%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL455+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 : n004.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 01:07:46 PM UTC 2026
% Result : Theorem 0.19s 0.51s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 8 unt; 4 def)
% Number of atoms : 61 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 21 |; 4 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,conjecture,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
~ r2,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f101,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y)))
| or_2 )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f102,plain,
( ( ~ is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl)))
| or_2 )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f101]) ).
fof(f103,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ or_2 ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f149,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f150,plain,
( ( ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f149]) ).
fof(f152,plain,
( ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))
| r2 ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f187,plain,
or_2,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f196,plain,
~ r2,
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f319,definition,
( sQ33_spl
<=> or_2 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( sQ33_spl
| ~ or_2 ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,definition,
! [X0,X1] :
( sQ34_spl
<=> is_a_theorem(implies(X0,or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f323,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f103,f319,f322]) ).
fof(f445,definition,
( sQ67_spl
<=> r2 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ67_spl
| r2 ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f449,definition,
( sQ68_spl
<=> is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( sQ68_spl
| ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( ~ sQ68_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f152,f445,f449]) ).
fof(f542,plain,
( sQ68_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f323]) ).
fof(f543,plain,
( sQ68_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f187]) ).
fof(f545,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f546,plain,
( ~ sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f196]) ).
fof(f547,plain,
~ sQ67_spl,
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f548,plain,
$false,
inference(sat_refutation,[status(thm)],[f325,f452,f543,f545,f547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL455+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n004.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 00:33:20 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.47 % Drodi V4.1.1
% 0.19/0.51 % Refutation found
% 0.19/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.57 % Elapsed time: 0.109889 seconds
% 0.26/0.57 % CPU time: 0.105423 seconds
% 0.26/0.57 % Total memory used: 2.671 MB
% 0.26/0.57 % Net memory used: 2.671 MB
%------------------------------------------------------------------------------