%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET118-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:09:25 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 7 unt; 2 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 41 ( 22 ~; 17 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/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(f164,negated_conjecture,
member(x,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f165,negated_conjecture,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f187,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(f275,plain,
! [U] :
( member(U,universal_class)
| ! [V,X,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f94]) ).
fof(f276,plain,
! [X0,X1,X2,X3] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f275]) ).
fof(f362,plain,
member(x,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f363,plain,
~ member(x,universal_class),
inference(cnf_transformation,[status(thm)],[f165]) ).
fof(f367,plain,
! [X0,X1,X2,X3] :
( member(X0,universal_class)
| ~ member(X2,X3)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f187,f276]) ).
fof(f370,definition,
! [X0,X1] :
( sQ0_spl
<=> ( member(X0,universal_class)
| ~ member(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f371,plain,
! [X0,X1] :
( ~ sQ0_spl
| member(X0,universal_class)
| ~ member(X0,X1) ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,definition,
! [X2,X3] :
( sQ1_spl
<=> ~ member(X2,X3) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f374,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ member(X0,X1) ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f367,f370,f373]) ).
fof(f382,plain,
( ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f362,f374]) ).
fof(f383,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f382]) ).
fof(f384,plain,
( ~ sQ0_spl
| member(x,universal_class) ),
inference(resolution,[status(thm)],[f362,f371]) ).
fof(f385,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f384,f363]) ).
fof(f386,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f387,plain,
$false,
inference(sat_refutation,[status(thm)],[f376,f383,f386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET118-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n004.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 04:54:19 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.50 % Drodi V4.1.1
% 0.17/0.51 % Refutation found
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.59 % Elapsed time: 0.123688 seconds
% 0.27/0.59 % CPU time: 0.114390 seconds
% 0.27/0.59 % Total memory used: 3.371 MB
% 0.27/0.59 % Net memory used: 3.367 MB
%------------------------------------------------------------------------------