TSTP Solution File: SEU187+2 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n019.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 20:41:24 EDT 2024

% Result   : Theorem 1.76s 0.60s
% Output   : CNFRefutation 2.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   41 (   7 unt;   0 def)
%            Number of atoms       :  149 (  45 equ)
%            Maximal formula atoms :   11 (   3 avg)
%            Number of connectives :  168 (  60   ~;  71   |;  24   &)
%                                         (  11 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   1 con; 0-3 aty)
%            Number of variables   :   89 (  71   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f11,axiom,
    ! [A] :
      ( A = empty_set
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( B = relation_dom(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f151,conjecture,
    ( relation_dom(empty_set) = empty_set
    & relation_rng(empty_set) = empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f152,negated_conjecture,
    ~ ( relation_dom(empty_set) = empty_set
      & relation_rng(empty_set) = empty_set ),
    inference(negated_conjecture,[status(cth)],[f151]) ).

fof(f209,plain,
    ! [A] :
      ( ( A != empty_set
        | ! [B] : ~ in(B,A) )
      & ( A = empty_set
        | ? [B] : in(B,A) ) ),
    inference(NNF_transformation,[status(esa)],[f11]) ).

fof(f210,plain,
    ( ! [A] :
        ( A != empty_set
        | ! [B] : ~ in(B,A) )
    & ! [A] :
        ( A = empty_set
        | ? [B] : in(B,A) ) ),
    inference(miniscoping,[status(esa)],[f209]) ).

fof(f211,plain,
    ( ! [A] :
        ( A != empty_set
        | ! [B] : ~ in(B,A) )
    & ! [A] :
        ( A = empty_set
        | in(sk0_7(A),A) ) ),
    inference(skolemization,[status(esa)],[f210]) ).

fof(f212,plain,
    ! [X0,X1] :
      ( X0 != empty_set
      | ~ in(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f211]) ).

fof(f271,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B = relation_dom(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f19]) ).

fof(f272,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ( B != relation_dom(A)
            | ! [C] :
                ( ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
          & ( B = relation_dom(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f271]) ).

fof(f273,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_dom(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(C,D),A) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f272]) ).

fof(f274,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_dom(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(C,sk0_18(C,B,A)),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ( ( ~ in(sk0_19(B,A),B)
                | ! [D] : ~ in(ordered_pair(sk0_19(B,A),D),A) )
              & ( in(sk0_19(B,A),B)
                | in(ordered_pair(sk0_19(B,A),sk0_20(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f273]) ).

fof(f278,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | X1 = relation_dom(X0)
      | in(sk0_19(X1,X0),X1)
      | in(ordered_pair(sk0_19(X1,X0),sk0_20(X1,X0)),X0) ),
    inference(cnf_transformation,[status(esa)],[f274]) ).

fof(f298,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( B = relation_rng(A)
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f23]) ).

fof(f299,plain,
    ! [A] :
      ( ~ relation(A)
      | ! [B] :
          ( ( B != relation_rng(A)
            | ! [C] :
                ( ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
          & ( B = relation_rng(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f298]) ).

fof(f300,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ? [C] :
                ( ( ~ in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) )
                & ( in(C,B)
                  | ? [D] : in(ordered_pair(D,C),A) ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f299]) ).

fof(f301,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(sk0_25(C,B,A),C),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ( ( ~ in(sk0_26(B,A),B)
                | ! [D] : ~ in(ordered_pair(D,sk0_26(B,A)),A) )
              & ( in(sk0_26(B,A),B)
                | in(ordered_pair(sk0_27(B,A),sk0_26(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f300]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( ~ relation(X0)
      | X1 = relation_rng(X0)
      | in(sk0_26(X1,X0),X1)
      | in(ordered_pair(sk0_27(X1,X0),sk0_26(X1,X0)),X0) ),
    inference(cnf_transformation,[status(esa)],[f301]) ).

fof(f377,plain,
    relation(empty_set),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f605,plain,
    ( relation_dom(empty_set) != empty_set
    | relation_rng(empty_set) != empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f152]) ).

fof(f606,plain,
    ( relation_dom(empty_set) != empty_set
    | relation_rng(empty_set) != empty_set ),
    inference(cnf_transformation,[status(esa)],[f605]) ).

fof(f657,plain,
    ( spl0_0
  <=> relation_dom(empty_set) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f659,plain,
    ( relation_dom(empty_set) != empty_set
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f657]) ).

fof(f660,plain,
    ( spl0_1
  <=> relation_rng(empty_set) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f662,plain,
    ( relation_rng(empty_set) != empty_set
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f660]) ).

fof(f663,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f606,f657,f660]) ).

fof(f672,plain,
    ! [X0] : ~ in(X0,empty_set),
    inference(equality_resolution,[status(esa)],[f212]) ).

fof(f1054,plain,
    ! [X0] :
      ( X0 = relation_dom(empty_set)
      | in(sk0_19(X0,empty_set),X0)
      | in(ordered_pair(sk0_19(X0,empty_set),sk0_20(X0,empty_set)),empty_set) ),
    inference(resolution,[status(thm)],[f278,f377]) ).

fof(f1055,plain,
    ! [X0] :
      ( X0 = relation_dom(empty_set)
      | in(sk0_19(X0,empty_set),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1054,f672]) ).

fof(f1059,plain,
    ! [X0] :
      ( X0 = relation_rng(empty_set)
      | in(sk0_26(X0,empty_set),X0)
      | in(ordered_pair(sk0_27(X0,empty_set),sk0_26(X0,empty_set)),empty_set) ),
    inference(resolution,[status(thm)],[f305,f377]) ).

fof(f1060,plain,
    ! [X0] :
      ( X0 = relation_rng(empty_set)
      | in(sk0_26(X0,empty_set),X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f1059,f672]) ).

fof(f1563,plain,
    empty_set = relation_dom(empty_set),
    inference(resolution,[status(thm)],[f1055,f672]) ).

fof(f1564,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1563,f659]) ).

fof(f1565,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f1564]) ).

fof(f1627,plain,
    empty_set = relation_rng(empty_set),
    inference(resolution,[status(thm)],[f1060,f672]) ).

fof(f1867,plain,
    ( empty_set != empty_set
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f1627,f662]) ).

fof(f1868,plain,
    ( $false
    | spl0_1 ),
    inference(trivial_equality_resolution,[status(esa)],[f1867]) ).

fof(f1869,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f1868]) ).

fof(f1870,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f663,f1565,f1869]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10  % Problem  : SEU187+2 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31  % Computer : n019.cluster.edu
% 0.09/0.31  % Model    : x86_64 x86_64
% 0.09/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31  % Memory   : 8042.1875MB
% 0.09/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31  % CPULimit : 300
% 0.09/0.31  % WCLimit  : 300
% 0.09/0.31  % DateTime : Mon Apr 29 19:42:59 EDT 2024
% 0.09/0.32  % CPUTime  : 
% 0.09/0.33  % Drodi V3.6.0
% 1.76/0.60  % Refutation found
% 1.76/0.60  % SZS status Theorem for theBenchmark: Theorem is valid
% 1.76/0.60  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.00/0.62  % Elapsed time: 0.304020 seconds
% 2.00/0.62  % CPU time: 2.172681 seconds
% 2.00/0.62  % Total memory used: 98.116 MB
% 2.00/0.62  % Net memory used: 97.178 MB
%------------------------------------------------------------------------------