%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM156-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 01:38:42 PM UTC 2026
% Result : Unsatisfiable 3.99s 1.11s
% Output : CNFRefutation 3.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 39 ( 18 unt; 0 def)
% Number of atoms : 69 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 29 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 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(f10,axiom,
! [Y,X] :
( member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
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(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] :
( member(null_class,X)
| ~ inductive(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f138,axiom,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
~ member(null_class,kind_1_ordinals),
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(f172,plain,
! [Y] :
( ! [X] : member(Y,unordered_pair(X,Y))
| ~ member(Y,universal_class) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f173,plain,
! [X0,X1] :
( member(X0,unordered_pair(X1,X0))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f175,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
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(f193,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f194,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f215,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f218,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f322,plain,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f347,plain,
~ member(null_class,kind_1_ordinals),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f369,plain,
member(null_class,omega),
inference(resolution,[status(thm)],[f215,f218]) ).
fof(f370,plain,
! [X0] :
( member(null_class,X0)
| ~ subclass(omega,X0) ),
inference(resolution,[status(thm)],[f369,f161]) ).
fof(f421,plain,
! [X0,X1,X2] :
( member(X0,intersection(complement(X1),complement(X2)))
| member(X0,union(X1,X2))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f194,f193]) ).
fof(f484,plain,
member(null_class,universal_class),
inference(resolution,[status(thm)],[f370,f164]) ).
fof(f487,plain,
! [X0] : member(null_class,unordered_pair(X0,null_class)),
inference(resolution,[status(thm)],[f484,f173]) ).
fof(f492,plain,
member(null_class,singleton(null_class)),
inference(paramodulation,[status(thm)],[f175,f487]) ).
fof(f3098,plain,
! [X0] :
( member(X0,intersection(complement(singleton(null_class)),complement(image(successor_relation,ordinal_numbers))))
| member(X0,kind_1_ordinals)
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f322,f421]) ).
fof(f3190,plain,
! [X0] :
( member(X0,complement(singleton(null_class)))
| member(X0,kind_1_ordinals)
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f3098,f188]) ).
fof(f3203,plain,
! [X0] :
( ~ member(X0,singleton(null_class))
| member(X0,kind_1_ordinals)
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f3190,f192]) ).
fof(f3213,plain,
( member(null_class,kind_1_ordinals)
| ~ member(null_class,universal_class) ),
inference(resolution,[status(thm)],[f3203,f492]) ).
fof(f3222,plain,
member(null_class,kind_1_ordinals),
inference(forward_subsumption_resolution,[status(thm)],[f3213,f484]) ).
fof(f3255,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f3222,f347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM156-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n018.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Mon Sep 21 02:11:15 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.49 % Drodi V4.1.1
% 3.99/1.11 % Refutation found
% 3.99/1.11 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.99/1.11 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.99/1.13 % Elapsed time: 0.652633 seconds
% 3.99/1.13 % CPU time: 4.911355 seconds
% 3.99/1.13 % Total memory used: 199.250 MB
% 3.99/1.13 % Net memory used: 192.385 MB
%------------------------------------------------------------------------------