%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU189+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n014.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 12:36:11 EDT 2023

% Result   : Theorem 0.12s 0.37s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   57 (  10 unt;   0 def)
%            Number of atoms       :  129 (  48 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  118 (  46   ~;  50   |;   8   &)
%                                         (   9 <=>;   4  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   8 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-1 aty)
%            Number of variables   :    8 (;   6   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f57,axiom,
    empty(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f64,axiom,
    ( empty(empty_set)
    & relation(empty_set) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f153,lemma,
    ( relation_dom(empty_set) = empty_set
    & relation_rng(empty_set) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f156,lemma,
    ! [A] :
      ( relation(A)
     => ( ( relation_dom(A) = empty_set
          | relation_rng(A) = empty_set )
       => A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f157,conjecture,
    ! [A] :
      ( relation(A)
     => ( relation_dom(A) = empty_set
      <=> relation_rng(A) = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f158,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ( relation_dom(A) = empty_set
        <=> relation_rng(A) = empty_set ) ),
    inference(negated_conjecture,[status(cth)],[f157]) ).

fof(f368,plain,
    empty(empty_set),
    inference(cnf_transformation,[status(esa)],[f57]) ).

fof(f381,plain,
    relation(empty_set),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f615,plain,
    relation_dom(empty_set) = empty_set,
    inference(cnf_transformation,[status(esa)],[f153]) ).

fof(f616,plain,
    relation_rng(empty_set) = empty_set,
    inference(cnf_transformation,[status(esa)],[f153]) ).

fof(f622,plain,
    ! [A] :
      ( ~ relation(A)
      | ( relation_dom(A) != empty_set
        & relation_rng(A) != empty_set )
      | A = empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f156]) ).

fof(f623,plain,
    ! [X0] :
      ( ~ relation(X0)
      | relation_dom(X0) != empty_set
      | X0 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f622]) ).

fof(f624,plain,
    ! [X0] :
      ( ~ relation(X0)
      | relation_rng(X0) != empty_set
      | X0 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f622]) ).

fof(f625,plain,
    ? [A] :
      ( relation(A)
      & ( relation_dom(A) = empty_set
      <~> relation_rng(A) = empty_set ) ),
    inference(pre_NNF_transformation,[status(esa)],[f158]) ).

fof(f626,plain,
    ? [A] :
      ( relation(A)
      & ( relation_dom(A) = empty_set
        | relation_rng(A) = empty_set )
      & ( relation_dom(A) != empty_set
        | relation_rng(A) != empty_set ) ),
    inference(NNF_transformation,[status(esa)],[f625]) ).

fof(f627,plain,
    ( relation(sk0_49)
    & ( relation_dom(sk0_49) = empty_set
      | relation_rng(sk0_49) = empty_set )
    & ( relation_dom(sk0_49) != empty_set
      | relation_rng(sk0_49) != empty_set ) ),
    inference(skolemization,[status(esa)],[f626]) ).

fof(f628,plain,
    relation(sk0_49),
    inference(cnf_transformation,[status(esa)],[f627]) ).

fof(f629,plain,
    ( relation_dom(sk0_49) = empty_set
    | relation_rng(sk0_49) = empty_set ),
    inference(cnf_transformation,[status(esa)],[f627]) ).

fof(f630,plain,
    ( relation_dom(sk0_49) != empty_set
    | relation_rng(sk0_49) != empty_set ),
    inference(cnf_transformation,[status(esa)],[f627]) ).

fof(f676,plain,
    ( spl0_0
  <=> relation_dom(sk0_49) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f677,plain,
    ( relation_dom(sk0_49) = empty_set
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f676]) ).

fof(f678,plain,
    ( relation_dom(sk0_49) != empty_set
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f676]) ).

fof(f679,plain,
    ( spl0_1
  <=> relation_rng(sk0_49) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f680,plain,
    ( relation_rng(sk0_49) = empty_set
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f679]) ).

fof(f681,plain,
    ( relation_rng(sk0_49) != empty_set
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f679]) ).

fof(f682,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f629,f676,f679]) ).

fof(f683,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f630,f676,f679]) ).

fof(f730,plain,
    ( spl0_2
  <=> empty(empty_set) ),
    introduced(split_symbol_definition) ).

fof(f732,plain,
    ( ~ empty(empty_set)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f730]) ).

fof(f735,plain,
    ( spl0_3
  <=> relation(empty_set) ),
    introduced(split_symbol_definition) ).

fof(f737,plain,
    ( ~ relation(empty_set)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f735]) ).

fof(f748,plain,
    ( spl0_4
  <=> empty_set = empty_set ),
    introduced(split_symbol_definition) ).

fof(f751,plain,
    ( ~ relation(empty_set)
    | empty_set = empty_set ),
    inference(resolution,[status(thm)],[f623,f615]) ).

fof(f752,plain,
    ( ~ spl0_3
    | spl0_4 ),
    inference(split_clause,[status(thm)],[f751,f735,f748]) ).

fof(f764,plain,
    ( spl0_5
  <=> relation(sk0_49) ),
    introduced(split_symbol_definition) ).

fof(f766,plain,
    ( ~ relation(sk0_49)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f764]) ).

fof(f767,plain,
    ( spl0_6
  <=> sk0_49 = empty_set ),
    introduced(split_symbol_definition) ).

fof(f768,plain,
    ( sk0_49 = empty_set
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f767]) ).

fof(f770,plain,
    ( ~ relation(sk0_49)
    | sk0_49 = empty_set
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f677,f623]) ).

fof(f771,plain,
    ( ~ spl0_5
    | spl0_6
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f770,f764,f767,f676]) ).

fof(f783,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f766,f628]) ).

fof(f784,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f783]) ).

fof(f785,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f737,f381]) ).

fof(f786,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f785]) ).

fof(f787,plain,
    ( ~ relation(sk0_49)
    | sk0_49 = empty_set
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f680,f624]) ).

fof(f788,plain,
    ( ~ spl0_5
    | spl0_6
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f787,f764,f767,f679]) ).

fof(f797,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f732,f368]) ).

fof(f798,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f797]) ).

fof(f800,plain,
    ( relation_dom(empty_set) != empty_set
    | ~ spl0_6
    | spl0_0 ),
    inference(backward_demodulation,[status(thm)],[f768,f678]) ).

fof(f801,plain,
    ( empty_set != empty_set
    | ~ spl0_6
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f615,f800]) ).

fof(f802,plain,
    ( $false
    | ~ spl0_6
    | spl0_0 ),
    inference(trivial_equality_resolution,[status(esa)],[f801]) ).

fof(f803,plain,
    ( ~ spl0_6
    | spl0_0 ),
    inference(contradiction_clause,[status(thm)],[f802]) ).

fof(f806,plain,
    ( relation_rng(empty_set) != empty_set
    | ~ spl0_6
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f768,f681]) ).

fof(f807,plain,
    ( empty_set != empty_set
    | ~ spl0_6
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f616,f806]) ).

fof(f808,plain,
    ( $false
    | ~ spl0_6
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f807]) ).

fof(f809,plain,
    ( ~ spl0_6
    | spl0_1 ),
    inference(contradiction_clause,[status(thm)],[f808]) ).

fof(f810,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f682,f683,f752,f771,f784,f786,f788,f798,f803,f809]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU189+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Tue May 30 09:09:04 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.36  % Drodi V3.5.1
% 0.12/0.37  % Refutation found
% 0.12/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.64  % Elapsed time: 0.080788 seconds
% 0.22/0.64  % CPU time: 0.041767 seconds
% 0.22/0.64  % Memory used: 4.316 MB
%------------------------------------------------------------------------------