%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:38:45 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 12 unt; 2 def)
% Number of atoms : 61 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 24 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
omega = null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f160,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f161,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f164,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f192,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f215,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f218,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f220,plain,
member(omega,universal_class),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f234,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f347,plain,
omega = null_class,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f355,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f164,f161]) ).
fof(f357,plain,
! [X0] :
( member(omega,X0)
| ~ inductive(X0) ),
inference(forward_demodulation,[status(thm)],[f347,f215]) ).
fof(f361,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = omega ),
inference(forward_demodulation,[status(thm)],[f347,f234]) ).
fof(f436,definition,
( sQ5_spl
<=> inductive(omega) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( sQ5_spl
| ~ inductive(omega) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f440,plain,
! [X0] :
( X0 = omega
| member(regular(X0),universal_class) ),
inference(resolution,[status(thm)],[f355,f361]) ).
fof(f477,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f218]) ).
fof(f478,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f490,plain,
! [X0] :
( complement(X0) = omega
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f192,f361]) ).
fof(f492,plain,
! [X0] :
( ~ inductive(complement(X0))
| ~ member(omega,X0) ),
inference(resolution,[status(thm)],[f192,f357]) ).
fof(f553,plain,
~ inductive(complement(universal_class)),
inference(resolution,[status(thm)],[f492,f220]) ).
fof(f639,plain,
( complement(universal_class) = omega
| complement(universal_class) = omega ),
inference(resolution,[status(thm)],[f490,f440]) ).
fof(f641,definition,
( sQ29_spl
<=> complement(universal_class) = omega ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( ~ sQ29_spl
| complement(universal_class) = omega ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f644,plain,
sQ29_spl,
inference(split_clause,[status(thm)],[f639,f641]) ).
fof(f652,plain,
( ~ sQ29_spl
| ~ inductive(omega) ),
inference(backward_demodulation,[status(thm)],[f642,f553]) ).
fof(f656,plain,
( ~ sQ29_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f652,f436,f641]) ).
fof(f666,plain,
$false,
inference(sat_refutation,[status(thm)],[f478,f644,f656]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM190-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n015.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 02:14:23 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.17/0.50 % Refutation found
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.55 % Elapsed time: 0.077919 seconds
% 0.22/0.55 % CPU time: 0.227074 seconds
% 0.22/0.55 % Total memory used: 108.312 MB
% 0.22/0.55 % Net memory used: 108.152 MB
%------------------------------------------------------------------------------