%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL491+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 : n011.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 0.14s 0.39s
% Output : CNFRefutation 0.14s
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,conjecture,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
~ or_2,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f93,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(f94,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)],[f93]) ).
fof(f96,plain,
( ~ is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl)))
| or_2 ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f141,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(f142,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)],[f141]) ).
fof(f143,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f172,plain,
r2,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f180,plain,
~ or_2,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f303,definition,
( sQ33_spl
<=> or_2 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( ~ sQ33_spl
| or_2 ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,definition,
! [X0,X1] :
( sQ34_spl
<=> is_a_theorem(implies(X0,or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f307,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f310,definition,
( sQ35_spl
<=> is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl))) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( sQ35_spl
| ~ is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl))) ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f313,plain,
( ~ sQ35_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f96,f303,f310]) ).
fof(f429,definition,
( sQ67_spl
<=> r2 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ67_spl
| ~ r2 ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( sQ34_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f143,f429,f306]) ).
fof(f542,plain,
( sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f431,f172]) ).
fof(f543,plain,
sQ67_spl,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f566,plain,
( sQ35_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f307]) ).
fof(f567,plain,
( sQ35_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f566]) ).
fof(f568,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f304,f180]) ).
fof(f569,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f570,plain,
$false,
inference(sat_refutation,[status(thm)],[f313,f432,f543,f567,f569]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL491+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 00:35:56 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.055482 seconds
% 0.14/0.43 % CPU time: 0.175962 seconds
% 0.14/0.43 % Total memory used: 83.164 MB
% 0.14/0.43 % Net memory used: 83.118 MB
%------------------------------------------------------------------------------