TSTP Solution File: SEU213+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU213+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n022.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  1 03:50:44 EDT 2024

% Result   : Theorem 0.62s 0.79s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  144 (  10 unt;   0 def)
%            Number of atoms       :  653 (  57 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  864 ( 355   ~; 368   |;  98   &)
%                                         (  21 <=>;  20  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   6 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   4 con; 0-4 aty)
%            Number of variables   :  312 ( 266   !;  46   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f595,plain,
    $false,
    inference(avatar_sat_refutation,[],[f186,f187,f188,f279,f293,f439,f529,f594]) ).

fof(f594,plain,
    ( ~ spl16_1
    | spl16_2
    | ~ spl16_4 ),
    inference(avatar_contradiction_clause,[],[f593]) ).

fof(f593,plain,
    ( $false
    | ~ spl16_1
    | spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f592,f99]) ).

fof(f99,plain,
    relation(sK2),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ( ( ~ in(apply(sK2,sK0),relation_dom(sK1))
      | ~ in(sK0,relation_dom(sK2))
      | ~ in(sK0,relation_dom(relation_composition(sK2,sK1))) )
    & ( ( in(apply(sK2,sK0),relation_dom(sK1))
        & in(sK0,relation_dom(sK2)) )
      | in(sK0,relation_dom(relation_composition(sK2,sK1))) )
    & function(sK2)
    & relation(sK2)
    & function(sK1)
    & relation(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f68,f70,f69]) ).

fof(f69,plain,
    ( ? [X0,X1] :
        ( ? [X2] :
            ( ( ~ in(apply(X2,X0),relation_dom(X1))
              | ~ in(X0,relation_dom(X2))
              | ~ in(X0,relation_dom(relation_composition(X2,X1))) )
            & ( ( in(apply(X2,X0),relation_dom(X1))
                & in(X0,relation_dom(X2)) )
              | in(X0,relation_dom(relation_composition(X2,X1))) )
            & function(X2)
            & relation(X2) )
        & function(X1)
        & relation(X1) )
   => ( ? [X2] :
          ( ( ~ in(apply(X2,sK0),relation_dom(sK1))
            | ~ in(sK0,relation_dom(X2))
            | ~ in(sK0,relation_dom(relation_composition(X2,sK1))) )
          & ( ( in(apply(X2,sK0),relation_dom(sK1))
              & in(sK0,relation_dom(X2)) )
            | in(sK0,relation_dom(relation_composition(X2,sK1))) )
          & function(X2)
          & relation(X2) )
      & function(sK1)
      & relation(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ( ? [X2] :
        ( ( ~ in(apply(X2,sK0),relation_dom(sK1))
          | ~ in(sK0,relation_dom(X2))
          | ~ in(sK0,relation_dom(relation_composition(X2,sK1))) )
        & ( ( in(apply(X2,sK0),relation_dom(sK1))
            & in(sK0,relation_dom(X2)) )
          | in(sK0,relation_dom(relation_composition(X2,sK1))) )
        & function(X2)
        & relation(X2) )
   => ( ( ~ in(apply(sK2,sK0),relation_dom(sK1))
        | ~ in(sK0,relation_dom(sK2))
        | ~ in(sK0,relation_dom(relation_composition(sK2,sK1))) )
      & ( ( in(apply(sK2,sK0),relation_dom(sK1))
          & in(sK0,relation_dom(sK2)) )
        | in(sK0,relation_dom(relation_composition(sK2,sK1))) )
      & function(sK2)
      & relation(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f68,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(apply(X2,X0),relation_dom(X1))
            | ~ in(X0,relation_dom(X2))
            | ~ in(X0,relation_dom(relation_composition(X2,X1))) )
          & ( ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) )
            | in(X0,relation_dom(relation_composition(X2,X1))) )
          & function(X2)
          & relation(X2) )
      & function(X1)
      & relation(X1) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( ~ in(apply(X2,X0),relation_dom(X1))
            | ~ in(X0,relation_dom(X2))
            | ~ in(X0,relation_dom(relation_composition(X2,X1))) )
          & ( ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) )
            | in(X0,relation_dom(relation_composition(X2,X1))) )
          & function(X2)
          & relation(X2) )
      & function(X1)
      & relation(X1) ),
    inference(nnf_transformation,[],[f45]) ).

fof(f45,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( in(X0,relation_dom(relation_composition(X2,X1)))
          <~> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) )
          & function(X2)
          & relation(X2) )
      & function(X1)
      & relation(X1) ),
    inference(flattening,[],[f44]) ).

fof(f44,plain,
    ? [X0,X1] :
      ( ? [X2] :
          ( ( in(X0,relation_dom(relation_composition(X2,X1)))
          <~> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) )
          & function(X2)
          & relation(X2) )
      & function(X1)
      & relation(X1) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f34,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( function(X1)
          & relation(X1) )
       => ! [X2] :
            ( ( function(X2)
              & relation(X2) )
           => ( in(X0,relation_dom(relation_composition(X2,X1)))
            <=> ( in(apply(X2,X0),relation_dom(X1))
                & in(X0,relation_dom(X2)) ) ) ) ),
    inference(negated_conjecture,[],[f33]) ).

fof(f33,conjecture,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(apply(X2,X0),relation_dom(X1))
              & in(X0,relation_dom(X2)) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KWCFEtNa1R/Vampire---4.8_17919',t21_funct_1) ).

fof(f592,plain,
    ( ~ relation(sK2)
    | ~ spl16_1
    | spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f591,f100]) ).

fof(f100,plain,
    function(sK2),
    inference(cnf_transformation,[],[f71]) ).

fof(f591,plain,
    ( ~ function(sK2)
    | ~ relation(sK2)
    | ~ spl16_1
    | spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f590,f181]) ).

fof(f181,plain,
    ( ~ in(sK0,relation_dom(sK2))
    | spl16_2 ),
    inference(avatar_component_clause,[],[f179]) ).

fof(f179,plain,
    ( spl16_2
  <=> in(sK0,relation_dom(sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_2])]) ).

fof(f590,plain,
    ( in(sK0,relation_dom(sK2))
    | ~ function(sK2)
    | ~ relation(sK2)
    | ~ spl16_1
    | spl16_2
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f588,f537]) ).

fof(f537,plain,
    ( ! [X0] : ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,X0)),sK2)
    | spl16_2 ),
    inference(subsumption_resolution,[],[f536,f99]) ).

fof(f536,plain,
    ( ! [X0] :
        ( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,X0)),sK2)
        | ~ relation(sK2) )
    | spl16_2 ),
    inference(resolution,[],[f181,f193]) ).

fof(f193,plain,
    ! [X0,X6,X5] :
      ( in(X5,relation_dom(X0))
      | ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X6)),X0)
      | ~ relation(X0) ),
    inference(backward_demodulation,[],[f166,f143]) ).

fof(f143,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    file('/export/starexec/sandbox2/tmp/tmp.KWCFEtNa1R/Vampire---4.8_17919',commutativity_k2_tarski) ).

fof(f166,plain,
    ! [X0,X6,X5] :
      ( in(X5,relation_dom(X0))
      | ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f155]) ).

fof(f155,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f110,f142]) ).

fof(f142,plain,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
    file('/export/starexec/sandbox2/tmp/tmp.KWCFEtNa1R/Vampire---4.8_17919',d5_tarski) ).

fof(f110,plain,
    ! [X0,X1,X6,X5] :
      ( in(X5,X1)
      | ~ in(ordered_pair(X5,X6),X0)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ( ( ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0)
                | ~ in(sK3(X0,X1),X1) )
              & ( in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0)
                | in(sK3(X0,X1),X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( in(ordered_pair(X5,sK5(X0,X5)),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f73,f76,f75,f74]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
            | ~ in(X2,X1) )
          & ( ? [X4] : in(ordered_pair(X2,X4),X0)
            | in(X2,X1) ) )
     => ( ( ! [X3] : ~ in(ordered_pair(sK3(X0,X1),X3),X0)
          | ~ in(sK3(X0,X1),X1) )
        & ( ? [X4] : in(ordered_pair(sK3(X0,X1),X4),X0)
          | in(sK3(X0,X1),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X4] : in(ordered_pair(sK3(X0,X1),X4),X0)
     => in(ordered_pair(sK3(X0,X1),sK4(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f76,plain,
    ! [X0,X5] :
      ( ? [X7] : in(ordered_pair(X5,X7),X0)
     => in(ordered_pair(X5,sK5(X0,X5)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f73,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X4] : in(ordered_pair(X2,X4),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X5] :
                ( ( in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( ? [X7] : in(ordered_pair(X5,X7),X0)
                  | ~ in(X5,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | in(X2,X1) ) ) )
          & ( ! [X2] :
                ( ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) ) )
            | relation_dom(X0) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation_dom(X0) = X1
        <=> ! [X2] :
              ( in(X2,X1)
            <=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KWCFEtNa1R/Vampire---4.8_17919',d4_relat_1) ).

fof(f588,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,empty_set)),sK2)
    | in(sK0,relation_dom(sK2))
    | ~ function(sK2)
    | ~ relation(sK2)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(superposition,[],[f526,f168]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( apply(X0,X1) = empty_set
      | in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f116]) ).

fof(f116,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X1) = X2
      | empty_set != X2
      | in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( ( apply(X0,X1) = X2
                | empty_set != X2 )
              & ( empty_set = X2
                | apply(X0,X1) != X2 ) )
            | in(X1,relation_dom(X0)) )
          & ( ( ( apply(X0,X1) = X2
                | ~ in(ordered_pair(X1,X2),X0) )
              & ( in(ordered_pair(X1,X2),X0)
                | apply(X0,X1) != X2 ) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( apply(X0,X1) = X2
            <=> empty_set = X2 )
            | in(X1,relation_dom(X0)) )
          & ( ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ( apply(X0,X1) = X2
            <=> empty_set = X2 )
            | in(X1,relation_dom(X0)) )
          & ( ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) )
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( ( ~ in(X1,relation_dom(X0))
           => ( apply(X0,X1) = X2
            <=> empty_set = X2 ) )
          & ( in(X1,relation_dom(X0))
           => ( apply(X0,X1) = X2
            <=> in(ordered_pair(X1,X2),X0) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KWCFEtNa1R/Vampire---4.8_17919',d4_funct_1) ).

fof(f526,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,apply(sK2,sK0))),sK2)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(backward_demodulation,[],[f490,f521]) ).

fof(f521,plain,
    ( apply(sK2,sK0) = sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0))
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(resolution,[],[f490,f309]) ).

fof(f309,plain,
    ! [X0,X1] :
      ( ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK2)
      | apply(sK2,X0) = X1 ),
    inference(subsumption_resolution,[],[f305,f99]) ).

fof(f305,plain,
    ! [X0,X1] :
      ( apply(sK2,X0) = X1
      | ~ in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK2)
      | ~ relation(sK2) ),
    inference(resolution,[],[f194,f100]) ).

fof(f194,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | apply(X0,X1) = X2
      | ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
      | ~ relation(X0) ),
    inference(backward_demodulation,[],[f189,f143]) ).

fof(f189,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X1) = X2
      | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(subsumption_resolution,[],[f157,f166]) ).

fof(f157,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X1) = X2
      | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
      | ~ in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f114,f142]) ).

fof(f114,plain,
    ! [X2,X0,X1] :
      ( apply(X0,X1) = X2
      | ~ in(ordered_pair(X1,X2),X0)
      | ~ in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f490,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0)))),sK2)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f489,f99]) ).

fof(f489,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0)))),sK2)
    | ~ relation(sK2)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f483,f97]) ).

fof(f97,plain,
    relation(sK1),
    inference(cnf_transformation,[],[f71]) ).

fof(f483,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0)))),sK2)
    | ~ relation(sK1)
    | ~ relation(sK2)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(resolution,[],[f449,f209]) ).

fof(f209,plain,
    ! [X0,X1,X8,X7] :
      ( ~ in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),relation_composition(X0,X1))
      | in(unordered_pair(singleton(X7),unordered_pair(X7,sK12(X0,X1,X7,X8))),X0)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f197,f143]) ).

fof(f197,plain,
    ! [X0,X1,X8,X7] :
      ( ~ in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),relation_composition(X0,X1))
      | in(unordered_pair(unordered_pair(X7,sK12(X0,X1,X7,X8)),singleton(X7)),X0)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(backward_demodulation,[],[f192,f143]) ).

fof(f192,plain,
    ! [X0,X1,X8,X7] :
      ( in(unordered_pair(unordered_pair(X7,sK12(X0,X1,X7,X8)),singleton(X7)),X0)
      | ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(subsumption_resolution,[],[f173,f131]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( relation(X1)
        & relation(X0) )
     => relation(relation_composition(X0,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmp.KWCFEtNa1R/Vampire---4.8_17919',dt_k5_relat_1) ).

fof(f173,plain,
    ! [X0,X1,X8,X7] :
      ( in(unordered_pair(unordered_pair(X7,sK12(X0,X1,X7,X8)),singleton(X7)),X0)
      | ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
      | ~ relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f164]) ).

fof(f164,plain,
    ! [X2,X0,X1,X8,X7] :
      ( in(unordered_pair(unordered_pair(X7,sK12(X0,X1,X7,X8)),singleton(X7)),X0)
      | ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
      | relation_composition(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f132,f142,f142]) ).

fof(f132,plain,
    ! [X2,X0,X1,X8,X7] :
      ( in(ordered_pair(X7,sK12(X0,X1,X7,X8)),X0)
      | ~ in(ordered_pair(X7,X8),X2)
      | relation_composition(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( relation_composition(X0,X1) = X2
                  | ( ( ! [X5] :
                          ( ~ in(ordered_pair(X5,sK10(X0,X1,X2)),X1)
                          | ~ in(ordered_pair(sK9(X0,X1,X2),X5),X0) )
                      | ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) )
                    & ( ( in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
                        & in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0) )
                      | in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) ) ) )
                & ( ! [X7,X8] :
                      ( ( in(ordered_pair(X7,X8),X2)
                        | ! [X9] :
                            ( ~ in(ordered_pair(X9,X8),X1)
                            | ~ in(ordered_pair(X7,X9),X0) ) )
                      & ( ( in(ordered_pair(sK12(X0,X1,X7,X8),X8),X1)
                          & in(ordered_pair(X7,sK12(X0,X1,X7,X8)),X0) )
                        | ~ in(ordered_pair(X7,X8),X2) ) )
                  | relation_composition(X0,X1) != X2 ) )
              | ~ relation(X2) )
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f86,f89,f88,f87]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ? [X3,X4] :
          ( ( ! [X5] :
                ( ~ in(ordered_pair(X5,X4),X1)
                | ~ in(ordered_pair(X3,X5),X0) )
            | ~ in(ordered_pair(X3,X4),X2) )
          & ( ? [X6] :
                ( in(ordered_pair(X6,X4),X1)
                & in(ordered_pair(X3,X6),X0) )
            | in(ordered_pair(X3,X4),X2) ) )
     => ( ( ! [X5] :
              ( ~ in(ordered_pair(X5,sK10(X0,X1,X2)),X1)
              | ~ in(ordered_pair(sK9(X0,X1,X2),X5),X0) )
          | ~ in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) )
        & ( ? [X6] :
              ( in(ordered_pair(X6,sK10(X0,X1,X2)),X1)
              & in(ordered_pair(sK9(X0,X1,X2),X6),X0) )
          | in(ordered_pair(sK9(X0,X1,X2),sK10(X0,X1,X2)),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ? [X6] :
          ( in(ordered_pair(X6,sK10(X0,X1,X2)),X1)
          & in(ordered_pair(sK9(X0,X1,X2),X6),X0) )
     => ( in(ordered_pair(sK11(X0,X1,X2),sK10(X0,X1,X2)),X1)
        & in(ordered_pair(sK9(X0,X1,X2),sK11(X0,X1,X2)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0,X1,X7,X8] :
      ( ? [X10] :
          ( in(ordered_pair(X10,X8),X1)
          & in(ordered_pair(X7,X10),X0) )
     => ( in(ordered_pair(sK12(X0,X1,X7,X8),X8),X1)
        & in(ordered_pair(X7,sK12(X0,X1,X7,X8)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( relation_composition(X0,X1) = X2
                  | ? [X3,X4] :
                      ( ( ! [X5] :
                            ( ~ in(ordered_pair(X5,X4),X1)
                            | ~ in(ordered_pair(X3,X5),X0) )
                        | ~ in(ordered_pair(X3,X4),X2) )
                      & ( ? [X6] :
                            ( in(ordered_pair(X6,X4),X1)
                            & in(ordered_pair(X3,X6),X0) )
                        | in(ordered_pair(X3,X4),X2) ) ) )
                & ( ! [X7,X8] :
                      ( ( in(ordered_pair(X7,X8),X2)
                        | ! [X9] :
                            ( ~ in(ordered_pair(X9,X8),X1)
                            | ~ in(ordered_pair(X7,X9),X0) ) )
                      & ( ? [X10] :
                            ( in(ordered_pair(X10,X8),X1)
                            & in(ordered_pair(X7,X10),X0) )
                        | ~ in(ordered_pair(X7,X8),X2) ) )
                  | relation_composition(X0,X1) != X2 ) )
              | ~ relation(X2) )
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( relation_composition(X0,X1) = X2
                  | ? [X3,X4] :
                      ( ( ! [X5] :
                            ( ~ in(ordered_pair(X5,X4),X1)
                            | ~ in(ordered_pair(X3,X5),X0) )
                        | ~ in(ordered_pair(X3,X4),X2) )
                      & ( ? [X5] :
                            ( in(ordered_pair(X5,X4),X1)
                            & in(ordered_pair(X3,X5),X0) )
                        | in(ordered_pair(X3,X4),X2) ) ) )
                & ( ! [X3,X4] :
                      ( ( in(ordered_pair(X3,X4),X2)
                        | ! [X5] :
                            ( ~ in(ordered_pair(X5,X4),X1)
                            | ~ in(ordered_pair(X3,X5),X0) ) )
                      & ( ? [X5] :
                            ( in(ordered_pair(X5,X4),X1)
                            & in(ordered_pair(X3,X5),X0) )
                        | ~ in(ordered_pair(X3,X4),X2) ) )
                  | relation_composition(X0,X1) != X2 ) )
              | ~ relation(X2) )
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( relation_composition(X0,X1) = X2
              <=> ! [X3,X4] :
                    ( in(ordered_pair(X3,X4),X2)
                  <=> ? [X5] :
                        ( in(ordered_pair(X5,X4),X1)
                        & in(ordered_pair(X3,X5),X0) ) ) )
              | ~ relation(X2) )
          | ~ relation(X1) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( relation(X1)
         => ! [X2] :
              ( relation(X2)
             => ( relation_composition(X0,X1) = X2
              <=> ! [X3,X4] :
                    ( in(ordered_pair(X3,X4),X2)
                  <=> ? [X5] :
                        ( in(ordered_pair(X5,X4),X1)
                        & in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.KWCFEtNa1R/Vampire---4.8_17919',d8_relat_1) ).

fof(f449,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK5(relation_composition(sK2,sK1),sK0))),relation_composition(sK2,sK1))
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f441,f274]) ).

fof(f274,plain,
    ( relation(relation_composition(sK2,sK1))
    | ~ spl16_4 ),
    inference(avatar_component_clause,[],[f273]) ).

fof(f273,plain,
    ( spl16_4
  <=> relation(relation_composition(sK2,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_4])]) ).

fof(f441,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK5(relation_composition(sK2,sK1),sK0))),relation_composition(sK2,sK1))
    | ~ relation(relation_composition(sK2,sK1))
    | ~ spl16_1 ),
    inference(resolution,[],[f176,f199]) ).

fof(f199,plain,
    ! [X0,X5] :
      ( ~ in(X5,relation_dom(X0))
      | in(unordered_pair(singleton(X5),unordered_pair(X5,sK5(X0,X5))),X0)
      | ~ relation(X0) ),
    inference(backward_demodulation,[],[f167,f143]) ).

fof(f167,plain,
    ! [X0,X5] :
      ( in(unordered_pair(unordered_pair(X5,sK5(X0,X5)),singleton(X5)),X0)
      | ~ in(X5,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f156]) ).

fof(f156,plain,
    ! [X0,X1,X5] :
      ( in(unordered_pair(unordered_pair(X5,sK5(X0,X5)),singleton(X5)),X0)
      | ~ in(X5,X1)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f109,f142]) ).

fof(f109,plain,
    ! [X0,X1,X5] :
      ( in(ordered_pair(X5,sK5(X0,X5)),X0)
      | ~ in(X5,X1)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f176,plain,
    ( in(sK0,relation_dom(relation_composition(sK2,sK1)))
    | ~ spl16_1 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f175,plain,
    ( spl16_1
  <=> in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_1])]) ).

fof(f529,plain,
    ( ~ spl16_1
    | spl16_3
    | ~ spl16_4 ),
    inference(avatar_contradiction_clause,[],[f528]) ).

fof(f528,plain,
    ( $false
    | ~ spl16_1
    | spl16_3
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f527,f477]) ).

fof(f477,plain,
    ( ! [X0] : ~ in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(X0,apply(sK2,sK0))),sK1)
    | spl16_3 ),
    inference(superposition,[],[f469,f143]) ).

fof(f469,plain,
    ( ! [X0] : ~ in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(apply(sK2,sK0),X0)),sK1)
    | spl16_3 ),
    inference(subsumption_resolution,[],[f467,f97]) ).

fof(f467,plain,
    ( ! [X0] :
        ( ~ in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(apply(sK2,sK0),X0)),sK1)
        | ~ relation(sK1) )
    | spl16_3 ),
    inference(resolution,[],[f185,f193]) ).

fof(f185,plain,
    ( ~ in(apply(sK2,sK0),relation_dom(sK1))
    | spl16_3 ),
    inference(avatar_component_clause,[],[f183]) ).

fof(f183,plain,
    ( spl16_3
  <=> in(apply(sK2,sK0),relation_dom(sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_3])]) ).

fof(f527,plain,
    ( in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(sK5(relation_composition(sK2,sK1),sK0),apply(sK2,sK0))),sK1)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(backward_demodulation,[],[f488,f521]) ).

fof(f488,plain,
    ( in(unordered_pair(singleton(sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0))),unordered_pair(sK5(relation_composition(sK2,sK1),sK0),sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0)))),sK1)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f487,f99]) ).

fof(f487,plain,
    ( in(unordered_pair(singleton(sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0))),unordered_pair(sK5(relation_composition(sK2,sK1),sK0),sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0)))),sK1)
    | ~ relation(sK2)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(subsumption_resolution,[],[f482,f97]) ).

fof(f482,plain,
    ( in(unordered_pair(singleton(sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0))),unordered_pair(sK5(relation_composition(sK2,sK1),sK0),sK12(sK2,sK1,sK0,sK5(relation_composition(sK2,sK1),sK0)))),sK1)
    | ~ relation(sK1)
    | ~ relation(sK2)
    | ~ spl16_1
    | ~ spl16_4 ),
    inference(resolution,[],[f449,f208]) ).

fof(f208,plain,
    ! [X0,X1,X8,X7] :
      ( ~ in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),relation_composition(X0,X1))
      | in(unordered_pair(singleton(sK12(X0,X1,X7,X8)),unordered_pair(X8,sK12(X0,X1,X7,X8))),X1)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f207,f143]) ).

fof(f207,plain,
    ! [X0,X1,X8,X7] :
      ( in(unordered_pair(singleton(sK12(X0,X1,X7,X8)),unordered_pair(sK12(X0,X1,X7,X8),X8)),X1)
      | ~ in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f196,f143]) ).

fof(f196,plain,
    ! [X0,X1,X8,X7] :
      ( ~ in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),relation_composition(X0,X1))
      | in(unordered_pair(unordered_pair(sK12(X0,X1,X7,X8),X8),singleton(sK12(X0,X1,X7,X8))),X1)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(backward_demodulation,[],[f191,f143]) ).

fof(f191,plain,
    ! [X0,X1,X8,X7] :
      ( in(unordered_pair(unordered_pair(sK12(X0,X1,X7,X8),X8),singleton(sK12(X0,X1,X7,X8))),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(subsumption_resolution,[],[f172,f131]) ).

fof(f172,plain,
    ! [X0,X1,X8,X7] :
      ( in(unordered_pair(unordered_pair(sK12(X0,X1,X7,X8),X8),singleton(sK12(X0,X1,X7,X8))),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
      | ~ relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f163]) ).

fof(f163,plain,
    ! [X2,X0,X1,X8,X7] :
      ( in(unordered_pair(unordered_pair(sK12(X0,X1,X7,X8),X8),singleton(sK12(X0,X1,X7,X8))),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
      | relation_composition(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f133,f142,f142]) ).

fof(f133,plain,
    ! [X2,X0,X1,X8,X7] :
      ( in(ordered_pair(sK12(X0,X1,X7,X8),X8),X1)
      | ~ in(ordered_pair(X7,X8),X2)
      | relation_composition(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f439,plain,
    ( ~ spl16_2
    | ~ spl16_3
    | ~ spl16_5 ),
    inference(avatar_contradiction_clause,[],[f438]) ).

fof(f438,plain,
    ( $false
    | ~ spl16_2
    | ~ spl16_3
    | ~ spl16_5 ),
    inference(subsumption_resolution,[],[f437,f97]) ).

fof(f437,plain,
    ( ~ relation(sK1)
    | ~ spl16_2
    | ~ spl16_3
    | ~ spl16_5 ),
    inference(subsumption_resolution,[],[f433,f278]) ).

fof(f278,plain,
    ( ! [X0] : ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,X0)),relation_composition(sK2,sK1))
    | ~ spl16_5 ),
    inference(avatar_component_clause,[],[f277]) ).

fof(f277,plain,
    ( spl16_5
  <=> ! [X0] : ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,X0)),relation_composition(sK2,sK1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl16_5])]) ).

fof(f433,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,apply(sK1,apply(sK2,sK0)))),relation_composition(sK2,sK1))
    | ~ relation(sK1)
    | ~ spl16_2
    | ~ spl16_3 ),
    inference(resolution,[],[f353,f321]) ).

fof(f321,plain,
    ( in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(apply(sK2,sK0),apply(sK1,apply(sK2,sK0)))),sK1)
    | ~ spl16_3 ),
    inference(subsumption_resolution,[],[f320,f97]) ).

fof(f320,plain,
    ( in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(apply(sK2,sK0),apply(sK1,apply(sK2,sK0)))),sK1)
    | ~ relation(sK1)
    | ~ spl16_3 ),
    inference(subsumption_resolution,[],[f314,f98]) ).

fof(f98,plain,
    function(sK1),
    inference(cnf_transformation,[],[f71]) ).

fof(f314,plain,
    ( in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(apply(sK2,sK0),apply(sK1,apply(sK2,sK0)))),sK1)
    | ~ function(sK1)
    | ~ relation(sK1)
    | ~ spl16_3 ),
    inference(resolution,[],[f198,f184]) ).

fof(f184,plain,
    ( in(apply(sK2,sK0),relation_dom(sK1))
    | ~ spl16_3 ),
    inference(avatar_component_clause,[],[f183]) ).

fof(f198,plain,
    ! [X0,X1] :
      ( ~ in(X1,relation_dom(X0))
      | in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(backward_demodulation,[],[f170,f143]) ).

fof(f170,plain,
    ! [X0,X1] :
      ( in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0)
      | ~ in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f158]) ).

fof(f158,plain,
    ! [X2,X0,X1] :
      ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
      | apply(X0,X1) != X2
      | ~ in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f113,f142]) ).

fof(f113,plain,
    ! [X2,X0,X1] :
      ( in(ordered_pair(X1,X2),X0)
      | apply(X0,X1) != X2
      | ~ in(X1,relation_dom(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f353,plain,
    ( ! [X0,X1] :
        ( ~ in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(apply(sK2,sK0),X0)),X1)
        | in(unordered_pair(singleton(sK0),unordered_pair(sK0,X0)),relation_composition(sK2,X1))
        | ~ relation(X1) )
    | ~ spl16_2 ),
    inference(subsumption_resolution,[],[f349,f99]) ).

fof(f349,plain,
    ( ! [X0,X1] :
        ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,X0)),relation_composition(sK2,X1))
        | ~ in(unordered_pair(singleton(apply(sK2,sK0)),unordered_pair(apply(sK2,sK0),X0)),X1)
        | ~ relation(X1)
        | ~ relation(sK2) )
    | ~ spl16_2 ),
    inference(resolution,[],[f206,f319]) ).

fof(f319,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,apply(sK2,sK0))),sK2)
    | ~ spl16_2 ),
    inference(subsumption_resolution,[],[f318,f99]) ).

fof(f318,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,apply(sK2,sK0))),sK2)
    | ~ relation(sK2)
    | ~ spl16_2 ),
    inference(subsumption_resolution,[],[f313,f100]) ).

fof(f313,plain,
    ( in(unordered_pair(singleton(sK0),unordered_pair(sK0,apply(sK2,sK0))),sK2)
    | ~ function(sK2)
    | ~ relation(sK2)
    | ~ spl16_2 ),
    inference(resolution,[],[f198,f180]) ).

fof(f180,plain,
    ( in(sK0,relation_dom(sK2))
    | ~ spl16_2 ),
    inference(avatar_component_clause,[],[f179]) ).

fof(f206,plain,
    ! [X0,X1,X8,X9,X7] :
      ( ~ in(unordered_pair(singleton(X7),unordered_pair(X7,X9)),X0)
      | in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),relation_composition(X0,X1))
      | ~ in(unordered_pair(singleton(X9),unordered_pair(X9,X8)),X1)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f205,f143]) ).

fof(f205,plain,
    ! [X0,X1,X8,X9,X7] :
      ( in(unordered_pair(singleton(X7),unordered_pair(X7,X8)),relation_composition(X0,X1))
      | ~ in(unordered_pair(singleton(X9),unordered_pair(X9,X8)),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(forward_demodulation,[],[f195,f143]) ).

fof(f195,plain,
    ! [X0,X1,X8,X9,X7] :
      ( ~ in(unordered_pair(singleton(X9),unordered_pair(X9,X8)),X1)
      | in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
      | ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(backward_demodulation,[],[f190,f143]) ).

fof(f190,plain,
    ! [X0,X1,X8,X9,X7] :
      ( in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
      | ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(subsumption_resolution,[],[f171,f131]) ).

fof(f171,plain,
    ! [X0,X1,X8,X9,X7] :
      ( in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),relation_composition(X0,X1))
      | ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
      | ~ relation(relation_composition(X0,X1))
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f162]) ).

fof(f162,plain,
    ! [X2,X0,X1,X8,X9,X7] :
      ( in(unordered_pair(unordered_pair(X7,X8),singleton(X7)),X2)
      | ~ in(unordered_pair(unordered_pair(X9,X8),singleton(X9)),X1)
      | ~ in(unordered_pair(unordered_pair(X7,X9),singleton(X7)),X0)
      | relation_composition(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(definition_unfolding,[],[f134,f142,f142,f142]) ).

fof(f134,plain,
    ! [X2,X0,X1,X8,X9,X7] :
      ( in(ordered_pair(X7,X8),X2)
      | ~ in(ordered_pair(X9,X8),X1)
      | ~ in(ordered_pair(X7,X9),X0)
      | relation_composition(X0,X1) != X2
      | ~ relation(X2)
      | ~ relation(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f90]) ).

fof(f293,plain,
    spl16_4,
    inference(avatar_contradiction_clause,[],[f292]) ).

fof(f292,plain,
    ( $false
    | spl16_4 ),
    inference(subsumption_resolution,[],[f291,f99]) ).

fof(f291,plain,
    ( ~ relation(sK2)
    | spl16_4 ),
    inference(subsumption_resolution,[],[f282,f97]) ).

fof(f282,plain,
    ( ~ relation(sK1)
    | ~ relation(sK2)
    | spl16_4 ),
    inference(resolution,[],[f275,f131]) ).

fof(f275,plain,
    ( ~ relation(relation_composition(sK2,sK1))
    | spl16_4 ),
    inference(avatar_component_clause,[],[f273]) ).

fof(f279,plain,
    ( ~ spl16_4
    | spl16_5
    | spl16_1 ),
    inference(avatar_split_clause,[],[f268,f175,f277,f273]) ).

fof(f268,plain,
    ( ! [X0] :
        ( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,X0)),relation_composition(sK2,sK1))
        | ~ relation(relation_composition(sK2,sK1)) )
    | spl16_1 ),
    inference(resolution,[],[f193,f177]) ).

fof(f177,plain,
    ( ~ in(sK0,relation_dom(relation_composition(sK2,sK1)))
    | spl16_1 ),
    inference(avatar_component_clause,[],[f175]) ).

fof(f188,plain,
    ( spl16_1
    | spl16_2 ),
    inference(avatar_split_clause,[],[f101,f179,f175]) ).

fof(f101,plain,
    ( in(sK0,relation_dom(sK2))
    | in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f187,plain,
    ( spl16_1
    | spl16_3 ),
    inference(avatar_split_clause,[],[f102,f183,f175]) ).

fof(f102,plain,
    ( in(apply(sK2,sK0),relation_dom(sK1))
    | in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f186,plain,
    ( ~ spl16_1
    | ~ spl16_2
    | ~ spl16_3 ),
    inference(avatar_split_clause,[],[f103,f183,f179,f175]) ).

fof(f103,plain,
    ( ~ in(apply(sK2,sK0),relation_dom(sK1))
    | ~ in(sK0,relation_dom(sK2))
    | ~ in(sK0,relation_dom(relation_composition(sK2,sK1))) ),
    inference(cnf_transformation,[],[f71]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU213+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35  % Computer : n022.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   : Tue Apr 30 16:11:58 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.KWCFEtNa1R/Vampire---4.8_17919
% 0.54/0.76  % (18116)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.54/0.76  % (18120)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.54/0.76  % (18122)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.54/0.76  % (18115)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.54/0.76  % (18117)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.54/0.76  % (18118)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.54/0.76  % (18119)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.54/0.76  % (18121)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.54/0.76  % (18120)Refutation not found, incomplete strategy% (18120)------------------------------
% 0.54/0.76  % (18120)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.76  % (18120)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.76  
% 0.54/0.76  % (18120)Memory used [KB]: 1119
% 0.54/0.76  % (18120)Time elapsed: 0.003 s
% 0.54/0.76  % (18120)Instructions burned: 5 (million)
% 0.54/0.76  % (18120)------------------------------
% 0.54/0.76  % (18120)------------------------------
% 0.54/0.76  % (18122)Refutation not found, incomplete strategy% (18122)------------------------------
% 0.54/0.76  % (18122)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.76  % (18122)Termination reason: Refutation not found, incomplete strategy
% 0.54/0.76  
% 0.54/0.76  % (18122)Memory used [KB]: 1085
% 0.54/0.76  % (18122)Time elapsed: 0.003 s
% 0.54/0.76  % (18122)Instructions burned: 6 (million)
% 0.54/0.76  % (18122)------------------------------
% 0.54/0.76  % (18122)------------------------------
% 0.54/0.76  % (18126)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.54/0.76  % (18127)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.54/0.77  % (18116)Instruction limit reached!
% 0.54/0.77  % (18116)------------------------------
% 0.54/0.77  % (18116)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.77  % (18116)Termination reason: Unknown
% 0.54/0.77  % (18116)Termination phase: Saturation
% 0.54/0.77  
% 0.54/0.77  % (18116)Memory used [KB]: 1617
% 0.54/0.77  % (18116)Time elapsed: 0.017 s
% 0.54/0.77  % (18116)Instructions burned: 52 (million)
% 0.54/0.77  % (18116)------------------------------
% 0.54/0.77  % (18116)------------------------------
% 0.54/0.78  % (18133)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.54/0.78  % (18118)Instruction limit reached!
% 0.54/0.78  % (18118)------------------------------
% 0.54/0.78  % (18118)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.78  % (18118)Termination reason: Unknown
% 0.54/0.78  % (18118)Termination phase: Saturation
% 0.54/0.78  
% 0.54/0.78  % (18118)Memory used [KB]: 1561
% 0.54/0.78  % (18118)Time elapsed: 0.019 s
% 0.54/0.78  % (18118)Instructions burned: 33 (million)
% 0.54/0.78  % (18118)------------------------------
% 0.54/0.78  % (18118)------------------------------
% 0.54/0.78  % (18126)Instruction limit reached!
% 0.54/0.78  % (18126)------------------------------
% 0.54/0.78  % (18126)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.78  % (18126)Termination reason: Unknown
% 0.54/0.78  % (18126)Termination phase: Saturation
% 0.62/0.78  
% 0.62/0.78  % (18126)Memory used [KB]: 2039
% 0.62/0.78  % (18126)Time elapsed: 0.017 s
% 0.62/0.78  % (18126)Instructions burned: 57 (million)
% 0.62/0.78  % (18127)Instruction limit reached!
% 0.62/0.78  % (18127)------------------------------
% 0.62/0.78  % (18127)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.78  % (18127)Termination reason: Unknown
% 0.62/0.78  % (18127)Termination phase: Saturation
% 0.62/0.78  
% 0.62/0.78  % (18127)Memory used [KB]: 1726
% 0.62/0.78  % (18127)Time elapsed: 0.017 s
% 0.62/0.78  % (18127)Instructions burned: 50 (million)
% 0.62/0.78  % (18127)------------------------------
% 0.62/0.78  % (18127)------------------------------
% 0.62/0.78  % (18126)------------------------------
% 0.62/0.78  % (18126)------------------------------
% 0.62/0.78  % (18119)Instruction limit reached!
% 0.62/0.78  % (18119)------------------------------
% 0.62/0.78  % (18119)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.78  % (18119)Termination reason: Unknown
% 0.62/0.78  % (18119)Termination phase: Saturation
% 0.62/0.78  
% 0.62/0.78  % (18119)Memory used [KB]: 1475
% 0.62/0.78  % (18119)Time elapsed: 0.022 s
% 0.62/0.78  % (18119)Instructions burned: 35 (million)
% 0.62/0.78  % (18119)------------------------------
% 0.62/0.78  % (18119)------------------------------
% 0.62/0.78  % (18137)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.62/0.78  % (18135)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.62/0.78  % (18138)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.62/0.78  % (18115)Instruction limit reached!
% 0.62/0.78  % (18115)------------------------------
% 0.62/0.78  % (18115)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.78  % (18115)Termination reason: Unknown
% 0.62/0.78  % (18115)Termination phase: Saturation
% 0.62/0.78  
% 0.62/0.78  % (18115)Memory used [KB]: 1401
% 0.62/0.78  % (18115)Time elapsed: 0.024 s
% 0.62/0.78  % (18115)Instructions burned: 35 (million)
% 0.62/0.78  % (18115)------------------------------
% 0.62/0.78  % (18115)------------------------------
% 0.62/0.78  % (18117)First to succeed.
% 0.62/0.78  % (18137)Refutation not found, incomplete strategy% (18137)------------------------------
% 0.62/0.78  % (18137)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.78  % (18137)Termination reason: Refutation not found, incomplete strategy
% 0.62/0.78  
% 0.62/0.78  % (18137)Memory used [KB]: 1147
% 0.62/0.78  % (18137)Time elapsed: 0.003 s
% 0.62/0.78  % (18137)Instructions burned: 8 (million)
% 0.62/0.78  % (18137)------------------------------
% 0.62/0.78  % (18137)------------------------------
% 0.62/0.78  % (18139)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.62/0.78  % (18141)lrs+1011_2:9_sil=2000:lsd=10:newcnf=on:i=117:sd=2:awrs=decay:ss=included:amm=off:ep=R_0 on Vampire---4 for (2995ds/117Mi)
% 0.62/0.79  % (18142)dis+1011_11:1_sil=2000:avsq=on:i=143:avsqr=1,16:ep=RS:rawr=on:aac=none:lsd=100:mep=off:fde=none:newcnf=on:bsr=unit_only_0 on Vampire---4 for (2995ds/143Mi)
% 0.62/0.79  % (18117)Refutation found. Thanks to Tanya!
% 0.62/0.79  % SZS status Theorem for Vampire---4
% 0.62/0.79  % SZS output start Proof for Vampire---4
% See solution above
% 0.62/0.79  % (18117)------------------------------
% 0.62/0.79  % (18117)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.62/0.79  % (18117)Termination reason: Refutation
% 0.62/0.79  
% 0.62/0.79  % (18117)Memory used [KB]: 1359
% 0.62/0.79  % (18117)Time elapsed: 0.029 s
% 0.62/0.79  % (18117)Instructions burned: 45 (million)
% 0.62/0.79  % (18117)------------------------------
% 0.62/0.79  % (18117)------------------------------
% 0.62/0.79  % (18088)Success in time 0.42 s
% 0.62/0.79  % Vampire---4.8 exiting
%------------------------------------------------------------------------------