%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET073-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:09:12 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.45s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 12 unt; 0 def)
% Number of atoms : 98 ( 49 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 77 ( 29 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 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(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(X),
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(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(f92,negated_conjecture,
member(x,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
unordered_pair(x,y) = 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(f109,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
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(f123,plain,
! [Z,Y] :
( member(Z,Y)
| ! [X] : ~ member(Z,intersection(X,Y)) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f124,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f126,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f168,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
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,
unordered_pair(x,y) = null_class,
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f205,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f109,f103]) ).
fof(f206,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f205]) ).
fof(f210,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(paramodulation,[status(thm)],[f200,f105]) ).
fof(f212,plain,
member(x,null_class),
inference(forward_subsumption_resolution,[status(thm)],[f210,f199]) ).
fof(f357,plain,
! [X0] :
( regular(singleton(X0)) = X0
| singleton(X0) = null_class ),
inference(resolution,[status(thm)],[f168,f206]) ).
fof(f435,plain,
! [X0] :
( singleton(X0) = null_class
| intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(paramodulation,[status(thm)],[f357,f169]) ).
fof(f437,plain,
! [X0,X1] :
( X1 = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f169,f122]) ).
fof(f439,plain,
! [X0] :
( intersection(singleton(X0),X0) = null_class
| singleton(X0) = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f435]) ).
fof(f490,plain,
! [X0,X1] :
( singleton(X1) = null_class
| member(X0,X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f439,f124]) ).
fof(f520,plain,
! [X0] :
( singleton(X0) = null_class
| member(x,X0) ),
inference(resolution,[status(thm)],[f490,f212]) ).
fof(f531,plain,
! [X0] :
( x = X0
| singleton(singleton(X0)) = null_class ),
inference(resolution,[status(thm)],[f520,f206]) ).
fof(f609,plain,
! [X0,X1] :
( x = X1
| X0 = singleton(X1)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f531,f206]) ).
fof(f670,plain,
! [X0] :
( x = X0
| x = singleton(X0) ),
inference(resolution,[status(thm)],[f609,f212]) ).
fof(f728,plain,
! [X0,X1] :
( x = X1
| X0 = X1
| ~ member(X0,x) ),
inference(paramodulation,[status(thm)],[f670,f206]) ).
fof(f1203,plain,
! [X0] :
( X0 = null_class
| member(x,X0) ),
inference(resolution,[status(thm)],[f437,f212]) ).
fof(f1212,plain,
! [X0] :
( x = X0
| x = X0
| x = null_class ),
inference(resolution,[status(thm)],[f1203,f728]) ).
fof(f1215,plain,
! [X0] :
( ~ member(x,X0)
| complement(X0) = null_class ),
inference(resolution,[status(thm)],[f1203,f126]) ).
fof(f1229,plain,
! [X0] :
( x = X0
| x = null_class ),
inference(duplicate_literals_removal,[status(thm)],[f1212]) ).
fof(f1246,plain,
! [X0] :
( x = X0
| null_class != X0 ),
inference(equality_factoring,[status(thm)],[f1229]) ).
fof(f1248,plain,
x = null_class,
inference(destructive_equality_resolution,[status(thm)],[f1246]) ).
fof(f1279,plain,
member(null_class,null_class),
inference(backward_demodulation,[status(thm)],[f1248,f212]) ).
fof(f1534,plain,
! [X0] :
( ~ member(null_class,X0)
| complement(X0) = null_class ),
inference(forward_demodulation,[status(thm)],[f1248,f1215]) ).
fof(f1536,plain,
complement(null_class) = null_class,
inference(resolution,[status(thm)],[f1534,f1279]) ).
fof(f1562,plain,
! [X0] :
( ~ member(X0,null_class)
| ~ member(X0,null_class) ),
inference(paramodulation,[status(thm)],[f1536,f126]) ).
fof(f1565,plain,
! [X0] : ~ member(X0,null_class),
inference(duplicate_literals_removal,[status(thm)],[f1562]) ).
fof(f1585,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f1279,f1565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET073-6 : 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 : n017.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 04:45:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.45 % Refutation found
% 0.09/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.48 % Elapsed time: 0.100688 seconds
% 0.09/0.48 % CPU time: 0.539549 seconds
% 0.09/0.48 % Total memory used: 114.866 MB
% 0.09/0.48 % Net memory used: 113.872 MB
%------------------------------------------------------------------------------