TSTP Solution File: SET096-6 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET096-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n015.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 : Wed May 31 12:33:58 EDT 2023

% Result   : Unsatisfiable 0.13s 0.37s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   67 (  17 unt;   0 def)
%            Number of atoms       :  134 (  37 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  117 (  50   ~;  61   |;   0   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   7 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   61 (;  61   !;   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(f5,axiom,
    ! [X,Y] :
      ( X != Y
      | subclass(X,Y) ),
    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(f8,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | U = X
      | U = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X] : unordered_pair(X,X) = singleton(X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f47,axiom,
    ! [X] :
      ( ~ inductive(X)
      | member(null_class,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f66,axiom,
    ! [X] :
      ( X = null_class
      | member(regular(X),X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f92,negated_conjecture,
    subclass(x,singleton(y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f93,negated_conjecture,
    x != null_class,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f94,negated_conjecture,
    singleton(y) != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f95,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f96,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f95]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X0,X1),X1)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f99,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ subclass(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f7]) ).

fof(f103,plain,
    ! [U,Y] :
      ( ! [X] :
          ( ~ member(U,unordered_pair(X,Y))
          | U = X )
      | U = Y ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f104,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f103]) ).

fof(f110,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f150,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | member(null_class,X0) ),
    inference(cnf_transformation,[status(esa)],[f47]) ).

fof(f153,plain,
    inductive(omega),
    inference(cnf_transformation,[status(esa)],[f50]) ).

fof(f169,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f200,plain,
    subclass(x,singleton(y)),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f201,plain,
    x != null_class,
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f202,plain,
    singleton(y) != x,
    inference(cnf_transformation,[status(esa)],[f94]) ).

fof(f203,plain,
    ! [X0] : subclass(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f100]) ).

fof(f206,plain,
    ( spl0_0
  <=> subclass(singleton(y),x) ),
    introduced(split_symbol_definition) ).

fof(f208,plain,
    ( ~ subclass(singleton(y),x)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f206]) ).

fof(f209,plain,
    ( spl0_1
  <=> singleton(y) = x ),
    introduced(split_symbol_definition) ).

fof(f210,plain,
    ( singleton(y) = x
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f209]) ).

fof(f212,plain,
    ( ~ subclass(singleton(y),x)
    | singleton(y) = x ),
    inference(resolution,[status(thm)],[f102,f200]) ).

fof(f213,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f212,f206,f209]) ).

fof(f243,plain,
    ! [X0,X1,X2,X3] :
      ( X0 = X1
      | X0 = X2
      | ~ subclass(X3,unordered_pair(X1,X2))
      | ~ member(X0,X3) ),
    inference(resolution,[status(thm)],[f104,f96]) ).

fof(f253,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | X0 = X1
      | ~ subclass(X2,singleton(X1))
      | ~ member(X0,X2) ),
    inference(paramodulation,[status(thm)],[f110,f243]) ).

fof(f254,plain,
    ! [X0,X1,X2] :
      ( X0 = X1
      | ~ subclass(X2,singleton(X1))
      | ~ member(X0,X2) ),
    inference(duplicate_literals_removal,[status(esa)],[f253]) ).

fof(f255,plain,
    ! [X0] :
      ( X0 = y
      | ~ member(X0,x) ),
    inference(resolution,[status(thm)],[f254,f200]) ).

fof(f256,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(X0,singleton(X1)) ),
    inference(resolution,[status(thm)],[f254,f203]) ).

fof(f257,plain,
    ( spl0_6
  <=> regular(x) = y ),
    introduced(split_symbol_definition) ).

fof(f258,plain,
    ( regular(x) = y
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f257]) ).

fof(f260,plain,
    ( spl0_7
  <=> x = null_class ),
    introduced(split_symbol_definition) ).

fof(f261,plain,
    ( x = null_class
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f260]) ).

fof(f263,plain,
    ( regular(x) = y
    | x = null_class ),
    inference(resolution,[status(thm)],[f255,f169]) ).

fof(f264,plain,
    ( spl0_6
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f263,f257,f260]) ).

fof(f275,plain,
    ( spl0_10
  <=> member(y,x) ),
    introduced(split_symbol_definition) ).

fof(f278,plain,
    ( x = null_class
    | member(y,x)
    | ~ spl0_6 ),
    inference(paramodulation,[status(thm)],[f258,f169]) ).

fof(f279,plain,
    ( spl0_7
    | spl0_10
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f278,f260,f275,f257]) ).

fof(f280,plain,
    ( $false
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f261,f201]) ).

fof(f281,plain,
    ~ spl0_7,
    inference(contradiction_clause,[status(thm)],[f280]) ).

fof(f466,plain,
    ! [X0,X1] :
      ( not_subclass_element(singleton(X0),X1) = X0
      | subclass(singleton(X0),X1) ),
    inference(resolution,[status(thm)],[f256,f97]) ).

fof(f479,plain,
    ( not_subclass_element(singleton(y),x) = y
    | spl0_0 ),
    inference(resolution,[status(thm)],[f466,f208]) ).

fof(f515,plain,
    ( $false
    | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f210,f202]) ).

fof(f516,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f515]) ).

fof(f677,plain,
    ( spl0_55
  <=> member(null_class,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f679,plain,
    ( ~ member(null_class,universal_class)
    | spl0_55 ),
    inference(component_clause,[status(thm)],[f677]) ).

fof(f723,plain,
    ! [X0] :
      ( ~ subclass(X0,universal_class)
      | ~ member(null_class,X0)
      | spl0_55 ),
    inference(resolution,[status(thm)],[f679,f96]) ).

fof(f724,plain,
    ! [X0] :
      ( ~ member(null_class,X0)
      | spl0_55 ),
    inference(forward_subsumption_resolution,[status(thm)],[f723,f99]) ).

fof(f727,plain,
    ! [X0] :
      ( ~ inductive(X0)
      | spl0_55 ),
    inference(backward_subsumption_resolution,[status(thm)],[f150,f724]) ).

fof(f734,plain,
    ( $false
    | spl0_55 ),
    inference(backward_subsumption_resolution,[status(thm)],[f153,f727]) ).

fof(f735,plain,
    spl0_55,
    inference(contradiction_clause,[status(thm)],[f734]) ).

fof(f787,plain,
    ( ~ member(y,x)
    | subclass(singleton(y),x)
    | spl0_0 ),
    inference(paramodulation,[status(thm)],[f479,f98]) ).

fof(f788,plain,
    ( ~ spl0_10
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f787,f275,f206]) ).

fof(f794,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f213,f264,f279,f281,f516,f735,f788]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET096-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 10:29:34 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.13/0.37  % Refutation found
% 0.13/0.37  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.38  % Elapsed time: 0.034548 seconds
% 0.19/0.38  % CPU time: 0.105057 seconds
% 0.19/0.38  % Memory used: 15.801 MB
%------------------------------------------------------------------------------