%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM078-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:38:37 PM UTC 2026
% Result : Unsatisfiable 0.11s 1.06s
% Output : CNFRefutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 13 unt; 0 def)
% Number of atoms : 141 ( 41 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 119 ( 48 ~; 71 |; 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 114 ( 114 !; 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(f7,axiom,
! [X,Y] :
( X = Y
| ~ subclass(Y,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,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(f22,axiom,
! [Z,X,Y] :
( member(Z,Y)
| ~ member(Z,intersection(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,X) ),
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(f66,axiom,
! [X] :
( member(regular(X),X)
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f161,negated_conjecture,
member(u,intersection(u,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f162,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f163,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f165,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f166,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f169,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f170,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f171,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f170]) ).
fof(f172,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f173,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f177,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f189,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f190,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
fof(f191,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f192,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f193,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f194,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f236,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f237,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f351,plain,
member(u,intersection(u,y)),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f361,plain,
member(u,u),
inference(resolution,[status(thm)],[f190,f351]) ).
fof(f369,plain,
! [X0] :
( member(u,intersection(X0,u))
| ~ member(u,X0) ),
inference(resolution,[status(thm)],[f193,f361]) ).
fof(f409,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f163,f166]) ).
fof(f413,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f164,f190]) ).
fof(f542,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f177,f171]) ).
fof(f543,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f542]) ).
fof(f550,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,unordered_pair(X0,X1)) ),
inference(resolution,[status(thm)],[f173,f409]) ).
fof(f644,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f413,f165]) ).
fof(f658,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f644]) ).
fof(f668,plain,
! [X0,X1] :
( X0 = intersection(X0,X1)
| ~ subclass(X0,intersection(X0,X1)) ),
inference(resolution,[status(thm)],[f658,f169]) ).
fof(f673,plain,
! [X0] :
( singleton(X0) = null_class
| regular(singleton(X0)) = X0 ),
inference(resolution,[status(thm)],[f543,f236]) ).
fof(f870,plain,
! [X0] :
( X0 = null_class
| subclass(null_class,X0) ),
inference(paramodulation,[status(thm)],[f237,f658]) ).
fof(f879,plain,
! [X0] :
( null_class = intersection(null_class,X0)
| intersection(null_class,X0) = null_class ),
inference(resolution,[status(thm)],[f870,f668]) ).
fof(f884,plain,
! [X0] : intersection(null_class,X0) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f879]) ).
fof(f918,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f884,f192]) ).
fof(f1263,plain,
! [X0,X1] :
( ~ member(X0,X1)
| member(X0,singleton(X0)) ),
inference(paramodulation,[status(thm)],[f177,f550]) ).
fof(f1270,plain,
! [X0] :
( member(u,intersection(singleton(u),u))
| ~ member(u,X0) ),
inference(resolution,[status(thm)],[f1263,f369]) ).
fof(f1288,plain,
! [X0] :
( singleton(X0) = null_class
| intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f673,f237]) ).
fof(f1290,plain,
! [X0] :
( singleton(X0) = null_class
| member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f673,f236]) ).
fof(f1291,plain,
! [X0] :
( intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f1288]) ).
fof(f1293,plain,
! [X0] :
( member(X0,singleton(X0))
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f1290]) ).
fof(f1300,plain,
( member(u,intersection(singleton(u),u))
| singleton(u) = null_class ),
inference(resolution,[status(thm)],[f1293,f369]) ).
fof(f1358,plain,
! [X0] :
( member(u,intersection(intersection(singleton(u),u),u))
| ~ member(u,X0) ),
inference(resolution,[status(thm)],[f1270,f369]) ).
fof(f1817,plain,
( singleton(u) = null_class
| member(u,null_class)
| singleton(u) = null_class ),
inference(paramodulation,[status(thm)],[f1291,f1300]) ).
fof(f1858,plain,
( member(u,null_class)
| singleton(u) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f1817]) ).
fof(f1876,plain,
! [X0] :
( member(u,X0)
| singleton(u) = null_class ),
inference(resolution,[status(thm)],[f1858,f918]) ).
fof(f1897,plain,
! [X0] :
( ~ member(u,X0)
| singleton(u) = null_class ),
inference(resolution,[status(thm)],[f1876,f194]) ).
fof(f1912,plain,
! [X0] :
( member(u,intersection(intersection(null_class,u),u))
| ~ member(u,X0) ),
inference(backward_demodulation,[status(thm)],[f1919,f1358]) ).
fof(f1919,plain,
singleton(u) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f1897,f1876]) ).
fof(f1920,plain,
! [X0] :
( member(u,intersection(null_class,u))
| ~ member(u,X0) ),
inference(forward_demodulation,[status(thm)],[f884,f1912]) ).
fof(f1921,plain,
! [X0] :
( member(u,null_class)
| ~ member(u,X0) ),
inference(forward_demodulation,[status(thm)],[f884,f1920]) ).
fof(f2026,plain,
! [X0,X1] :
( member(u,X1)
| ~ member(u,X0) ),
inference(resolution,[status(thm)],[f1921,f918]) ).
fof(f2030,plain,
! [X0] : member(u,X0),
inference(resolution,[status(thm)],[f2026,f361]) ).
fof(f2060,plain,
! [X0] : ~ member(u,X0),
inference(resolution,[status(thm)],[f2030,f194]) ).
fof(f2075,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2060,f2030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM078-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n015.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Mon Sep 21 02:06:06 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.58 % Drodi V4.1.1
% 0.11/1.06 % Refutation found
% 0.11/1.06 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/1.06 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.46/1.09 % Elapsed time: 0.512008 seconds
% 3.46/1.09 % CPU time: 3.810659 seconds
% 3.46/1.09 % Total memory used: 170.740 MB
% 3.46/1.09 % Net memory used: 164.207 MB
%------------------------------------------------------------------------------