%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET096-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 02:09:19 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 41 ( 15 unt; 0 def)
% Number of atoms : 80 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 72 ( 33 ~; 39 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 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(f5,axiom,
! [X,Y] :
( subclass(X,Y)
| X != Y ),
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(f12,axiom,
! [X] : unordered_pair(X,X) = singleton(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(f92,negated_conjecture,
subclass(x,singleton(y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
x != null_class,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,negated_conjecture,
singleton(y) != x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f95,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f96,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f98,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f100,plain,
! [X0,X1] :
( subclass(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f103,plain,
! [U,Y] :
( U = Y
| ! [X] :
( U = X
| ~ member(U,unordered_pair(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f104,plain,
! [X0,X1,X2] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f110,plain,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f169,plain,
! [X0] :
( member(regular(X0),X0)
| X0 = null_class ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f200,plain,
subclass(x,singleton(y)),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f201,plain,
x != null_class,
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f202,plain,
singleton(y) != x,
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f203,plain,
! [X0] : subclass(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f100]) ).
fof(f206,plain,
( singleton(y) = x
| ~ subclass(singleton(y),x) ),
inference(resolution,[status(thm)],[f102,f200]) ).
fof(f209,plain,
~ subclass(singleton(y),x),
inference(forward_subsumption_resolution,[status(thm)],[f206,f202]) ).
fof(f214,plain,
! [X0,X1,X2,X3] :
( ~ member(X0,X3)
| ~ subclass(X3,unordered_pair(X1,X2))
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[f104,f96]) ).
fof(f222,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ subclass(X2,singleton(X1))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f110,f214]) ).
fof(f223,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ subclass(X2,singleton(X1))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(thm)],[f222]) ).
fof(f224,plain,
! [X0] :
( ~ member(X0,x)
| X0 = y ),
inference(resolution,[status(thm)],[f223,f200]) ).
fof(f225,plain,
! [X0,X1] :
( ~ member(X0,singleton(X1))
| X0 = X1 ),
inference(resolution,[status(thm)],[f223,f203]) ).
fof(f228,plain,
! [X0,X1] :
( subclass(singleton(X0),X1)
| not_subclass_element(singleton(X0),X1) = X0 ),
inference(resolution,[status(thm)],[f225,f97]) ).
fof(f266,plain,
not_subclass_element(singleton(y),x) = y,
inference(resolution,[status(thm)],[f228,f209]) ).
fof(f275,plain,
( subclass(singleton(y),x)
| ~ member(y,x) ),
inference(paramodulation,[status(thm)],[f266,f98]) ).
fof(f279,plain,
~ member(y,x),
inference(forward_subsumption_resolution,[status(thm)],[f275,f209]) ).
fof(f324,plain,
( regular(x) = y
| x = null_class ),
inference(resolution,[status(thm)],[f169,f224]) ).
fof(f328,plain,
regular(x) = y,
inference(forward_subsumption_resolution,[status(thm)],[f324,f201]) ).
fof(f329,plain,
( member(y,x)
| x = null_class ),
inference(paramodulation,[status(thm)],[f328,f169]) ).
fof(f330,plain,
member(y,x),
inference(forward_subsumption_resolution,[status(thm)],[f329,f201]) ).
fof(f331,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f330,f279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET096-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n007.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Mon Sep 21 04:49:56 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 0.13/5.40 % Refutation found
% 0.13/5.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.43 % Elapsed time: 0.049690 seconds
% 0.13/5.43 % CPU time: 0.152119 seconds
% 0.13/5.43 % Total memory used: 53.446 MB
% 0.13/5.43 % Net memory used: 53.326 MB
%------------------------------------------------------------------------------