TSTP Solution File: SET073-6 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET073-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 20:38:59 EDT 2024

% Result   : Unsatisfiable 0.17s 0.37s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   42 (   9 unt;   0 def)
%            Number of atoms       :   85 (  27 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   76 (  33   ~;  41   |;   0   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   51 (  51   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | U = X
      | U = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,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(f21,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    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(f67,axiom,
    ! [X] :
      ( X = null_class
      | intersection(X,regular(X)) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f92,negated_conjecture,
    member(x,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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(f104,plain,
    ! [X] :
      ( ~ member(X,universal_class)
      | ! [Y] : member(X,unordered_pair(X,Y)) ),
    inference(miniscoping,[status(esa)],[f9]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | member(X0,unordered_pair(X0,X1)) ),
    inference(cnf_transformation,[status(esa)],[f104]) ).

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

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

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

fof(f199,plain,
    member(x,universal_class),
    inference(cnf_transformation,[status(esa)],[f92]) ).

fof(f200,plain,
    unordered_pair(x,y) = null_class,
    inference(cnf_transformation,[status(esa)],[f93]) ).

fof(f207,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f109,f103]) ).

fof(f208,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f207]) ).

fof(f209,plain,
    ( spl0_0
  <=> member(x,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f211,plain,
    ( ~ member(x,universal_class)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f209]) ).

fof(f212,plain,
    ( spl0_1
  <=> member(x,null_class) ),
    introduced(split_symbol_definition) ).

fof(f213,plain,
    ( member(x,null_class)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f212]) ).

fof(f215,plain,
    ( ~ member(x,universal_class)
    | member(x,null_class) ),
    inference(paramodulation,[status(thm)],[f200,f105]) ).

fof(f216,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f215,f209,f212]) ).

fof(f218,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f211,f199]) ).

fof(f219,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f218]) ).

fof(f247,plain,
    ! [X0,X1] :
      ( ~ member(X0,null_class)
      | member(X0,X1)
      | X1 = null_class ),
    inference(paramodulation,[status(thm)],[f169,f122]) ).

fof(f256,plain,
    ! [X0] :
      ( member(x,X0)
      | X0 = null_class
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f213,f247]) ).

fof(f278,plain,
    ! [X0] :
      ( singleton(X0) = null_class
      | x = X0
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f256,f208]) ).

fof(f286,plain,
    ! [X0,X1] :
      ( ~ member(X0,null_class)
      | X0 = X1
      | x = X1
      | ~ spl0_1 ),
    inference(paramodulation,[status(thm)],[f278,f208]) ).

fof(f295,plain,
    ! [X0] :
      ( x = X0
      | x = X0
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f286,f213]) ).

fof(f296,plain,
    ! [X0] :
      ( x = X0
      | ~ spl0_1 ),
    inference(duplicate_literals_removal,[status(esa)],[f295]) ).

fof(f316,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ spl0_1 ),
    inference(paramodulation,[status(thm)],[f296,f296]) ).

fof(f319,plain,
    ! [X0] :
      ( member(X0,null_class)
      | ~ spl0_1 ),
    inference(paramodulation,[status(thm)],[f296,f213]) ).

fof(f323,plain,
    ! [X0,X1] :
      ( member(X0,X1)
      | ~ spl0_1 ),
    inference(paramodulation,[status(thm)],[f316,f319]) ).

fof(f332,plain,
    ! [X0,X1] :
      ( ~ member(X0,X1)
      | ~ spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f126,f323]) ).

fof(f333,plain,
    ( $false
    | ~ spl0_1 ),
    inference(backward_subsumption_resolution,[status(thm)],[f323,f332]) ).

fof(f334,plain,
    ~ spl0_1,
    inference(contradiction_clause,[status(thm)],[f333]) ).

fof(f335,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f216,f219,f334]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET073-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.03/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n011.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Mon Apr 29 21:41:01 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  % Drodi V3.6.0
% 0.17/0.37  % Refutation found
% 0.17/0.37  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.38  % Elapsed time: 0.057014 seconds
% 0.17/0.38  % CPU time: 0.337991 seconds
% 0.17/0.38  % Total memory used: 65.362 MB
% 0.17/0.38  % Net memory used: 64.850 MB
%------------------------------------------------------------------------------