%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET232-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 02:09:41 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.51s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 26 ( 8 unt; 2 def)
% Number of atoms : 44 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 35 ( 17 ~; 16 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
~ subclass(cross_product(x,y),z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
~ member(first(not_subclass_element(cross_product(x,y),z)),x),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f132,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f137,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f246,plain,
~ subclass(cross_product(x,y),z),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
~ member(first(not_subclass_element(cross_product(x,y),z)),x),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f328,plain,
! [X0,X1,X2] :
( subclass(cross_product(X0,X1),X2)
| ordered_pair(first(not_subclass_element(cross_product(X0,X1),X2)),second(not_subclass_element(cross_product(X0,X1),X2))) = not_subclass_element(cross_product(X0,X1),X2) ),
inference(resolution,[status(thm)],[f138,f117]) ).
fof(f357,plain,
ordered_pair(first(not_subclass_element(cross_product(x,y),z)),second(not_subclass_element(cross_product(x,y),z))) = not_subclass_element(cross_product(x,y),z),
inference(resolution,[status(thm)],[f328,f246]) ).
fof(f385,plain,
! [X0,X1] :
( member(first(not_subclass_element(cross_product(x,y),z)),X0)
| ~ member(not_subclass_element(cross_product(x,y),z),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f357,f133]) ).
fof(f405,definition,
( sQ9_spl
<=> subclass(cross_product(x,y),z) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ9_spl
| subclass(cross_product(x,y),z) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f409,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f406,f246]) ).
fof(f410,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f492,plain,
( subclass(cross_product(x,y),z)
| member(first(not_subclass_element(cross_product(x,y),z)),x) ),
inference(resolution,[status(thm)],[f385,f117]) ).
fof(f505,definition,
( sQ12_spl
<=> member(first(not_subclass_element(cross_product(x,y),z)),x) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( ~ sQ12_spl
| member(first(not_subclass_element(cross_product(x,y),z)),x) ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f508,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f492,f505,f405]) ).
fof(f517,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f506,f247]) ).
fof(f518,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f519,plain,
$false,
inference(sat_refutation,[status(thm)],[f410,f508,f518]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET232-6 : 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 : n009.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 05:02:28 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.41 % Drodi V4.1.1
% 0.10/0.51 % Refutation found
% 0.10/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.52 % Elapsed time: 0.145813 seconds
% 0.10/0.52 % CPU time: 0.579769 seconds
% 0.10/0.52 % Total memory used: 75.995 MB
% 0.10/0.52 % Net memory used: 75.156 MB
%------------------------------------------------------------------------------