%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU224+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 20:41:35 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   36 (   3 unt;   0 def)
%            Number of atoms       :  124 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  137 (  49   ~;  51   |;  25   &)
%                                         (   8 <=>;   3  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   38 (  29   !;   9   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f117,conjecture,
    ! [A,B,C] :
      ( ( relation(C)
        & function(C) )
     => ( in(B,relation_dom(relation_dom_restriction(C,A)))
      <=> ( in(B,relation_dom(C))
          & in(B,A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f118,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( relation(C)
          & function(C) )
       => ( in(B,relation_dom(relation_dom_restriction(C,A)))
        <=> ( in(B,relation_dom(C))
            & in(B,A) ) ) ),
    inference(negated_conjecture,[status(cth)],[f117]) ).

fof(f228,lemma,
    ! [A,B,C] :
      ( relation(C)
     => ( in(A,relation_dom(relation_dom_restriction(C,B)))
      <=> ( in(A,B)
          & in(A,relation_dom(C)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f638,plain,
    ? [A,B,C] :
      ( relation(C)
      & function(C)
      & ( in(B,relation_dom(relation_dom_restriction(C,A)))
      <~> ( in(B,relation_dom(C))
          & in(B,A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f118]) ).

fof(f639,plain,
    ? [A,B,C] :
      ( relation(C)
      & function(C)
      & ( in(B,relation_dom(relation_dom_restriction(C,A)))
        | ( in(B,relation_dom(C))
          & in(B,A) ) )
      & ( ~ in(B,relation_dom(relation_dom_restriction(C,A)))
        | ~ in(B,relation_dom(C))
        | ~ in(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f638]) ).

fof(f640,plain,
    ? [C] :
      ( relation(C)
      & function(C)
      & ? [A,B] :
          ( ( in(B,relation_dom(relation_dom_restriction(C,A)))
            | ( in(B,relation_dom(C))
              & in(B,A) ) )
          & ( ~ in(B,relation_dom(relation_dom_restriction(C,A)))
            | ~ in(B,relation_dom(C))
            | ~ in(B,A) ) ) ),
    inference(miniscoping,[status(esa)],[f639]) ).

fof(f641,plain,
    ( relation(sk0_55)
    & function(sk0_55)
    & ( in(sk0_57,relation_dom(relation_dom_restriction(sk0_55,sk0_56)))
      | ( in(sk0_57,relation_dom(sk0_55))
        & in(sk0_57,sk0_56) ) )
    & ( ~ in(sk0_57,relation_dom(relation_dom_restriction(sk0_55,sk0_56)))
      | ~ in(sk0_57,relation_dom(sk0_55))
      | ~ in(sk0_57,sk0_56) ) ),
    inference(skolemization,[status(esa)],[f640]) ).

fof(f642,plain,
    relation(sk0_55),
    inference(cnf_transformation,[status(esa)],[f641]) ).

fof(f644,plain,
    ( in(sk0_57,relation_dom(relation_dom_restriction(sk0_55,sk0_56)))
    | in(sk0_57,relation_dom(sk0_55)) ),
    inference(cnf_transformation,[status(esa)],[f641]) ).

fof(f645,plain,
    ( in(sk0_57,relation_dom(relation_dom_restriction(sk0_55,sk0_56)))
    | in(sk0_57,sk0_56) ),
    inference(cnf_transformation,[status(esa)],[f641]) ).

fof(f646,plain,
    ( ~ in(sk0_57,relation_dom(relation_dom_restriction(sk0_55,sk0_56)))
    | ~ in(sk0_57,relation_dom(sk0_55))
    | ~ in(sk0_57,sk0_56) ),
    inference(cnf_transformation,[status(esa)],[f641]) ).

fof(f985,plain,
    ! [A,B,C] :
      ( ~ relation(C)
      | ( in(A,relation_dom(relation_dom_restriction(C,B)))
      <=> ( in(A,B)
          & in(A,relation_dom(C)) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f228]) ).

fof(f986,plain,
    ! [A,B,C] :
      ( ~ relation(C)
      | ( ( ~ in(A,relation_dom(relation_dom_restriction(C,B)))
          | ( in(A,B)
            & in(A,relation_dom(C)) ) )
        & ( in(A,relation_dom(relation_dom_restriction(C,B)))
          | ~ in(A,B)
          | ~ in(A,relation_dom(C)) ) ) ),
    inference(NNF_transformation,[status(esa)],[f985]) ).

fof(f987,plain,
    ! [C] :
      ( ~ relation(C)
      | ( ! [A,B] :
            ( ~ in(A,relation_dom(relation_dom_restriction(C,B)))
            | ( in(A,B)
              & in(A,relation_dom(C)) ) )
        & ! [A,B] :
            ( in(A,relation_dom(relation_dom_restriction(C,B)))
            | ~ in(A,B)
            | ~ in(A,relation_dom(C)) ) ) ),
    inference(miniscoping,[status(esa)],[f986]) ).

fof(f988,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
      | in(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f987]) ).

fof(f989,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | ~ in(X1,relation_dom(relation_dom_restriction(X0,X2)))
      | in(X1,relation_dom(X0)) ),
    inference(cnf_transformation,[status(esa)],[f987]) ).

fof(f990,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,relation_dom(relation_dom_restriction(X0,X2)))
      | ~ in(X1,X2)
      | ~ in(X1,relation_dom(X0)) ),
    inference(cnf_transformation,[status(esa)],[f987]) ).

fof(f1044,plain,
    ( spl0_0
  <=> in(sk0_57,relation_dom(relation_dom_restriction(sk0_55,sk0_56))) ),
    introduced(split_symbol_definition) ).

fof(f1045,plain,
    ( in(sk0_57,relation_dom(relation_dom_restriction(sk0_55,sk0_56)))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f1044]) ).

fof(f1046,plain,
    ( ~ in(sk0_57,relation_dom(relation_dom_restriction(sk0_55,sk0_56)))
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f1044]) ).

fof(f1047,plain,
    ( spl0_1
  <=> in(sk0_57,relation_dom(sk0_55)) ),
    introduced(split_symbol_definition) ).

fof(f1050,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f644,f1044,f1047]) ).

fof(f1051,plain,
    ( spl0_2
  <=> in(sk0_57,sk0_56) ),
    introduced(split_symbol_definition) ).

fof(f1054,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f645,f1044,f1051]) ).

fof(f1055,plain,
    ( ~ spl0_0
    | ~ spl0_1
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f646,f1044,f1047,f1051]) ).

fof(f1146,plain,
    ( spl0_3
  <=> relation(sk0_55) ),
    introduced(split_symbol_definition) ).

fof(f1148,plain,
    ( ~ relation(sk0_55)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f1146]) ).

fof(f1149,plain,
    ( ~ relation(sk0_55)
    | in(sk0_57,relation_dom(sk0_55))
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f1045,f989]) ).

fof(f1150,plain,
    ( ~ spl0_3
    | spl0_1
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f1149,f1146,f1047,f1044]) ).

fof(f1151,plain,
    ( ~ relation(sk0_55)
    | in(sk0_57,sk0_56)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f1045,f988]) ).

fof(f1152,plain,
    ( ~ spl0_3
    | spl0_2
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f1151,f1146,f1051,f1044]) ).

fof(f1154,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1148,f642]) ).

fof(f1155,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f1154]) ).

fof(f1158,plain,
    ( ~ relation(sk0_55)
    | ~ in(sk0_57,sk0_56)
    | ~ in(sk0_57,relation_dom(sk0_55))
    | spl0_0 ),
    inference(resolution,[status(thm)],[f1046,f990]) ).

fof(f1159,plain,
    ( ~ spl0_3
    | ~ spl0_2
    | ~ spl0_1
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f1158,f1146,f1051,f1047,f1044]) ).

fof(f1160,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f1050,f1054,f1055,f1150,f1152,f1155,f1159]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SEU224+2 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon Apr 29 19:37:17 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.14/0.37  % Drodi V3.6.0
% 0.14/0.38  % Refutation found
% 0.14/0.38  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40  % Elapsed time: 0.041002 seconds
% 0.14/0.40  % CPU time: 0.071484 seconds
% 0.14/0.40  % Total memory used: 19.736 MB
% 0.14/0.40  % Net memory used: 19.671 MB
%------------------------------------------------------------------------------