%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET067-6 : 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 02:09:10 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 12 unt; 0 def)
% Number of atoms : 57 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 24 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 44 ( 44 !; 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(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(f92,negated_conjecture,
~ subclass(singleton(x),unordered_pair(x,y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f94,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f96,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f97,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f101,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f102,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [X] :
( ! [Y] : member(X,unordered_pair(X,Y))
| ~ member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f104,plain,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f108,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f198,plain,
~ subclass(singleton(x),unordered_pair(x,y)),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f206,plain,
! [X0,X1] :
( X0 = X1
| X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(paramodulation,[status(thm)],[f108,f102]) ).
fof(f207,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X0,singleton(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f206]) ).
fof(f216,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[f207,f95]) ).
fof(f222,plain,
not_subclass_element(singleton(x),unordered_pair(x,y)) = x,
inference(resolution,[status(thm)],[f216,f198]) ).
fof(f244,plain,
( subclass(singleton(x),unordered_pair(x,y))
| ~ member(x,unordered_pair(x,y)) ),
inference(paramodulation,[status(thm)],[f222,f96]) ).
fof(f245,plain,
( subclass(singleton(x),unordered_pair(x,y))
| member(x,singleton(x)) ),
inference(paramodulation,[status(thm)],[f222,f95]) ).
fof(f246,plain,
~ member(x,unordered_pair(x,y)),
inference(forward_subsumption_resolution,[status(thm)],[f244,f198]) ).
fof(f247,plain,
member(x,singleton(x)),
inference(forward_subsumption_resolution,[status(thm)],[f245,f198]) ).
fof(f249,plain,
~ member(x,universal_class),
inference(resolution,[status(thm)],[f246,f104]) ).
fof(f251,plain,
! [X0] :
( ~ member(x,X0)
| ~ subclass(X0,universal_class) ),
inference(resolution,[status(thm)],[f249,f94]) ).
fof(f252,plain,
! [X0] : ~ member(x,X0),
inference(forward_subsumption_resolution,[status(thm)],[f251,f97]) ).
fof(f254,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f247,f252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET067-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n015.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:52:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.065928 seconds
% 0.10/0.44 % CPU time: 0.170574 seconds
% 0.10/0.44 % Total memory used: 104.928 MB
% 0.10/0.44 % Net memory used: 104.836 MB
%------------------------------------------------------------------------------