) ).
fof(f5068,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f5067]) ).
fof(f5069,plain,
$false,
inference(sat_refutation,[status(thm)],[f203,f222,f237,f270,f369,f485,f492,f499,f506,f513,f524,f526,f528,f530,f556,f558,f592,f611,f616,f5066,f5068]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL458+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n002.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 00:35:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 4.37/0.99 % Refutation found
% 4.37/0.99 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.37/0.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.43/1.05 % Elapsed time: 0.666185 seconds
% 2.43/1.05 % CPU time: 4.928370 seconds
% 2.43/1.05 % Total memory used: 191.124 MB
% 2.43/1.05 % Net memory used: 184.827 MB
%------------------------------------------------------------------------------