%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET231-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 0.09s 5.78s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 7 unt; 0 def)
% Number of atoms : 17 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 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(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) != not_subclass_element(cross_product(x,y),z),
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(f137,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f246,plain,
~ subclass(cross_product(x,y),z),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) != not_subclass_element(cross_product(x,y),z),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f264,plain,
! [X0,X1] : ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1)),
inference(resolution,[status(thm)],[f138,f247]) ).
fof(f265,plain,
subclass(cross_product(x,y),z),
inference(resolution,[status(thm)],[f264,f117]) ).
fof(f266,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f265,f246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET231-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.74 % Computer : n002.cluster.edu
% 0.09/5.74 % Model : x86_64 x86_64
% 0.09/5.74 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.74 % Memory : 8046.5625MB
% 0.09/5.74 % OS : Linux 6.8.0-71-generic
% 0.09/5.74 % CPULimit : 300
% 0.09/5.74 % WCLimit : 300
% 0.09/5.74 % DateTime : Mon Sep 21 05:04:25 UTC 2026
% 0.09/5.74 % CPUTime :
% 0.09/5.76 % Drodi V4.1.1
% 0.09/5.78 % Refutation found
% 0.09/5.78 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.80 % Elapsed time: 0.051769 seconds
% 0.14/5.80 % CPU time: 0.142584 seconds
% 0.14/5.80 % Total memory used: 85.841 MB
% 0.14/5.80 % Net memory used: 85.797 MB
%------------------------------------------------------------------------------