TSTP Solution File: SET103-6 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET103-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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 20:39:09 EDT 2024

% Result   : Unsatisfiable 0.18s 0.49s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   29 (  14 unt;   0 def)
%            Number of atoms       :   52 (  26 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   40 (  17   ~;  23   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   39 (  39   !;   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(f4,axiom,
    ! [X] : subclass(X,universal_class),
    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(f13,axiom,
    ! [X,Y] : unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y),
    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,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f93,negated_conjecture,
    ~ member(y,universal_class),
    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(f98,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f102,plain,
    ! [U,Y] :
      ( ! [X] :
          ( ~ member(U,unordered_pair(X,Y))
          | U = X )
      | U = Y ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f103,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f109,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f110,plain,
    ! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f168,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f199,plain,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f200,plain,
    ~ member(y,universal_class),
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f205,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f109,f103]) ).

fof(f206,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f205]) ).

fof(f252,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(X0,universal_class) ),
    inference(resolution,[status(thm)],[f95,f98]) ).

fof(f574,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | regular(singleton(X0)) = X0 ),
    inference(resolution,[status(thm)],[f168,f206]) ).

fof(f588,plain,
    ! [X0] :
      ( member(regular(X0),universal_class)
      | X0 = null_class ),
    inference(resolution,[status(thm)],[f252,f168]) ).

fof(f1058,plain,
    ! [X0] :
      ( member(X0,universal_class)
      | singleton(X0) = null_class
      | singleton(X0) = null_class ),
    inference(paramodulation,[status(thm)],[f574,f588]) ).

fof(f1059,plain,
    ! [X0] :
      ( member(X0,universal_class)
      | singleton(X0) = null_class ),
    inference(duplicate_literals_removal,[status(esa)],[f1058]) ).

fof(f1679,plain,
    singleton(y) = null_class,
    inference(resolution,[status(thm)],[f1059,f200]) ).

fof(f1701,plain,
    ! [X0] : unordered_pair(singleton(X0),unordered_pair(X0,null_class)) = ordered_pair(X0,y),
    inference(paramodulation,[status(thm)],[f1679,f110]) ).

fof(f2382,plain,
    ordered_pair(x,y) != ordered_pair(x,y),
    inference(backward_demodulation,[status(thm)],[f1701,f199]) ).

fof(f2383,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f2382]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET103-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35  % Computer : n018.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Mon Apr 29 21:46:13 EDT 2024
% 0.12/0.35  % CPUTime  : 
% 0.12/0.36  % Drodi V3.6.0
% 0.18/0.49  % Refutation found
% 0.18/0.49  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/0.49  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.50  % Elapsed time: 0.140203 seconds
% 0.18/0.50  % CPU time: 0.979495 seconds
% 0.18/0.50  % Total memory used: 79.216 MB
% 0.18/0.50  % Net memory used: 78.425 MB
%------------------------------------------------------------------------------