%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SYN413+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n028.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 12:46:46 EDT 2023

% Result   : Theorem 0.17s 0.55s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   21 (   5 unt;   0 def)
%            Number of atoms       :   59 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   62 (  24   ~;  19   |;  13   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   2 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   1 con; 0-1 aty)
%            Number of variables   :   41 (;  31   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,conjecture,
    ( ! [Z] :
      ? [Y] :
      ! [X] :
        ( f(X,Y)
      <=> ( f(X,Z)
          & ~ f(X,X) ) )
   => ~ ? [V] :
        ! [U] : f(U,V) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,negated_conjecture,
    ~ ( ! [Z] :
        ? [Y] :
        ! [X] :
          ( f(X,Y)
        <=> ( f(X,Z)
            & ~ f(X,X) ) )
     => ~ ? [V] :
          ! [U] : f(U,V) ),
    inference(negated_conjecture,[status(cth)],[f1]) ).

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

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

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

fof(f6,plain,
    ( ! [Z] :
        ( ! [X] :
            ( ~ f(X,sk0_0(Z))
            | ( f(X,Z)
              & ~ f(X,X) ) )
        & ! [X] :
            ( f(X,sk0_0(Z))
            | ~ f(X,Z)
            | f(X,X) ) )
    & ! [U] : f(U,sk0_1) ),
    inference(skolemization,[status(esa)],[f5]) ).

fof(f7,plain,
    ! [X0,X1] :
      ( ~ f(X0,sk0_0(X1))
      | f(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f8,plain,
    ! [X0,X1] :
      ( ~ f(X0,sk0_0(X1))
      | ~ f(X0,X0) ),
    inference(cnf_transformation,[status(esa)],[f6]) ).

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

fof(f10,plain,
    ! [X0] : f(X0,sk0_1),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f11,plain,
    ! [X0] :
      ( f(X0,sk0_0(sk0_1))
      | f(X0,X0) ),
    inference(resolution,[status(thm)],[f9,f10]) ).

fof(f25,plain,
    ! [X0] :
      ( f(sk0_0(X0),sk0_0(sk0_1))
      | ~ f(sk0_0(X0),sk0_0(X0)) ),
    inference(resolution,[status(thm)],[f11,f8]) ).

fof(f26,plain,
    ! [X0] : ~ f(sk0_0(X0),sk0_0(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f25,f8]) ).

fof(f27,plain,
    ! [X0] :
      ( f(sk0_0(X0),sk0_0(sk0_1))
      | f(sk0_0(X0),X0) ),
    inference(resolution,[status(thm)],[f11,f7]) ).

fof(f36,plain,
    ( spl0_3
  <=> f(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_0(sk0_1))) ),
    introduced(split_symbol_definition) ).

fof(f37,plain,
    ( f(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_0(sk0_1)))
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f36]) ).

fof(f49,plain,
    ( f(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_0(sk0_1)))
    | f(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_0(sk0_1))) ),
    inference(resolution,[status(thm)],[f27,f9]) ).

fof(f50,plain,
    spl0_3,
    inference(split_clause,[status(thm)],[f49,f36]) ).

fof(f56,plain,
    ( $false
    | ~ spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f37,f26]) ).

fof(f57,plain,
    ~ spl0_3,
    inference(contradiction_clause,[status(thm)],[f56]) ).

fof(f58,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f50,f57]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SYN413+1 : TPTP v8.1.2. Released v2.0.0.
% 0.06/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n028.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 : Tue May 30 10:40:47 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  % Drodi V3.5.1
% 0.17/0.55  % Refutation found
% 0.17/0.55  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.55  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.55  % Elapsed time: 0.011081 seconds
% 0.17/0.55  % CPU time: 0.013594 seconds
% 0.17/0.55  % Memory used: 562.884 KB
%------------------------------------------------------------------------------