%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL489+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 01:07:50 PM UTC 2026
% Result : Theorem 22.95s 3.43s
% Output : CNFRefutation 22.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 26
% Syntax : Number of formulae : 166 ( 90 unt; 0 def)
% Number of atoms : 304 ( 57 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 240 ( 102 ~; 95 |; 26 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 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 : 276 ( 257 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ and_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(f85,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f86,plain,
( ( ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f85]) ).
fof(f88,plain,
( ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl))))
| and_3 ),
inference(cnf_transformation,[status(thm)],[f86]) ).
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,
~ and_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(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))),
inference(backward_subsumption_resolution,[status(thm)],[f88,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(f208,plain,
! [X0,X1,X2] : implies(X0,implies(X1,not(X2))) = not(and(X0,and(X1,X2))),
inference(paramodulation,[status(thm)],[f194,f192]) ).
fof(f209,plain,
! [X0,X1,X2] : and(X0,and(X1,not(X2))) = not(implies(X0,implies(X1,X2))),
inference(paramodulation,[status(thm)],[f192,f194]) ).
fof(f214,plain,
! [X0,X1,X2] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(paramodulation,[status(thm)],[f194,f181]) ).
fof(f217,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(paramodulation,[status(thm)],[f181,f186]) ).
fof(f218,plain,
! [X0] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(paramodulation,[status(thm)],[f181,f185]) ).
fof(f220,plain,
! [X0] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(forward_demodulation,[status(thm)],[f214,f218]) ).
fof(f228,plain,
! [X0,X1,X2] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(paramodulation,[status(thm)],[f192,f196]) ).
fof(f232,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(paramodulation,[status(thm)],[f196,f217]) ).
fof(f234,plain,
! [X0,X1] : and(not(X0),X1) = not(or(X0,not(X1))),
inference(paramodulation,[status(thm)],[f196,f194]) ).
fof(f237,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(f248,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,not(not(X0))))),
inference(paramodulation,[status(thm)],[f181,f232]) ).
fof(f252,plain,
! [X0,X1] : is_a_theorem(not(and(X0,and(X1,not(X0))))),
inference(forward_demodulation,[status(thm)],[f208,f248]) ).
fof(f253,plain,
! [X0,X1] : is_a_theorem(not(not(implies(X0,implies(X1,X0))))),
inference(forward_demodulation,[status(thm)],[f209,f252]) ).
fof(f263,plain,
! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f187,f184]) ).
fof(f266,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f181,f187]) ).
fof(f310,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(paramodulation,[status(thm)],[f181,f263]) ).
fof(f338,plain,
! [X0,X1] : is_a_theorem(not(not(implies(X0,or(X1,X0))))),
inference(paramodulation,[status(thm)],[f196,f253]) ).
fof(f370,plain,
! [X0,X1] : equiv(X0,not(X1)) = and(implies(X0,not(X1)),or(X1,X0)),
inference(paramodulation,[status(thm)],[f196,f183]) ).
fof(f385,plain,
! [X0,X1] : and(not(not(X0)),X1) = not(implies(X0,not(X1))),
inference(paramodulation,[status(thm)],[f181,f234]) ).
fof(f402,plain,
! [X0,X1] : and(not(not(X0)),X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f194,f385]) ).
fof(f413,plain,
! [X0,X1,X2] : and(not(and(X0,X1)),X2) = and(implies(X0,not(X1)),X2),
inference(paramodulation,[status(thm)],[f194,f402]) ).
fof(f416,plain,
! [X0,X1] : equiv(X0,not(X1)) = and(not(and(X0,X1)),or(X1,X0)),
inference(backward_demodulation,[status(thm)],[f413,f370]) ).
fof(f461,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(or(not(implies(X0,or(X1,X0))),X2)) ),
inference(resolution,[status(thm)],[f237,f338]) ).
fof(f467,plain,
! [X0,X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(X0,or(X1,X0)),X2)) ),
inference(forward_demodulation,[status(thm)],[f181,f461]) ).
fof(f549,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[f310,f220]) ).
fof(f562,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(f564,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(f568,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f181,f564]) ).
fof(f572,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f549,f184]) ).
fof(f591,plain,
! [X0] :
( is_a_theorem(and(X0,not(not(X0))))
| ~ is_a_theorem(not(not(X0))) ),
inference(paramodulation,[status(thm)],[f402,f572]) ).
fof(f593,plain,
! [X0] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(paramodulation,[status(thm)],[f183,f572]) ).
fof(f705,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(f707,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f181,f705]) ).
fof(f710,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X2,X0),implies(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f707,f184]) ).
fof(f719,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)],[f710,f184]) ).
fof(f1781,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),not(not(X0)))),
inference(paramodulation,[status(thm)],[f228,f220]) ).
fof(f1855,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),not(not(X0)))),
inference(forward_demodulation,[status(thm)],[f196,f1781]) ).
fof(f1917,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(resolution,[status(thm)],[f1855,f184]) ).
fof(f2380,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = and(implies(X0,X1),or(not(X1),X0)),
inference(paramodulation,[status(thm)],[f192,f416]) ).
fof(f2395,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = and(implies(X0,X1),implies(X1,X0)),
inference(forward_demodulation,[status(thm)],[f181,f2380]) ).
fof(f2397,plain,
! [X0,X1] : equiv(X0,not(not(X1))) = equiv(X0,X1),
inference(forward_demodulation,[status(thm)],[f183,f2395]) ).
fof(f2427,plain,
! [X0,X1] :
( X0 = not(not(X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2397,f190]) ).
fof(f2441,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,X0))
| X0 = not(not(X0)) ),
inference(resolution,[status(thm)],[f2427,f593]) ).
fof(f2447,plain,
! [X0] : or(X0,X0) = not(not(or(X0,X0))),
inference(resolution,[status(thm)],[f2441,f187]) ).
fof(f2468,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)],[f214,f2441]) ).
fof(f2489,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,f2468]) ).
fof(f2616,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,f562]) ).
fof(f2622,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,f2616]) ).
fof(f3401,plain,
! [X0] : or(not(X0),not(X0)) = not(and(not(not(X0)),X0)),
inference(paramodulation,[status(thm)],[f234,f2447]) ).
fof(f3466,plain,
! [X0] : implies(X0,not(X0)) = not(and(not(not(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f181,f3401]) ).
fof(f3469,plain,
! [X0] : implies(X0,not(X0)) = not(and(X0,X0)),
inference(forward_demodulation,[status(thm)],[f402,f3466]) ).
fof(f3845,plain,
! [X0] : is_a_theorem(or(X0,not(and(X0,X0)))),
inference(paramodulation,[status(thm)],[f3469,f232]) ).
fof(f3846,plain,
! [X0] : and(X0,X0) = not(not(and(X0,X0))),
inference(paramodulation,[status(thm)],[f3469,f194]) ).
fof(f4115,plain,
! [X0] : and(not(not(X0)),not(not(X0))) = not(not(and(X0,not(not(X0))))),
inference(paramodulation,[status(thm)],[f402,f3846]) ).
fof(f4195,plain,
! [X0] : and(X0,not(not(X0))) = not(not(and(X0,not(not(X0))))),
inference(forward_demodulation,[status(thm)],[f402,f4115]) ).
fof(f4196,plain,
! [X0] : and(X0,not(not(X0))) = not(implies(X0,not(X0))),
inference(forward_demodulation,[status(thm)],[f192,f4195]) ).
fof(f4201,plain,
! [X0] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(not(not(X0))) ),
inference(backward_demodulation,[status(thm)],[f4202,f591]) ).
fof(f4202,plain,
! [X0] : and(X0,not(not(X0))) = and(X0,X0),
inference(forward_demodulation,[status(thm)],[f194,f4196]) ).
fof(f4722,plain,
! [X0] : is_a_theorem(implies(and(X0,X0),X0)),
inference(resolution,[status(thm)],[f3845,f310]) ).
fof(f4776,plain,
! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X0,X0)) ),
inference(resolution,[status(thm)],[f4722,f184]) ).
fof(f4826,plain,
! [X0] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(equiv(X0,X0)) ),
inference(paramodulation,[status(thm)],[f183,f4776]) ).
fof(f5485,plain,
! [X0] :
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(and(X0,X0)) ),
inference(resolution,[status(thm)],[f4201,f1917]) ).
fof(f5519,plain,
! [X0] :
( ~ is_a_theorem(or(implies(X0,X0),implies(X0,X0)))
| is_a_theorem(equiv(X0,X0)) ),
inference(paramodulation,[status(thm)],[f183,f5485]) ).
fof(f8458,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X1,X1))),
inference(resolution,[status(thm)],[f467,f568]) ).
fof(f8512,plain,
! [X0] : is_a_theorem(equiv(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f5519,f8458]) ).
fof(f8515,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[f4826,f8512]) ).
fof(f8895,plain,
! [X0,X1] : is_a_theorem(or(and(X0,X1),implies(X0,not(X1)))),
inference(paramodulation,[status(thm)],[f214,f8515]) ).
fof(f8897,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(paramodulation,[status(thm)],[f196,f8515]) ).
fof(f8901,plain,
! [X0,X1] : implies(X0,not(X1)) = not(and(X0,X1)),
inference(backward_subsumption_resolution,[status(thm)],[f2489,f8895]) ).
fof(f15833,plain,
! [X0] :
( ~ is_a_theorem(implies(sK17_skl,X0))
| ~ is_a_theorem(implies(X0,implies(sK18_skl,and(sK17_skl,sK18_skl)))) ),
inference(resolution,[status(thm)],[f719,f193]) ).
fof(f15899,plain,
~ is_a_theorem(implies(sK17_skl,or(and(sK17_skl,sK18_skl),not(sK18_skl)))),
inference(resolution,[status(thm)],[f15833,f266]) ).
fof(f15994,plain,
~ is_a_theorem(or(and(sK17_skl,sK18_skl),implies(sK17_skl,not(sK18_skl)))),
inference(resolution,[status(thm)],[f15899,f2622]) ).
fof(f16001,plain,
~ is_a_theorem(or(and(sK17_skl,sK18_skl),not(and(sK17_skl,sK18_skl)))),
inference(forward_demodulation,[status(thm)],[f8901,f15994]) ).
fof(f16002,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f16001,f8897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL489+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 00:30:56 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 22.95/3.43 % Refutation found
% 22.95/3.43 % SZS status Theorem for theBenchmark: Theorem is valid
% 22.95/3.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.72/3.54 % Elapsed time: 3.158288 seconds
% 4.72/3.54 % CPU time: 24.602185 seconds
% 4.72/3.54 % Total memory used: 571.853 MB
% 4.72/3.54 % Net memory used: 540.002 MB
%------------------------------------------------------------------------------