%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL518+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:07:54 PM UTC 2026
% Result : Theorem 0.22s 0.73s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 18
% Syntax : Number of formulae : 103 ( 63 unt; 0 def)
% Number of atoms : 184 ( 26 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 136 ( 55 ~; 52 |; 18 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 166 ( 155 !; 11 ?)
% 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(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(f22,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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,
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(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,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ r1,
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(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(f135,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(f136,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)],[f135]) ).
fof(f138,plain,
( ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))
| r1 ),
inference(cnf_transformation,[status(thm)],[f136]) ).
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(f165,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f166,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f168,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f169,plain,
kn1,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f170,plain,
kn2,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f171,plain,
kn3,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(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,
~ r1,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f177,plain,
~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f138,f176]) ).
fof(f178,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f49,f168]) ).
fof(f180,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f113,f169]) ).
fof(f181,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f117,f170]) ).
fof(f182,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f162,f173]) ).
fof(f187,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f160,f166]) ).
fof(f189,plain,
! [X0,X1,X2] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2),
inference(paramodulation,[status(thm)],[f187,f182]) ).
fof(f190,plain,
! [X0,X1] :
( or(X0,X1) = implies(not(X0),X1)
| ~ op_or ),
inference(forward_demodulation,[status(thm)],[f187,f156]) ).
fof(f197,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f190,f165]) ).
fof(f199,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(paramodulation,[status(thm)],[f197,f180]) ).
fof(f207,plain,
! [X0,X1] :
( and(X0,X1) = not(implies(X0,not(X1)))
| ~ op_and ),
inference(forward_demodulation,[status(thm)],[f182,f158]) ).
fof(f208,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f207,f174]) ).
fof(f209,plain,
! [X0,X1] : and(not(X0),X1) = not(or(X0,not(X1))),
inference(paramodulation,[status(thm)],[f197,f208]) ).
fof(f215,plain,
! [X0,X1,X2] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(paramodulation,[status(thm)],[f208,f197]) ).
fof(f217,plain,
! [X0,X1,X2] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(paramodulation,[status(thm)],[f208,f182]) ).
fof(f220,plain,
! [X0,X1] : and(not(not(X0)),X1) = not(implies(X0,not(X1))),
inference(paramodulation,[status(thm)],[f182,f209]) ).
fof(f230,plain,
! [X0,X1,X2] : implies(or(X0,not(X1)),X2) = or(and(not(X0),X1),X2),
inference(paramodulation,[status(thm)],[f209,f182]) ).
fof(f231,plain,
! [X0,X1] : and(not(not(X0)),X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f208,f220]) ).
fof(f236,plain,
! [X0,X1,X2] : and(not(implies(X0,X1)),X2) = and(and(X0,not(X1)),X2),
inference(paramodulation,[status(thm)],[f187,f231]) ).
fof(f237,plain,
! [X0] : is_a_theorem(or(not(X0),and(X0,not(not(X0))))),
inference(paramodulation,[status(thm)],[f231,f199]) ).
fof(f241,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),not(not(X0)))),
inference(paramodulation,[status(thm)],[f231,f181]) ).
fof(f243,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,not(not(X0))))),
inference(forward_demodulation,[status(thm)],[f182,f237]) ).
fof(f250,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),and(X0,not(not(not(not(X0))))))),
inference(paramodulation,[status(thm)],[f231,f243]) ).
fof(f254,plain,
! [X0] : is_a_theorem(or(not(X0),and(X0,not(not(not(not(X0))))))),
inference(forward_demodulation,[status(thm)],[f197,f250]) ).
fof(f255,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,not(not(not(not(X0))))))),
inference(forward_demodulation,[status(thm)],[f182,f254]) ).
fof(f299,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),not(not(X0)))),
inference(paramodulation,[status(thm)],[f189,f241]) ).
fof(f320,plain,
! [X0,X1] : is_a_theorem(or(or(X0,X1),not(not(not(X0))))),
inference(paramodulation,[status(thm)],[f197,f299]) ).
fof(f451,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)],[f197,f121]) ).
fof(f452,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)],[f451,f171]) ).
fof(f453,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)],[f452,f178]) ).
fof(f1404,plain,
! [X0,X1] : is_a_theorem(or(and(and(X0,not(not(not(not(X0))))),X1),not(and(X1,X0)))),
inference(resolution,[status(thm)],[f453,f255]) ).
fof(f1428,plain,
! [X0,X1] : is_a_theorem(or(and(not(implies(X0,not(not(not(X0))))),X1),not(and(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f236,f1404]) ).
fof(f1429,plain,
! [X0,X1] : is_a_theorem(implies(or(implies(X0,not(not(not(X0)))),not(X1)),not(and(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f230,f1428]) ).
fof(f1430,plain,
! [X0,X1] : is_a_theorem(implies(implies(and(X0,not(not(X0))),not(X1)),not(and(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f215,f1429]) ).
fof(f1431,plain,
! [X0,X1] : is_a_theorem(or(and(and(X0,not(not(X0))),X1),not(and(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f217,f1430]) ).
fof(f1432,plain,
! [X0,X1] : is_a_theorem(or(and(not(implies(X0,not(X0))),X1),not(and(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f236,f1431]) ).
fof(f1433,plain,
! [X0,X1] : is_a_theorem(implies(or(implies(X0,not(X0)),not(X1)),not(and(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f230,f1432]) ).
fof(f1434,plain,
! [X0,X1] : is_a_theorem(implies(implies(and(X0,X0),not(X1)),not(and(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f215,f1433]) ).
fof(f1435,plain,
! [X0,X1] : is_a_theorem(or(and(and(X0,X0),X1),not(and(X1,X0)))),
inference(forward_demodulation,[status(thm)],[f217,f1434]) ).
fof(f1485,plain,
! [X0,X1] : is_a_theorem(or(and(not(implies(not(X0),X0)),X1),not(and(X1,not(X0))))),
inference(paramodulation,[status(thm)],[f236,f1435]) ).
fof(f1504,plain,
! [X0,X1] : is_a_theorem(implies(or(implies(not(X0),X0),not(X1)),not(and(X1,not(X0))))),
inference(forward_demodulation,[status(thm)],[f230,f1485]) ).
fof(f1505,plain,
! [X0,X1] : is_a_theorem(implies(or(or(X0,X0),not(X1)),not(and(X1,not(X0))))),
inference(forward_demodulation,[status(thm)],[f197,f1504]) ).
fof(f1506,plain,
! [X0,X1] : is_a_theorem(implies(or(or(X0,X0),not(X1)),implies(X1,X0))),
inference(forward_demodulation,[status(thm)],[f187,f1505]) ).
fof(f1577,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(or(X0,X0),not(X1))) ),
inference(resolution,[status(thm)],[f1506,f178]) ).
fof(f1706,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(resolution,[status(thm)],[f1577,f320]) ).
fof(f1722,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[status(thm)],[f197,f1706]) ).
fof(f1723,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[status(thm)],[f182,f1722]) ).
fof(f1790,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(paramodulation,[status(thm)],[f197,f1723]) ).
fof(f1801,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[f1790,f1577]) ).
fof(f1821,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f177,f1801]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL518+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 % Computer : n018.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 00:38:44 UTC 2026
% 0.19/0.50 % CPUTime :
% 0.19/0.53 % Drodi V4.1.1
% 0.22/0.73 % Refutation found
% 0.22/0.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.78 % Elapsed time: 0.253588 seconds
% 0.22/0.78 % CPU time: 1.564400 seconds
% 0.22/0.78 % Total memory used: 116.103 MB
% 0.22/0.78 % Net memory used: 114.937 MB
%------------------------------------------------------------------------------