%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET216-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 02:09:39 PM UTC 2026
% Result : Unsatisfiable 225.99s 29.02s
% Output : CNFRefutation 225.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 34 ( 8 unt; 0 def)
% Number of atoms : 62 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 53 ( 25 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 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(f14,axiom,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(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(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(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
~ subclass(cross_product(x,intersection(y,z)),cross_product(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f131,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,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(f136,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f141,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f142,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f245,plain,
~ subclass(cross_product(x,intersection(y,z)),cross_product(x,y)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f422,plain,
! [X0,X1,X2] :
( subclass(cross_product(X0,X1),X2)
| ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2) ),
inference(resolution,[status(thm)],[f137,f116]) ).
fof(f2848,plain,
ordered_pair(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)))) = not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),
inference(resolution,[status(thm)],[f422,f245]) ).
fof(f2946,plain,
! [X0,X1] :
( member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),X1)
| ~ member(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2848,f134]) ).
fof(f2947,plain,
! [X0,X1] :
( member(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),X0)
| ~ member(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f2848,f132]) ).
fof(f5426,plain,
( subclass(cross_product(x,intersection(y,z)),cross_product(x,y))
| member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),intersection(y,z)) ),
inference(resolution,[status(thm)],[f2946,f116]) ).
fof(f5428,plain,
member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),intersection(y,z)),
inference(forward_subsumption_resolution,[status(thm)],[f5426,f245]) ).
fof(f6087,plain,
member(second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),y),
inference(resolution,[status(thm)],[f5428,f142]) ).
fof(f6096,plain,
! [X0,X1] :
( member(ordered_pair(X0,second(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)))),cross_product(X1,y))
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f6087,f135]) ).
fof(f6338,plain,
! [X0] :
( member(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y)),cross_product(X0,y))
| ~ member(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),X0) ),
inference(paramodulation,[status(thm)],[f2848,f6096]) ).
fof(f7347,plain,
( subclass(cross_product(x,intersection(y,z)),cross_product(x,y))
| member(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),x) ),
inference(resolution,[status(thm)],[f2947,f116]) ).
fof(f7349,plain,
member(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),x),
inference(forward_subsumption_resolution,[status(thm)],[f7347,f245]) ).
fof(f11143,plain,
( subclass(cross_product(x,intersection(y,z)),cross_product(x,y))
| ~ member(first(not_subclass_element(cross_product(x,intersection(y,z)),cross_product(x,y))),x) ),
inference(resolution,[status(thm)],[f6338,f117]) ).
fof(f11151,plain,
subclass(cross_product(x,intersection(y,z)),cross_product(x,y)),
inference(forward_subsumption_resolution,[status(thm)],[f11143,f7349]) ).
fof(f11152,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f11151,f245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET216-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Mon Sep 21 05:02:59 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 225.99/29.02 % Refutation found
% 225.99/29.02 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 225.99/29.02 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 28.50/29.18 % Elapsed time: 28.738150 seconds
% 28.50/29.18 % CPU time: 226.742112 seconds
% 28.50/29.18 % Total memory used: 752.907 MB
% 28.50/29.18 % Net memory used: 670.021 MB
%------------------------------------------------------------------------------