TSTP Solution File: SEU221+3 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU221+3 : 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_uns --cores 0 -t %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 Aug 31 18:27:37 EDT 2022

% Result   : Theorem 0.21s 0.49s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   80 (  12 unt;   0 def)
%            Number of atoms       :  407 ( 124 equ)
%            Maximal formula atoms :   19 (   5 avg)
%            Number of connectives :  544 ( 217   ~; 201   |;  99   &)
%                                         (   8 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   1 con; 0-2 aty)
%            Number of variables   :  104 (  87   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f344,plain,
    $false,
    inference(subsumption_resolution,[],[f343,f190]) ).

fof(f190,plain,
    relation(sK9),
    inference(cnf_transformation,[],[f122]) ).

fof(f122,plain,
    ( function(sK9)
    & relation(sK9)
    & one_to_one(sK9)
    & ~ one_to_one(function_inverse(sK9)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f62,f121]) ).

fof(f121,plain,
    ( ? [X0] :
        ( function(X0)
        & relation(X0)
        & one_to_one(X0)
        & ~ one_to_one(function_inverse(X0)) )
   => ( function(sK9)
      & relation(sK9)
      & one_to_one(sK9)
      & ~ one_to_one(function_inverse(sK9)) ) ),
    introduced(choice_axiom,[]) ).

fof(f62,plain,
    ? [X0] :
      ( function(X0)
      & relation(X0)
      & one_to_one(X0)
      & ~ one_to_one(function_inverse(X0)) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ? [X0] :
      ( ~ one_to_one(function_inverse(X0))
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,negated_conjecture,
    ~ ! [X0] :
        ( ( function(X0)
          & relation(X0) )
       => ( one_to_one(X0)
         => one_to_one(function_inverse(X0)) ) ),
    inference(negated_conjecture,[],[f38]) ).

fof(f38,conjecture,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => one_to_one(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).

fof(f343,plain,
    ~ relation(sK9),
    inference(subsumption_resolution,[],[f341,f191]) ).

fof(f191,plain,
    function(sK9),
    inference(cnf_transformation,[],[f122]) ).

fof(f341,plain,
    ( ~ function(sK9)
    | ~ relation(sK9) ),
    inference(resolution,[],[f340,f187]) ).

fof(f187,plain,
    ! [X0] :
      ( function(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(function_inverse(X0))
        & relation(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).

fof(f340,plain,
    ~ function(function_inverse(sK9)),
    inference(subsumption_resolution,[],[f339,f281]) ).

fof(f281,plain,
    sK14(function_inverse(sK9)) != sK15(function_inverse(sK9)),
    inference(subsumption_resolution,[],[f280,f190]) ).

fof(f280,plain,
    ( ~ relation(sK9)
    | sK14(function_inverse(sK9)) != sK15(function_inverse(sK9)) ),
    inference(subsumption_resolution,[],[f278,f191]) ).

fof(f278,plain,
    ( sK14(function_inverse(sK9)) != sK15(function_inverse(sK9))
    | ~ function(sK9)
    | ~ relation(sK9) ),
    inference(resolution,[],[f277,f187]) ).

fof(f277,plain,
    ( ~ function(function_inverse(sK9))
    | sK14(function_inverse(sK9)) != sK15(function_inverse(sK9)) ),
    inference(subsumption_resolution,[],[f249,f245]) ).

fof(f245,plain,
    relation(function_inverse(sK9)),
    inference(subsumption_resolution,[],[f243,f190]) ).

fof(f243,plain,
    ( relation(function_inverse(sK9))
    | ~ relation(sK9) ),
    inference(resolution,[],[f191,f186]) ).

fof(f186,plain,
    ! [X0] :
      ( ~ function(X0)
      | relation(function_inverse(X0))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f249,plain,
    ( ~ relation(function_inverse(sK9))
    | sK14(function_inverse(sK9)) != sK15(function_inverse(sK9))
    | ~ function(function_inverse(sK9)) ),
    inference(resolution,[],[f188,f212]) ).

fof(f212,plain,
    ! [X0] :
      ( one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0)
      | sK15(X0) != sK14(X0) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f138,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ( ( one_to_one(X0)
          | ( apply(X0,sK15(X0)) = apply(X0,sK14(X0))
            & in(sK14(X0),relation_dom(X0))
            & sK15(X0) != sK14(X0)
            & in(sK15(X0),relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( apply(X0,X3) != apply(X0,X4)
              | ~ in(X3,relation_dom(X0))
              | X3 = X4
              | ~ in(X4,relation_dom(X0)) )
          | ~ one_to_one(X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f136,f137]) ).

fof(f137,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( apply(X0,X1) = apply(X0,X2)
          & in(X1,relation_dom(X0))
          & X1 != X2
          & in(X2,relation_dom(X0)) )
     => ( apply(X0,sK15(X0)) = apply(X0,sK14(X0))
        & in(sK14(X0),relation_dom(X0))
        & sK15(X0) != sK14(X0)
        & in(sK15(X0),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f136,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( apply(X0,X1) = apply(X0,X2)
              & in(X1,relation_dom(X0))
              & X1 != X2
              & in(X2,relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( apply(X0,X3) != apply(X0,X4)
              | ~ in(X3,relation_dom(X0))
              | X3 = X4
              | ~ in(X4,relation_dom(X0)) )
          | ~ one_to_one(X0) ) ) ),
    inference(rectify,[],[f135]) ).

fof(f135,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( apply(X0,X1) = apply(X0,X2)
              & in(X1,relation_dom(X0))
              & X1 != X2
              & in(X2,relation_dom(X0)) ) )
        & ( ! [X1,X2] :
              ( apply(X0,X1) != apply(X0,X2)
              | ~ in(X1,relation_dom(X0))
              | X1 = X2
              | ~ in(X2,relation_dom(X0)) )
          | ~ one_to_one(X0) ) ) ),
    inference(nnf_transformation,[],[f74]) ).

fof(f74,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( apply(X0,X1) != apply(X0,X2)
            | ~ in(X1,relation_dom(X0))
            | X1 = X2
            | ~ in(X2,relation_dom(X0)) ) ) ),
    inference(flattening,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( ( ! [X2,X1] :
            ( X1 = X2
            | ~ in(X1,relation_dom(X0))
            | ~ in(X2,relation_dom(X0))
            | apply(X0,X1) != apply(X0,X2) )
      <=> one_to_one(X0) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( ! [X2,X1] :
            ( ( in(X1,relation_dom(X0))
              & in(X2,relation_dom(X0))
              & apply(X0,X1) = apply(X0,X2) )
           => X1 = X2 )
      <=> one_to_one(X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).

fof(f188,plain,
    ~ one_to_one(function_inverse(sK9)),
    inference(cnf_transformation,[],[f122]) ).

fof(f339,plain,
    ( sK14(function_inverse(sK9)) = sK15(function_inverse(sK9))
    | ~ function(function_inverse(sK9)) ),
    inference(forward_demodulation,[],[f338,f319]) ).

fof(f319,plain,
    sK14(function_inverse(sK9)) = apply(sK9,apply(function_inverse(sK9),sK14(function_inverse(sK9)))),
    inference(subsumption_resolution,[],[f318,f191]) ).

fof(f318,plain,
    ( ~ function(sK9)
    | sK14(function_inverse(sK9)) = apply(sK9,apply(function_inverse(sK9),sK14(function_inverse(sK9)))) ),
    inference(subsumption_resolution,[],[f316,f190]) ).

fof(f316,plain,
    ( sK14(function_inverse(sK9)) = apply(sK9,apply(function_inverse(sK9),sK14(function_inverse(sK9))))
    | ~ relation(sK9)
    | ~ function(sK9) ),
    inference(resolution,[],[f296,f187]) ).

fof(f296,plain,
    ( ~ function(function_inverse(sK9))
    | sK14(function_inverse(sK9)) = apply(sK9,apply(function_inverse(sK9),sK14(function_inverse(sK9)))) ),
    inference(resolution,[],[f295,f258]) ).

fof(f258,plain,
    ( in(sK14(function_inverse(sK9)),relation_dom(function_inverse(sK9)))
    | ~ function(function_inverse(sK9)) ),
    inference(subsumption_resolution,[],[f246,f245]) ).

fof(f246,plain,
    ( ~ relation(function_inverse(sK9))
    | in(sK14(function_inverse(sK9)),relation_dom(function_inverse(sK9)))
    | ~ function(function_inverse(sK9)) ),
    inference(resolution,[],[f188,f213]) ).

fof(f213,plain,
    ! [X0] :
      ( one_to_one(X0)
      | ~ function(X0)
      | in(sK14(X0),relation_dom(X0))
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f295,plain,
    ! [X4] :
      ( ~ in(X4,relation_dom(function_inverse(sK9)))
      | apply(sK9,apply(function_inverse(sK9),X4)) = X4 ),
    inference(forward_demodulation,[],[f294,f254]) ).

fof(f254,plain,
    relation_rng(sK9) = relation_dom(function_inverse(sK9)),
    inference(subsumption_resolution,[],[f253,f190]) ).

fof(f253,plain,
    ( ~ relation(sK9)
    | relation_rng(sK9) = relation_dom(function_inverse(sK9)) ),
    inference(subsumption_resolution,[],[f242,f191]) ).

fof(f242,plain,
    ( ~ function(sK9)
    | relation_rng(sK9) = relation_dom(function_inverse(sK9))
    | ~ relation(sK9) ),
    inference(subsumption_resolution,[],[f241,f186]) ).

fof(f241,plain,
    ( ~ relation(sK9)
    | ~ function(sK9)
    | relation_rng(sK9) = relation_dom(function_inverse(sK9))
    | ~ relation(function_inverse(sK9)) ),
    inference(subsumption_resolution,[],[f231,f187]) ).

fof(f231,plain,
    ( ~ function(function_inverse(sK9))
    | relation_rng(sK9) = relation_dom(function_inverse(sK9))
    | ~ relation(function_inverse(sK9))
    | ~ relation(sK9)
    | ~ function(sK9) ),
    inference(resolution,[],[f189,f230]) ).

fof(f230,plain,
    ! [X0] :
      ( ~ one_to_one(X0)
      | relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(function_inverse(X0))
      | ~ relation(X0)
      | ~ function(function_inverse(X0)) ),
    inference(equality_resolution,[],[f163]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ~ one_to_one(X0)
      | relation_rng(X0) = relation_dom(X1)
      | function_inverse(X0) != X1
      | ~ relation(X1)
      | ~ function(X1)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f113]) ).

fof(f113,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ one_to_one(X0)
      | ! [X1] :
          ( ( ( ( ! [X2,X3] :
                    ( ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0))
                      | ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) ) )
                    & sP0(X0,X2,X3,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 )
            & ( function_inverse(X0) = X1
              | ( sK4(X0,X1) = apply(X0,sK5(X0,X1))
                & in(sK5(X0,X1),relation_dom(X0))
                & ( sK5(X0,X1) != apply(X1,sK4(X0,X1))
                  | ~ in(sK4(X0,X1),relation_rng(X0)) ) )
              | ~ sP0(X0,sK4(X0,X1),sK5(X0,X1),X1)
              | relation_rng(X0) != relation_dom(X1) ) )
          | ~ relation(X1)
          | ~ function(X1) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f111,f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ? [X4,X5] :
          ( ( apply(X0,X5) = X4
            & in(X5,relation_dom(X0))
            & ( apply(X1,X4) != X5
              | ~ in(X4,relation_rng(X0)) ) )
          | ~ sP0(X0,X4,X5,X1) )
     => ( ( sK4(X0,X1) = apply(X0,sK5(X0,X1))
          & in(sK5(X0,X1),relation_dom(X0))
          & ( sK5(X0,X1) != apply(X1,sK4(X0,X1))
            | ~ in(sK4(X0,X1),relation_rng(X0)) ) )
        | ~ sP0(X0,sK4(X0,X1),sK5(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ one_to_one(X0)
      | ! [X1] :
          ( ( ( ( ! [X2,X3] :
                    ( ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0))
                      | ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) ) )
                    & sP0(X0,X2,X3,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 )
            & ( function_inverse(X0) = X1
              | ? [X4,X5] :
                  ( ( apply(X0,X5) = X4
                    & in(X5,relation_dom(X0))
                    & ( apply(X1,X4) != X5
                      | ~ in(X4,relation_rng(X0)) ) )
                  | ~ sP0(X0,X4,X5,X1) )
              | relation_rng(X0) != relation_dom(X1) ) )
          | ~ relation(X1)
          | ~ function(X1) )
      | ~ relation(X0) ),
    inference(rectify,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ one_to_one(X0)
      | ! [X1] :
          ( ( ( ( ! [X2,X3] :
                    ( ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0))
                      | ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) ) )
                    & sP0(X0,X2,X3,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 )
            & ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( apply(X0,X3) = X2
                    & in(X3,relation_dom(X0))
                    & ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) ) )
                  | ~ sP0(X0,X2,X3,X1) )
              | relation_rng(X0) != relation_dom(X1) ) )
          | ~ relation(X1)
          | ~ function(X1) )
      | ~ relation(X0) ),
    inference(flattening,[],[f109]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ one_to_one(X0)
      | ! [X1] :
          ( ( ( ( ! [X2,X3] :
                    ( ( apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0))
                      | ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) ) )
                    & sP0(X0,X2,X3,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 )
            & ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( apply(X0,X3) = X2
                    & in(X3,relation_dom(X0))
                    & ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) ) )
                  | ~ sP0(X0,X2,X3,X1) )
              | relation_rng(X0) != relation_dom(X1) ) )
          | ~ relation(X1)
          | ~ function(X1) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ one_to_one(X0)
      | ! [X1] :
          ( ( ( ! [X2,X3] :
                  ( ( apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0))
                    | ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) ) )
                  & sP0(X0,X2,X3,X1) )
              & relation_rng(X0) = relation_dom(X1) )
          <=> function_inverse(X0) = X1 )
          | ~ relation(X1)
          | ~ function(X1) )
      | ~ relation(X0) ),
    inference(definition_folding,[],[f72,f96]) ).

fof(f96,plain,
    ! [X0,X2,X3,X1] :
      ( sP0(X0,X2,X3,X1)
    <=> ( ~ in(X2,relation_rng(X0))
        | ( apply(X0,X3) = X2
          & in(X3,relation_dom(X0)) )
        | apply(X1,X2) != X3 ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f72,plain,
    ! [X0] :
      ( ~ function(X0)
      | ~ one_to_one(X0)
      | ! [X1] :
          ( ( ( ! [X2,X3] :
                  ( ( apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0))
                    | ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) ) )
                  & ( ~ in(X2,relation_rng(X0))
                    | ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                    | apply(X1,X2) != X3 ) )
              & relation_rng(X0) = relation_dom(X1) )
          <=> function_inverse(X0) = X1 )
          | ~ relation(X1)
          | ~ function(X1) )
      | ~ relation(X0) ),
    inference(flattening,[],[f71]) ).

fof(f71,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( relation_rng(X0) = relation_dom(X1)
              & ! [X3,X2] :
                  ( ( ( apply(X0,X3) = X2
                      & in(X3,relation_dom(X0)) )
                    | apply(X1,X2) != X3
                    | ~ in(X2,relation_rng(X0)) )
                  & ( ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) )
                    | apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0)) ) ) ) )
          | ~ relation(X1)
          | ~ function(X1) )
      | ~ one_to_one(X0)
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0] :
      ( ( relation(X0)
        & function(X0) )
     => ( one_to_one(X0)
       => ! [X1] :
            ( ( relation(X1)
              & function(X1) )
           => ( function_inverse(X0) = X1
            <=> ( relation_rng(X0) = relation_dom(X1)
                & ! [X3,X2] :
                    ( ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                     => ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) ) )
                    & ( ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) )
                     => ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).

fof(f189,plain,
    one_to_one(sK9),
    inference(cnf_transformation,[],[f122]) ).

fof(f294,plain,
    ! [X4] :
      ( ~ in(X4,relation_rng(sK9))
      | apply(sK9,apply(function_inverse(sK9),X4)) = X4 ),
    inference(subsumption_resolution,[],[f293,f191]) ).

fof(f293,plain,
    ! [X4] :
      ( ~ in(X4,relation_rng(sK9))
      | apply(sK9,apply(function_inverse(sK9),X4)) = X4
      | ~ function(sK9) ),
    inference(subsumption_resolution,[],[f235,f190]) ).

fof(f235,plain,
    ! [X4] :
      ( ~ in(X4,relation_rng(sK9))
      | ~ relation(sK9)
      | ~ function(sK9)
      | apply(sK9,apply(function_inverse(sK9),X4)) = X4 ),
    inference(resolution,[],[f189,f221]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( ~ one_to_one(X1)
      | ~ function(X1)
      | ~ in(X0,relation_rng(X1))
      | ~ relation(X1)
      | apply(X1,apply(function_inverse(X1),X0)) = X0 ),
    inference(cnf_transformation,[],[f142]) ).

fof(f142,plain,
    ! [X0,X1] :
      ( ~ one_to_one(X1)
      | ~ in(X0,relation_rng(X1))
      | ~ relation(X1)
      | ( apply(X1,apply(function_inverse(X1),X0)) = X0
        & apply(relation_composition(function_inverse(X1),X1),X0) = X0 )
      | ~ function(X1) ),
    inference(rectify,[],[f59]) ).

fof(f59,plain,
    ! [X1,X0] :
      ( ~ one_to_one(X0)
      | ~ in(X1,relation_rng(X0))
      | ~ relation(X0)
      | ( apply(X0,apply(function_inverse(X0),X1)) = X1
        & apply(relation_composition(function_inverse(X0),X0),X1) = X1 )
      | ~ function(X0) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ! [X1,X0] :
      ( ( apply(X0,apply(function_inverse(X0),X1)) = X1
        & apply(relation_composition(function_inverse(X0),X0),X1) = X1 )
      | ~ one_to_one(X0)
      | ~ in(X1,relation_rng(X0))
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X1,X0] :
      ( ( relation(X0)
        & function(X0) )
     => ( ( one_to_one(X0)
          & in(X1,relation_rng(X0)) )
       => ( apply(X0,apply(function_inverse(X0),X1)) = X1
          & apply(relation_composition(function_inverse(X0),X0),X1) = X1 ) ) ),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X1,X0] :
      ( ( function(X1)
        & relation(X1) )
     => ( ( one_to_one(X1)
          & in(X0,relation_rng(X1)) )
       => ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
          & apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).

fof(f338,plain,
    ( ~ function(function_inverse(sK9))
    | apply(sK9,apply(function_inverse(sK9),sK14(function_inverse(sK9)))) = sK15(function_inverse(sK9)) ),
    inference(forward_demodulation,[],[f297,f323]) ).

fof(f323,plain,
    apply(function_inverse(sK9),sK14(function_inverse(sK9))) = apply(function_inverse(sK9),sK15(function_inverse(sK9))),
    inference(subsumption_resolution,[],[f322,f190]) ).

fof(f322,plain,
    ( apply(function_inverse(sK9),sK14(function_inverse(sK9))) = apply(function_inverse(sK9),sK15(function_inverse(sK9)))
    | ~ relation(sK9) ),
    inference(subsumption_resolution,[],[f320,f191]) ).

fof(f320,plain,
    ( ~ function(sK9)
    | apply(function_inverse(sK9),sK14(function_inverse(sK9))) = apply(function_inverse(sK9),sK15(function_inverse(sK9)))
    | ~ relation(sK9) ),
    inference(resolution,[],[f308,f187]) ).

fof(f308,plain,
    ( ~ function(function_inverse(sK9))
    | apply(function_inverse(sK9),sK14(function_inverse(sK9))) = apply(function_inverse(sK9),sK15(function_inverse(sK9))) ),
    inference(subsumption_resolution,[],[f250,f245]) ).

fof(f250,plain,
    ( apply(function_inverse(sK9),sK14(function_inverse(sK9))) = apply(function_inverse(sK9),sK15(function_inverse(sK9)))
    | ~ relation(function_inverse(sK9))
    | ~ function(function_inverse(sK9)) ),
    inference(resolution,[],[f188,f214]) ).

fof(f214,plain,
    ! [X0] :
      ( one_to_one(X0)
      | apply(X0,sK15(X0)) = apply(X0,sK14(X0))
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f138]) ).

fof(f297,plain,
    ( ~ function(function_inverse(sK9))
    | apply(sK9,apply(function_inverse(sK9),sK15(function_inverse(sK9)))) = sK15(function_inverse(sK9)) ),
    inference(resolution,[],[f295,f271]) ).

fof(f271,plain,
    ( in(sK15(function_inverse(sK9)),relation_dom(function_inverse(sK9)))
    | ~ function(function_inverse(sK9)) ),
    inference(subsumption_resolution,[],[f247,f245]) ).

fof(f247,plain,
    ( ~ relation(function_inverse(sK9))
    | ~ function(function_inverse(sK9))
    | in(sK15(function_inverse(sK9)),relation_dom(function_inverse(sK9))) ),
    inference(resolution,[],[f188,f211]) ).

fof(f211,plain,
    ! [X0] :
      ( one_to_one(X0)
      | ~ relation(X0)
      | ~ function(X0)
      | in(sK15(X0),relation_dom(X0)) ),
    inference(cnf_transformation,[],[f138]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU221+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 15:01:00 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.21/0.44  % (23452)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.21/0.46  % (23457)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.47  % (23480)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 0.21/0.48  % (23464)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.21/0.48  % (23457)First to succeed.
% 0.21/0.49  % (23457)Refutation found. Thanks to Tanya!
% 0.21/0.49  % SZS status Theorem for theBenchmark
% 0.21/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49  % (23457)------------------------------
% 0.21/0.49  % (23457)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49  % (23457)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49  % (23457)Termination reason: Refutation
% 0.21/0.49  
% 0.21/0.49  % (23457)Memory used [KB]: 1663
% 0.21/0.49  % (23457)Time elapsed: 0.070 s
% 0.21/0.49  % (23457)Instructions burned: 8 (million)
% 0.21/0.49  % (23457)------------------------------
% 0.21/0.49  % (23457)------------------------------
% 0.21/0.49  % (23451)Success in time 0.136 s
%------------------------------------------------------------------------------