%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET382-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 02:09:52 PM UTC 2026
% Result : Unsatisfiable 2.76s 0.71s
% Output : CNFRefutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 76 ( 8 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 74 ( 35 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 69 ( 69 !; 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(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [Z,X,Y] :
( member(Z,X)
| ~ member(Z,intersection(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(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,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,
restrict(x,universal_class,universal_class) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f115,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f116,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
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(f142,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f143,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f142]) ).
fof(f146,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f246,plain,
subclass(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
restrict(x,universal_class,universal_class) != x,
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f252,plain,
! [X0] :
( member(X0,cross_product(universal_class,universal_class))
| ~ member(X0,x) ),
inference(resolution,[status(thm)],[f116,f246]) ).
fof(f365,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f143,f117]) ).
fof(f387,plain,
! [X0,X1,X2] :
( subclass(X0,intersection(X1,X2))
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X2)
| ~ member(not_subclass_element(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f146,f118]) ).
fof(f1977,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f365,f118]) ).
fof(f2015,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f1977]) ).
fof(f2206,plain,
! [X0,X1,X2] : subclass(restrict(X0,X1,X2),X0),
inference(paramodulation,[status(thm)],[f151,f2015]) ).
fof(f2240,plain,
! [X0,X1,X2] :
( X0 = restrict(X0,X1,X2)
| ~ subclass(X0,restrict(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f2206,f122]) ).
fof(f2290,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),x)
| subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
| ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),X1) ),
inference(resolution,[status(thm)],[f387,f252]) ).
fof(f2355,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),x)
| subclass(X0,intersection(X1,cross_product(universal_class,universal_class)))
| ~ member(not_subclass_element(X0,restrict(X1,universal_class,universal_class)),X1) ),
inference(forward_demodulation,[status(thm)],[f151,f2290]) ).
fof(f2356,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,intersection(X1,cross_product(universal_class,universal_class))),x)
| subclass(X0,restrict(X1,universal_class,universal_class))
| ~ member(not_subclass_element(X0,restrict(X1,universal_class,universal_class)),X1) ),
inference(forward_demodulation,[status(thm)],[f151,f2355]) ).
fof(f2357,plain,
! [X0,X1] :
( ~ member(not_subclass_element(X0,restrict(X1,universal_class,universal_class)),x)
| subclass(X0,restrict(X1,universal_class,universal_class))
| ~ member(not_subclass_element(X0,restrict(X1,universal_class,universal_class)),X1) ),
inference(forward_demodulation,[status(thm)],[f151,f2356]) ).
fof(f2423,plain,
! [X0] :
( subclass(x,restrict(X0,universal_class,universal_class))
| subclass(x,restrict(X0,universal_class,universal_class))
| ~ member(not_subclass_element(x,restrict(X0,universal_class,universal_class)),X0) ),
inference(resolution,[status(thm)],[f2357,f117]) ).
fof(f2434,plain,
! [X0] :
( subclass(x,restrict(X0,universal_class,universal_class))
| ~ member(not_subclass_element(x,restrict(X0,universal_class,universal_class)),X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2423]) ).
fof(f3546,plain,
( subclass(x,restrict(x,universal_class,universal_class))
| subclass(x,restrict(x,universal_class,universal_class)) ),
inference(resolution,[status(thm)],[f2434,f117]) ).
fof(f3581,plain,
subclass(x,restrict(x,universal_class,universal_class)),
inference(duplicate_literals_removal,[status(thm)],[f3546]) ).
fof(f3585,plain,
x = restrict(x,universal_class,universal_class),
inference(resolution,[status(thm)],[f3581,f2240]) ).
fof(f3588,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3585,f247]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET382-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 05:13:07 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 2.76/0.71 % Refutation found
% 2.76/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 2.76/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.76/0.74 % Elapsed time: 0.423661 seconds
% 2.76/0.74 % CPU time: 3.038920 seconds
% 2.76/0.74 % Total memory used: 164.229 MB
% 2.76/0.74 % Net memory used: 157.014 MB
%------------------------------------------------------------------------------