%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET021-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 02:08:55 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 43 ( 12 unt; 0 def)
% Number of atoms : 87 ( 22 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 91 ( 47 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 101 ( 101 !; 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(f4,axiom,
! [X] : subclass(X,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f14,axiom,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U,X,V,Y] :
( member(ordered_pair(U,V),cross_product(X,Y))
| ~ member(V,Y)
| ~ member(U,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f93,negated_conjecture,
second(ordered_pair(u,v)) != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f94,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f95,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f98,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
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(f111,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X2),cross_product(X1,X3))
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f116,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f199,plain,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f200,plain,
second(ordered_pair(u,v)) != v,
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f209,plain,
! [X0,X1,X2,X3,X4] :
( ~ member(ordered_pair(X3,X0),cross_product(X4,unordered_pair(X1,X2)))
| X0 = X2
| X0 = X1 ),
inference(resolution,[status(thm)],[f103,f114]) ).
fof(f252,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X2,X0),cross_product(X3,singleton(X1)))
| X0 = X1
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f109,f209]) ).
fof(f265,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X2,X0),cross_product(X3,singleton(X1)))
| X0 = X1 ),
inference(duplicate_literals_removal,[status(thm)],[f252]) ).
fof(f271,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(paramodulation,[status(thm)],[f109,f105]) ).
fof(f334,plain,
ordered_pair(first(ordered_pair(u,v)),second(ordered_pair(u,v))) = ordered_pair(u,v),
inference(resolution,[status(thm)],[f117,f199]) ).
fof(f348,plain,
! [X0,X1] :
( ~ member(ordered_pair(u,v),cross_product(X1,singleton(X0)))
| second(ordered_pair(u,v)) = X0 ),
inference(paramodulation,[status(thm)],[f334,f265]) ).
fof(f357,plain,
! [X0,X1] :
( ~ member(v,singleton(X0))
| ~ member(u,X1)
| second(ordered_pair(u,v)) = X0 ),
inference(resolution,[status(thm)],[f348,f115]) ).
fof(f527,plain,
! [X0] :
( ~ member(u,X0)
| second(ordered_pair(u,v)) = v
| ~ member(v,universal_class) ),
inference(resolution,[status(thm)],[f271,f357]) ).
fof(f530,plain,
! [X0] :
( ~ member(u,X0)
| ~ member(v,universal_class) ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f200]) ).
fof(f573,plain,
! [X0,X1] :
( ~ member(v,X1)
| ~ subclass(X1,universal_class)
| ~ member(u,X0) ),
inference(resolution,[status(thm)],[f530,f95]) ).
fof(f576,plain,
! [X0,X1] :
( ~ member(v,X1)
| ~ member(u,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f98]) ).
fof(f586,plain,
! [X0,X1,X2,X3] :
( ~ member(ordered_pair(X1,v),cross_product(X2,X3))
| ~ member(u,X0) ),
inference(resolution,[status(thm)],[f576,f114]) ).
fof(f612,plain,
! [X0] : ~ member(u,X0),
inference(resolution,[status(thm)],[f586,f199]) ).
fof(f627,plain,
! [X0,X1,X2] : ~ member(ordered_pair(u,X0),cross_product(X1,X2)),
inference(resolution,[status(thm)],[f612,f112]) ).
fof(f634,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f199,f627]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET021-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n019.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 04:43:34 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.084617 seconds
% 0.13/0.44 % CPU time: 0.363147 seconds
% 0.13/0.44 % Total memory used: 110.642 MB
% 0.13/0.44 % Net memory used: 109.942 MB
%------------------------------------------------------------------------------