TSTP Solution File: SET788+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 20:40:21 EDT 2024

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   43 (   1 unt;   0 def)
%            Number of atoms       :  154 (   0 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  173 (  62   ~;  78   |;  16   &)
%                                         (  14 <=>;   2  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    9 (   8 usr;   7 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   52 (  44   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ( ! [X,Y] :
        ( equalish(X,Y)
      <=> ! [Z] :
            ( a_member_of(Z,X)
          <=> a_member_of(Z,Y) ) )
   => ! [X,Y] :
        ( equalish(X,Y)
      <=> equalish(Y,X) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ ( ! [X,Y] :
          ( equalish(X,Y)
        <=> ! [Z] :
              ( a_member_of(Z,X)
            <=> a_member_of(Z,Y) ) )
     => ! [X,Y] :
          ( equalish(X,Y)
        <=> equalish(Y,X) ) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

fof(f3,plain,
    ( ! [X,Y] :
        ( equalish(X,Y)
      <=> ! [Z] :
            ( a_member_of(Z,X)
          <=> a_member_of(Z,Y) ) )
    & ? [X,Y] :
        ( equalish(X,Y)
      <~> equalish(Y,X) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f4,plain,
    ( ! [X,Y] :
        ( ( ~ equalish(X,Y)
          | ! [Z] :
              ( ( ~ a_member_of(Z,X)
                | a_member_of(Z,Y) )
              & ( a_member_of(Z,X)
                | ~ a_member_of(Z,Y) ) ) )
        & ( equalish(X,Y)
          | ? [Z] :
              ( ( ~ a_member_of(Z,X)
                | ~ a_member_of(Z,Y) )
              & ( a_member_of(Z,X)
                | a_member_of(Z,Y) ) ) ) )
    & ? [X,Y] :
        ( ( equalish(X,Y)
          | equalish(Y,X) )
        & ( ~ equalish(X,Y)
          | ~ equalish(Y,X) ) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f5,plain,
    ( ! [X,Y] :
        ( ~ equalish(X,Y)
        | ( ! [Z] :
              ( ~ a_member_of(Z,X)
              | a_member_of(Z,Y) )
          & ! [Z] :
              ( a_member_of(Z,X)
              | ~ a_member_of(Z,Y) ) ) )
    & ! [X,Y] :
        ( equalish(X,Y)
        | ? [Z] :
            ( ( ~ a_member_of(Z,X)
              | ~ a_member_of(Z,Y) )
            & ( a_member_of(Z,X)
              | a_member_of(Z,Y) ) ) )
    & ? [X,Y] :
        ( ( equalish(X,Y)
          | equalish(Y,X) )
        & ( ~ equalish(X,Y)
          | ~ equalish(Y,X) ) ) ),
    inference(miniscoping,[status(esa)],[f4]) ).

fof(f6,plain,
    ( ! [X,Y] :
        ( ~ equalish(X,Y)
        | ( ! [Z] :
              ( ~ a_member_of(Z,X)
              | a_member_of(Z,Y) )
          & ! [Z] :
              ( a_member_of(Z,X)
              | ~ a_member_of(Z,Y) ) ) )
    & ! [X,Y] :
        ( equalish(X,Y)
        | ( ( ~ a_member_of(sk0_0(Y,X),X)
            | ~ a_member_of(sk0_0(Y,X),Y) )
          & ( a_member_of(sk0_0(Y,X),X)
            | a_member_of(sk0_0(Y,X),Y) ) ) )
    & ( equalish(sk0_1,sk0_2)
      | equalish(sk0_2,sk0_1) )
    & ( ~ equalish(sk0_1,sk0_2)
      | ~ equalish(sk0_2,sk0_1) ) ),
    inference(skolemization,[status(esa)],[f5]) ).

fof(f7,plain,
    ! [X0,X1,X2] :
      ( ~ equalish(X0,X1)
      | ~ a_member_of(X2,X0)
      | a_member_of(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f8,plain,
    ! [X0,X1,X2] :
      ( ~ equalish(X0,X1)
      | a_member_of(X2,X0)
      | ~ a_member_of(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f9,plain,
    ! [X0,X1] :
      ( equalish(X0,X1)
      | ~ a_member_of(sk0_0(X1,X0),X0)
      | ~ a_member_of(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( equalish(X0,X1)
      | a_member_of(sk0_0(X1,X0),X0)
      | a_member_of(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f11,plain,
    ( equalish(sk0_1,sk0_2)
    | equalish(sk0_2,sk0_1) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f12,plain,
    ( ~ equalish(sk0_1,sk0_2)
    | ~ equalish(sk0_2,sk0_1) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f13,plain,
    ( spl0_0
  <=> equalish(sk0_1,sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f14,plain,
    ( equalish(sk0_1,sk0_2)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f13]) ).

fof(f16,plain,
    ( spl0_1
  <=> equalish(sk0_2,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f17,plain,
    ( equalish(sk0_2,sk0_1)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f16]) ).

fof(f19,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f11,f13,f16]) ).

fof(f20,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f12,f13,f16]) ).

fof(f25,plain,
    ! [X0] :
      ( a_member_of(X0,sk0_2)
      | ~ a_member_of(X0,sk0_1)
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f17,f8]) ).

fof(f26,plain,
    ! [X0] :
      ( ~ a_member_of(X0,sk0_2)
      | a_member_of(X0,sk0_1)
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f17,f7]) ).

fof(f38,plain,
    ! [X0] :
      ( a_member_of(sk0_0(X0,sk0_1),sk0_2)
      | equalish(sk0_1,X0)
      | a_member_of(sk0_0(X0,sk0_1),X0)
      | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f25,f10]) ).

fof(f46,plain,
    ( spl0_5
  <=> a_member_of(sk0_0(sk0_2,sk0_1),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f49,plain,
    ( a_member_of(sk0_0(sk0_2,sk0_1),sk0_2)
    | equalish(sk0_1,sk0_2)
    | ~ spl0_1 ),
    inference(factoring,[status(esa)],[f38]) ).

fof(f50,plain,
    ( spl0_5
    | spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f49,f46,f13,f16]) ).

fof(f51,plain,
    ( spl0_6
  <=> a_member_of(sk0_0(sk0_2,sk0_1),sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f52,plain,
    ( a_member_of(sk0_0(sk0_2,sk0_1),sk0_1)
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f51]) ).

fof(f54,plain,
    ( a_member_of(sk0_0(sk0_2,sk0_1),sk0_1)
    | equalish(sk0_1,sk0_2)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f26,f38]) ).

fof(f55,plain,
    ( spl0_6
    | spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f54,f51,f13,f16]) ).

fof(f73,plain,
    ( spl0_9
  <=> a_member_of(sk0_0(sk0_1,sk0_2),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f74,plain,
    ( a_member_of(sk0_0(sk0_1,sk0_2),sk0_2)
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f73]) ).

fof(f86,plain,
    ( spl0_11
  <=> a_member_of(sk0_0(sk0_1,sk0_2),sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f94,plain,
    ( equalish(sk0_1,sk0_2)
    | ~ a_member_of(sk0_0(sk0_2,sk0_1),sk0_2)
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f52,f9]) ).

fof(f95,plain,
    ( spl0_0
    | ~ spl0_5
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f94,f13,f46,f51]) ).

fof(f96,plain,
    ! [X0] :
      ( a_member_of(X0,sk0_1)
      | ~ a_member_of(X0,sk0_2)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f14,f8]) ).

fof(f97,plain,
    ! [X0] :
      ( ~ a_member_of(X0,sk0_1)
      | a_member_of(X0,sk0_2)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f14,f7]) ).

fof(f103,plain,
    ! [X0] :
      ( a_member_of(sk0_0(X0,sk0_2),sk0_1)
      | equalish(sk0_2,X0)
      | a_member_of(sk0_0(X0,sk0_2),X0)
      | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f96,f10]) ).

fof(f110,plain,
    ( equalish(sk0_2,sk0_1)
    | a_member_of(sk0_0(sk0_1,sk0_2),sk0_2)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f103,f97]) ).

fof(f111,plain,
    ( spl0_1
    | spl0_9
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f110,f16,f73,f13]) ).

fof(f119,plain,
    ( a_member_of(sk0_0(sk0_1,sk0_2),sk0_1)
    | equalish(sk0_2,sk0_1)
    | ~ spl0_0 ),
    inference(factoring,[status(esa)],[f103]) ).

fof(f120,plain,
    ( spl0_11
    | spl0_1
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f119,f86,f16,f13]) ).

fof(f134,plain,
    ( equalish(sk0_2,sk0_1)
    | ~ a_member_of(sk0_0(sk0_1,sk0_2),sk0_1)
    | ~ spl0_9 ),
    inference(resolution,[status(thm)],[f74,f9]) ).

fof(f135,plain,
    ( spl0_1
    | ~ spl0_11
    | ~ spl0_9 ),
    inference(split_clause,[status(thm)],[f134,f16,f86,f73]) ).

fof(f136,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f19,f20,f50,f55,f95,f111,f120,f135]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n031.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Mon Apr 29 22:22:58 EDT 2024
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.6.0
% 0.13/0.36  % Refutation found
% 0.13/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38  % Elapsed time: 0.024452 seconds
% 0.20/0.38  % CPU time: 0.064756 seconds
% 0.20/0.38  % Total memory used: 2.450 MB
% 0.20/0.38  % Net memory used: 2.400 MB
%------------------------------------------------------------------------------