TSTP Solution File: SET076+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET076+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 20:39:00 EDT 2024

% Result   : Theorem 0.16s 0.41s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   42 (   7 unt;   0 def)
%            Number of atoms       :  115 (  20 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  112 (  39   ~;  43   |;  19   &)
%                                         (   8 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   52 (  47   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( U = X
          | U = Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f44,conjecture,
    ! [X,Y,Z] :
      ( ( member(X,Z)
        & member(Y,Z) )
     => subclass(unordered_pair(X,Y),Z) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,negated_conjecture,
    ~ ! [X,Y,Z] :
        ( ( member(X,Z)
          & member(Y,Z) )
       => subclass(unordered_pair(X,Y),Z) ),
    inference(negated_conjecture,[status(cth)],[f44]) ).

fof(f46,plain,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( ~ member(U,X)
          | member(U,Y) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f47,plain,
    ! [X,Y] :
      ( ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
      & ( subclass(X,Y)
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ( ! [X,Y] :
        ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
    & ! [X,Y] :
        ( subclass(X,Y)
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) ) ) ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ( ! [X,Y] :
        ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
    & ! [X,Y] :
        ( subclass(X,Y)
        | ( member(sk0_0(Y,X),X)
          & ~ member(sk0_0(Y,X),Y) ) ) ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f59,plain,
    ! [U,X,Y] :
      ( ( ~ member(U,unordered_pair(X,Y))
        | ( member(U,universal_class)
          & ( U = X
            | U = Y ) ) )
      & ( member(U,unordered_pair(X,Y))
        | ~ member(U,universal_class)
        | ( U != X
          & U != Y ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f60,plain,
    ( ! [U,X,Y] :
        ( ~ member(U,unordered_pair(X,Y))
        | ( member(U,universal_class)
          & ( U = X
            | U = Y ) ) )
    & ! [U,X,Y] :
        ( member(U,unordered_pair(X,Y))
        | ~ member(U,universal_class)
        | ( U != X
          & U != Y ) ) ),
    inference(miniscoping,[status(esa)],[f59]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f191,plain,
    ? [X,Y,Z] :
      ( member(X,Z)
      & member(Y,Z)
      & ~ subclass(unordered_pair(X,Y),Z) ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f192,plain,
    ( member(sk0_7,sk0_9)
    & member(sk0_8,sk0_9)
    & ~ subclass(unordered_pair(sk0_7,sk0_8),sk0_9) ),
    inference(skolemization,[status(esa)],[f191]) ).

fof(f193,plain,
    member(sk0_7,sk0_9),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f194,plain,
    member(sk0_8,sk0_9),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f195,plain,
    ~ subclass(unordered_pair(sk0_7,sk0_8),sk0_9),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f249,plain,
    ! [X0,X1,X2] :
      ( subclass(unordered_pair(X0,X1),X2)
      | sk0_0(X2,unordered_pair(X0,X1)) = X0
      | sk0_0(X2,unordered_pair(X0,X1)) = X1 ),
    inference(resolution,[status(thm)],[f51,f62]) ).

fof(f1164,plain,
    ( spl0_18
  <=> sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_7 ),
    introduced(split_symbol_definition) ).

fof(f1165,plain,
    ( sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_7
    | ~ spl0_18 ),
    inference(component_clause,[status(thm)],[f1164]) ).

fof(f1167,plain,
    ( spl0_19
  <=> sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_8 ),
    introduced(split_symbol_definition) ).

fof(f1168,plain,
    ( sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_8
    | ~ spl0_19 ),
    inference(component_clause,[status(thm)],[f1167]) ).

fof(f1170,plain,
    ( sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_7
    | sk0_0(sk0_9,unordered_pair(sk0_7,sk0_8)) = sk0_8 ),
    inference(resolution,[status(thm)],[f249,f195]) ).

fof(f1171,plain,
    ( spl0_18
    | spl0_19 ),
    inference(split_clause,[status(thm)],[f1170,f1164,f1167]) ).

fof(f1412,plain,
    ( spl0_22
  <=> subclass(unordered_pair(sk0_7,sk0_8),sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f1413,plain,
    ( subclass(unordered_pair(sk0_7,sk0_8),sk0_9)
    | ~ spl0_22 ),
    inference(component_clause,[status(thm)],[f1412]) ).

fof(f1420,plain,
    ( spl0_24
  <=> member(sk0_7,sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f1422,plain,
    ( ~ member(sk0_7,sk0_9)
    | spl0_24 ),
    inference(component_clause,[status(thm)],[f1420]) ).

fof(f1423,plain,
    ( subclass(unordered_pair(sk0_7,sk0_8),sk0_9)
    | ~ member(sk0_7,sk0_9)
    | ~ spl0_18 ),
    inference(paramodulation,[status(thm)],[f1165,f52]) ).

fof(f1424,plain,
    ( spl0_22
    | ~ spl0_24
    | ~ spl0_18 ),
    inference(split_clause,[status(thm)],[f1423,f1412,f1420,f1164]) ).

fof(f1430,plain,
    ( $false
    | ~ spl0_22 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1413,f195]) ).

fof(f1431,plain,
    ~ spl0_22,
    inference(contradiction_clause,[status(thm)],[f1430]) ).

fof(f1437,plain,
    ( spl0_27
  <=> member(sk0_8,sk0_9) ),
    introduced(split_symbol_definition) ).

fof(f1439,plain,
    ( ~ member(sk0_8,sk0_9)
    | spl0_27 ),
    inference(component_clause,[status(thm)],[f1437]) ).

fof(f1440,plain,
    ( subclass(unordered_pair(sk0_7,sk0_8),sk0_9)
    | ~ member(sk0_8,sk0_9)
    | ~ spl0_19 ),
    inference(paramodulation,[status(thm)],[f1168,f52]) ).

fof(f1441,plain,
    ( spl0_22
    | ~ spl0_27
    | ~ spl0_19 ),
    inference(split_clause,[status(thm)],[f1440,f1412,f1437,f1167]) ).

fof(f1447,plain,
    ( $false
    | spl0_27 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1439,f194]) ).

fof(f1448,plain,
    spl0_27,
    inference(contradiction_clause,[status(thm)],[f1447]) ).

fof(f1449,plain,
    ( $false
    | spl0_24 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1422,f193]) ).

fof(f1450,plain,
    spl0_24,
    inference(contradiction_clause,[status(thm)],[f1449]) ).

fof(f1451,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1171,f1424,f1431,f1441,f1448,f1450]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13  % Problem  : SET076+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.05/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.34  % Computer : n004.cluster.edu
% 0.10/0.34  % Model    : x86_64 x86_64
% 0.10/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34  % Memory   : 8042.1875MB
% 0.10/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.34  % CPULimit : 300
% 0.10/0.34  % WCLimit  : 300
% 0.10/0.34  % DateTime : Mon Apr 29 21:43:18 EDT 2024
% 0.10/0.34  % CPUTime  : 
% 0.10/0.35  % Drodi V3.6.0
% 0.16/0.41  % Refutation found
% 0.16/0.41  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.41  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.42  % Elapsed time: 0.076674 seconds
% 0.16/0.42  % CPU time: 0.478939 seconds
% 0.16/0.42  % Total memory used: 68.795 MB
% 0.16/0.42  % Net memory used: 68.099 MB
%------------------------------------------------------------------------------