%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET230-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 02:09:41 PM UTC 2026
% Result : Unsatisfiable 0.15s 15.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 9 unt; 0 def)
% Number of atoms : 84 ( 17 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 85 ( 41 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 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 : 60 ( 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
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(f113,negated_conjecture,
cross_product(u,u) = cross_product(w,w),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
u != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f118,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f122,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f134,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f189,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f246,plain,
cross_product(u,u) = cross_product(w,w),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
u != w,
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f253,plain,
! [X0,X1] :
( member(X1,w)
| ~ member(ordered_pair(X0,X1),cross_product(u,u)) ),
inference(paramodulation,[status(thm)],[f246,f135]) ).
fof(f254,plain,
! [X0,X1] :
( member(X1,w)
| ~ member(X1,u)
| ~ member(X0,u) ),
inference(resolution,[status(thm)],[f136,f253]) ).
fof(f258,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),cross_product(u,u))
| ~ member(X1,w)
| ~ member(X0,w) ),
inference(paramodulation,[status(thm)],[f246,f136]) ).
fof(f261,plain,
! [X0,X1] :
( member(X1,u)
| ~ member(X1,w)
| ~ member(X0,w) ),
inference(resolution,[status(thm)],[f258,f135]) ).
fof(f266,plain,
! [X0,X1] :
( member(not_subclass_element(w,X0),u)
| ~ member(X1,w)
| subclass(w,X0) ),
inference(resolution,[status(thm)],[f117,f261]) ).
fof(f267,plain,
! [X0,X1] :
( member(not_subclass_element(u,X0),w)
| ~ member(X1,u)
| subclass(u,X0) ),
inference(resolution,[status(thm)],[f117,f254]) ).
fof(f271,plain,
! [X0] :
( subclass(w,u)
| ~ member(X0,w)
| subclass(w,u) ),
inference(resolution,[status(thm)],[f266,f118]) ).
fof(f273,plain,
! [X0] :
( ~ member(X0,w)
| subclass(w,u) ),
inference(duplicate_literals_removal,[status(thm)],[f271]) ).
fof(f275,plain,
! [X0] :
( subclass(u,w)
| ~ member(X0,u)
| subclass(u,w) ),
inference(resolution,[status(thm)],[f267,f118]) ).
fof(f277,plain,
! [X0] :
( ~ member(X0,u)
| subclass(u,w) ),
inference(duplicate_literals_removal,[status(thm)],[f275]) ).
fof(f289,plain,
! [X0] :
( member(regular(w),u)
| ~ member(X0,w)
| w = null_class ),
inference(resolution,[status(thm)],[f189,f261]) ).
fof(f292,plain,
! [X0] :
( ~ member(X0,u)
| w = u
| ~ subclass(w,u) ),
inference(resolution,[status(thm)],[f122,f277]) ).
fof(f296,plain,
! [X0] :
( ~ member(X0,u)
| ~ subclass(w,u) ),
inference(forward_subsumption_resolution,[status(thm)],[f292,f247]) ).
fof(f305,plain,
! [X0,X1] :
( ~ member(X1,w)
| ~ member(X0,u) ),
inference(resolution,[status(thm)],[f296,f273]) ).
fof(f311,plain,
! [X0,X1] :
( ~ member(X1,u)
| ~ member(X0,u) ),
inference(backward_subsumption_resolution,[status(thm)],[f254,f305]) ).
fof(f329,plain,
! [X0] :
( u = null_class
| ~ member(X0,u) ),
inference(resolution,[status(thm)],[f311,f189]) ).
fof(f332,plain,
! [X0] :
( ~ member(X0,w)
| w = null_class ),
inference(forward_subsumption_resolution,[status(thm)],[f289,f305]) ).
fof(f333,plain,
( w = null_class
| w = null_class ),
inference(resolution,[status(thm)],[f332,f189]) ).
fof(f336,plain,
w = null_class,
inference(duplicate_literals_removal,[status(thm)],[f333]) ).
fof(f348,plain,
u != null_class,
inference(backward_demodulation,[status(thm)],[f336,f247]) ).
fof(f375,plain,
! [X0] : ~ member(X0,u),
inference(forward_subsumption_resolution,[status(thm)],[f329,f348]) ).
fof(f376,plain,
u = null_class,
inference(resolution,[status(thm)],[f375,f189]) ).
fof(f379,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f376,f348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET230-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/15.40 % Computer : n010.cluster.edu
% 0.12/15.40 % Model : x86_64 x86_64
% 0.12/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.40 % Memory : 8046.5625MB
% 0.12/15.40 % OS : Linux 6.8.0-71-generic
% 0.12/15.40 % CPULimit : 300
% 0.12/15.40 % WCLimit : 300
% 0.15/15.40 % DateTime : Mon Sep 21 05:02:13 UTC 2026
% 0.15/15.40 % CPUTime :
% 0.15/15.42 % Drodi V4.1.1
% 0.15/15.44 % Refutation found
% 0.15/15.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/15.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/15.47 % Elapsed time: 0.058711 seconds
% 0.15/15.47 % CPU time: 0.178446 seconds
% 0.15/15.47 % Total memory used: 93.015 MB
% 0.15/15.47 % Net memory used: 92.902 MB
%------------------------------------------------------------------------------