%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL495+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 : n026.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 01:07:51 PM UTC 2026
% Result : Theorem 62.80s 18.37s
% Output : CNFRefutation 49.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 26
% Syntax : Number of formulae : 175 ( 97 unt; 0 def)
% Number of atoms : 315 ( 59 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 245 ( 105 ~; 97 |; 26 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-2 aty)
% Number of variables : 293 ( 274 !; 19 ?)
% 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(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(f22,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),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(f24,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
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(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_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_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,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ equivalence_3,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,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(f48,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)],[f47]) ).
fof(f49,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)],[f48]) ).
fof(f50,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)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f55,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f56,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)],[f55]) ).
fof(f57,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)],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f109,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(f110,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)],[f109]) ).
fof(f112,plain,
( ~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl))))
| equivalence_3 ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f137,plain,
( ( ? [P] : ~ is_a_theorem(implies(or(P,P),P))
| r1 )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f138,plain,
( ( ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))
| r1 )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f137]) ).
fof(f139,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f141,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(f142,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)],[f141]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f145,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f146,plain,
( ( ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f145]) ).
fof(f147,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[status(thm)],[f146]) ).
fof(f149,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| r4 )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f150,plain,
( ( ~ is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl))))
| r4 )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl]),skolemize(P,sK49_skl),skolemize(Q,sK50_skl),skolemize(R,sK51_skl)],[f149]) ).
fof(f151,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f153,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(f154,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)],[f153]) ).
fof(f155,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))
| ~ r5 ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f157,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f158,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f159,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f160,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f161,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f162,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f163,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f164,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f165,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f166,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f167,plain,
op_implies_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f168,plain,
op_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f169,plain,
op_equiv,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f170,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f171,plain,
r1,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f172,plain,
r2,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f173,plain,
r3,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f174,plain,
r4,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f175,plain,
r5,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f176,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f177,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f178,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f180,plain,
~ equivalence_3,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f181,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(backward_subsumption_resolution,[status(thm)],[f164,f167]) ).
fof(f182,plain,
! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))),
inference(backward_subsumption_resolution,[status(thm)],[f160,f168]) ).
fof(f183,plain,
! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f166,f169]) ).
fof(f184,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f170]) ).
fof(f185,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(backward_subsumption_resolution,[status(thm)],[f139,f171]) ).
fof(f186,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,X0))),
inference(backward_subsumption_resolution,[status(thm)],[f143,f172]) ).
fof(f187,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(backward_subsumption_resolution,[status(thm)],[f147,f173]) ).
fof(f188,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(backward_subsumption_resolution,[status(thm)],[f151,f174]) ).
fof(f189,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(backward_subsumption_resolution,[status(thm)],[f155,f175]) ).
fof(f190,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[f58,f176]) ).
fof(f191,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(backward_subsumption_resolution,[status(thm)],[f158,f177]) ).
fof(f192,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(backward_subsumption_resolution,[status(thm)],[f162,f178]) ).
fof(f193,plain,
~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))),
inference(backward_subsumption_resolution,[status(thm)],[f112,f180]) ).
fof(f194,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_demodulation,[status(thm)],[f181,f182]) ).
fof(f196,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(backward_demodulation,[status(thm)],[f192,f191]) ).
fof(f213,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(paramodulation,[status(thm)],[f181,f186]) ).
fof(f214,plain,
! [X0] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(paramodulation,[status(thm)],[f181,f185]) ).
fof(f223,plain,
! [X0,X1,X2] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(paramodulation,[status(thm)],[f192,f196]) ).
fof(f226,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f196,f213]) ).
fof(f230,plain,
! [X0,X1] : equiv(X0,not(X1)) = and(implies(X0,not(X1)),or(X1,X0)),
inference(paramodulation,[status(thm)],[f196,f183]) ).
fof(f232,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(paramodulation,[status(thm)],[f196,f184]) ).
fof(f234,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,not(not(X0))))),
inference(paramodulation,[status(thm)],[f181,f226]) ).
fof(f243,plain,
! [X0,X1] : and(not(X0),X1) = not(or(X0,not(X1))),
inference(paramodulation,[status(thm)],[f196,f194]) ).
fof(f245,plain,
! [X0,X1,X2] : and(X0,and(X1,not(X2))) = not(implies(X0,implies(X1,X2))),
inference(paramodulation,[status(thm)],[f192,f194]) ).
fof(f249,plain,
! [X0,X1,X2] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(paramodulation,[status(thm)],[f194,f181]) ).
fof(f250,plain,
! [X0,X1,X2] : implies(X0,implies(X1,not(X2))) = not(and(X0,and(X1,X2))),
inference(paramodulation,[status(thm)],[f194,f192]) ).
fof(f254,plain,
! [X0] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(backward_demodulation,[status(thm)],[f249,f214]) ).
fof(f255,plain,
! [X0,X1] : is_a_theorem(not(and(X0,and(X1,not(X0))))),
inference(backward_demodulation,[status(thm)],[f250,f234]) ).
fof(f256,plain,
! [X0,X1] : is_a_theorem(not(not(implies(X0,implies(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f245,f255]) ).
fof(f258,plain,
! [X0] : is_a_theorem(or(equiv(X0,X0),not(implies(X0,X0)))),
inference(paramodulation,[status(thm)],[f183,f254]) ).
fof(f267,plain,
! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f187,f184]) ).
fof(f270,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f181,f187]) ).
fof(f314,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f181,f267]) ).
fof(f353,plain,
! [X0,X1] : is_a_theorem(not(not(implies(X0,or(X1,X0))))),
inference(paramodulation,[status(thm)],[f196,f256]) ).
fof(f387,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(or(not(implies(X0,or(X1,X0))),X2)) ),
inference(resolution,[status(thm)],[f232,f353]) ).
fof(f392,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,or(X1,X0)),X2)) ),
inference(forward_demodulation,[status(thm)],[f181,f387]) ).
fof(f407,plain,
! [X0,X1] : and(not(not(X0)),X1) = not(implies(X0,not(X1))),
inference(paramodulation,[status(thm)],[f181,f243]) ).
fof(f426,plain,
! [X0,X1] : and(not(not(X0)),X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f194,f407]) ).
fof(f436,plain,
! [X0,X1,X2] : and(not(and(X0,X1)),X2) = and(implies(X0,not(X1)),X2),
inference(paramodulation,[status(thm)],[f194,f426]) ).
fof(f440,plain,
! [X0,X1] : equiv(X0,not(X1)) = and(not(and(X0,X1)),or(X1,X0)),
inference(backward_demodulation,[status(thm)],[f436,f230]) ).
fof(f504,plain,
! [X0] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(resolution,[status(thm)],[f314,f258]) ).
fof(f505,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[f314,f254]) ).
fof(f517,plain,
! [X0,X1,X2] :
( is_a_theorem(or(X1,or(X0,X2)))
| ~ is_a_theorem(or(X0,or(X1,X2))) ),
inference(resolution,[status(thm)],[f188,f184]) ).
fof(f519,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(paramodulation,[status(thm)],[f181,f188]) ).
fof(f523,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f181,f519]) ).
fof(f530,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f181,f189]) ).
fof(f532,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f181,f530]) ).
fof(f534,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f504,f184]) ).
fof(f546,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f532,f184]) ).
fof(f555,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f546,f184]) ).
fof(f561,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f505,f184]) ).
fof(f918,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),not(not(X0)))),
inference(paramodulation,[status(thm)],[f223,f254]) ).
fof(f973,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),not(not(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f918]) ).
fof(f1068,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[status(thm)],[f973,f184]) ).
fof(f1428,plain,
! [X0,X1,X2] : equiv(X0,implies(X1,not(X2))) = and(implies(X0,implies(X1,not(X2))),or(and(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f249,f183]) ).
fof(f1480,plain,
! [X0,X1,X2] : equiv(X0,implies(X1,not(X2))) = and(not(and(X0,and(X1,X2))),or(and(X1,X2),X0)),
inference(forward_demodulation,[status(thm)],[f250,f1428]) ).
fof(f1484,plain,
! [X0,X1,X2] : equiv(X0,implies(X1,not(X2))) = equiv(X0,not(and(X1,X2))),
inference(forward_demodulation,[status(thm)],[f440,f1480]) ).
fof(f2175,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = and(implies(X0,X1),or(not(X1),X0)),
inference(paramodulation,[status(thm)],[f192,f440]) ).
fof(f2188,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f181,f2175]) ).
fof(f2193,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = equiv(X0,X1),
inference(forward_demodulation,[status(thm)],[f183,f2188]) ).
fof(f2215,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,or(X0,X2)))
| ~ is_a_theorem(or(X0,or(not(X1),X2))) ),
inference(paramodulation,[status(thm)],[f181,f517]) ).
fof(f2221,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(X1,or(X0,X2)))
| ~ is_a_theorem(or(X0,implies(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f181,f2215]) ).
fof(f2234,plain,
! [X0,X1] :
( X0 = not(not(X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2193,f190]) ).
fof(f2258,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,X0))
| X0 = not(not(X0)) ),
inference(resolution,[status(thm)],[f2234,f534]) ).
fof(f2266,plain,
! [X0] : or(X0,X0) = not(not(or(X0,X0))),
inference(resolution,[status(thm)],[f2258,f187]) ).
fof(f2287,plain,
! [X0,X1] :
( ~ is_a_theorem(or(and(X0,X1),implies(X0,not(X1))))
| implies(X0,not(X1)) = not(not(implies(X0,not(X1)))) ),
inference(paramodulation,[status(thm)],[f249,f2258]) ).
fof(f2309,plain,
! [X0,X1] :
( ~ is_a_theorem(or(and(X0,X1),implies(X0,not(X1))))
| implies(X0,not(X1)) = not(and(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f194,f2287]) ).
fof(f2860,plain,
! [X0] : or(not(X0),not(X0)) = not(and(not(not(X0)),X0)),
inference(paramodulation,[status(thm)],[f243,f2266]) ).
fof(f2923,plain,
! [X0] : implies(X0,not(X0)) = not(and(not(not(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f181,f2860]) ).
fof(f2926,plain,
! [X0] : implies(X0,not(X0)) = not(and(X0,X0)),
inference(forward_demodulation,[status(thm)],[f426,f2923]) ).
fof(f3199,plain,
! [X0] : or(X0,not(not(X0))) = not(and(not(X0),not(X0))),
inference(paramodulation,[status(thm)],[f196,f2926]) ).
fof(f3221,plain,
! [X0] : is_a_theorem(or(X0,not(and(X0,X0)))),
inference(paramodulation,[status(thm)],[f2926,f226]) ).
fof(f3255,plain,
! [X0] : or(X0,not(not(X0))) = implies(not(X0),X0),
inference(forward_demodulation,[status(thm)],[f192,f3199]) ).
fof(f3258,plain,
! [X0] : or(X0,not(not(X0))) = or(X0,X0),
inference(forward_demodulation,[status(thm)],[f196,f3255]) ).
fof(f3330,plain,
! [X0] : is_a_theorem(implies(and(X0,X0),X0)),
inference(resolution,[status(thm)],[f3221,f314]) ).
fof(f3384,plain,
! [X0] : is_a_theorem(implies(equiv(X0,X0),implies(X0,X0))),
inference(paramodulation,[status(thm)],[f183,f3330]) ).
fof(f3400,plain,
! [X0] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(equiv(X0,X0)) ),
inference(resolution,[status(thm)],[f3384,f184]) ).
fof(f3436,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,not(X1)),implies(X0,not(X1))))
| ~ is_a_theorem(equiv(implies(X0,not(X1)),not(and(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f1484,f3400]) ).
fof(f3440,plain,
! [X0,X1] :
( is_a_theorem(or(and(X0,X1),implies(X0,not(X1))))
| ~ is_a_theorem(equiv(implies(X0,not(X1)),not(and(X0,X1)))) ),
inference(forward_demodulation,[status(thm)],[f249,f3436]) ).
fof(f3551,plain,
! [X0] : and(not(X0),not(X0)) = not(or(X0,X0)),
inference(paramodulation,[status(thm)],[f3258,f243]) ).
fof(f5656,plain,
! [X0] :
( is_a_theorem(not(or(X0,X0)))
| ~ is_a_theorem(not(X0)) ),
inference(paramodulation,[status(thm)],[f3551,f561]) ).
fof(f6196,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(not(or(not(X0),not(X0)))) ),
inference(resolution,[status(thm)],[f5656,f1068]) ).
fof(f6207,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(and(not(not(X0)),X0)) ),
inference(forward_demodulation,[status(thm)],[f243,f6196]) ).
fof(f6208,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(and(X0,X0)) ),
inference(forward_demodulation,[status(thm)],[f426,f6207]) ).
fof(f6241,plain,
! [X0] :
( ~ is_a_theorem(or(implies(X0,X0),implies(X0,X0)))
| is_a_theorem(equiv(X0,X0)) ),
inference(paramodulation,[status(thm)],[f183,f6208]) ).
fof(f7221,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f392,f523]) ).
fof(f7276,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f6241,f7221]) ).
fof(f7279,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f3400,f7276]) ).
fof(f7652,plain,
! [X0,X1] : is_a_theorem(equiv(implies(X0,not(X1)),not(and(X0,X1)))),
inference(paramodulation,[status(thm)],[f1484,f7276]) ).
fof(f7653,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),implies(X0,not(X1)))),
inference(backward_subsumption_resolution,[status(thm)],[f3440,f7652]) ).
fof(f7654,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and(X0,X1)),
inference(backward_subsumption_resolution,[status(thm)],[f2309,f7653]) ).
fof(f7841,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(paramodulation,[status(thm)],[f196,f7279]) ).
fof(f16094,plain,
! [X0] :
( ~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),X0))
| ~ is_a_theorem(implies(X0,implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))) ),
inference(resolution,[status(thm)],[f555,f193]) ).
fof(f16223,plain,
~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),or(equiv(sK30_skl,sK31_skl),not(implies(sK31_skl,sK30_skl))))),
inference(resolution,[status(thm)],[f16094,f270]) ).
fof(f17228,plain,
~ is_a_theorem(or(equiv(sK30_skl,sK31_skl),implies(implies(sK30_skl,sK31_skl),not(implies(sK31_skl,sK30_skl))))),
inference(resolution,[status(thm)],[f16223,f2221]) ).
fof(f17235,plain,
~ is_a_theorem(or(equiv(sK30_skl,sK31_skl),not(and(implies(sK30_skl,sK31_skl),implies(sK31_skl,sK30_skl))))),
inference(forward_demodulation,[status(thm)],[f7654,f17228]) ).
fof(f17236,plain,
~ is_a_theorem(or(equiv(sK30_skl,sK31_skl),not(equiv(sK30_skl,sK31_skl)))),
inference(forward_demodulation,[status(thm)],[f183,f17235]) ).
fof(f17237,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f17236,f7841]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL495+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n026.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Mon Sep 21 00:39:18 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.39 % Drodi V4.1.1
% 62.80/18.37 % Refutation found
% 62.80/18.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 62.80/18.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.08/18.59 % Elapsed time: 8.180617 seconds
% 14.08/18.59 % CPU time: 64.424003 seconds
% 14.08/18.59 % Total memory used: 833.168 MB
% 14.08/18.59 % Net memory used: 795.354 MB
%------------------------------------------------------------------------------