%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL496+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 : 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 01:07:51 PM UTC 2026
% Result : Theorem 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 23 unt; 0 def)
% Number of atoms : 106 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 102 ( 42 ~; 37 |; 16 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-2 aty)
% Number of variables : 93 ( 80 !; 13 ?)
% 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(f19,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
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(f30,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
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(f45,conjecture,
cn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ cn1,
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(f125,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| cn1 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f126,plain,
( ( ~ is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl))))
| cn1 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl,sK40_skl]),skolemize(P,sK38_skl),skolemize(Q,sK39_skl),skolemize(R,sK40_skl)],[f125]) ).
fof(f128,plain,
( ~ is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl))))
| cn1 ),
inference(cnf_transformation,[status(thm)],[f126]) ).
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(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(f167,plain,
op_implies_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f170,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f174,plain,
r4,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f175,plain,
r5,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f180,plain,
~ cn1,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f181,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,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f164,f167]) ).
fof(f360,plain,
! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(forward_subsumption_resolution,[status(thm)],[f151,f174]) ).
fof(f361,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(paramodulation,[status(thm)],[f185,f360]) ).
fof(f365,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f185,f361]) ).
fof(f371,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),or(not(X1),implies(X0,X2)))),
inference(paramodulation,[status(thm)],[f185,f365]) ).
fof(f377,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(X1,implies(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f185,f371]) ).
fof(f409,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[f155,f175]) ).
fof(f413,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(paramodulation,[status(thm)],[f185,f409]) ).
fof(f415,plain,
! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f185,f413]) ).
fof(f448,plain,
~ is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl)))),
inference(forward_subsumption_resolution,[status(thm)],[f128,f180]) ).
fof(f449,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl)))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f448,f181]) ).
fof(f450,plain,
~ is_a_theorem(implies(implies(sK39_skl,sK40_skl),implies(implies(sK38_skl,sK39_skl),implies(sK38_skl,sK40_skl)))),
inference(resolution,[status(thm)],[f449,f377]) ).
fof(f457,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f450,f415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL496+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 00:34:06 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.44 % Refutation found
% 0.12/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.46 % Elapsed time: 0.094907 seconds
% 0.12/0.46 % CPU time: 0.578920 seconds
% 0.12/0.46 % Total memory used: 96.398 MB
% 0.12/0.46 % Net memory used: 95.955 MB
%------------------------------------------------------------------------------