%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL520+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 : n007.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 1.26s 0.67s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 91 ( 51 unt; 0 def)
% Number of atoms : 172 ( 23 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 136 ( 55 ~; 52 |; 18 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 152 ( 140 !; 12 ?)
% 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(f24,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,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,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ r3,
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(f143,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(f144,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)],[f143]) ).
fof(f146,plain,
( ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))
| r3 ),
inference(cnf_transformation,[status(thm)],[f144]) ).
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,
~ r3,
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(backward_subsumption_resolution,[status(thm)],[f49,f168]) ).
fof(f179,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f117,f170]) ).
fof(f181,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f113,f169]) ).
fof(f184,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f162,f173]) ).
fof(f186,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f160,f166]) ).
fof(f188,plain,
! [X0,X1,X2] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2),
inference(paramodulation,[status(thm)],[f186,f184]) ).
fof(f189,plain,
! [X0,X1] :
( or(X0,X1) = implies(not(X0),X1)
| ~ op_or ),
inference(forward_demodulation,[status(thm)],[f186,f156]) ).
fof(f196,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f189,f165]) ).
fof(f197,plain,
! [X0,X1,X2] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(paramodulation,[status(thm)],[f186,f196]) ).
fof(f198,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(paramodulation,[status(thm)],[f196,f181]) ).
fof(f206,plain,
! [X0,X1] :
( and(X0,X1) = not(implies(X0,not(X1)))
| ~ op_and ),
inference(forward_demodulation,[status(thm)],[f184,f158]) ).
fof(f207,plain,
! [X0,X1] : and(X0,X1) = not(implies(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f206,f174]) ).
fof(f208,plain,
! [X0,X1] : and(not(X0),X1) = not(or(X0,not(X1))),
inference(paramodulation,[status(thm)],[f196,f207]) ).
fof(f219,plain,
! [X0,X1] : and(not(not(X0)),X1) = not(implies(X0,not(X1))),
inference(paramodulation,[status(thm)],[f184,f208]) ).
fof(f230,plain,
! [X0,X1] : and(not(not(X0)),X1) = and(X0,X1),
inference(forward_demodulation,[status(thm)],[f207,f219]) ).
fof(f241,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),not(not(X0)))),
inference(paramodulation,[status(thm)],[f230,f179]) ).
fof(f267,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)],[f196,f121]) ).
fof(f268,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)],[f267,f171]) ).
fof(f270,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))),
inference(paramodulation,[status(thm)],[f196,f268]) ).
fof(f274,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f186,f270]) ).
fof(f277,plain,
~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f146,f176]) ).
fof(f328,plain,
! [X0,X1] : is_a_theorem(or(implies(X0,X1),not(not(X0)))),
inference(paramodulation,[status(thm)],[f188,f241]) ).
fof(f374,plain,
! [X0,X1] : is_a_theorem(or(or(X0,X1),not(not(not(X0))))),
inference(paramodulation,[status(thm)],[f196,f328]) ).
fof(f619,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0)))),
inference(paramodulation,[status(thm)],[f197,f274]) ).
fof(f629,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f196,f619]) ).
fof(f633,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f629,f177]) ).
fof(f661,plain,
! [X0,X1] : is_a_theorem(implies(implies(and(not(X0),not(X0)),X1),or(X1,X0))),
inference(resolution,[status(thm)],[f633,f198]) ).
fof(f672,plain,
! [X0,X1] : is_a_theorem(implies(or(implies(not(X0),X0),X1),or(X1,X0))),
inference(forward_demodulation,[status(thm)],[f188,f661]) ).
fof(f673,plain,
! [X0,X1] : is_a_theorem(implies(or(or(X0,X0),X1),or(X1,X0))),
inference(forward_demodulation,[status(thm)],[f196,f672]) ).
fof(f974,plain,
! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(or(X0,X0),X1)) ),
inference(resolution,[status(thm)],[f673,f177]) ).
fof(f986,plain,
! [X0] : is_a_theorem(or(not(not(not(X0))),X0)),
inference(resolution,[status(thm)],[f974,f374]) ).
fof(f994,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(forward_demodulation,[status(thm)],[f184,f986]) ).
fof(f995,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[status(thm)],[f196,f994]) ).
fof(f996,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(forward_demodulation,[status(thm)],[f184,f995]) ).
fof(f1010,plain,
! [X0] : is_a_theorem(or(X0,not(X0))),
inference(paramodulation,[status(thm)],[f196,f996]) ).
fof(f1017,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),X1),or(X1,X0))),
inference(resolution,[status(thm)],[f1010,f633]) ).
fof(f1027,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_demodulation,[status(thm)],[f196,f1017]) ).
fof(f1150,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f277,f1027]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL520+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n007.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Mon Sep 21 00:34:36 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 1.26/0.67 % Refutation found
% 1.26/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.26/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.26/0.71 % Elapsed time: 0.330971 seconds
% 1.26/0.71 % CPU time: 2.376166 seconds
% 1.26/0.71 % Total memory used: 155.917 MB
% 1.26/0.71 % Net memory used: 152.097 MB
%------------------------------------------------------------------------------