%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM051-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 01:38:35 PM UTC 2026
% Result : Unsatisfiable 1.03s 0.71s
% Output : CNFRefutation 1.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 13 unt; 0 def)
% Number of atoms : 82 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 39 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 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(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/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/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(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,axiom,
! [Y,X] :
( connected(X,Y)
| ~ subclass(cross_product(Y,Y),union(identity_relation,symmetrization_of(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
~ connected(x,null_class),
file('/export/starexec/sandbox/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(f162,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f164,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f170,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f171,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f175,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f179,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f180,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f179]) ).
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(f192,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f234,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f295,plain,
! [X0,X1] :
( connected(X1,X0)
| ~ subclass(cross_product(X0,X0),union(identity_relation,symmetrization_of(X1))) ),
inference(cnf_transformation,[status(thm)],[f117]) ).
fof(f347,plain,
~ connected(x,null_class),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f368,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ subclass(X2,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[f171,f161]) ).
fof(f369,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,unordered_pair(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f164]) ).
fof(f403,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = null_class ),
inference(resolution,[status(thm)],[f234,f161]) ).
fof(f422,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[status(thm)],[f192,f234]) ).
fof(f514,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f175,f369]) ).
fof(f516,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ subclass(singleton(X0),X2)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f514,f161]) ).
fof(f811,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f422,f403]) ).
fof(f823,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f811]) ).
fof(f828,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[f823,f164]) ).
fof(f843,plain,
! [X0] :
( ~ member(X0,universal_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f828,f192]) ).
fof(f1009,plain,
~ subclass(cross_product(null_class,null_class),union(identity_relation,symmetrization_of(x))),
inference(resolution,[status(thm)],[f295,f347]) ).
fof(f1012,plain,
member(not_subclass_element(cross_product(null_class,null_class),union(identity_relation,symmetrization_of(x))),cross_product(null_class,null_class)),
inference(resolution,[status(thm)],[f1009,f162]) ).
fof(f1013,plain,
ordered_pair(first(not_subclass_element(cross_product(null_class,null_class),union(identity_relation,symmetrization_of(x)))),second(not_subclass_element(cross_product(null_class,null_class),union(identity_relation,symmetrization_of(x))))) = not_subclass_element(cross_product(null_class,null_class),union(identity_relation,symmetrization_of(x))),
inference(resolution,[status(thm)],[f1012,f183]) ).
fof(f1047,plain,
! [X0,X1] :
( member(second(not_subclass_element(cross_product(null_class,null_class),union(identity_relation,symmetrization_of(x)))),X1)
| ~ member(not_subclass_element(cross_product(null_class,null_class),union(identity_relation,symmetrization_of(x))),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1013,f180]) ).
fof(f1149,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f516,f164]) ).
fof(f1154,plain,
! [X0] : ~ member(X0,null_class),
inference(backward_subsumption_resolution,[status(thm)],[f843,f1149]) ).
fof(f2194,plain,
member(second(not_subclass_element(cross_product(null_class,null_class),union(identity_relation,symmetrization_of(x)))),null_class),
inference(resolution,[status(thm)],[f1047,f1012]) ).
fof(f2199,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2194,f1154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM051-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Mon Sep 21 02:02:32 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 1.03/0.71 % Refutation found
% 1.03/0.71 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.03/0.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.34/0.73 % Elapsed time: 0.334746 seconds
% 0.34/0.73 % CPU time: 2.357204 seconds
% 0.34/0.73 % Total memory used: 153.847 MB
% 0.34/0.73 % Net memory used: 149.135 MB
%------------------------------------------------------------------------------