%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM094-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 01:38:38 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.62s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 73 ( 24 unt; 0 def)
% Number of atoms : 142 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 129 ( 60 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-3 aty)
% Number of variables : 122 ( 122 !; 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(f23,axiom,
! [Z,X,Y] :
( member(Z,intersection(X,Y))
| ~ member(Z,Y)
| ~ member(Z,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(f29,axiom,
! [X,Y,Xr] : intersection(cross_product(X,Y),Xr) = restrict(Xr,X,Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [X,Z] :
( ~ member(Z,domain_of(X))
| restrict(X,singleton(Z),universal_class) != null_class ),
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(f67,axiom,
! [X] :
( intersection(X,regular(X)) = null_class
| X = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f124,axiom,
! [Xr,Y,U] :
( member(least(Xr,U),U)
| U = null_class
| ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,axiom,
! [Xr,Y,Z] :
( subclass(Y,Z)
| ~ section(Xr,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
well_ordering(xr,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f160,negated_conjecture,
section(xr,w,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f161,negated_conjecture,
~ member(least(xr,intersection(complement(w),y)),y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f162,negated_conjecture,
y != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f163,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f164,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f165,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f166,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f167,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f170,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f190,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f191,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f192,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f193,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f194,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f196,plain,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f200,plain,
! [X0,X1,X2] : intersection(cross_product(X0,X1),X2) = restrict(X2,X0,X1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f201,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| restrict(X0,singleton(X1),universal_class) != null_class ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f237,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f238,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f305,plain,
! [Xr,U] :
( member(least(Xr,U),U)
| U = null_class
| ! [Y] :
( ~ subclass(U,Y)
| ~ well_ordering(Xr,Y) ) ),
inference(miniscoping,[status(thm)],[f124]) ).
fof(f306,plain,
! [X0,X1,X2] :
( member(least(X0,X2),X2)
| X2 = null_class
| ~ subclass(X2,X1)
| ~ well_ordering(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f305]) ).
fof(f317,plain,
! [Y,Z] :
( subclass(Y,Z)
| ! [Xr] : ~ section(Xr,Y,Z) ),
inference(miniscoping,[status(thm)],[f131]) ).
fof(f318,plain,
! [X0,X1,X2] :
( subclass(X1,X2)
| ~ section(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f317]) ).
fof(f350,plain,
well_ordering(xr,y),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f351,plain,
section(xr,w,y),
inference(cnf_transformation,[status(thm)],[f160]) ).
fof(f352,plain,
~ member(least(xr,intersection(complement(w),y)),y),
inference(cnf_transformation,[status(thm)],[f161]) ).
fof(f353,plain,
y != w,
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f360,plain,
subclass(w,y),
inference(resolution,[status(thm)],[f318,f351]) ).
fof(f368,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f164,f167]) ).
fof(f370,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f165,f193]) ).
fof(f371,plain,
! [X0,X1,X2] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f165,f191]) ).
fof(f386,plain,
! [X0,X1,X2,X3] :
( member(least(X0,intersection(X2,X3)),X3)
| intersection(X2,X3) = null_class
| ~ subclass(intersection(X2,X3),X1)
| ~ well_ordering(X0,X1) ),
inference(resolution,[status(thm)],[f306,f193]) ).
fof(f414,plain,
( y = w
| ~ subclass(y,w) ),
inference(resolution,[status(thm)],[f170,f360]) ).
fof(f417,plain,
~ subclass(y,w),
inference(forward_subsumption_resolution,[status(thm)],[f414,f353]) ).
fof(f465,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X1)
| subclass(intersection(X0,X1),X1) ),
inference(resolution,[status(thm)],[f370,f166]) ).
fof(f476,plain,
! [X0,X1] : subclass(intersection(X0,X1),X1),
inference(duplicate_literals_removal,[status(thm)],[f465]) ).
fof(f481,plain,
! [X0,X1,X2] : subclass(restrict(X0,X1,X2),X0),
inference(paramodulation,[status(thm)],[f200,f476]) ).
fof(f483,plain,
! [X0,X1,X2] :
( X0 = restrict(X0,X1,X2)
| ~ subclass(X0,restrict(X0,X1,X2)) ),
inference(resolution,[status(thm)],[f481,f170]) ).
fof(f495,plain,
! [X0,X1] :
( subclass(intersection(X0,X1),X0)
| subclass(intersection(X0,X1),X0) ),
inference(resolution,[status(thm)],[f371,f166]) ).
fof(f506,plain,
! [X0,X1] : subclass(intersection(X0,X1),X0),
inference(duplicate_literals_removal,[status(thm)],[f495]) ).
fof(f821,plain,
! [X0] :
( intersection(complement(w),y) = null_class
| ~ subclass(intersection(complement(w),y),X0)
| ~ well_ordering(xr,X0) ),
inference(resolution,[status(thm)],[f386,f352]) ).
fof(f924,plain,
! [X0] :
( X0 = null_class
| subclass(null_class,X0) ),
inference(paramodulation,[status(thm)],[f238,f506]) ).
fof(f940,plain,
( intersection(complement(w),y) = null_class
| ~ well_ordering(xr,y) ),
inference(resolution,[status(thm)],[f821,f476]) ).
fof(f943,plain,
intersection(complement(w),y) = null_class,
inference(forward_subsumption_resolution,[status(thm)],[f940,f350]) ).
fof(f944,plain,
! [X0,X1] :
( null_class = restrict(null_class,X0,X1)
| restrict(null_class,X0,X1) = null_class ),
inference(resolution,[status(thm)],[f924,f483]) ).
fof(f948,plain,
! [X0,X1] : restrict(null_class,X0,X1) = null_class,
inference(duplicate_literals_removal,[status(thm)],[f944]) ).
fof(f986,plain,
! [X0] : ~ member(X0,domain_of(null_class)),
inference(resolution,[status(thm)],[f948,f201]) ).
fof(f999,plain,
domain_of(null_class) = null_class,
inference(resolution,[status(thm)],[f986,f237]) ).
fof(f1030,plain,
! [X0] : ~ member(X0,null_class),
inference(backward_demodulation,[status(thm)],[f999,f986]) ).
fof(f1109,plain,
! [X0] :
( member(X0,null_class)
| ~ member(X0,y)
| ~ member(X0,complement(w)) ),
inference(paramodulation,[status(thm)],[f943,f194]) ).
fof(f1119,plain,
! [X0] :
( ~ member(X0,y)
| ~ member(X0,complement(w)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1109,f1030]) ).
fof(f1238,plain,
! [X0] :
( member(X0,w)
| ~ member(X0,universal_class)
| ~ member(X0,y) ),
inference(resolution,[status(thm)],[f1119,f196]) ).
fof(f1239,plain,
! [X0] :
( member(X0,w)
| ~ member(X0,y) ),
inference(forward_subsumption_resolution,[status(thm)],[f1238,f368]) ).
fof(f1244,plain,
! [X0] :
( subclass(X0,w)
| ~ member(not_subclass_element(X0,w),y) ),
inference(resolution,[status(thm)],[f1239,f166]) ).
fof(f1712,plain,
( subclass(y,w)
| subclass(y,w) ),
inference(resolution,[status(thm)],[f1244,f165]) ).
fof(f1719,plain,
subclass(y,w),
inference(duplicate_literals_removal,[status(thm)],[f1712]) ).
fof(f1720,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1719,f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM094-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n004.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 02:04:19 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.46 % Drodi V4.1.1
% 0.16/0.62 % Refutation found
% 0.16/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.66 % Elapsed time: 0.210237 seconds
% 0.16/0.66 % CPU time: 1.195841 seconds
% 0.16/0.66 % Total memory used: 124.096 MB
% 0.16/0.66 % Net memory used: 122.890 MB
%------------------------------------------------------------------------------