%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET097-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.18s 0.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 17 unt; 0 def)
% Number of atoms : 83 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 82 ( 43 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
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(f106,axiom,
! [Z] :
( member(not_subclass_element(Z,null_class),Z)
| Z = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f139,axiom,
! [X,Y] :
( subclass(singleton(X),Y)
| ~ member(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,negated_conjecture,
~ 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,
singleton(not_subclass_element(x,null_class)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f145,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f147,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f148,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f151,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f175,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f177,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f265,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f267,plain,
! [X0] :
( X0 = null_class
| ~ subclass(X0,null_class) ),
inference(cnf_transformation,[status(thm)],[f105]) ).
fof(f268,plain,
! [X0] :
( member(not_subclass_element(X0,null_class),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f310,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f312,plain,
~ 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)),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f313,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f314,plain,
x != null_class,
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f318,plain,
subclass(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),
inference(resolution,[status(thm)],[f146,f312]) ).
fof(f326,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f145,f148]) ).
fof(f332,plain,
intersection(complement(singleton(not_subclass_element(x,null_class))),x) = null_class,
inference(resolution,[status(thm)],[f318,f267]) ).
fof(f358,plain,
! [X0] :
( member(X0,null_class)
| ~ member(X0,x)
| ~ member(X0,complement(singleton(not_subclass_element(x,null_class)))) ),
inference(paramodulation,[status(thm)],[f332,f175]) ).
fof(f360,plain,
! [X0] :
( ~ member(X0,x)
| ~ member(X0,complement(singleton(not_subclass_element(x,null_class)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f358,f265]) ).
fof(f388,plain,
! [X0] :
( ~ member(X0,x)
| member(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f177,f360]) ).
fof(f437,plain,
! [X0] :
( subclass(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),x)
| ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),universal_class) ),
inference(resolution,[status(thm)],[f388,f147]) ).
fof(f487,plain,
! [X0] :
( subclass(X0,singleton(not_subclass_element(x,null_class)))
| ~ member(not_subclass_element(X0,singleton(not_subclass_element(x,null_class))),x) ),
inference(backward_subsumption_resolution,[status(thm)],[f437,f326]) ).
fof(f526,plain,
( subclass(x,singleton(not_subclass_element(x,null_class)))
| subclass(x,singleton(not_subclass_element(x,null_class))) ),
inference(resolution,[status(thm)],[f487,f146]) ).
fof(f529,plain,
subclass(x,singleton(not_subclass_element(x,null_class))),
inference(duplicate_literals_removal,[status(thm)],[f526]) ).
fof(f624,plain,
( singleton(not_subclass_element(x,null_class)) = x
| ~ subclass(singleton(not_subclass_element(x,null_class)),x) ),
inference(resolution,[status(thm)],[f529,f151]) ).
fof(f626,plain,
~ subclass(singleton(not_subclass_element(x,null_class)),x),
inference(forward_subsumption_resolution,[status(thm)],[f624,f313]) ).
fof(f627,plain,
~ member(not_subclass_element(x,null_class),x),
inference(resolution,[status(thm)],[f626,f310]) ).
fof(f628,plain,
x = null_class,
inference(resolution,[status(thm)],[f627,f268]) ).
fof(f632,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f628,f314]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET097-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n001.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Mon Sep 21 04:58:13 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.18/0.44 % Drodi V4.1.1
% 0.18/0.49 % Refutation found
% 0.18/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.52 % Elapsed time: 0.093704 seconds
% 0.18/0.52 % CPU time: 0.391353 seconds
% 0.18/0.52 % Total memory used: 97.277 MB
% 0.18/0.52 % Net memory used: 96.964 MB
%------------------------------------------------------------------------------