%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET098-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:09:20 PM UTC 2026
% Result : Unsatisfiable 0.24s 0.54s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 14 unt; 3 def)
% Number of atoms : 62 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 49 ( 23 ~; 23 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f103,axiom,
! [Z] : ~ member(Z,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f105,axiom,
! [X] :
( X = null_class
| ~ subclass(X,null_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [X] :
( X = null_class
| singleton(not_subclass_element(X,null_class)) = X
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X,null_class))),X),null_class),intersection(complement(singleton(not_subclass_element(X,null_class))),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f142,negated_conjecture,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,negated_conjecture,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f147,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f174,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f175,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f174]) ).
fof(f266,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f268,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f313,plain,
! [X0] :
( X0 = null_class
| singleton(not_subclass_element(X0,null_class)) = X0
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(X0,null_class))),X0),null_class),intersection(complement(singleton(not_subclass_element(X0,null_class))),X0)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f314,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f315,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f316,plain,
x != null_class,
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f330,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f175,f147]) ).
fof(f723,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[status(thm)],[f330,f314]) ).
fof(f826,plain,
intersection(complement(singleton(not_subclass_element(x,null_class))),x) = null_class,
inference(resolution,[status(thm)],[f723,f268]) ).
fof(f841,plain,
( x = null_class
| singleton(not_subclass_element(x,null_class)) = x
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),null_class) ),
inference(paramodulation,[status(thm)],[f826,f313]) ).
fof(f850,definition,
( sQ30_spl
<=> member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),null_class) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f851,plain,
( ~ sQ30_spl
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),null_class) ),
inference(component_clause,[status(thm)],[f850]) ).
fof(f853,definition,
( sQ31_spl
<=> singleton(not_subclass_element(x,null_class)) = x ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f854,plain,
( ~ sQ31_spl
| singleton(not_subclass_element(x,null_class)) = x ),
inference(component_clause,[status(thm)],[f853]) ).
fof(f856,definition,
( sQ32_spl
<=> x = null_class ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f857,plain,
( ~ sQ32_spl
| x = null_class ),
inference(component_clause,[status(thm)],[f856]) ).
fof(f859,plain,
( sQ32_spl
| sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f841,f850,f853,f856]) ).
fof(f866,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f857,f316]) ).
fof(f867,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f866]) ).
fof(f868,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f854,f315]) ).
fof(f869,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f868]) ).
fof(f870,plain,
( ~ sQ30_spl
| member(not_subclass_element(null_class,null_class),null_class) ),
inference(forward_demodulation,[status(thm)],[f826,f851]) ).
fof(f871,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f870,f266]) ).
fof(f872,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f871]) ).
fof(f873,plain,
$false,
inference(sat_refutation,[status(thm)],[f859,f867,f869,f872]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET098-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n004.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 04:52:34 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.24/0.54 % Refutation found
% 0.24/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.24/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.57 % Elapsed time: 0.129325 seconds
% 0.24/0.57 % CPU time: 0.574176 seconds
% 0.24/0.57 % Total memory used: 113.213 MB
% 0.24/0.57 % Net memory used: 112.669 MB
%------------------------------------------------------------------------------