TSTP Solution File: SEU177+2 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 12:36:08 EDT 2023

% Result   : Theorem 0.18s 0.35s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   34 (   4 unt;   0 def)
%            Number of atoms       :  142 (  18 equ)
%            Maximal formula atoms :   11 (   4 avg)
%            Number of connectives :  172 (  64   ~;  65   |;  26   &)
%                                         (  11 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :   92 (;  70   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,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(f21,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(f94,conjecture,
    ! [A,B,C] :
      ( relation(C)
     => ( in(ordered_pair(A,B),C)
       => ( in(A,relation_dom(C))
          & in(B,relation_rng(C)) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f95,negated_conjecture,
    ~ ! [A,B,C] :
        ( relation(C)
       => ( in(ordered_pair(A,B),C)
         => ( in(A,relation_dom(C))
            & in(B,relation_rng(C)) ) ) ),
    inference(negated_conjecture,[status(cth)],[f94]) ).

fof(f237,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)],[f17]) ).

fof(f238,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)],[f237]) ).

fof(f239,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)],[f238]) ).

fof(f240,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_dom(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(C,sk0_15(C,B,A)),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(C,D),A) ) ) )
        & ! [B] :
            ( B = relation_dom(A)
            | ( ( ~ in(sk0_16(B,A),B)
                | ! [D] : ~ in(ordered_pair(sk0_16(B,A),D),A) )
              & ( in(sk0_16(B,A),B)
                | in(ordered_pair(sk0_16(B,A),sk0_17(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f239]) ).

fof(f242,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != relation_dom(X0)
      | in(X2,X1)
      | ~ in(ordered_pair(X2,X3),X0) ),
    inference(cnf_transformation,[status(esa)],[f240]) ).

fof(f264,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)],[f21]) ).

fof(f265,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)],[f264]) ).

fof(f266,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)],[f265]) ).

fof(f267,plain,
    ! [A] :
      ( ~ relation(A)
      | ( ! [B] :
            ( B != relation_rng(A)
            | ( ! [C] :
                  ( ~ in(C,B)
                  | in(ordered_pair(sk0_22(C,B,A),C),A) )
              & ! [C] :
                  ( in(C,B)
                  | ! [D] : ~ in(ordered_pair(D,C),A) ) ) )
        & ! [B] :
            ( B = relation_rng(A)
            | ( ( ~ in(sk0_23(B,A),B)
                | ! [D] : ~ in(ordered_pair(D,sk0_23(B,A)),A) )
              & ( in(sk0_23(B,A),B)
                | in(ordered_pair(sk0_24(B,A),sk0_23(B,A)),A) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f266]) ).

fof(f269,plain,
    ! [X0,X1,X2,X3] :
      ( ~ relation(X0)
      | X1 != relation_rng(X0)
      | in(X2,X1)
      | ~ in(ordered_pair(X3,X2),X0) ),
    inference(cnf_transformation,[status(esa)],[f267]) ).

fof(f419,plain,
    ? [A,B,C] :
      ( relation(C)
      & in(ordered_pair(A,B),C)
      & ( ~ in(A,relation_dom(C))
        | ~ in(B,relation_rng(C)) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f95]) ).

fof(f420,plain,
    ? [C] :
      ( relation(C)
      & ? [A,B] :
          ( in(ordered_pair(A,B),C)
          & ( ~ in(A,relation_dom(C))
            | ~ in(B,relation_rng(C)) ) ) ),
    inference(miniscoping,[status(esa)],[f419]) ).

fof(f421,plain,
    ( relation(sk0_34)
    & in(ordered_pair(sk0_35,sk0_36),sk0_34)
    & ( ~ in(sk0_35,relation_dom(sk0_34))
      | ~ in(sk0_36,relation_rng(sk0_34)) ) ),
    inference(skolemization,[status(esa)],[f420]) ).

fof(f422,plain,
    relation(sk0_34),
    inference(cnf_transformation,[status(esa)],[f421]) ).

fof(f423,plain,
    in(ordered_pair(sk0_35,sk0_36),sk0_34),
    inference(cnf_transformation,[status(esa)],[f421]) ).

fof(f424,plain,
    ( ~ in(sk0_35,relation_dom(sk0_34))
    | ~ in(sk0_36,relation_rng(sk0_34)) ),
    inference(cnf_transformation,[status(esa)],[f421]) ).

fof(f561,plain,
    ( spl0_0
  <=> in(sk0_35,relation_dom(sk0_34)) ),
    introduced(split_symbol_definition) ).

fof(f564,plain,
    ( spl0_1
  <=> in(sk0_36,relation_rng(sk0_34)) ),
    introduced(split_symbol_definition) ).

fof(f567,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f424,f561,f564]) ).

fof(f592,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,relation_dom(X0))
      | ~ in(ordered_pair(X1,X2),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f242]) ).

fof(f600,plain,
    ! [X0,X1,X2] :
      ( ~ relation(X0)
      | in(X1,relation_rng(X0))
      | ~ in(ordered_pair(X2,X1),X0) ),
    inference(destructive_equality_resolution,[status(esa)],[f269]) ).

fof(f610,plain,
    ( spl0_2
  <=> relation(sk0_34) ),
    introduced(split_symbol_definition) ).

fof(f612,plain,
    ( ~ relation(sk0_34)
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f610]) ).

fof(f613,plain,
    ( ~ relation(sk0_34)
    | in(sk0_35,relation_dom(sk0_34)) ),
    inference(resolution,[status(thm)],[f592,f423]) ).

fof(f614,plain,
    ( ~ spl0_2
    | spl0_0 ),
    inference(split_clause,[status(thm)],[f613,f610,f561]) ).

fof(f615,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f612,f422]) ).

fof(f616,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f615]) ).

fof(f617,plain,
    ( ~ relation(sk0_34)
    | in(sk0_36,relation_rng(sk0_34)) ),
    inference(resolution,[status(thm)],[f600,f423]) ).

fof(f618,plain,
    ( ~ spl0_2
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f617,f610,f564]) ).

fof(f619,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f567,f614,f616,f618]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU177+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 09:30:12 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.34  % Drodi V3.5.1
% 0.18/0.35  % Refutation found
% 0.18/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.37  % Elapsed time: 0.032402 seconds
% 0.18/0.37  % CPU time: 0.046930 seconds
% 0.18/0.37  % Memory used: 16.508 MB
%------------------------------------------------------------------------------