%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET202-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 72.97s 9.67s
% Output : CNFRefutation 72.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 69 ( 11 unt; 9 def)
% Number of atoms : 137 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 129 ( 61 ~; 59 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,U] :
( member(U,Y)
| ~ member(U,X)
| ~ subclass(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( subclass(X,Y)
| member(not_subclass_element(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( subclass(X,Y)
| ~ member(not_subclass_element(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : subclass(X,universal_class),
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(f15,axiom,
! [U,V,X,Y] :
( member(V,Y)
| ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
file('/export/starexec/sandbox2/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/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(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f113,negated_conjecture,
~ subclass(cross_product(x,y),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,plain,
! [Y,U] :
( member(U,Y)
| ! [X] :
( ~ member(U,X)
| ~ subclass(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f115,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f117,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f118,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f131,plain,
! [U,X] :
( member(U,X)
| ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [V,Y] :
( member(V,Y)
| ! [U,X] : ~ member(ordered_pair(U,V),cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,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(f136,plain,
! [Z] :
( ordered_pair(first(Z),second(Z)) = Z
| ! [X,Y] : ~ member(Z,cross_product(X,Y)) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ordered_pair(first(X0),second(X0)) = X0
| ~ member(X0,cross_product(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f172,plain,
inductive(omega),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f245,plain,
~ subclass(cross_product(x,y),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[status(thm)],[f113]) ).
fof(f253,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(resolution,[status(thm)],[f118,f115]) ).
fof(f1048,definition,
! [X2] :
( sQ63_spl
<=> ~ inductive(X2) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1049,plain,
! [X0] :
( ~ sQ63_spl
| ~ inductive(X0) ),
inference(component_clause,[status(thm)],[f1048]) ).
fof(f1055,plain,
( ~ sQ63_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f172,f1049]) ).
fof(f1636,plain,
! [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)
| subclass(cross_product(X0,X1),X2) ),
inference(resolution,[status(thm)],[f116,f137]) ).
fof(f2762,definition,
( sQ92_spl
<=> subclass(cross_product(x,y),cross_product(universal_class,universal_class)) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f2763,plain,
( ~ sQ92_spl
| subclass(cross_product(x,y),cross_product(universal_class,universal_class)) ),
inference(component_clause,[status(thm)],[f2762]) ).
fof(f2824,plain,
( ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2763,f245]) ).
fof(f2825,plain,
~ sQ92_spl,
inference(contradiction_clause,[status(thm)],[f2824]) ).
fof(f4245,definition,
( sQ161_spl
<=> subclass(cross_product(universal_class,universal_class),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f4247,plain,
( sQ161_spl
| ~ subclass(cross_product(universal_class,universal_class),universal_class) ),
inference(component_clause,[status(thm)],[f4245]) ).
fof(f4249,plain,
( sQ161_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4247,f118]) ).
fof(f4250,plain,
sQ161_spl,
inference(contradiction_clause,[status(thm)],[f4249]) ).
fof(f6711,plain,
ordered_pair(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class)))) = not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class)),
inference(resolution,[status(thm)],[f1636,f245]) ).
fof(f6864,plain,
! [X0,X1] :
( member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X0)
| ~ member(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class)),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f6711,f132]) ).
fof(f6865,plain,
! [X0,X1] :
( member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X1)
| ~ member(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class)),cross_product(X0,X1)) ),
inference(paramodulation,[status(thm)],[f6711,f134]) ).
fof(f6866,plain,
! [X0,X1] :
( member(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class)),cross_product(X0,X1))
| ~ member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X1)
| ~ member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X0) ),
inference(paramodulation,[status(thm)],[f6711,f135]) ).
fof(f6908,definition,
( sQ214_spl
<=> member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f6910,plain,
( sQ214_spl
| ~ member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),universal_class) ),
inference(component_clause,[status(thm)],[f6908]) ).
fof(f6912,definition,
( sQ215_spl
<=> member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),universal_class) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f6914,plain,
( sQ215_spl
| ~ member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),universal_class) ),
inference(component_clause,[status(thm)],[f6912]) ).
fof(f8669,plain,
( subclass(cross_product(x,y),cross_product(universal_class,universal_class))
| member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),x) ),
inference(resolution,[status(thm)],[f6864,f116]) ).
fof(f8677,definition,
( sQ253_spl
<=> member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),x) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f8678,plain,
( ~ sQ253_spl
| member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),x) ),
inference(component_clause,[status(thm)],[f8677]) ).
fof(f8680,plain,
( sQ92_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f8669,f8677,f2762]) ).
fof(f8726,plain,
( subclass(cross_product(x,y),cross_product(universal_class,universal_class))
| member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),y) ),
inference(resolution,[status(thm)],[f6865,f116]) ).
fof(f8735,definition,
( sQ255_spl
<=> member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),y) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f8736,plain,
( ~ sQ255_spl
| member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),y) ),
inference(component_clause,[status(thm)],[f8735]) ).
fof(f8738,plain,
( sQ92_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f8726,f8735,f2762]) ).
fof(f8751,plain,
( subclass(cross_product(x,y),cross_product(universal_class,universal_class))
| ~ member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),universal_class)
| ~ member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),universal_class) ),
inference(resolution,[status(thm)],[f6866,f117]) ).
fof(f8754,definition,
! [X0] :
( sQ257_spl
<=> ~ member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X0) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f8755,plain,
! [X0] :
( ~ sQ257_spl
| ~ member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X0) ),
inference(component_clause,[status(thm)],[f8754]) ).
fof(f8764,definition,
! [X1] :
( sQ260_spl
<=> ~ member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X1) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f8765,plain,
! [X0] :
( ~ sQ260_spl
| ~ member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X0) ),
inference(component_clause,[status(thm)],[f8764]) ).
fof(f8768,plain,
( sQ92_spl
| ~ sQ215_spl
| ~ sQ214_spl ),
inference(split_clause,[status(thm)],[f8751,f6908,f6912,f2762]) ).
fof(f8775,plain,
( ~ sQ255_spl
| ~ sQ260_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f8736,f8765]) ).
fof(f8779,plain,
( ~ sQ253_spl
| ~ sQ257_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f8678,f8755]) ).
fof(f8786,plain,
( ~ sQ253_spl
| ~ sQ257_spl ),
inference(contradiction_clause,[status(thm)],[f8779]) ).
fof(f8787,plain,
( ~ sQ255_spl
| ~ sQ260_spl ),
inference(contradiction_clause,[status(thm)],[f8775]) ).
fof(f10173,plain,
~ sQ63_spl,
inference(contradiction_clause,[status(thm)],[f1055]) ).
fof(f11758,plain,
! [X0] :
( sQ215_spl
| ~ member(second(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X0) ),
inference(resolution,[status(thm)],[f6914,f253]) ).
fof(f11759,plain,
( sQ215_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f11758,f8764,f6912]) ).
fof(f14364,plain,
! [X0] :
( sQ214_spl
| ~ member(first(not_subclass_element(cross_product(x,y),cross_product(universal_class,universal_class))),X0) ),
inference(resolution,[status(thm)],[f6910,f253]) ).
fof(f14365,plain,
( sQ214_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f14364,f8754,f6908]) ).
fof(f14366,plain,
$false,
inference(sat_refutation,[status(thm)],[f2825,f4250,f8680,f8738,f8768,f8786,f8787,f10173,f11759,f14365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET202-6 : 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 : n016.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 05:05:08 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 72.97/9.67 % Refutation found
% 72.97/9.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 72.97/9.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.55/9.73 % Elapsed time: 9.354156 seconds
% 18.55/9.73 % CPU time: 73.850427 seconds
% 18.55/9.73 % Total memory used: 530.024 MB
% 18.55/9.73 % Net memory used: 460.680 MB
%------------------------------------------------------------------------------