%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET021-7 : 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 02:08:56 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f95,axiom,
! [U,V,X,Y] :
( member(V,universal_class)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f152,axiom,
! [W,X,Y,Z] :
( X = Z
| ~ member(X,universal_class)
| ordered_pair(W,X) != ordered_pair(Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f158,negated_conjecture,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f159,negated_conjecture,
second(ordered_pair(u,v)) != v,
file('/export/starexec/sandbox/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(f271,plain,
! [V] :
( member(V,universal_class)
| ! [U,X,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f272,plain,
! [X0,X1,X2,X3] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f271]) ).
fof(f343,plain,
! [X,Z] :
( X = Z
| ~ member(X,universal_class)
| ! [W,Y] : ordered_pair(W,X) != ordered_pair(Y,Z) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f344,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ member(X1,universal_class)
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f343]) ).
fof(f350,plain,
member(ordered_pair(u,v),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f351,plain,
second(ordered_pair(u,v)) != v,
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f418,plain,
! [X0,X1,X2,X3] :
( X1 = second(ordered_pair(X0,X1))
| ~ member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(resolution,[status(thm)],[f183,f344]) ).
fof(f420,plain,
! [X0,X1,X2,X3] :
( X1 = second(ordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f418,f272]) ).
fof(f422,plain,
v = second(ordered_pair(u,v)),
inference(resolution,[status(thm)],[f420,f350]) ).
fof(f424,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f422,f351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET021-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 04:38:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.071416 seconds
% 0.13/0.44 % CPU time: 0.180761 seconds
% 0.13/0.44 % Total memory used: 107.562 MB
% 0.13/0.44 % Net memory used: 107.425 MB
%------------------------------------------------------------------------------