%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET122-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:09:26 PM UTC 2026
% Result : Unsatisfiable 4.02s 1.00s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 9 unt; 0 def)
% Number of atoms : 49 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 14 ~; 22 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 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 : 38 ( 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,axiom,
! [U,V,X,Y] :
( member(V,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(f155,axiom,
! [X] :
( second(X) = X
| member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f157,axiom,
! [X] :
( second(X) = X
| ordered_pair(first(X),second(X)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f167,axiom,
! [X,Y] :
( second(ordered_pair(X,Y)) = ordered_pair(X,Y)
| member(X,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f168,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f169,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f281,plain,
! [V] :
( member(V,universal_class)
| ! [U,X,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f95]) ).
fof(f282,plain,
! [X0,X1,X2,X3] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f351,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(f352,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ member(X0,universal_class)
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f351]) ).
fof(f357,plain,
! [X0] :
( second(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f359,plain,
! [X0] :
( second(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f370,plain,
! [X] :
( ! [Y] : second(ordered_pair(X,Y)) = ordered_pair(X,Y)
| member(X,universal_class) ),
inference(miniscoping,[status(thm)],[f167]) ).
fof(f371,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = ordered_pair(X0,X1)
| member(X0,universal_class) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f372,plain,
~ member(y,universal_class),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f373,plain,
second(ordered_pair(x,y)) != ordered_pair(x,y),
inference(cnf_transformation,[status(thm)],[f169]) ).
fof(f1568,plain,
! [X0,X1] :
( X0 = first(ordered_pair(X0,X1))
| ~ member(X0,universal_class)
| second(ordered_pair(X0,X1)) = ordered_pair(X0,X1) ),
inference(resolution,[status(thm)],[f359,f352]) ).
fof(f1608,plain,
! [X0,X1] :
( X0 = first(ordered_pair(X0,X1))
| second(ordered_pair(X0,X1)) = ordered_pair(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1568,f371]) ).
fof(f1645,plain,
x = first(ordered_pair(x,y)),
inference(resolution,[status(thm)],[f1608,f373]) ).
fof(f1661,plain,
( second(ordered_pair(x,y)) = ordered_pair(x,y)
| ordered_pair(x,second(ordered_pair(x,y))) = ordered_pair(x,y) ),
inference(paramodulation,[status(thm)],[f1645,f359]) ).
fof(f1666,plain,
ordered_pair(x,second(ordered_pair(x,y))) = ordered_pair(x,y),
inference(forward_subsumption_resolution,[status(thm)],[f1661,f373]) ).
fof(f5557,plain,
( second(ordered_pair(x,y)) = ordered_pair(x,y)
| member(ordered_pair(x,second(ordered_pair(x,y))),cross_product(universal_class,universal_class)) ),
inference(paramodulation,[status(thm)],[f1645,f357]) ).
fof(f5567,plain,
( second(ordered_pair(x,y)) = ordered_pair(x,y)
| member(ordered_pair(x,y),cross_product(universal_class,universal_class)) ),
inference(forward_demodulation,[status(thm)],[f1666,f5557]) ).
fof(f5568,plain,
member(ordered_pair(x,y),cross_product(universal_class,universal_class)),
inference(forward_subsumption_resolution,[status(thm)],[f5567,f373]) ).
fof(f5575,plain,
member(y,universal_class),
inference(resolution,[status(thm)],[f5568,f282]) ).
fof(f5586,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f5575,f372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET122-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n017.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 04:50:12 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 4.02/1.00 % Refutation found
% 4.02/1.00 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 4.02/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.13/1.02 % Elapsed time: 0.653970 seconds
% 2.13/1.02 % CPU time: 4.901063 seconds
% 2.13/1.02 % Total memory used: 178.785 MB
% 2.13/1.02 % Net memory used: 169.239 MB
%------------------------------------------------------------------------------