TSTP Solution File: SET068-7 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET068-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n027.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 20:38:57 EDT 2024

% Result   : Unsatisfiable 0.20s 0.37s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   54 (  16 unt;   0 def)
%            Number of atoms       :  102 (  25 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   83 (  35   ~;  46   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   3 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   70 (  70   !;   0   ?)

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

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

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

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

fof(f5,axiom,
    ! [X,Y] :
      ( X != Y
      | subclass(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | U = X
      | U = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

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

fof(f104,axiom,
    ! [X] : subclass(null_class,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f108,axiom,
    ! [X,Y] : unordered_pair(X,Y) = unordered_pair(Y,X),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f109,negated_conjecture,
    ~ subclass(singleton(y),unordered_pair(x,y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f110,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f111,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f110]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X0,X1),X1)
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f114,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( X0 != X1
      | subclass(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f5]) ).

fof(f118,plain,
    ! [U,Y] :
      ( ! [X] :
          ( ~ member(U,unordered_pair(X,Y))
          | U = X )
      | U = Y ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f119,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f118]) ).

fof(f120,plain,
    ! [X] :
      ( ~ member(X,universal_class)
      | ! [Y] : member(X,unordered_pair(X,Y)) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f120]) ).

fof(f125,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f184,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f232,plain,
    ! [X0] : subclass(null_class,X0),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f236,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f237,plain,
    ~ subclass(singleton(y),unordered_pair(x,y)),
    inference(cnf_transformation,[status(esa)],[f109]) ).

fof(f238,plain,
    ! [X0] : subclass(X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f115]) ).

fof(f242,plain,
    ~ subclass(singleton(y),unordered_pair(y,x)),
    inference(paramodulation,[status(thm)],[f236,f237]) ).

fof(f250,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f125,f119]) ).

fof(f251,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f250]) ).

fof(f255,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X0,X1))
      | ~ subclass(X2,universal_class)
      | ~ member(X0,X2) ),
    inference(resolution,[status(thm)],[f121,f111]) ).

fof(f256,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X0,X1))
      | ~ member(X0,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f255,f114]) ).

fof(f282,plain,
    ! [X0,X1] :
      ( subclass(singleton(X0),X1)
      | not_subclass_element(singleton(X0),X1) = X0 ),
    inference(resolution,[status(thm)],[f112,f251]) ).

fof(f286,plain,
    ! [X0,X1,X2] :
      ( subclass(X0,X1)
      | ~ subclass(X2,X1)
      | ~ member(not_subclass_element(X0,X1),X2) ),
    inference(resolution,[status(thm)],[f113,f111]) ).

fof(f447,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | regular(singleton(X0)) = X0 ),
    inference(resolution,[status(thm)],[f184,f251]) ).

fof(f638,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | member(X0,singleton(X0))
      | singleton(X0) = null_class ),
    inference(paramodulation,[status(thm)],[f447,f184]) ).

fof(f639,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | member(X0,singleton(X0)) ),
    inference(duplicate_literals_removal,[status(esa)],[f638]) ).

fof(f682,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(not_subclass_element(X0,X1),X1) ),
    inference(resolution,[status(thm)],[f286,f238]) ).

fof(f686,plain,
    not_subclass_element(singleton(y),unordered_pair(y,x)) = y,
    inference(resolution,[status(thm)],[f282,f242]) ).

fof(f696,plain,
    ( spl0_12
  <=> subclass(singleton(y),unordered_pair(y,x)) ),
    introduced(split_symbol_definition) ).

fof(f697,plain,
    ( subclass(singleton(y),unordered_pair(y,x))
    | ~ spl0_12 ),
    inference(component_clause,[status(thm)],[f696]) ).

fof(f699,plain,
    ( spl0_13
  <=> member(y,unordered_pair(y,x)) ),
    introduced(split_symbol_definition) ).

fof(f701,plain,
    ( ~ member(y,unordered_pair(y,x))
    | spl0_13 ),
    inference(component_clause,[status(thm)],[f699]) ).

fof(f702,plain,
    ( subclass(singleton(y),unordered_pair(y,x))
    | ~ member(y,unordered_pair(y,x)) ),
    inference(paramodulation,[status(thm)],[f686,f682]) ).

fof(f703,plain,
    ( spl0_12
    | ~ spl0_13 ),
    inference(split_clause,[status(thm)],[f702,f696,f699]) ).

fof(f704,plain,
    ! [X0] :
      ( ~ member(y,X0)
      | spl0_13 ),
    inference(resolution,[status(thm)],[f701,f256]) ).

fof(f714,plain,
    ( singleton(y) = null_class
    | spl0_13 ),
    inference(resolution,[status(thm)],[f704,f639]) ).

fof(f717,plain,
    ( $false
    | ~ spl0_12 ),
    inference(forward_subsumption_resolution,[status(thm)],[f697,f242]) ).

fof(f718,plain,
    ~ spl0_12,
    inference(contradiction_clause,[status(thm)],[f717]) ).

fof(f728,plain,
    ( ~ subclass(null_class,unordered_pair(y,x))
    | spl0_13 ),
    inference(backward_demodulation,[status(thm)],[f714,f242]) ).

fof(f729,plain,
    ( $false
    | spl0_13 ),
    inference(forward_subsumption_resolution,[status(thm)],[f728,f232]) ).

fof(f730,plain,
    spl0_13,
    inference(contradiction_clause,[status(thm)],[f729]) ).

fof(f731,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f703,f718,f730]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET068-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n027.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 22:05:47 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.20/0.36  % Drodi V3.6.0
% 0.20/0.37  % Refutation found
% 0.20/0.37  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38  % Elapsed time: 0.032122 seconds
% 0.20/0.38  % CPU time: 0.106226 seconds
% 0.20/0.38  % Total memory used: 22.336 MB
% 0.20/0.38  % Net memory used: 22.237 MB
%------------------------------------------------------------------------------