%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET257-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 02:09:44 PM UTC 2026
% Result : Unsatisfiable 46.94s 6.44s
% Output : CNFRefutation 46.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 58 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 24 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 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 : 76 ( 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
restrict(cross_product(x,y),x,y) != cross_product(x,y),
file('/export/starexec/sandbox/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(f121,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
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(f145,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f150,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f151,plain,
! [X0,X1,X2] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f245,plain,
restrict(cross_product(x,y),x,y) != cross_product(x,y),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( member(X0,X1)
| ~ member(X0,restrict(X1,X2,X3)) ),
inference(paramodulation,[status(thm)],[f150,f142]) ).
fof(f339,plain,
! [X0,X1,X2,X3] :
( member(X0,restrict(X3,X1,X2))
| ~ member(X0,X3)
| ~ member(X0,cross_product(X1,X2)) ),
inference(paramodulation,[status(thm)],[f151,f145]) ).
fof(f351,plain,
! [X0,X1,X2,X3] :
( subclass(restrict(X0,X1,X2),X3)
| member(not_subclass_element(restrict(X0,X1,X2),X3),X0) ),
inference(resolution,[status(thm)],[f321,f116]) ).
fof(f382,plain,
! [X0,X1,X2,X3] :
( subclass(X0,restrict(X1,X2,X3))
| ~ member(not_subclass_element(X0,restrict(X1,X2,X3)),X1)
| ~ member(not_subclass_element(X0,restrict(X1,X2,X3)),cross_product(X2,X3)) ),
inference(resolution,[status(thm)],[f339,f117]) ).
fof(f437,plain,
! [X0,X1,X2] :
( subclass(restrict(X0,X1,X2),X0)
| subclass(restrict(X0,X1,X2),X0) ),
inference(resolution,[status(thm)],[f351,f117]) ).
fof(f448,plain,
! [X0,X1,X2] : subclass(restrict(X0,X1,X2),X0),
inference(duplicate_literals_removal,[status(thm)],[f437]) ).
fof(f464,plain,
! [X0,X1,X2] :
( X0 = restrict(X0,X1,X2)
| ~ subclass(X0,restrict(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f448,f121]) ).
fof(f672,plain,
! [X0,X1,X2] :
( subclass(cross_product(X0,X1),restrict(X2,X0,X1))
| subclass(cross_product(X0,X1),restrict(X2,X0,X1))
| ~ member(not_subclass_element(cross_product(X0,X1),restrict(X2,X0,X1)),X2) ),
inference(resolution,[status(thm)],[f382,f116]) ).
fof(f681,plain,
! [X0,X1,X2] :
( subclass(cross_product(X0,X1),restrict(X2,X0,X1))
| ~ member(not_subclass_element(cross_product(X0,X1),restrict(X2,X0,X1)),X2) ),
inference(duplicate_literals_removal,[status(thm)],[f672]) ).
fof(f21811,plain,
! [X0,X1] :
( subclass(cross_product(X0,X1),restrict(cross_product(X0,X1),X0,X1))
| subclass(cross_product(X0,X1),restrict(cross_product(X0,X1),X0,X1)) ),
inference(resolution,[status(thm)],[f681,f116]) ).
fof(f21868,plain,
! [X0,X1] : subclass(cross_product(X0,X1),restrict(cross_product(X0,X1),X0,X1)),
inference(duplicate_literals_removal,[status(thm)],[f21811]) ).
fof(f21892,plain,
! [X0,X1] : cross_product(X0,X1) = restrict(cross_product(X0,X1),X0,X1),
inference(resolution,[status(thm)],[f21868,f464]) ).
fof(f21897,plain,
cross_product(x,y) != cross_product(x,y),
inference(backward_demodulation,[status(thm)],[f21892,f245]) ).
fof(f22018,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f21897]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET257-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n007.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 05:01:35 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 46.94/6.44 % Refutation found
% 46.94/6.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 46.94/6.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.62/6.52 % Elapsed time: 6.075913 seconds
% 7.62/6.52 % CPU time: 47.561156 seconds
% 7.62/6.52 % Total memory used: 372.484 MB
% 7.62/6.52 % Net memory used: 333.649 MB
%------------------------------------------------------------------------------