%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET154-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 02:09:30 PM UTC 2026
% Result : Unsatisfiable 30.92s 4.39s
% Output : CNFRefutation 20.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 16 unt; 0 def)
% Number of atoms : 103 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 88 ( 38 ~; 50 |; 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 : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 83 !; 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(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
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(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(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(f25,axiom,
! [Z,X] :
( member(Z,X)
| member(Z,complement(X))
| ~ member(Z,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,Y] : complement(intersection(complement(X),complement(Y))) = union(X,Y),
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(f113,negated_conjecture,
union(complement(x),x) != universal_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
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(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(f143,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f144,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f146,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f147,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f148,plain,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f188,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f245,plain,
union(complement(x),x) != universal_class,
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f569,plain,
! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) ),
inference(resolution,[status(thm)],[f117,f147]) ).
fof(f629,plain,
! [X0] :
( subclass(universal_class,complement(X0))
| member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ),
inference(resolution,[status(thm)],[f569,f116]) ).
fof(f634,plain,
! [X0] :
( member(not_subclass_element(universal_class,complement(X0)),X0)
| subclass(universal_class,complement(X0)) ),
inference(duplicate_literals_removal,[status(thm)],[f629]) ).
fof(f647,plain,
! [X0] :
( ~ member(not_subclass_element(universal_class,complement(complement(X0))),X0)
| subclass(universal_class,complement(complement(X0))) ),
inference(resolution,[status(thm)],[f634,f146]) ).
fof(f664,plain,
( subclass(universal_class,complement(complement(universal_class)))
| subclass(universal_class,complement(complement(universal_class))) ),
inference(resolution,[status(thm)],[f647,f116]) ).
fof(f671,plain,
subclass(universal_class,complement(complement(universal_class))),
inference(duplicate_literals_removal,[status(thm)],[f664]) ).
fof(f810,plain,
! [X0] :
( ~ member(regular(complement(X0)),X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f188,f146]) ).
fof(f811,plain,
! [X0,X1] :
( member(regular(X0),X1)
| ~ subclass(X0,X1)
| X0 = null_class ),
inference(resolution,[status(thm)],[f188,f115]) ).
fof(f814,plain,
( complement(complement(universal_class)) = universal_class
| ~ subclass(complement(complement(universal_class)),universal_class) ),
inference(resolution,[status(thm)],[f121,f671]) ).
fof(f821,plain,
complement(complement(universal_class)) = universal_class,
inference(forward_subsumption_resolution,[status(thm)],[f814,f118]) ).
fof(f930,plain,
! [X0,X1,X2] :
( subclass(intersection(X0,X1),X2)
| member(not_subclass_element(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f142,f116]) ).
fof(f934,plain,
! [X0,X1] :
( intersection(X0,X1) = null_class
| member(regular(intersection(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f144,f188]) ).
fof(f2655,plain,
! [X0] :
( complement(X0) = null_class
| ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f811,f810]) ).
fof(f2669,plain,
! [X0,X1] :
( ~ member(regular(X0),X1)
| ~ subclass(X0,complement(X1))
| X0 = null_class ),
inference(resolution,[status(thm)],[f811,f146]) ).
fof(f2673,plain,
! [X0] :
( ~ subclass(complement(X0),X0)
| complement(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f2655]) ).
fof(f2677,plain,
complement(universal_class) = null_class,
inference(resolution,[status(thm)],[f2673,f118]) ).
fof(f2723,plain,
complement(null_class) = universal_class,
inference(backward_demodulation,[status(thm)],[f2677,f821]) ).
fof(f6736,plain,
! [X0,X1] :
( ~ subclass(intersection(X0,X1),complement(X1))
| intersection(X0,X1) = null_class
| intersection(X0,X1) = null_class ),
inference(resolution,[status(thm)],[f934,f2669]) ).
fof(f6774,plain,
! [X0,X1] :
( ~ subclass(intersection(X0,X1),complement(X1))
| intersection(X0,X1) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f6736]) ).
fof(f8436,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f930,f117]) ).
fof(f8486,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f8436]) ).
fof(f13731,plain,
! [X0] : intersection(complement(X0),X0) = null_class,
inference(resolution,[status(thm)],[f6774,f8486]) ).
fof(f13841,plain,
! [X0] : complement(null_class) = union(complement(X0),X0),
inference(paramodulation,[status(thm)],[f13731,f148]) ).
fof(f13913,plain,
! [X0] : universal_class = union(complement(X0),X0),
inference(forward_demodulation,[status(thm)],[f2723,f13841]) ).
fof(f13964,plain,
universal_class != universal_class,
inference(backward_demodulation,[status(thm)],[f13913,f245]) ).
fof(f14025,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f13964]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET154-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 04:59:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 30.92/4.39 % Refutation found
% 30.92/4.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 30.92/4.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.09/4.80 % Elapsed time: 4.411225 seconds
% 2.09/4.80 % CPU time: 32.426732 seconds
% 2.09/4.80 % Total memory used: 544.897 MB
% 2.09/4.80 % Net memory used: 510.354 MB
%------------------------------------------------------------------------------