TSTP Solution File: SET120-7 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET120-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 12:34:04 EDT 2023

% Result   : Unsatisfiable 42.72s 5.87s
% Output   : CNFRefutation 43.35s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   65 (  27 unt;   0 def)
%            Number of atoms       :  112 (  41 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   91 (  44   ~;  44   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   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   :   97 (;  97   !;   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(f11,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    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(f14,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [U,X,V,Y] :
      ( ~ member(U,X)
      | ~ member(V,Y)
      | member(ordered_pair(U,V),cross_product(X,Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f107,axiom,
    member(null_class,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f116,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | unordered_pair(X,Y) != null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f126,axiom,
    ! [X] :
      ( member(X,universal_class)
      | singleton(X) = null_class ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f145,axiom,
    ! [X,Y] : member(ordered_pair(X,Y),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f151,axiom,
    ! [W,X,Y,Z] :
      ( ordered_pair(W,X) != ordered_pair(Y,Z)
      | ~ member(W,universal_class)
      | W = Y ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f155,axiom,
    ! [X] :
      ( member(ordered_pair(first(X),second(X)),cross_product(universal_class,universal_class))
      | second(X) = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f159,axiom,
    ! [U,V] :
      ( ~ member(ordered_pair(U,V),cross_product(universal_class,universal_class))
      | second(ordered_pair(U,V)) = V ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f163,axiom,
    ! [X] :
      ( ordered_pair(first(X),second(X)) = X
      | second(X) = X ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f166,negated_conjecture,
    ~ member(x,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f167,negated_conjecture,
    second(ordered_pair(x,y)) != ordered_pair(x,y),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f168,plain,
    ! [Y,U] :
      ( ! [X] :
          ( ~ subclass(X,Y)
          | ~ member(U,X) )
      | member(U,Y) ),
    inference(miniscoping,[status(esa)],[f1]) ).

fof(f169,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f168]) ).

fof(f172,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f182,plain,
    ! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
    inference(cnf_transformation,[status(esa)],[f11]) ).

fof(f183,plain,
    ! [X0] : unordered_pair(X0,X0) = singleton(X0),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f185,plain,
    ! [U,X] :
      ( ! [V,Y] : ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,X) ),
    inference(miniscoping,[status(esa)],[f14]) ).

fof(f186,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(ordered_pair(X0,X1),cross_product(X2,X3))
      | member(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f185]) ).

fof(f189,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,X1)
      | ~ member(X2,X3)
      | member(ordered_pair(X0,X2),cross_product(X1,X3)) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f293,plain,
    member(null_class,universal_class),
    inference(cnf_transformation,[status(esa)],[f107]) ).

fof(f307,plain,
    ! [X] :
      ( ~ member(X,universal_class)
      | ! [Y] : unordered_pair(X,Y) != null_class ),
    inference(miniscoping,[status(esa)],[f116]) ).

fof(f308,plain,
    ! [X0,X1] :
      ( ~ member(X0,universal_class)
      | unordered_pair(X0,X1) != null_class ),
    inference(cnf_transformation,[status(esa)],[f307]) ).

fof(f320,plain,
    ! [X0] :
      ( member(X0,universal_class)
      | singleton(X0) = null_class ),
    inference(cnf_transformation,[status(esa)],[f126]) ).

fof(f340,plain,
    ! [X0,X1] : member(ordered_pair(X0,X1),universal_class),
    inference(cnf_transformation,[status(esa)],[f145]) ).

fof(f349,plain,
    ! [W,Y] :
      ( ! [X,Z] : ordered_pair(W,X) != ordered_pair(Y,Z)
      | ~ member(W,universal_class)
      | W = Y ),
    inference(miniscoping,[status(esa)],[f151]) ).

fof(f350,plain,
    ! [X0,X1,X2,X3] :
      ( ordered_pair(X0,X1) != ordered_pair(X2,X3)
      | ~ member(X0,universal_class)
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f349]) ).

fof(f355,plain,
    ! [X0] :
      ( member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class))
      | second(X0) = X0 ),
    inference(cnf_transformation,[status(esa)],[f155]) ).

fof(f359,plain,
    ! [X0,X1] :
      ( ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class))
      | second(ordered_pair(X0,X1)) = X1 ),
    inference(cnf_transformation,[status(esa)],[f159]) ).

fof(f363,plain,
    ! [X0] :
      ( ordered_pair(first(X0),second(X0)) = X0
      | second(X0) = X0 ),
    inference(cnf_transformation,[status(esa)],[f163]) ).

fof(f366,plain,
    ~ member(x,universal_class),
    inference(cnf_transformation,[status(esa)],[f166]) ).

fof(f367,plain,
    second(ordered_pair(x,y)) != ordered_pair(x,y),
    inference(cnf_transformation,[status(esa)],[f167]) ).

fof(f374,plain,
    ! [X0] :
      ( ~ subclass(X0,universal_class)
      | ~ member(x,X0) ),
    inference(resolution,[status(thm)],[f169,f366]) ).

fof(f375,plain,
    ! [X0] : ~ member(x,X0),
    inference(forward_subsumption_resolution,[status(thm)],[f374,f172]) ).

fof(f692,plain,
    ! [X0,X1,X2,X3] :
      ( ~ member(X0,X1)
      | member(ordered_pair(ordered_pair(X2,X3),X0),cross_product(universal_class,X1)) ),
    inference(resolution,[status(thm)],[f189,f340]) ).

fof(f696,plain,
    ! [X0,X1] : member(ordered_pair(ordered_pair(X0,X1),null_class),cross_product(universal_class,universal_class)),
    inference(resolution,[status(thm)],[f692,f293]) ).

fof(f703,plain,
    ! [X0,X1,X2,X3] : member(ordered_pair(ordered_pair(X0,X1),unordered_pair(X2,X3)),cross_product(universal_class,universal_class)),
    inference(resolution,[status(thm)],[f692,f182]) ).

fof(f1411,plain,
    ! [X0,X1,X2,X3] : second(ordered_pair(ordered_pair(X0,X1),unordered_pair(X2,X3))) = unordered_pair(X2,X3),
    inference(resolution,[status(thm)],[f359,f703]) ).

fof(f1414,plain,
    ! [X0,X1] : second(ordered_pair(ordered_pair(X0,X1),null_class)) = null_class,
    inference(resolution,[status(thm)],[f359,f696]) ).

fof(f1423,plain,
    ! [X0,X1,X2] : second(ordered_pair(ordered_pair(X0,X1),singleton(X2))) = unordered_pair(X2,X2),
    inference(paramodulation,[status(thm)],[f183,f1411]) ).

fof(f1644,plain,
    singleton(x) = null_class,
    inference(resolution,[status(thm)],[f320,f375]) ).

fof(f1665,plain,
    ! [X0,X1] : second(ordered_pair(ordered_pair(X0,X1),null_class)) = unordered_pair(x,x),
    inference(paramodulation,[status(thm)],[f1644,f1423]) ).

fof(f1716,plain,
    ( spl0_46
  <=> null_class = null_class ),
    introduced(split_symbol_definition) ).

fof(f1718,plain,
    ( null_class != null_class
    | spl0_46 ),
    inference(component_clause,[status(thm)],[f1716]) ).

fof(f1724,plain,
    ( $false
    | spl0_46 ),
    inference(trivial_equality_resolution,[status(esa)],[f1718]) ).

fof(f1725,plain,
    spl0_46,
    inference(contradiction_clause,[status(thm)],[f1724]) ).

fof(f2016,plain,
    null_class = unordered_pair(x,x),
    inference(paramodulation,[status(thm)],[f1414,f1665]) ).

fof(f2667,plain,
    ( spl0_92
  <=> member(x,universal_class) ),
    introduced(split_symbol_definition) ).

fof(f2878,plain,
    ( ~ member(x,universal_class)
    | null_class != null_class ),
    inference(paramodulation,[status(thm)],[f2016,f308]) ).

fof(f2879,plain,
    ( ~ spl0_92
    | ~ spl0_46 ),
    inference(split_clause,[status(thm)],[f2878,f2667,f1716]) ).

fof(f22647,plain,
    ! [X0,X1] :
      ( second(ordered_pair(X0,X1)) = ordered_pair(X0,X1)
      | ~ member(first(ordered_pair(X0,X1)),universal_class)
      | first(ordered_pair(X0,X1)) = X0 ),
    inference(resolution,[status(thm)],[f363,f350]) ).

fof(f38201,plain,
    ! [X0] :
      ( second(X0) = X0
      | member(first(X0),universal_class) ),
    inference(resolution,[status(thm)],[f355,f186]) ).

fof(f40156,plain,
    ! [X0,X1] :
      ( second(ordered_pair(X0,X1)) = ordered_pair(X0,X1)
      | first(ordered_pair(X0,X1)) = X0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f22647,f38201]) ).

fof(f40157,plain,
    first(ordered_pair(x,y)) = x,
    inference(resolution,[status(thm)],[f40156,f367]) ).

fof(f40222,plain,
    ( spl0_1538
  <=> second(ordered_pair(x,y)) = ordered_pair(x,y) ),
    introduced(split_symbol_definition) ).

fof(f40223,plain,
    ( second(ordered_pair(x,y)) = ordered_pair(x,y)
    | ~ spl0_1538 ),
    inference(component_clause,[status(thm)],[f40222]) ).

fof(f40227,plain,
    ( second(ordered_pair(x,y)) = ordered_pair(x,y)
    | member(x,universal_class) ),
    inference(paramodulation,[status(thm)],[f40157,f38201]) ).

fof(f40228,plain,
    ( spl0_1538
    | spl0_92 ),
    inference(split_clause,[status(thm)],[f40227,f40222,f2667]) ).

fof(f40262,plain,
    ( $false
    | ~ spl0_1538 ),
    inference(forward_subsumption_resolution,[status(thm)],[f40223,f367]) ).

fof(f40263,plain,
    ~ spl0_1538,
    inference(contradiction_clause,[status(thm)],[f40262]) ).

fof(f40264,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1725,f2879,f40228,f40263]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SET120-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.09/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33  % Computer : n022.cluster.edu
% 0.10/0.33  % Model    : x86_64 x86_64
% 0.10/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33  % Memory   : 8042.1875MB
% 0.10/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33  % CPULimit : 300
% 0.10/0.33  % WCLimit  : 300
% 0.10/0.33  % DateTime : Tue May 30 10:19:57 EDT 2023
% 0.10/0.33  % CPUTime  : 
% 0.10/0.34  % Drodi V3.5.1
% 42.72/5.87  % Refutation found
% 42.72/5.87  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 42.72/5.87  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 43.35/5.95  % Elapsed time: 5.607353 seconds
% 43.35/5.95  % CPU time: 43.654600 seconds
% 43.35/5.95  % Memory used: 278.685 MB
%------------------------------------------------------------------------------