TSTP Solution File: SEU003+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU003+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n020.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 Aug 31 18:31:42 EDT 2022

% Result   : Theorem 1.71s 0.61s
% Output   : Refutation 1.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   25
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   69 (  14 unt;   0 def)
%            Number of atoms       :  329 (  51 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  385 ( 125   ~; 144   |;  84   &)
%                                         (  13 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   2 con; 0-2 aty)
%            Number of variables   :  135 ( 110   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f891,plain,
    $false,
    inference(subsumption_resolution,[],[f885,f149]) ).

fof(f149,plain,
    ~ subset(relation_rng(sK1),relation_dom(sK0)),
    inference(cnf_transformation,[],[f95]) ).

fof(f95,plain,
    ( ~ subset(relation_rng(sK1),relation_dom(sK0))
    & relation(sK1)
    & relation_dom(sK1) = relation_dom(relation_composition(sK1,sK0))
    & function(sK1)
    & relation(sK0)
    & function(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f60,f94,f93]) ).

fof(f93,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ~ subset(relation_rng(X1),relation_dom(X0))
            & relation(X1)
            & relation_dom(X1) = relation_dom(relation_composition(X1,X0))
            & function(X1) )
        & relation(X0)
        & function(X0) )
   => ( ? [X1] :
          ( ~ subset(relation_rng(X1),relation_dom(sK0))
          & relation(X1)
          & relation_dom(X1) = relation_dom(relation_composition(X1,sK0))
          & function(X1) )
      & relation(sK0)
      & function(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f94,plain,
    ( ? [X1] :
        ( ~ subset(relation_rng(X1),relation_dom(sK0))
        & relation(X1)
        & relation_dom(X1) = relation_dom(relation_composition(X1,sK0))
        & function(X1) )
   => ( ~ subset(relation_rng(sK1),relation_dom(sK0))
      & relation(sK1)
      & relation_dom(sK1) = relation_dom(relation_composition(sK1,sK0))
      & function(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ subset(relation_rng(X1),relation_dom(X0))
          & relation(X1)
          & relation_dom(X1) = relation_dom(relation_composition(X1,X0))
          & function(X1) )
      & relation(X0)
      & function(X0) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ? [X0] :
      ( ? [X1] :
          ( ~ subset(relation_rng(X1),relation_dom(X0))
          & relation_dom(X1) = relation_dom(relation_composition(X1,X0))
          & function(X1)
          & relation(X1) )
      & relation(X0)
      & function(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,negated_conjecture,
    ~ ! [X0] :
        ( ( relation(X0)
          & function(X0) )
       => ! [X1] :
            ( ( function(X1)
              & relation(X1) )
           => ( relation_dom(X1) = relation_dom(relation_composition(X1,X0))
             => subset(relation_rng(X1),relation_dom(X0)) ) ) ),
    inference(negated_conjecture,[],[f30]) ).

fof(f30,conjecture,
    ! [X0] :
      ( ( relation(X0)
        & function(X0) )
     => ! [X1] :
          ( ( function(X1)
            & relation(X1) )
         => ( relation_dom(X1) = relation_dom(relation_composition(X1,X0))
           => subset(relation_rng(X1),relation_dom(X0)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_funct_1) ).

fof(f885,plain,
    subset(relation_rng(sK1),relation_dom(sK0)),
    inference(resolution,[],[f841,f209]) ).

fof(f209,plain,
    ! [X0,X1] :
      ( in(sK14(X0,X1),X0)
      | subset(X1,X0) ),
    inference(consistent_polarity_flipping,[],[f186]) ).

fof(f186,plain,
    ! [X0,X1] :
      ( ~ in(sK14(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f124,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ( in(sK14(X0,X1),X1)
          & ~ in(sK14(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f122,f123]) ).

fof(f123,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( in(X3,X1)
          & ~ in(X3,X0) )
     => ( in(sK14(X0,X1),X1)
        & ~ in(sK14(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X3] :
            ( in(X3,X1)
            & ~ in(X3,X0) ) ) ),
    inference(rectify,[],[f121]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) )
      & ( subset(X1,X0)
        | ? [X2] :
            ( in(X2,X1)
            & ~ in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) )
    <=> subset(X1,X0) ),
    inference(rectify,[],[f4]) ).

fof(f4,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f841,plain,
    ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(sK0)),
    inference(subsumption_resolution,[],[f840,f149]) ).

fof(f840,plain,
    ( ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(sK0))
    | subset(relation_rng(sK1),relation_dom(sK0)) ),
    inference(resolution,[],[f772,f199]) ).

fof(f199,plain,
    ! [X0,X1] :
      ( ~ in(sK14(X0,X1),X1)
      | subset(X1,X0) ),
    inference(consistent_polarity_flipping,[],[f187]) ).

fof(f187,plain,
    ! [X0,X1] :
      ( in(sK14(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f772,plain,
    ( in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_rng(sK1))
    | ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(sK0)) ),
    inference(subsumption_resolution,[],[f771,f216]) ).

fof(f216,plain,
    ~ relation(sK1),
    inference(consistent_polarity_flipping,[],[f148]) ).

fof(f148,plain,
    relation(sK1),
    inference(cnf_transformation,[],[f95]) ).

fof(f771,plain,
    ( relation(sK1)
    | ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(sK0))
    | in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_rng(sK1)) ),
    inference(subsumption_resolution,[],[f768,f195]) ).

fof(f195,plain,
    ~ function(sK1),
    inference(consistent_polarity_flipping,[],[f146]) ).

fof(f146,plain,
    function(sK1),
    inference(cnf_transformation,[],[f95]) ).

fof(f768,plain,
    ( ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(sK0))
    | function(sK1)
    | in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_rng(sK1))
    | relation(sK1) ),
    inference(resolution,[],[f767,f196]) ).

fof(f196,plain,
    ! [X2,X0] :
      ( ~ in(sK9(X0,X2),relation_dom(X0))
      | in(X2,relation_rng(X0))
      | function(X0)
      | relation(X0) ),
    inference(consistent_polarity_flipping,[],[f190]) ).

fof(f190,plain,
    ! [X2,X0] :
      ( ~ relation(X0)
      | ~ in(X2,relation_rng(X0))
      | in(sK9(X0,X2),relation_dom(X0))
      | ~ function(X0) ),
    inference(equality_resolution,[],[f176]) ).

fof(f176,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | in(sK9(X0,X2),relation_dom(X0))
      | ~ in(X2,X1)
      | relation_rng(X0) != X1 ),
    inference(cnf_transformation,[],[f116]) ).

fof(f116,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1] :
          ( ( ! [X2] :
                ( ( ( apply(X0,sK9(X0,X2)) = X2
                    & in(sK9(X0,X2),relation_dom(X0)) )
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X4] :
                      ( apply(X0,X4) != X2
                      | ~ in(X4,relation_dom(X0)) ) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ( ( ~ in(sK10(X0,X1),X1)
                | ! [X6] :
                    ( apply(X0,X6) != sK10(X0,X1)
                    | ~ in(X6,relation_dom(X0)) ) )
              & ( in(sK10(X0,X1),X1)
                | ( sK10(X0,X1) = apply(X0,sK11(X0,X1))
                  & in(sK11(X0,X1),relation_dom(X0)) ) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11])],[f112,f115,f114,f113]) ).

fof(f113,plain,
    ! [X0,X2] :
      ( ? [X3] :
          ( apply(X0,X3) = X2
          & in(X3,relation_dom(X0)) )
     => ( apply(X0,sK9(X0,X2)) = X2
        & in(sK9(X0,X2),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ( ~ in(X5,X1)
            | ! [X6] :
                ( apply(X0,X6) != X5
                | ~ in(X6,relation_dom(X0)) ) )
          & ( in(X5,X1)
            | ? [X7] :
                ( apply(X0,X7) = X5
                & in(X7,relation_dom(X0)) ) ) )
     => ( ( ~ in(sK10(X0,X1),X1)
          | ! [X6] :
              ( apply(X0,X6) != sK10(X0,X1)
              | ~ in(X6,relation_dom(X0)) ) )
        & ( in(sK10(X0,X1),X1)
          | ? [X7] :
              ( sK10(X0,X1) = apply(X0,X7)
              & in(X7,relation_dom(X0)) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ! [X0,X1] :
      ( ? [X7] :
          ( sK10(X0,X1) = apply(X0,X7)
          & in(X7,relation_dom(X0)) )
     => ( sK10(X0,X1) = apply(X0,sK11(X0,X1))
        & in(sK11(X0,X1),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f112,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1] :
          ( ( ! [X2] :
                ( ( ? [X3] :
                      ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X4] :
                      ( apply(X0,X4) != X2
                      | ~ in(X4,relation_dom(X0)) ) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ? [X5] :
                ( ( ~ in(X5,X1)
                  | ! [X6] :
                      ( apply(X0,X6) != X5
                      | ~ in(X6,relation_dom(X0)) ) )
                & ( in(X5,X1)
                  | ? [X7] :
                      ( apply(X0,X7) = X5
                      & in(X7,relation_dom(X0)) ) ) ) ) ) ),
    inference(rectify,[],[f111]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1] :
          ( ( ! [X2] :
                ( ( ? [X3] :
                      ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X3] :
                      ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) ) ) )
            | relation_rng(X0) != X1 )
          & ( relation_rng(X0) = X1
            | ? [X2] :
                ( ( ~ in(X2,X1)
                  | ! [X3] :
                      ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) ) )
                & ( in(X2,X1)
                  | ? [X3] :
                      ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) ) ) ) ) ) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ relation(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) )
            <=> in(X2,X1) )
        <=> relation_rng(X0) = X1 ) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) )
            <=> in(X2,X1) )
        <=> relation_rng(X0) = X1 )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1] :
          ( ! [X2] :
              ( ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) )
            <=> in(X2,X1) )
        <=> relation_rng(X0) = X1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).

fof(f767,plain,
    ( in(sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1))),relation_dom(sK1))
    | ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(sK0)) ),
    inference(subsumption_resolution,[],[f766,f207]) ).

fof(f207,plain,
    ~ relation(sK0),
    inference(consistent_polarity_flipping,[],[f145]) ).

fof(f145,plain,
    relation(sK0),
    inference(cnf_transformation,[],[f95]) ).

fof(f766,plain,
    ( relation(sK0)
    | in(sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1))),relation_dom(sK1))
    | ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(sK0)) ),
    inference(subsumption_resolution,[],[f760,f214]) ).

fof(f214,plain,
    ~ function(sK0),
    inference(consistent_polarity_flipping,[],[f144]) ).

fof(f144,plain,
    function(sK0),
    inference(cnf_transformation,[],[f95]) ).

fof(f760,plain,
    ( ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(sK0))
    | function(sK0)
    | relation(sK0)
    | in(sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1))),relation_dom(sK1)) ),
    inference(superposition,[],[f537,f147]) ).

fof(f147,plain,
    relation_dom(sK1) = relation_dom(relation_composition(sK1,sK0)),
    inference(cnf_transformation,[],[f95]) ).

fof(f537,plain,
    ! [X1] :
      ( in(sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1))),relation_dom(relation_composition(sK1,X1)))
      | relation(X1)
      | function(X1)
      | ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(X1)) ),
    inference(subsumption_resolution,[],[f536,f216]) ).

fof(f536,plain,
    ! [X1] :
      ( relation(sK1)
      | relation(X1)
      | function(X1)
      | in(sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1))),relation_dom(relation_composition(sK1,X1)))
      | ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(X1)) ),
    inference(subsumption_resolution,[],[f533,f195]) ).

fof(f533,plain,
    ! [X1] :
      ( function(sK1)
      | ~ in(sK14(relation_dom(sK0),relation_rng(sK1)),relation_dom(X1))
      | in(sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1))),relation_dom(relation_composition(sK1,X1)))
      | relation(X1)
      | relation(sK1)
      | function(X1) ),
    inference(superposition,[],[f206,f526]) ).

fof(f526,plain,
    sK14(relation_dom(sK0),relation_rng(sK1)) = apply(sK1,sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1)))),
    inference(subsumption_resolution,[],[f525,f216]) ).

fof(f525,plain,
    ( sK14(relation_dom(sK0),relation_rng(sK1)) = apply(sK1,sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1))))
    | relation(sK1) ),
    inference(subsumption_resolution,[],[f523,f195]) ).

fof(f523,plain,
    ( sK14(relation_dom(sK0),relation_rng(sK1)) = apply(sK1,sK9(sK1,sK14(relation_dom(sK0),relation_rng(sK1))))
    | function(sK1)
    | relation(sK1) ),
    inference(resolution,[],[f301,f149]) ).

fof(f301,plain,
    ! [X0,X1] :
      ( subset(relation_rng(X0),X1)
      | relation(X0)
      | function(X0)
      | apply(X0,sK9(X0,sK14(X1,relation_rng(X0)))) = sK14(X1,relation_rng(X0)) ),
    inference(resolution,[],[f237,f199]) ).

fof(f237,plain,
    ! [X2,X0] :
      ( in(X2,relation_rng(X0))
      | function(X0)
      | apply(X0,sK9(X0,X2)) = X2
      | relation(X0) ),
    inference(consistent_polarity_flipping,[],[f189]) ).

fof(f189,plain,
    ! [X2,X0] :
      ( apply(X0,sK9(X0,X2)) = X2
      | ~ function(X0)
      | ~ relation(X0)
      | ~ in(X2,relation_rng(X0)) ),
    inference(equality_resolution,[],[f177]) ).

fof(f177,plain,
    ! [X2,X0,X1] :
      ( ~ function(X0)
      | ~ relation(X0)
      | apply(X0,sK9(X0,X2)) = X2
      | ~ in(X2,X1)
      | relation_rng(X0) != X1 ),
    inference(cnf_transformation,[],[f116]) ).

fof(f206,plain,
    ! [X2,X0,X1] :
      ( ~ in(apply(X2,X0),relation_dom(X1))
      | function(X2)
      | relation(X1)
      | function(X1)
      | in(X0,relation_dom(relation_composition(X2,X1)))
      | relation(X2) ),
    inference(consistent_polarity_flipping,[],[f133]) ).

fof(f133,plain,
    ! [X2,X0,X1] :
      ( ~ relation(X2)
      | ~ relation(X1)
      | ~ function(X1)
      | ~ in(X0,relation_dom(relation_composition(X2,X1)))
      | in(apply(X2,X0),relation_dom(X1))
      | ~ function(X2) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f87,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(X0,relation_dom(relation_composition(X2,X1)))
              | ~ in(apply(X2,X0),relation_dom(X1))
              | ~ in(X0,relation_dom(X2)) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(rectify,[],[f86]) ).

fof(f86,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( ( ( in(apply(X2,X1),relation_dom(X0))
                & in(X1,relation_dom(X2)) )
              | ~ in(X1,relation_dom(relation_composition(X2,X0))) )
            & ( in(X1,relation_dom(relation_composition(X2,X0)))
              | ~ in(apply(X2,X1),relation_dom(X0))
              | ~ in(X1,relation_dom(X2)) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(flattening,[],[f85]) ).

fof(f85,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( ( ( in(apply(X2,X1),relation_dom(X0))
                & in(X1,relation_dom(X2)) )
              | ~ in(X1,relation_dom(relation_composition(X2,X0))) )
            & ( in(X1,relation_dom(relation_composition(X2,X0)))
              | ~ in(apply(X2,X1),relation_dom(X0))
              | ~ in(X1,relation_dom(X2)) ) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(nnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( ( in(apply(X2,X1),relation_dom(X0))
              & in(X1,relation_dom(X2)) )
          <=> in(X1,relation_dom(relation_composition(X2,X0))) )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(flattening,[],[f70]) ).

fof(f70,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( ( in(apply(X2,X1),relation_dom(X0))
              & in(X1,relation_dom(X2)) )
          <=> in(X1,relation_dom(relation_composition(X2,X0))) )
          | ~ relation(X2)
          | ~ function(X2) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X1,X0] :
      ( ( relation(X0)
        & function(X0) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( ( in(apply(X2,X1),relation_dom(X0))
              & in(X1,relation_dom(X2)) )
          <=> in(X1,relation_dom(relation_composition(X2,X0))) ) ) ),
    inference(rectify,[],[f29]) ).

fof(f29,axiom,
    ! [X1,X0] :
      ( ( function(X1)
        & relation(X1) )
     => ! [X2] :
          ( ( relation(X2)
            & function(X2) )
         => ( in(X0,relation_dom(relation_composition(X2,X1)))
          <=> ( in(X0,relation_dom(X2))
              & in(apply(X2,X0),relation_dom(X1)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SEU003+1 : TPTP v8.1.0. Released v3.2.0.
% 0.14/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n020.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 Aug 30 14:36:15 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.48  % (1149)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.48  % (1122)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.51  % (1123)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51  % (1122)Instruction limit reached!
% 0.21/0.51  % (1122)------------------------------
% 0.21/0.51  % (1122)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.51  % (1122)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.51  % (1122)Termination reason: Unknown
% 0.21/0.51  % (1122)Termination phase: Saturation
% 0.21/0.51  
% 0.21/0.51  % (1122)Memory used [KB]: 1407
% 0.21/0.51  % (1122)Time elapsed: 0.085 s
% 0.21/0.51  % (1122)Instructions burned: 38 (million)
% 0.21/0.51  % (1122)------------------------------
% 0.21/0.51  % (1122)------------------------------
% 0.21/0.51  % (1142)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.52  % (1146)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.52  % (1132)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.52  % (1136)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.21/0.53  % (1150)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.53  % (1125)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.21/0.53  % (1127)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53  % (1151)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.53  % (1124)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.53  % (1120)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.21/0.54  % (1138)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.21/0.54  % (1121)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.54  % (1152)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.21/0.54  % (1135)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.21/0.54  % (1121)Refutation not found, incomplete strategy% (1121)------------------------------
% 0.21/0.54  % (1121)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54  % (1121)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54  % (1121)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.54  
% 0.21/0.54  % (1121)Memory used [KB]: 5628
% 0.21/0.54  % (1121)Time elapsed: 0.137 s
% 0.21/0.54  % (1121)Instructions burned: 6 (million)
% 0.21/0.54  % (1121)------------------------------
% 0.21/0.54  % (1121)------------------------------
% 0.21/0.54  % (1137)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.54  % (1143)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.21/0.54  % (1144)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.55  % (1129)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.55  % (1139)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.55  % (1129)Instruction limit reached!
% 0.21/0.55  % (1129)------------------------------
% 0.21/0.55  % (1129)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.55  % (1129)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.55  % (1129)Termination reason: Unknown
% 0.21/0.55  % (1129)Termination phase: Property scanning
% 0.21/0.55  
% 0.21/0.55  % (1129)Memory used [KB]: 895
% 0.21/0.55  % (1129)Time elapsed: 0.002 s
% 0.21/0.55  % (1129)Instructions burned: 3 (million)
% 0.21/0.55  % (1129)------------------------------
% 0.21/0.55  % (1129)------------------------------
% 0.21/0.55  % (1133)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.55  % (1145)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.21/0.55  % (1149)Instruction limit reached!
% 0.21/0.55  % (1149)------------------------------
% 0.21/0.55  % (1149)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.55  % (1149)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.55  % (1149)Termination reason: Unknown
% 0.21/0.55  % (1149)Termination phase: Saturation
% 0.21/0.55  
% 0.21/0.55  % (1149)Memory used [KB]: 6780
% 0.21/0.55  % (1149)Time elapsed: 0.054 s
% 0.21/0.55  % (1149)Instructions burned: 68 (million)
% 0.21/0.55  % (1149)------------------------------
% 0.21/0.55  % (1149)------------------------------
% 0.21/0.55  % (1147)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.55  TRYING [1]
% 0.21/0.55  TRYING [2]
% 0.21/0.55  % (1134)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.55  TRYING [1]
% 1.52/0.55  TRYING [2]
% 1.52/0.55  TRYING [3]
% 1.52/0.55  % (1128)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.52/0.56  TRYING [3]
% 1.52/0.56  % (1130)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.52/0.56  % (1128)Instruction limit reached!
% 1.52/0.56  % (1128)------------------------------
% 1.52/0.56  % (1128)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.56  % (1128)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.56  % (1128)Termination reason: Unknown
% 1.52/0.56  % (1128)Termination phase: Saturation
% 1.52/0.56  
% 1.52/0.56  % (1128)Memory used [KB]: 5628
% 1.52/0.56  % (1128)Time elapsed: 0.127 s
% 1.52/0.56  % (1128)Instructions burned: 8 (million)
% 1.52/0.56  % (1128)------------------------------
% 1.52/0.56  % (1128)------------------------------
% 1.52/0.56  % (1131)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.52/0.56  % (1148)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.52/0.57  TRYING [1]
% 1.52/0.57  TRYING [2]
% 1.52/0.57  TRYING [3]
% 1.71/0.58  TRYING [4]
% 1.71/0.58  TRYING [4]
% 1.71/0.59  TRYING [4]
% 1.71/0.60  % (1142)First to succeed.
% 1.71/0.60  % (1227)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/388Mi)
% 1.71/0.60  % (1127)Instruction limit reached!
% 1.71/0.60  % (1127)------------------------------
% 1.71/0.60  % (1127)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.60  % (1127)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.60  % (1127)Termination reason: Unknown
% 1.71/0.60  % (1127)Termination phase: Finite model building SAT solving
% 1.71/0.60  
% 1.71/0.60  % (1127)Memory used [KB]: 7036
% 1.71/0.60  % (1127)Time elapsed: 0.169 s
% 1.71/0.60  % (1127)Instructions burned: 51 (million)
% 1.71/0.60  % (1127)------------------------------
% 1.71/0.60  % (1127)------------------------------
% 1.71/0.61  % (1123)Instruction limit reached!
% 1.71/0.61  % (1123)------------------------------
% 1.71/0.61  % (1123)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.61  % (1123)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.61  % (1123)Termination reason: Unknown
% 1.71/0.61  % (1123)Termination phase: Saturation
% 1.71/0.61  
% 1.71/0.61  % (1123)Memory used [KB]: 5884
% 1.71/0.61  % (1123)Time elapsed: 0.198 s
% 1.71/0.61  % (1123)Instructions burned: 51 (million)
% 1.71/0.61  % (1123)------------------------------
% 1.71/0.61  % (1123)------------------------------
% 1.71/0.61  TRYING [5]
% 1.71/0.61  % (1142)Refutation found. Thanks to Tanya!
% 1.71/0.61  % SZS status Theorem for theBenchmark
% 1.71/0.61  % SZS output start Proof for theBenchmark
% See solution above
% 1.71/0.62  % (1142)------------------------------
% 1.71/0.62  % (1142)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.62  % (1142)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.62  % (1142)Termination reason: Refutation
% 1.71/0.62  
% 1.71/0.62  % (1142)Memory used [KB]: 1407
% 1.71/0.62  % (1142)Time elapsed: 0.209 s
% 1.71/0.62  % (1142)Instructions burned: 42 (million)
% 1.71/0.62  % (1142)------------------------------
% 1.71/0.62  % (1142)------------------------------
% 1.71/0.62  % (1116)Success in time 0.255 s
%------------------------------------------------------------------------------