TSTP Solution File: SET497-6 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET497-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 20:39:45 EDT 2024

% Result   : Unsatisfiable 9.09s 1.46s
% Output   : CNFRefutation 9.09s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   56 (  14 unt;   0 def)
%            Number of atoms       :  111 (  33 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   97 (  42   ~;  52   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   57 (  57   !;   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(f4,axiom,
    ! [X] : subclass(X,universal_class),
    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(f23,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,X)
      | ~ member(Z,Y)
      | member(Z,intersection(X,Y)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,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(f67,axiom,
    ! [X] :
      ( X = null_class
      | intersection(X,regular(X)) = null_class ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f113,negated_conjecture,
    member(z,diagonalise(element_relation)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f114,negated_conjecture,
    member(z,z),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f115,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f116,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f115]) ).

fof(f119,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f123,plain,
    ! [U,Y] :
      ( ! [X] :
          ( ~ member(U,unordered_pair(X,Y))
          | U = X )
      | U = Y ),
    inference(miniscoping,[status(esa)],[f8]) ).

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

fof(f125,plain,
    ! [X] :
      ( ~ member(X,universal_class)
      | ! [Y] : member(X,unordered_pair(X,Y)) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f126,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f125]) ).

fof(f130,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f146,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,X1)
      | ~ member(X0,X2)
      | member(X0,intersection(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f147,plain,
    ! [X0,X1] :
      ( ~ member(X0,complement(X1))
      | ~ member(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f189,plain,
    ! [X0] :
      ( X0 = null_class
      | member(regular(X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f66]) ).

fof(f190,plain,
    ! [X0] :
      ( X0 = null_class
      | intersection(X0,regular(X0)) = null_class ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f246,plain,
    member(z,diagonalise(element_relation)),
    inference(cnf_transformation,[status(esa)],[f113]) ).

fof(f247,plain,
    member(z,z),
    inference(cnf_transformation,[status(esa)],[f114]) ).

fof(f254,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | member(X0,universal_class) ),
    inference(resolution,[status(thm)],[f116,f119]) ).

fof(f265,plain,
    ! [X0] :
      ( member(regular(X0),universal_class)
      | X0 = null_class ),
    inference(resolution,[status(thm)],[f254,f189]) ).

fof(f270,plain,
    member(z,universal_class),
    inference(resolution,[status(thm)],[f254,f246]) ).

fof(f318,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f130,f124]) ).

fof(f319,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f318]) ).

fof(f327,plain,
    ! [X0] : member(z,unordered_pair(z,X0)),
    inference(resolution,[status(thm)],[f126,f270]) ).

fof(f348,plain,
    member(z,singleton(z)),
    inference(paramodulation,[status(thm)],[f130,f327]) ).

fof(f354,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | regular(singleton(X0)) = X0 ),
    inference(resolution,[status(thm)],[f189,f319]) ).

fof(f738,plain,
    ! [X0] :
      ( complement(X0) = null_class
      | ~ member(regular(complement(X0)),X0) ),
    inference(resolution,[status(thm)],[f189,f147]) ).

fof(f775,plain,
    ! [X0] :
      ( ~ member(z,X0)
      | member(z,intersection(singleton(z),X0)) ),
    inference(resolution,[status(thm)],[f146,f348]) ).

fof(f1855,plain,
    ( spl0_65
  <=> member(z,null_class) ),
    introduced(split_symbol_definition) ).

fof(f1856,plain,
    ( member(z,null_class)
    | ~ spl0_65 ),
    inference(component_clause,[status(thm)],[f1855]) ).

fof(f1969,plain,
    member(z,intersection(singleton(z),z)),
    inference(resolution,[status(thm)],[f775,f247]) ).

fof(f1987,plain,
    ( spl0_72
  <=> singleton(z) = null_class ),
    introduced(split_symbol_definition) ).

fof(f1988,plain,
    ( singleton(z) = null_class
    | ~ spl0_72 ),
    inference(component_clause,[status(thm)],[f1987]) ).

fof(f2007,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | intersection(singleton(X0),X0) = null_class
      | singleton(X0) = null_class ),
    inference(paramodulation,[status(thm)],[f354,f190]) ).

fof(f2008,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | intersection(singleton(X0),X0) = null_class ),
    inference(duplicate_literals_removal,[status(esa)],[f2007]) ).

fof(f2175,plain,
    ( member(z,null_class)
    | ~ spl0_72 ),
    inference(backward_demodulation,[status(thm)],[f1988,f348]) ).

fof(f13688,plain,
    ( spl0_429
  <=> complement(universal_class) = null_class ),
    introduced(split_symbol_definition) ).

fof(f13689,plain,
    ( complement(universal_class) = null_class
    | ~ spl0_429 ),
    inference(component_clause,[status(thm)],[f13688]) ).

fof(f13691,plain,
    ( complement(universal_class) = null_class
    | complement(universal_class) = null_class ),
    inference(resolution,[status(thm)],[f738,f265]) ).

fof(f13692,plain,
    spl0_429,
    inference(split_clause,[status(thm)],[f13691,f13688]) ).

fof(f13722,plain,
    ( member(z,null_class)
    | singleton(z) = null_class ),
    inference(paramodulation,[status(thm)],[f2008,f1969]) ).

fof(f13723,plain,
    ( spl0_65
    | spl0_72 ),
    inference(split_clause,[status(thm)],[f13722,f1855,f1987]) ).

fof(f14476,plain,
    ! [X0] :
      ( ~ member(X0,null_class)
      | ~ member(X0,universal_class)
      | ~ spl0_429 ),
    inference(paramodulation,[status(thm)],[f13689,f147]) ).

fof(f14477,plain,
    ! [X0] :
      ( ~ member(X0,null_class)
      | ~ spl0_429 ),
    inference(forward_subsumption_resolution,[status(thm)],[f14476,f254]) ).

fof(f14478,plain,
    ( $false
    | ~ spl0_429
    | ~ spl0_72 ),
    inference(backward_subsumption_resolution,[status(thm)],[f2175,f14477]) ).

fof(f14479,plain,
    ( ~ spl0_429
    | ~ spl0_72 ),
    inference(contradiction_clause,[status(thm)],[f14478]) ).

fof(f14485,plain,
    ( $false
    | ~ spl0_429
    | ~ spl0_65 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1856,f14477]) ).

fof(f14486,plain,
    ( ~ spl0_429
    | ~ spl0_65 ),
    inference(contradiction_clause,[status(thm)],[f14485]) ).

fof(f14487,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f13692,f13723,f14479,f14486]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : SET497-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.08  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27  % Computer : n005.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 300
% 0.07/0.27  % DateTime : Mon Apr 29 21:22:11 EDT 2024
% 0.07/0.27  % CPUTime  : 
% 0.07/0.27  % Drodi V3.6.0
% 9.09/1.46  % Refutation found
% 9.09/1.46  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.09/1.46  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.49/1.50  % Elapsed time: 1.219621 seconds
% 9.49/1.50  % CPU time: 9.511140 seconds
% 9.49/1.50  % Total memory used: 151.551 MB
% 9.49/1.50  % Net memory used: 144.402 MB
%------------------------------------------------------------------------------