%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL483+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 01:07:49 PM UTC 2026
% Result : Theorem 0.22s 0.51s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 20 unt; 0 def)
% Number of atoms : 62 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 45 ( 20 ~; 16 |; 4 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 48 ( 44 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
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(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_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ modus_tollens,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f61,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
( ( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f61]) ).
fof(f64,plain,
( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens ),
inference(cnf_transformation,[status(thm)],[f62]) ).
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(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(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(f167,plain,
op_implies_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f173,plain,
r3,
inference(cnf_transformation,[status(thm)],[f38]) ).
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,
~ modus_tollens,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f184,plain,
~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f64,f180]) ).
fof(f189,plain,
! [X0,X1] : implies(X0,X1) = or(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f164,f167]) ).
fof(f196,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f147,f173]) ).
fof(f199,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(paramodulation,[status(thm)],[f189,f196]) ).
fof(f229,plain,
! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f158,f177]) ).
fof(f240,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(backward_demodulation,[status(thm)],[f241,f229]) ).
fof(f241,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f162,f178]) ).
fof(f250,plain,
~ is_a_theorem(implies(or(sK5_skl,not(sK4_skl)),implies(sK4_skl,sK5_skl))),
inference(backward_demodulation,[status(thm)],[f240,f184]) ).
fof(f300,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f250,f199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL483+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.46 % Computer : n007.cluster.edu
% 0.22/0.46 % Model : x86_64 x86_64
% 0.22/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.46 % Memory : 8046.5625MB
% 0.22/0.46 % OS : Linux 6.8.0-71-generic
% 0.22/0.46 % CPULimit : 300
% 0.22/0.46 % WCLimit : 300
% 0.22/0.46 % DateTime : Mon Sep 21 00:32:06 UTC 2026
% 0.22/0.47 % CPUTime :
% 0.22/0.49 % Drodi V4.1.1
% 0.22/0.51 % Refutation found
% 0.22/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.22/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.62 % Elapsed time: 0.139583 seconds
% 0.25/0.62 % CPU time: 0.134198 seconds
% 0.25/0.62 % Total memory used: 18.821 MB
% 0.25/0.62 % Net memory used: 18.788 MB
%------------------------------------------------------------------------------