%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET079-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 02:09:14 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 27 unt; 0 def)
% Number of atoms : 89 ( 37 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 25 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [U,X,Y] :
( U = Y
| U = X
| ~ member(U,unordered_pair(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : member(unordered_pair(X,Y),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(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(f24,axiom,
! [Z,X] :
( ~ member(Z,X)
| ~ member(Z,complement(X)) ),
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(f92,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
singleton(x) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f103,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f105,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f108,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f109,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f110,plain,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f121,plain,
! [Z,X] :
( member(Z,X)
| ! [Y] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f122,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f126,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f169,plain,
! [X0] :
( intersection(X0,regular(X0)) = null_class
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f199,plain,
member(x,universal_class),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f200,plain,
singleton(x) = null_class,
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f204,plain,
! [X0] : member(singleton(X0),universal_class),
inference(paramodulation,[status(thm)],[f109,f108]) ).
fof(f210,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f109,f103]) ).
fof(f211,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f210]) ).
fof(f213,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f109,f105]) ).
fof(f214,plain,
member(null_class,universal_class),
inference(paramodulation,[status(thm)],[f200,f204]) ).
fof(f221,plain,
! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,x),
inference(paramodulation,[status(thm)],[f200,f110]) ).
fof(f223,plain,
! [X0,X1] :
( member(singleton(X0),ordered_pair(X0,X1))
| ~ member(singleton(X0),universal_class) ),
inference(paramodulation,[status(thm)],[f110,f105]) ).
fof(f228,plain,
! [X0,X1] : member(singleton(X0),ordered_pair(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f223,f204]) ).
fof(f242,plain,
! [X0] :
( X0 = x
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f200,f211]) ).
fof(f251,plain,
unordered_pair(singleton(null_class),singleton(null_class)) = ordered_pair(null_class,x),
inference(paramodulation,[status(thm)],[f109,f221]) ).
fof(f256,plain,
singleton(singleton(null_class)) = ordered_pair(null_class,x),
inference(forward_demodulation,[status(thm)],[f109,f251]) ).
fof(f298,plain,
member(singleton(null_class),singleton(singleton(null_class))),
inference(paramodulation,[status(thm)],[f256,f228]) ).
fof(f373,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f169,f122]) ).
fof(f375,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(paramodulation,[status(thm)],[f200,f213]) ).
fof(f376,plain,
member(x,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f375,f199]) ).
fof(f744,plain,
! [X0] :
( X0 = null_class
| member(x,X0) ),
inference(resolution,[status(thm)],[f373,f376]) ).
fof(f756,plain,
! [X0] :
( x = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f744,f211]) ).
fof(f779,plain,
( x = singleton(null_class)
| member(singleton(null_class),null_class) ),
inference(paramodulation,[status(thm)],[f756,f298]) ).
fof(f801,plain,
! [X0] :
( x = X0
| member(X0,null_class)
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f756,f213]) ).
fof(f812,plain,
x = singleton(null_class),
inference(forward_subsumption_resolution,[status(thm)],[f779,f242]) ).
fof(f816,plain,
! [X0] :
( x = X0
| ~ member(X0,universal_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f801,f242]) ).
fof(f835,plain,
( x = null_class
| x = null_class ),
inference(paramodulation,[status(thm)],[f756,f812]) ).
fof(f844,plain,
( member(null_class,x)
| ~ member(null_class,universal_class) ),
inference(paramodulation,[status(thm)],[f812,f213]) ).
fof(f873,plain,
x = null_class,
inference(duplicate_literals_removal,[status(thm)],[f835]) ).
fof(f877,plain,
member(null_class,x),
inference(forward_subsumption_resolution,[status(thm)],[f844,f214]) ).
fof(f971,plain,
member(x,x),
inference(forward_demodulation,[status(thm)],[f873,f877]) ).
fof(f988,plain,
! [X0] : x = singleton(X0),
inference(resolution,[status(thm)],[f816,f204]) ).
fof(f1018,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,x) ),
inference(backward_demodulation,[status(thm)],[f988,f211]) ).
fof(f1062,plain,
! [X0] : x = X0,
inference(resolution,[status(thm)],[f1018,f971]) ).
fof(f1083,plain,
! [X0] : member(x,X0),
inference(paramodulation,[status(thm)],[f1062,f971]) ).
fof(f1089,plain,
! [X0] : ~ member(x,X0),
inference(resolution,[status(thm)],[f1083,f126]) ).
fof(f1092,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1089,f1083]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET079-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:53:51 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.46 % Refutation found
% 0.11/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.49 % Elapsed time: 0.098438 seconds
% 0.11/0.49 % CPU time: 0.483855 seconds
% 0.11/0.49 % Total memory used: 113.171 MB
% 0.11/0.49 % Net memory used: 112.346 MB
%------------------------------------------------------------------------------