%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM159-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 01:38:43 PM UTC 2026
% Result : Unsatisfiable 126.94s 37.62s
% Output : CNFRefutation 126.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 63 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 57 ( 26 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 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(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ 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(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,
~ subclass(image(successor_relation,ordinal_numbers),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(f162,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f163,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f164,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f189,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f190,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
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(f322,plain,
union(singleton(null_class),image(successor_relation,ordinal_numbers)) = kind_1_ordinals,
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f347,plain,
~ subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f357,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f164,f161]) ).
fof(f442,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(f1268,plain,
! [X0,X1,X2] :
( member(X0,complement(X2))
| member(X0,union(X1,X2))
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f442,f190]) ).
fof(f1283,plain,
! [X0] :
( member(X0,complement(image(successor_relation,ordinal_numbers)))
| member(X0,kind_1_ordinals)
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f322,f1268]) ).
fof(f1293,plain,
! [X0] :
( ~ member(X0,image(successor_relation,ordinal_numbers))
| member(X0,kind_1_ordinals)
| ~ member(X0,universal_class) ),
inference(resolution,[status(thm)],[f1283,f192]) ).
fof(f1294,plain,
! [X0] :
( ~ member(X0,image(successor_relation,ordinal_numbers))
| member(X0,kind_1_ordinals) ),
inference(forward_subsumption_resolution,[status(thm)],[f1293,f357]) ).
fof(f1335,plain,
! [X0] :
( subclass(image(successor_relation,ordinal_numbers),X0)
| member(not_subclass_element(image(successor_relation,ordinal_numbers),X0),kind_1_ordinals) ),
inference(resolution,[status(thm)],[f1294,f162]) ).
fof(f1337,plain,
( subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals)
| subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals) ),
inference(resolution,[status(thm)],[f1335,f163]) ).
fof(f1338,plain,
subclass(image(successor_relation,ordinal_numbers),kind_1_ordinals),
inference(duplicate_literals_removal,[status(thm)],[f1337]) ).
fof(f1339,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1338,f347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM159-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.15/21.52 % CPULimit : 300
% 0.15/21.52 % WCLimit : 300
% 0.15/21.52 % DateTime : Mon Sep 21 02:09:05 UTC 2026
% 0.15/21.53 % CPUTime :
% 0.15/21.55 % Drodi V4.1.1
% 126.94/37.62 % Refutation found
% 126.94/37.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 126.94/37.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.52/37.73 % Elapsed time: 16.181242 seconds
% 12.52/37.73 % CPU time: 128.060618 seconds
% 12.52/37.73 % Total memory used: 691.650 MB
% 12.52/37.73 % Net memory used: 606.050 MB
%------------------------------------------------------------------------------