%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM217-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 01:38:47 PM UTC 2026
% Result : Unsatisfiable 0.28s 0.87s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 81 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 32 ~; 37 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
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(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [Xr,X,Y] : intersection(Xr,cross_product(X,Y)) = restrict(Xr,X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f140,axiom,
! [X] : subclass(rest_of(X),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [U,V,X] :
( member(U,domain_of(X))
| ~ member(ordered_pair(U,V),rest_of(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
rest_of(null_class) != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f160,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f161,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f164,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f182,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f187,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f188,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f192,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f196,plain,
! [X0,X1,X2] : intersection(X0,cross_product(X1,X2)) = restrict(X0,X1,X2),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f198,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f234,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f324,plain,
! [X0] : subclass(rest_of(X0),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f325,plain,
! [U,X] :
( member(U,domain_of(X))
| ! [V] : ~ member(ordered_pair(U,V),rest_of(X)) ),
inference(miniscoping,[status(thm)],[f141]) ).
fof(f326,plain,
! [X0,X1,X2] :
( member(X0,domain_of(X2))
| ~ member(ordered_pair(X0,X1),rest_of(X2)) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f347,plain,
rest_of(null_class) != null_class,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f378,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = null_class ),
inference(resolution,[status(thm)],[f234,f161]) ).
fof(f474,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f192,f234]) ).
fof(f540,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f188,f234]) ).
fof(f869,plain,
! [X0] :
( member(regular(rest_of(X0)),cross_product(universal_class,universal_class))
| rest_of(X0) = null_class ),
inference(resolution,[status(thm)],[f378,f324]) ).
fof(f870,plain,
! [X0] :
( member(regular(X0),universal_class)
| X0 = null_class ),
inference(resolution,[status(thm)],[f378,f164]) ).
fof(f890,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(resolution,[status(thm)],[f474,f870]) ).
fof(f899,plain,
complement(universal_class) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f890]) ).
fof(f909,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f899,f192]) ).
fof(f936,plain,
! [X0] :
( ordered_pair(first(regular(rest_of(X0))),second(regular(rest_of(X0)))) = regular(rest_of(X0))
| rest_of(X0) = null_class ),
inference(resolution,[status(thm)],[f869,f183]) ).
fof(f952,plain,
! [X0,X1] :
( rest_of(X0) = null_class
| member(first(regular(rest_of(X0))),domain_of(X1))
| ~ member(regular(rest_of(X0)),rest_of(X1)) ),
inference(paramodulation,[status(thm)],[f936,f326]) ).
fof(f970,plain,
! [X0] :
( rest_of(X0) = null_class
| rest_of(X0) = null_class
| member(first(regular(rest_of(X0))),domain_of(X0)) ),
inference(resolution,[status(thm)],[f952,f234]) ).
fof(f971,plain,
! [X0] :
( rest_of(X0) = null_class
| member(first(regular(rest_of(X0))),domain_of(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f970]) ).
fof(f972,plain,
! [X0] :
( restrict(X0,singleton(first(regular(rest_of(X0)))),universal_class) != null_class
| rest_of(X0) = null_class ),
inference(resolution,[status(thm)],[f971,f198]) ).
fof(f1898,plain,
! [X0] :
( ~ member(regular(intersection(null_class,X0)),universal_class)
| intersection(null_class,X0) = null_class ),
inference(resolution,[status(thm)],[f540,f909]) ).
fof(f1953,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f1898,f870]) ).
fof(f1992,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(paramodulation,[status(thm)],[f196,f1953]) ).
fof(f2012,plain,
rest_of(null_class) = null_class,
inference(resolution,[status(thm)],[f1992,f972]) ).
fof(f2041,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2012,f347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM217-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n014.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 02:13:19 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 0.28/0.87 % Refutation found
% 0.28/0.87 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.28/0.87 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.28/0.92 % Elapsed time: 0.445161 seconds
% 0.28/0.92 % CPU time: 2.983198 seconds
% 0.28/0.92 % Total memory used: 144.086 MB
% 0.28/0.92 % Net memory used: 140.143 MB
%------------------------------------------------------------------------------