%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL517+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 : n005.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 0.09s 0.61s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 44 unt; 0 def)
% Number of atoms : 168 ( 10 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 143 ( 60 ~; 56 |; 18 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 141 ( 130 !; 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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
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(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ cn3,
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(f131,plain,
( ( ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P))
| cn3 )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f132,plain,
( ( ~ is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))
| cn3 )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f131]) ).
fof(f134,plain,
( ~ is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))
| cn3 ),
inference(cnf_transformation,[status(thm)],[f132]) ).
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(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(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(f176,plain,
~ cn3,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f177,plain,
~ is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f134,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(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] :
( or(X0,X1) = implies(not(X0),X1)
| ~ op_or ),
inference(forward_demodulation,[status(thm)],[f187,f156]) ).
fof(f192,plain,
~ is_a_theorem(implies(or(sK43_skl,sK43_skl),sK43_skl)),
inference(backward_demodulation,[status(thm)],[f195,f177]) ).
fof(f195,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f189,f165]) ).
fof(f196,plain,
! [X0,X1,X2] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(paramodulation,[status(thm)],[f187,f195]) ).
fof(f197,plain,
! [X0] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(paramodulation,[status(thm)],[f195,f180]) ).
fof(f198,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0)) ),
inference(paramodulation,[status(thm)],[f195,f178]) ).
fof(f401,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)],[f195,f121]) ).
fof(f402,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)],[f401,f171]) ).
fof(f405,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),not(and(X2,not(X0)))))),
inference(paramodulation,[status(thm)],[f195,f402]) ).
fof(f416,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f187,f405]) ).
fof(f421,plain,
! [X0,X1,X2] :
( is_a_theorem(or(and(X1,X2),implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f416,f178]) ).
fof(f424,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),implies(not(X2),X0)))),
inference(paramodulation,[status(thm)],[f196,f416]) ).
fof(f431,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(forward_demodulation,[status(thm)],[f195,f424]) ).
fof(f437,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[f431,f178]) ).
fof(f447,plain,
! [X0,X1] : is_a_theorem(implies(implies(and(not(X0),not(X0)),X1),or(X1,X0))),
inference(resolution,[status(thm)],[f437,f197]) ).
fof(f470,plain,
! [X0,X1] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(implies(and(not(X0),not(X0)),X1)) ),
inference(resolution,[status(thm)],[f447,f178]) ).
fof(f486,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(resolution,[status(thm)],[f470,f181]) ).
fof(f498,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(resolution,[status(thm)],[f486,f437]) ).
fof(f500,plain,
! [X0] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(not(X0))) ),
inference(resolution,[status(thm)],[f486,f198]) ).
fof(f506,plain,
! [X0,X1] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f498,f178]) ).
fof(f550,plain,
! [X0,X1] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(resolution,[status(thm)],[f506,f181]) ).
fof(f551,plain,
! [X0] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(resolution,[status(thm)],[f506,f180]) ).
fof(f555,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(not(and(X0,X1)),X2),or(X2,X0))),
inference(resolution,[status(thm)],[f550,f437]) ).
fof(f561,plain,
! [X0,X1] : is_a_theorem(or(X0,implies(X0,X1))),
inference(paramodulation,[status(thm)],[f187,f550]) ).
fof(f565,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(and(X0,X1),X2),or(X2,X0))),
inference(forward_demodulation,[status(thm)],[f195,f555]) ).
fof(f567,plain,
! [X0,X1,X2] : is_a_theorem(or(and(implies(X0,X1),X2),implies(X2,X0))),
inference(resolution,[status(thm)],[f561,f421]) ).
fof(f575,plain,
! [X0] :
( is_a_theorem(not(X0))
| ~ is_a_theorem(not(and(X0,X0))) ),
inference(resolution,[status(thm)],[f551,f198]) ).
fof(f602,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(paramodulation,[status(thm)],[f187,f575]) ).
fof(f604,plain,
! [X0] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(forward_demodulation,[status(thm)],[f195,f602]) ).
fof(f675,plain,
! [X0,X1,X2] :
( is_a_theorem(or(X2,X0))
| ~ is_a_theorem(or(and(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f565,f178]) ).
fof(f757,plain,
! [X0,X1,X2] : is_a_theorem(or(implies(X0,X1),implies(X1,X2))),
inference(resolution,[status(thm)],[f675,f567]) ).
fof(f784,plain,
! [X0] : is_a_theorem(not(not(implies(X0,X0)))),
inference(resolution,[status(thm)],[f757,f604]) ).
fof(f794,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[f784,f500]) ).
fof(f802,plain,
! [X0] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(resolution,[status(thm)],[f794,f470]) ).
fof(f809,plain,
! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)),
inference(forward_demodulation,[status(thm)],[f196,f802]) ).
fof(f810,plain,
! [X0] : is_a_theorem(implies(or(X0,X0),X0)),
inference(forward_demodulation,[status(thm)],[f195,f809]) ).
fof(f835,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f192,f810]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL517+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n005.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Mon Sep 21 00:36:49 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.58 % Drodi V4.1.1
% 0.09/0.61 % Refutation found
% 0.09/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.65 % Elapsed time: 0.065287 seconds
% 0.13/0.65 % CPU time: 0.238640 seconds
% 0.13/0.65 % Total memory used: 87.072 MB
% 0.13/0.65 % Net memory used: 86.907 MB
%------------------------------------------------------------------------------