TSTP Solution File: SYN966+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SYN966+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n016.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 12:48:30 EDT 2023

% Result   : Theorem 0.11s 0.27s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   30 (   4 unt;   0 def)
%            Number of atoms       :  102 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  115 (  43   ~;  42   |;  17   &)
%                                         (   9 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   48 (;  40   !;   8   ?)

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

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

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

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

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

fof(f6,plain,
    ( ! [X,Y] :
        ( ~ eq(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] :
        ( eq(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) ) ) )
    & eq(sk0_1,sk0_2)
    & ~ eq(sk0_2,sk0_1) ),
    inference(skolemization,[status(esa)],[f5]) ).

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

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

fof(f9,plain,
    ! [X0,X1] :
      ( eq(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] :
      ( eq(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,
    eq(sk0_1,sk0_2),
    inference(cnf_transformation,[status(esa)],[f6]) ).

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

fof(f13,plain,
    ( spl0_0
  <=> a_member_of(sk0_0(sk0_1,sk0_2),sk0_2) ),
    introduced(split_symbol_definition) ).

fof(f15,plain,
    ( ~ a_member_of(sk0_0(sk0_1,sk0_2),sk0_2)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f13]) ).

fof(f16,plain,
    ( spl0_1
  <=> a_member_of(sk0_0(sk0_1,sk0_2),sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f18,plain,
    ( ~ a_member_of(sk0_0(sk0_1,sk0_2),sk0_1)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f16]) ).

fof(f19,plain,
    ( ~ a_member_of(sk0_0(sk0_1,sk0_2),sk0_2)
    | ~ a_member_of(sk0_0(sk0_1,sk0_2),sk0_1) ),
    inference(resolution,[status(thm)],[f9,f12]) ).

fof(f20,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f19,f13,f16]) ).

fof(f22,plain,
    ! [X0] :
      ( ~ eq(X0,sk0_2)
      | ~ a_member_of(sk0_0(sk0_1,sk0_2),X0)
      | spl0_0 ),
    inference(resolution,[status(thm)],[f15,f7]) ).

fof(f24,plain,
    ( ~ a_member_of(sk0_0(sk0_1,sk0_2),sk0_1)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f22,f11]) ).

fof(f26,plain,
    ( spl0_2
  <=> eq(sk0_2,sk0_1) ),
    introduced(split_symbol_definition) ).

fof(f27,plain,
    ( eq(sk0_2,sk0_1)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f26]) ).

fof(f29,plain,
    ( eq(sk0_2,sk0_1)
    | a_member_of(sk0_0(sk0_1,sk0_2),sk0_2)
    | spl0_0 ),
    inference(resolution,[status(thm)],[f24,f10]) ).

fof(f30,plain,
    ( spl0_2
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f29,f26,f13]) ).

fof(f33,plain,
    ( $false
    | ~ spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f27,f12]) ).

fof(f34,plain,
    ~ spl0_2,
    inference(contradiction_clause,[status(thm)],[f33]) ).

fof(f37,plain,
    ! [X0] :
      ( ~ eq(sk0_1,X0)
      | ~ a_member_of(sk0_0(sk0_1,sk0_2),X0)
      | spl0_1 ),
    inference(resolution,[status(thm)],[f18,f8]) ).

fof(f39,plain,
    ( ~ a_member_of(sk0_0(sk0_1,sk0_2),sk0_2)
    | spl0_1 ),
    inference(resolution,[status(thm)],[f37,f11]) ).

fof(f40,plain,
    ( ~ spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f39,f13,f16]) ).

fof(f42,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f20,f30,f34,f40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07  % Problem  : SYN966+1 : TPTP v8.1.2. Released v3.1.0.
% 0.02/0.07  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26  % Computer : n016.cluster.edu
% 0.07/0.26  % Model    : x86_64 x86_64
% 0.07/0.26  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26  % Memory   : 8042.1875MB
% 0.07/0.26  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26  % CPULimit : 300
% 0.07/0.26  % WCLimit  : 300
% 0.07/0.26  % DateTime : Tue May 30 10:53:58 EDT 2023
% 0.07/0.26  % CPUTime  : 
% 0.07/0.26  % Drodi V3.5.1
% 0.11/0.27  % Refutation found
% 0.11/0.27  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.27  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.28  % Elapsed time: 0.015133 seconds
% 0.11/0.28  % CPU time: 0.022766 seconds
% 0.11/0.28  % Memory used: 1.833 MB
%------------------------------------------------------------------------------