%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL469+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 01:07:48 PM UTC 2026
% Result : Theorem 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 15 unt; 0 def)
% Number of atoms : 53 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 41 ( 18 ~; 15 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
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(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f87,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f88,plain,
( ( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X,sK19_skl),skolemize(Y,sK20_skl)],[f87]) ).
fof(f90,plain,
( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f127,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q)))
| cn2 )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f128,plain,
( ( ~ is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl)))
| cn2 )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41_skl,sK42_skl]),skolemize(P,sK41_skl),skolemize(Q,sK42_skl)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[status(thm)],[f128]) ).
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(f170,plain,
cn2,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f174,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f176,plain,
~ or_1,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f181,plain,
~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f90,f176]) ).
fof(f185,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(forward_subsumption_resolution,[status(thm)],[f129,f170]) ).
fof(f192,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f160,f174]) ).
fof(f197,plain,
! [X0,X1] :
( or(X0,X1) = implies(not(X0),X1)
| ~ op_or ),
inference(forward_demodulation,[status(thm)],[f192,f156]) ).
fof(f205,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))),
inference(backward_demodulation,[status(thm)],[f206,f185]) ).
fof(f206,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f197,f165]) ).
fof(f222,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f181,f205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n007.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 00:33:06 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.19/0.49 % Refutation found
% 0.19/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.57 % Elapsed time: 0.108992 seconds
% 0.27/0.57 % CPU time: 0.117920 seconds
% 0.27/0.57 % Total memory used: 10.707 MB
% 0.27/0.57 % Net memory used: 10.701 MB
%------------------------------------------------------------------------------