TSTP Solution File: SET064-6 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET064-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 20:38:56 EDT 2024

% Result   : Unsatisfiable 0.21s 0.40s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   63 (  18 unt;   0 def)
%            Number of atoms       :  115 (  19 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   91 (  39   ~;  47   |;   0   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   6 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   68 (  68   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X,Y] :
      ( ~ subclass(X,Y)
      | ~ subclass(Y,X)
      | X = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f50,axiom,
    inductive(omega),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f67,axiom,
    ! [X] :
      ( X = null_class
      | intersection(X,regular(X)) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f75,axiom,
    intersection(inverse(subset_relation),subset_relation) = identity_relation,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f92,negated_conjecture,
    z != null_class,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f93,negated_conjecture,
    ~ member(not_subclass_element(z,null_class),z),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f94,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f95,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f94]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X0,X1),X1)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f98,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f121,plain,
    ! [Z,X] :
      ( ! [Y] : ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f122,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f121]) ).

fof(f123,plain,
    ! [Z,Y] :
      ( ! [X] : ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f124,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,intersection(X1,X2))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f123]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f152,plain,
    inductive(omega),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f169,plain,
    ! [X0] :
      ( X0 = null_class
      | intersection(X0,regular(X0)) = null_class ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f177,plain,
    intersection(inverse(subset_relation),subset_relation) = identity_relation,
    inference(cnf_transformation,[status(esa)],[f75]) ).

fof(f199,plain,
    z != null_class,
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f200,plain,
    ~ member(not_subclass_element(z,null_class),z),
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f204,plain,
    subclass(z,null_class),
    inference(resolution,[status(thm)],[f96,f200]) ).

fof(f210,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | member(not_subclass_element(X0,X2),X1)
      | subclass(X0,X2) ),
    inference(resolution,[status(thm)],[f95,f96]) ).

fof(f226,plain,
    ( spl0_2
  <=> subclass(null_class,z) ),
    introduced(split_symbol_definition) ).

fof(f228,plain,
    ( ~ subclass(null_class,z)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f226]) ).

fof(f229,plain,
    ( spl0_3
  <=> null_class = z ),
    introduced(split_symbol_definition) ).

fof(f230,plain,
    ( null_class = z
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f229]) ).

fof(f232,plain,
    ( ~ subclass(null_class,z)
    | null_class = z ),
    inference(resolution,[status(thm)],[f101,f204]) ).

fof(f233,plain,
    ( ~ spl0_2
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f232,f226,f229]) ).

fof(f246,plain,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(complement(X0),X1),X0)
      | subclass(complement(X0),X1) ),
    inference(resolution,[status(thm)],[f126,f96]) ).

fof(f265,plain,
    ! [X0,X1] :
      ( subclass(complement(X0),X1)
      | ~ subclass(complement(X0),X0)
      | subclass(complement(X0),X1) ),
    inference(resolution,[status(thm)],[f246,f210]) ).

fof(f266,plain,
    ! [X0,X1] :
      ( subclass(complement(X0),X1)
      | ~ subclass(complement(X0),X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f265]) ).

fof(f267,plain,
    ! [X0] : subclass(complement(universal_class),X0),
    inference(resolution,[status(thm)],[f266,f98]) ).

fof(f281,plain,
    ! [X0] :
      ( ~ subclass(X0,complement(universal_class))
      | X0 = complement(universal_class) ),
    inference(resolution,[status(thm)],[f267,f101]) ).

fof(f302,plain,
    ( spl0_11
  <=> complement(universal_class) = null_class ),
    introduced(split_symbol_definition) ).

fof(f405,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f230,f199]) ).

fof(f406,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f405]) ).

fof(f482,plain,
    ( spl0_29
  <=> inductive(omega) ),
    introduced(split_symbol_definition) ).

fof(f484,plain,
    ( ~ inductive(omega)
    | spl0_29 ),
    inference(component_clause,[status(thm)],[f482]) ).

fof(f488,plain,
    ( $false
    | spl0_29 ),
    inference(forward_subsumption_resolution,[status(thm)],[f484,f152]) ).

fof(f489,plain,
    spl0_29,
    inference(contradiction_clause,[status(thm)],[f488]) ).

fof(f584,plain,
    ! [X0,X1,X2] :
      ( member(not_subclass_element(intersection(X0,X1),X2),X0)
      | subclass(intersection(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f122,f96]) ).

fof(f591,plain,
    ! [X0] :
      ( ~ member(X0,identity_relation)
      | member(X0,subset_relation) ),
    inference(paramodulation,[status(thm)],[f177,f124]) ).

fof(f610,plain,
    ! [X0] :
      ( member(not_subclass_element(identity_relation,X0),subset_relation)
      | subclass(identity_relation,X0) ),
    inference(resolution,[status(thm)],[f591,f96]) ).

fof(f1059,plain,
    ( spl0_110
  <=> subclass(identity_relation,subset_relation) ),
    introduced(split_symbol_definition) ).

fof(f1062,plain,
    ( subclass(identity_relation,subset_relation)
    | subclass(identity_relation,subset_relation) ),
    inference(resolution,[status(thm)],[f610,f97]) ).

fof(f1063,plain,
    spl0_110,
    inference(split_clause,[status(thm)],[f1062,f1059]) ).

fof(f1081,plain,
    ! [X0,X1] :
      ( subclass(intersection(X0,X1),X0)
      | subclass(intersection(X0,X1),X0) ),
    inference(resolution,[status(thm)],[f584,f97]) ).

fof(f1082,plain,
    ! [X0,X1] : subclass(intersection(X0,X1),X0),
    inference(duplicate_literals_removal,[status(esa)],[f1081]) ).

fof(f1129,plain,
    ! [X0] :
      ( subclass(null_class,X0)
      | X0 = null_class ),
    inference(paramodulation,[status(thm)],[f169,f1082]) ).

fof(f1162,plain,
    ( z = null_class
    | spl0_2 ),
    inference(resolution,[status(thm)],[f1129,f228]) ).

fof(f1163,plain,
    ( spl0_3
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f1162,f229,f226]) ).

fof(f1197,plain,
    ( complement(universal_class) = null_class
    | null_class = complement(universal_class) ),
    inference(resolution,[status(thm)],[f1129,f281]) ).

fof(f1198,plain,
    spl0_11,
    inference(split_clause,[status(thm)],[f1197,f302]) ).

fof(f1212,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f233,f406,f489,f1063,f1163,f1198]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET064-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 21:31:55 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  % Drodi V3.6.0
% 0.21/0.40  % Refutation found
% 0.21/0.40  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.42  % Elapsed time: 0.063086 seconds
% 0.21/0.42  % CPU time: 0.355435 seconds
% 0.21/0.42  % Total memory used: 64.395 MB
% 0.21/0.42  % Net memory used: 64.240 MB
%------------------------------------------------------------------------------