%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:09:38 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 9 unt; 2 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 16 |; 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 : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [U,V,X,Y] :
( member(U,X)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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/sandbox/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
member(ordered_pair(u,v),cross_product(x,y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f114,negated_conjecture,
~ member(ordered_pair(v,u),cross_product(y,x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f134,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f136,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(f246,plain,
member(ordered_pair(u,v),cross_product(x,y)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f247,plain,
~ member(ordered_pair(v,u),cross_product(y,x)),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f252,plain,
member(u,x),
inference(resolution,[status(thm)],[f133,f246]) ).
fof(f253,plain,
member(v,y),
inference(resolution,[status(thm)],[f135,f246]) ).
fof(f254,plain,
( ~ member(u,x)
| ~ member(v,y) ),
inference(resolution,[status(thm)],[f136,f247]) ).
fof(f257,definition,
( sQ0_spl
<=> member(v,y) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ0_spl
| ~ member(v,y) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ1_spl
<=> member(u,x) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ1_spl
| ~ member(u,x) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f254,f257,f260]) ).
fof(f272,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f253]) ).
fof(f273,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f272]) ).
fof(f274,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f262,f252]) ).
fof(f275,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f274]) ).
fof(f276,plain,
$false,
inference(sat_refutation,[status(thm)],[f263,f273,f275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET204-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n020.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Mon Sep 21 05:01:24 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.13/5.40 % Refutation found
% 0.13/5.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.45 % Elapsed time: 0.058596 seconds
% 0.13/5.45 % CPU time: 0.115205 seconds
% 0.13/5.45 % Total memory used: 42.868 MB
% 0.13/5.45 % Net memory used: 42.843 MB
%------------------------------------------------------------------------------