%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET235-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 0.10s 0.62s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 36 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 15 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 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 : 27 ( 27 !; 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(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
subclass(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
~ member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,negated_conjecture,
~ subclass(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f117,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f138,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f139,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f247,plain,
subclass(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f248,plain,
~ member(ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))),x),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f249,plain,
~ subclass(x,y),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f257,plain,
! [X0,X1,X2] :
( member(not_subclass_element(X0,X1),X2)
| ~ subclass(X0,X2)
| subclass(X0,X1) ),
inference(resolution,[status(thm)],[f118,f117]) ).
fof(f270,plain,
! [X0] :
( member(not_subclass_element(x,X0),cross_product(universal_class,universal_class))
| subclass(x,X0) ),
inference(resolution,[status(thm)],[f257,f247]) ).
fof(f302,plain,
! [X0] :
( ordered_pair(first(not_subclass_element(x,X0)),second(not_subclass_element(x,X0))) = not_subclass_element(x,X0)
| subclass(x,X0) ),
inference(resolution,[status(thm)],[f270,f139]) ).
fof(f307,plain,
ordered_pair(first(not_subclass_element(x,y)),second(not_subclass_element(x,y))) = not_subclass_element(x,y),
inference(resolution,[status(thm)],[f302,f249]) ).
fof(f334,plain,
~ member(not_subclass_element(x,y),x),
inference(backward_demodulation,[status(thm)],[f307,f248]) ).
fof(f341,plain,
subclass(x,y),
inference(resolution,[status(thm)],[f334,f118]) ).
fof(f342,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f341,f249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET235-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n013.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Mon Sep 21 05:02:08 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.59 % Drodi V4.1.1
% 0.10/0.62 % Refutation found
% 0.10/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.65 % Elapsed time: 0.058676 seconds
% 0.15/0.65 % CPU time: 0.173941 seconds
% 0.15/0.65 % Total memory used: 106.251 MB
% 0.15/0.65 % Net memory used: 106.130 MB
%------------------------------------------------------------------------------