%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL519+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 : 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 01:07:54 PM UTC 2026
% Result : Theorem 12.72s 2.04s
% Output : CNFRefutation 12.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of formulae : 140 ( 74 unt; 0 def)
% Number of atoms : 261 ( 46 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 208 ( 87 ~; 84 |; 22 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 12 con; 0-2 aty)
% Number of variables : 256 ( 242 !; 14 ?)
% 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(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(f23,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
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(f31,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
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(f34,axiom,
op_equiv,
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(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ r2,
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(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(f139,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f140,plain,
( ( ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f139]) ).
fof(f142,plain,
( ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))
| r2 ),
inference(cnf_transformation,[status(thm)],[f140]) ).
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(f157,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f158,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(thm)],[f157]) ).
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(f161,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f162,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(thm)],[f161]) ).
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(f173,plain,
op_implies_or,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f174,plain,
op_and,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f176,plain,
~ r2,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f177,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f168]) ).
fof(f178,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f172]) ).
fof(f179,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f113,f169]) ).
fof(f180,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f179,f177]) ).
fof(f182,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f117,f170]) ).
fof(f183,plain,
! [X0,X1] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X0,X1)) ),
inference(resolution,[status(thm)],[f182,f177]) ).
fof(f184,plain,
! [X0,X1] : is_a_theorem(and(implies(and(X0,X1),X0),implies(and(X0,X1),X0))),
inference(resolution,[status(thm)],[f182,f180]) ).
fof(f185,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f162,f173]) ).
fof(f187,plain,
~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f142,f176]) ).
fof(f188,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f160,f166]) ).
fof(f190,plain,
! [X0,X1,X2] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2),
inference(paramodulation,[status(thm)],[f188,f185]) ).
fof(f191,plain,
! [X0,X1] :
( or(X0,X1) = implies(not(X0),X1)
| ~ op_or ),
inference(forward_demodulation,[status(thm)],[f188,f156]) ).
fof(f198,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f191,f165]) ).
fof(f199,plain,
! [X0,X1,X2] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(paramodulation,[status(thm)],[f188,f198]) ).
fof(f201,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(paramodulation,[status(thm)],[f198,f177]) ).
fof(f209,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(not(not(X0))) ),
inference(paramodulation,[status(thm)],[f185,f201]) ).
fof(f210,plain,
! [X0,X1] :
( and(X0,X1) = not(implies(X0,not(X1)))
| ~ op_and ),
inference(forward_demodulation,[status(thm)],[f185,f158]) ).
fof(f211,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f210,f174]) ).
fof(f212,plain,
! [X0,X1] : and(not(X0),X1) = not(or(X0,not(X1))),
inference(paramodulation,[status(thm)],[f198,f211]) ).
fof(f222,plain,
! [X0,X1] : and(not(not(X0)),X1) = not(implies(X0,not(X1))),
inference(paramodulation,[status(thm)],[f185,f212]) ).
fof(f230,plain,
! [X0,X1,X2] : implies(X0,or(X1,not(X2))) = not(and(X0,and(not(X1),X2))),
inference(paramodulation,[status(thm)],[f212,f188]) ).
fof(f232,plain,
! [X0,X1] : and(not(not(X0)),X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f211,f222]) ).
fof(f236,plain,
! [X0,X1,X2] : and(not(and(X0,X1)),X2) = and(implies(X0,not(X1)),X2),
inference(paramodulation,[status(thm)],[f211,f232]) ).
fof(f240,plain,
! [X0,X1] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(and(X0,X1)) ),
inference(paramodulation,[status(thm)],[f232,f183]) ).
fof(f257,plain,
! [X0,X1] :
( is_a_theorem(not(not(not(not(X0)))))
| ~ is_a_theorem(and(X0,X1)) ),
inference(paramodulation,[status(thm)],[f232,f240]) ).
fof(f271,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f164,f167]) ).
fof(f273,plain,
! [X0,X1] : equiv(X0,not(X1)) = and(implies(X0,not(X1)),or(X1,X0)),
inference(paramodulation,[status(thm)],[f198,f271]) ).
fof(f278,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(paramodulation,[status(thm)],[f271,f179]) ).
fof(f283,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f278,f177]) ).
fof(f392,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(not(not(X0)))) ),
inference(paramodulation,[status(thm)],[f198,f209]) ).
fof(f592,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0)))))
| ~ kn3 ),
inference(forward_demodulation,[status(thm)],[f198,f121]) ).
fof(f593,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(forward_subsumption_resolution,[status(thm)],[f592,f171]) ).
fof(f595,plain,
! [X0,X1,X2] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f593,f177]) ).
fof(f601,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))),
inference(paramodulation,[status(thm)],[f198,f593]) ).
fof(f608,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f188,f601]) ).
fof(f835,plain,
! [X0,X1] : is_a_theorem(not(not(not(not(implies(and(X0,X1),X0)))))),
inference(resolution,[status(thm)],[f184,f257]) ).
fof(f920,plain,
! [X0,X1] : is_a_theorem(not(not(not(and(and(not(X0),X1),X0))))),
inference(paramodulation,[status(thm)],[f211,f835]) ).
fof(f921,plain,
! [X0,X1] : is_a_theorem(not(not(not(not(or(implies(X0,X1),X0)))))),
inference(paramodulation,[status(thm)],[f190,f835]) ).
fof(f1758,plain,
! [X0,X1] : equiv(X0,not(X1)) = and(not(and(X0,X1)),or(X1,X0)),
inference(forward_demodulation,[status(thm)],[f236,f273]) ).
fof(f1759,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = and(implies(X0,X1),or(not(X1),X0)),
inference(paramodulation,[status(thm)],[f188,f1758]) ).
fof(f1790,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f185,f1759]) ).
fof(f1791,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = equiv(X0,X1),
inference(forward_demodulation,[status(thm)],[f271,f1790]) ).
fof(f1831,plain,
! [X0,X1] :
( X0 = not(not(X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1791,f178]) ).
fof(f1895,plain,
! [X0,X1] : is_a_theorem(or(and(and(X0,X0),X1),not(and(X1,X0)))),
inference(resolution,[status(thm)],[f595,f179]) ).
fof(f1900,plain,
! [X0,X1,X2] :
( is_a_theorem(or(and(X1,X2),not(and(X2,not(X0)))))
| ~ is_a_theorem(or(X0,X1)) ),
inference(paramodulation,[status(thm)],[f198,f595]) ).
fof(f1907,plain,
! [X0,X1,X2] :
( is_a_theorem(or(and(X1,X2),implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f188,f1900]) ).
fof(f2126,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(or(and(and(not(X0),X1),X0),X2)) ),
inference(resolution,[status(thm)],[f392,f920]) ).
fof(f2128,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(or(not(or(implies(X0,X1),X0)),X2)) ),
inference(resolution,[status(thm)],[f392,f921]) ).
fof(f2135,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(or(implies(X0,X1),X0),X2)) ),
inference(forward_demodulation,[status(thm)],[f185,f2128]) ).
fof(f2214,plain,
! [X0,X1,X2] : is_a_theorem(or(and(X0,X1),implies(X1,implies(X0,X2)))),
inference(resolution,[status(thm)],[f608,f2135]) ).
fof(f2312,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(X1),implies(X0,X2)))),
inference(paramodulation,[status(thm)],[f199,f2214]) ).
fof(f2333,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f198,f2312]) ).
fof(f2689,plain,
! [X0,X1,X2] :
( is_a_theorem(or(X1,implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f2333,f177]) ).
fof(f8051,plain,
! [X0] : is_a_theorem(not(and(X0,not(X0)))),
inference(resolution,[status(thm)],[f2126,f1895]) ).
fof(f8078,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[status(thm)],[f188,f8051]) ).
fof(f8090,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f283,f8078]) ).
fof(f8094,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(resolution,[status(thm)],[f8078,f2689]) ).
fof(f8095,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(resolution,[status(thm)],[f8078,f595]) ).
fof(f8116,plain,
! [X0] : X0 = not(not(X0)),
inference(resolution,[status(thm)],[f8090,f1831]) ).
fof(f8176,plain,
! [X0,X1] : or(X0,not(X1)) = not(and(not(X0),X1)),
inference(paramodulation,[status(thm)],[f212,f8116]) ).
fof(f8179,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and(X0,X1)),
inference(paramodulation,[status(thm)],[f211,f8116]) ).
fof(f10226,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),not(and(not(X1),X0)))),
inference(paramodulation,[status(thm)],[f199,f8095]) ).
fof(f10233,plain,
! [X0,X1] : is_a_theorem(or(and(not(X0),X1),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f188,f8095]) ).
fof(f10244,plain,
! [X0,X1] : is_a_theorem(not(and(implies(X0,X1),and(not(X1),X0)))),
inference(forward_demodulation,[status(thm)],[f8179,f10226]) ).
fof(f10245,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(forward_demodulation,[status(thm)],[f230,f10244]) ).
fof(f14359,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(not(and(not(X0),X1))) ),
inference(resolution,[status(thm)],[f10233,f201]) ).
fof(f14390,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(forward_demodulation,[status(thm)],[f8176,f14359]) ).
fof(f40151,plain,
! [X0,X1,X2] : is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0))),
inference(resolution,[status(thm)],[f1907,f8094]) ).
fof(f46548,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),implies(not(X2),X0))),
inference(paramodulation,[status(thm)],[f199,f40151]) ).
fof(f46589,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(implies(X0,X1),X2),or(X2,X0))),
inference(forward_demodulation,[status(thm)],[f198,f46548]) ).
fof(f48099,plain,
! [X0,X1,X2] :
( is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f46589,f177]) ).
fof(f49218,plain,
! [X0,X1] : is_a_theorem(or(or(X0,not(X1)),X1)),
inference(resolution,[status(thm)],[f48099,f10245]) ).
fof(f49346,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,not(not(X0))))),
inference(resolution,[status(thm)],[f49218,f14390]) ).
fof(f49381,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,X0))),
inference(forward_demodulation,[status(thm)],[f8116,f49346]) ).
fof(f49394,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f187,f49381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL519+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n006.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 00:36:42 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 12.72/2.04 % Refutation found
% 12.72/2.04 % SZS status Theorem for theBenchmark: Theorem is valid
% 12.72/2.04 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.92/2.15 % Elapsed time: 1.785984 seconds
% 5.92/2.15 % CPU time: 13.584918 seconds
% 5.92/2.15 % Total memory used: 309.949 MB
% 5.92/2.15 % Net memory used: 297.463 MB
%------------------------------------------------------------------------------