%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET020-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 6 unt; 0 def)
% Number of atoms : 32 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
! [Z,X,Y] :
( ordered_pair(first(Z),second(Z)) = Z
| ~ member(Z,cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [U,V,X,Y] :
( member(U,universal_class)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f151,axiom,
! [W,X,Y,Z] :
( W = Y
| ~ member(W,universal_class)
| ordered_pair(W,X) != ordered_pair(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f158,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
first(ordered_pair(u,v)) != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f182,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f182]) ).
fof(f269,plain,
! [U] :
( member(U,universal_class)
| ! [V,X,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f94]) ).
fof(f270,plain,
! [X0,X1,X2,X3] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f341,plain,
! [W,Y] :
( W = Y
| ~ member(W,universal_class)
| ! [X,Z] : ordered_pair(W,X) != ordered_pair(Y,Z) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f342,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ member(X0,universal_class)
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f341]) ).
fof(f350,plain,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f351,plain,
first(ordered_pair(u,v)) != u,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f419,plain,
! [X0,X1,X2,X3] :
( X0 = first(ordered_pair(X0,X1))
| ~ member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(resolution,[status(thm)],[f183,f342]) ).
fof(f421,plain,
! [X0,X1,X2,X3] :
( X0 = first(ordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f419,f270]) ).
fof(f438,plain,
u = first(ordered_pair(u,v)),
inference(resolution,[status(thm)],[f421,f350]) ).
fof(f440,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f438,f351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET020-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:45:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.39 % 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
% 0.14/0.44 % Elapsed time: 0.067082 seconds
% 0.14/0.44 % CPU time: 0.167609 seconds
% 0.14/0.44 % Total memory used: 53.905 MB
% 0.14/0.44 % Net memory used: 53.821 MB
%------------------------------------------------------------------------------