TSTP Solution File: SEU221+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SEU221+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n016.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 : Thu Aug 31 17:57:02 EDT 2023

% Result   : Theorem 0.21s 0.46s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   75 (  11 unt;   0 def)
%            Number of atoms       :  406 ( 119 equ)
%            Maximal formula atoms :   19 (   5 avg)
%            Number of connectives :  548 ( 217   ~; 211   |;  95   &)
%                                         (   8 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-2 aty)
%            Number of variables   :  103 (;  86   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f953,plain,
    $false,
    inference(unit_resulting_resolution,[],[f257,f260,f216,f952,f164]) ).

fof(f164,plain,
    ! [X0] :
      ( sK5(X0) != sK6(X0)
      | one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ( sK5(X0) != sK6(X0)
            & apply(X0,sK5(X0)) = apply(X0,sK6(X0))
            & in(sK6(X0),relation_dom(X0))
            & in(sK5(X0),relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | apply(X0,X3) != apply(X0,X4)
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f102,f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & apply(X0,X1) = apply(X0,X2)
          & in(X2,relation_dom(X0))
          & in(X1,relation_dom(X0)) )
     => ( sK5(X0) != sK6(X0)
        & apply(X0,sK5(X0)) = apply(X0,sK6(X0))
        & in(sK6(X0),relation_dom(X0))
        & in(sK5(X0),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f102,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( X1 != X2
              & apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | apply(X0,X3) != apply(X0,X4)
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( X1 != X2
              & apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) ) )
        & ( ! [X1,X2] :
              ( X1 = X2
              | apply(X0,X1) != apply(X0,X2)
              | ~ in(X2,relation_dom(X0))
              | ~ in(X1,relation_dom(X0)) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( X1 = X2
            | apply(X0,X1) != apply(X0,X2)
            | ~ in(X2,relation_dom(X0))
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( X1 = X2
            | apply(X0,X1) != apply(X0,X2)
            | ~ in(X2,relation_dom(X0))
            | ~ in(X1,relation_dom(X0)) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
      <=> ! [X1,X2] :
            ( ( apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.IV7ReKMQsI/Vampire---4.8_5356',d8_funct_1) ).

fof(f952,plain,
    sK6(sF18) = sK5(sF18),
    inference(subsumption_resolution,[],[f951,f257]) ).

fof(f951,plain,
    ( sK6(sF18) = sK5(sF18)
    | ~ relation(sF18) ),
    inference(subsumption_resolution,[],[f950,f260]) ).

fof(f950,plain,
    ( sK6(sF18) = sK5(sF18)
    | ~ function(sF18)
    | ~ relation(sF18) ),
    inference(subsumption_resolution,[],[f949,f216]) ).

fof(f949,plain,
    ( sK6(sF18) = sK5(sF18)
    | one_to_one(sF18)
    | ~ function(sF18)
    | ~ relation(sF18) ),
    inference(resolution,[],[f948,f161]) ).

fof(f161,plain,
    ! [X0] :
      ( in(sK5(X0),relation_dom(X0))
      | one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f948,plain,
    ( ~ in(sK5(sF18),relation_dom(sF18))
    | sK6(sF18) = sK5(sF18) ),
    inference(subsumption_resolution,[],[f947,f257]) ).

fof(f947,plain,
    ( sK6(sF18) = sK5(sF18)
    | ~ in(sK5(sF18),relation_dom(sF18))
    | ~ relation(sF18) ),
    inference(subsumption_resolution,[],[f946,f260]) ).

fof(f946,plain,
    ( sK6(sF18) = sK5(sF18)
    | ~ in(sK5(sF18),relation_dom(sF18))
    | ~ function(sF18)
    | ~ relation(sF18) ),
    inference(subsumption_resolution,[],[f945,f216]) ).

fof(f945,plain,
    ( sK6(sF18) = sK5(sF18)
    | ~ in(sK5(sF18),relation_dom(sF18))
    | one_to_one(sF18)
    | ~ function(sF18)
    | ~ relation(sF18) ),
    inference(resolution,[],[f932,f162]) ).

fof(f162,plain,
    ! [X0] :
      ( in(sK6(X0),relation_dom(X0))
      | one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f932,plain,
    ( ~ in(sK6(sF18),relation_dom(sF18))
    | sK6(sF18) = sK5(sF18)
    | ~ in(sK5(sF18),relation_dom(sF18)) ),
    inference(superposition,[],[f919,f886]) ).

fof(f886,plain,
    ! [X0] :
      ( apply(sK1,apply(sF18,X0)) = X0
      | ~ in(X0,relation_dom(sF18)) ),
    inference(forward_demodulation,[],[f885,f512]) ).

fof(f512,plain,
    relation_rng(sK1) = relation_dom(sF18),
    inference(subsumption_resolution,[],[f511,f125]) ).

fof(f125,plain,
    relation(sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( ~ one_to_one(function_inverse(sK1))
    & one_to_one(sK1)
    & function(sK1)
    & relation(sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f48,f89]) ).

fof(f89,plain,
    ( ? [X0] :
        ( ~ one_to_one(function_inverse(X0))
        & one_to_one(X0)
        & function(X0)
        & relation(X0) )
   => ( ~ one_to_one(function_inverse(sK1))
      & one_to_one(sK1)
      & function(sK1)
      & relation(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f48,plain,
    ? [X0] :
      ( ~ one_to_one(function_inverse(X0))
      & one_to_one(X0)
      & function(X0)
      & relation(X0) ),
    inference(flattening,[],[f47]) ).

fof(f47,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/tmp/tmp.IV7ReKMQsI/Vampire---4.8_5356',t62_funct_1) ).

fof(f511,plain,
    ( relation_rng(sK1) = relation_dom(sF18)
    | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f510,f126]) ).

fof(f126,plain,
    function(sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f510,plain,
    ( relation_rng(sK1) = relation_dom(sF18)
    | ~ function(sK1)
    | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f497,f127]) ).

fof(f127,plain,
    one_to_one(sK1),
    inference(cnf_transformation,[],[f90]) ).

fof(f497,plain,
    ( relation_rng(sK1) = relation_dom(sF18)
    | ~ one_to_one(sK1)
    | ~ function(sK1)
    | ~ relation(sK1) ),
    inference(superposition,[],[f224,f215]) ).

fof(f215,plain,
    function_inverse(sK1) = sF18,
    introduced(function_definition,[]) ).

fof(f224,plain,
    ! [X0] :
      ( relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(subsumption_resolution,[],[f223,f146]) ).

fof(f146,plain,
    ! [X0] :
      ( relation(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ( function(function_inverse(X0))
        & relation(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f59]) ).

fof(f59,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/tmp/tmp.IV7ReKMQsI/Vampire---4.8_5356',dt_k2_funct_1) ).

fof(f223,plain,
    ! [X0] :
      ( relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ relation(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(subsumption_resolution,[],[f212,f147]) ).

fof(f147,plain,
    ! [X0] :
      ( function(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f212,plain,
    ! [X0] :
      ( relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ function(function_inverse(X0))
      | ~ relation(function_inverse(X0))
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f153]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( relation_rng(X0) = relation_dom(X1)
      | function_inverse(X0) != X1
      | ~ function(X1)
      | ~ relation(X1)
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ( ( sK4(X0,X1) != apply(X1,sK3(X0,X1))
                  | ~ in(sK3(X0,X1),relation_rng(X0)) )
                & sK3(X0,X1) = apply(X0,sK4(X0,X1))
                & in(sK4(X0,X1),relation_dom(X0)) )
              | ~ sP0(sK3(X0,X1),sK4(X0,X1),X0,X1)
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X4,X5] :
                    ( ( ( apply(X1,X4) = X5
                        & in(X4,relation_rng(X0)) )
                      | apply(X0,X5) != X4
                      | ~ in(X5,relation_dom(X0)) )
                    & sP0(X4,X5,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f98,f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( ( ( apply(X1,X2) != X3
              | ~ in(X2,relation_rng(X0)) )
            & apply(X0,X3) = X2
            & in(X3,relation_dom(X0)) )
          | ~ sP0(X2,X3,X0,X1) )
     => ( ( ( sK4(X0,X1) != apply(X1,sK3(X0,X1))
            | ~ in(sK3(X0,X1),relation_rng(X0)) )
          & sK3(X0,X1) = apply(X0,sK4(X0,X1))
          & in(sK4(X0,X1),relation_dom(X0)) )
        | ~ sP0(sK3(X0,X1),sK4(X0,X1),X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) )
                    & apply(X0,X3) = X2
                    & in(X3,relation_dom(X0)) )
                  | ~ sP0(X2,X3,X0,X1) )
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X4,X5] :
                    ( ( ( apply(X1,X4) = X5
                        & in(X4,relation_rng(X0)) )
                      | apply(X0,X5) != X4
                      | ~ in(X5,relation_dom(X0)) )
                    & sP0(X4,X5,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f97]) ).

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

fof(f96,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( function_inverse(X0) = X1
              | ? [X2,X3] :
                  ( ( ( apply(X1,X2) != X3
                      | ~ in(X2,relation_rng(X0)) )
                    & apply(X0,X3) = X2
                    & in(X3,relation_dom(X0)) )
                  | ~ sP0(X2,X3,X0,X1) )
              | relation_rng(X0) != relation_dom(X1) )
            & ( ( ! [X2,X3] :
                    ( ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                      | apply(X0,X3) != X2
                      | ~ in(X3,relation_dom(X0)) )
                    & sP0(X2,X3,X0,X1) )
                & relation_rng(X0) = relation_dom(X1) )
              | function_inverse(X0) != X1 ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( apply(X1,X2) = X3
                      & in(X2,relation_rng(X0)) )
                    | apply(X0,X3) != X2
                    | ~ in(X3,relation_dom(X0)) )
                  & sP0(X2,X3,X0,X1) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(definition_folding,[],[f62,f87]) ).

fof(f87,plain,
    ! [X2,X3,X0,X1] :
      ( sP0(X2,X3,X0,X1)
    <=> ( ( apply(X0,X3) = X2
          & in(X3,relation_dom(X0)) )
        | apply(X1,X2) != X3
        | ~ in(X2,relation_rng(X0)) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f62,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( 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)) ) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( function_inverse(X0) = X1
          <=> ( ! [X2,X3] :
                  ( ( ( 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)) ) )
              & relation_rng(X0) = relation_dom(X1) ) )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ! [X1] :
            ( ( function(X1)
              & relation(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)) ) )
                    & ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                     => ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) ) ) )
                & relation_rng(X0) = relation_dom(X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.IV7ReKMQsI/Vampire---4.8_5356',t54_funct_1) ).

fof(f885,plain,
    ! [X0] :
      ( apply(sK1,apply(sF18,X0)) = X0
      | ~ in(X0,relation_rng(sK1)) ),
    inference(subsumption_resolution,[],[f884,f125]) ).

fof(f884,plain,
    ! [X0] :
      ( apply(sK1,apply(sF18,X0)) = X0
      | ~ in(X0,relation_rng(sK1))
      | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f883,f126]) ).

fof(f883,plain,
    ! [X0] :
      ( apply(sK1,apply(sF18,X0)) = X0
      | ~ in(X0,relation_rng(sK1))
      | ~ function(sK1)
      | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f870,f127]) ).

fof(f870,plain,
    ! [X0] :
      ( apply(sK1,apply(sF18,X0)) = X0
      | ~ in(X0,relation_rng(sK1))
      | ~ one_to_one(sK1)
      | ~ function(sK1)
      | ~ relation(sK1) ),
    inference(superposition,[],[f181,f215]) ).

fof(f181,plain,
    ! [X0,X1] :
      ( apply(X1,apply(function_inverse(X1),X0)) = X0
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        & apply(X1,apply(function_inverse(X1),X0)) = X0 )
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
        & apply(X1,apply(function_inverse(X1),X0)) = X0 )
      | ~ in(X0,relation_rng(X1))
      | ~ one_to_one(X1)
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => ( ( in(X0,relation_rng(X1))
          & one_to_one(X1) )
       => ( apply(relation_composition(function_inverse(X1),X1),X0) = X0
          & apply(X1,apply(function_inverse(X1),X0)) = X0 ) ) ),
    file('/export/starexec/sandbox2/tmp/tmp.IV7ReKMQsI/Vampire---4.8_5356',t57_funct_1) ).

fof(f919,plain,
    ( sK6(sF18) = apply(sK1,apply(sF18,sK5(sF18)))
    | ~ in(sK6(sF18),relation_dom(sF18)) ),
    inference(subsumption_resolution,[],[f918,f257]) ).

fof(f918,plain,
    ( sK6(sF18) = apply(sK1,apply(sF18,sK5(sF18)))
    | ~ in(sK6(sF18),relation_dom(sF18))
    | ~ relation(sF18) ),
    inference(subsumption_resolution,[],[f917,f260]) ).

fof(f917,plain,
    ( sK6(sF18) = apply(sK1,apply(sF18,sK5(sF18)))
    | ~ in(sK6(sF18),relation_dom(sF18))
    | ~ function(sF18)
    | ~ relation(sF18) ),
    inference(subsumption_resolution,[],[f909,f216]) ).

fof(f909,plain,
    ( sK6(sF18) = apply(sK1,apply(sF18,sK5(sF18)))
    | ~ in(sK6(sF18),relation_dom(sF18))
    | one_to_one(sF18)
    | ~ function(sF18)
    | ~ relation(sF18) ),
    inference(superposition,[],[f886,f163]) ).

fof(f163,plain,
    ! [X0] :
      ( apply(X0,sK5(X0)) = apply(X0,sK6(X0))
      | one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f216,plain,
    ~ one_to_one(sF18),
    inference(definition_folding,[],[f128,f215]) ).

fof(f128,plain,
    ~ one_to_one(function_inverse(sK1)),
    inference(cnf_transformation,[],[f90]) ).

fof(f260,plain,
    function(sF18),
    inference(subsumption_resolution,[],[f259,f125]) ).

fof(f259,plain,
    ( function(sF18)
    | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f258,f126]) ).

fof(f258,plain,
    ( function(sF18)
    | ~ function(sK1)
    | ~ relation(sK1) ),
    inference(superposition,[],[f147,f215]) ).

fof(f257,plain,
    relation(sF18),
    inference(subsumption_resolution,[],[f256,f125]) ).

fof(f256,plain,
    ( relation(sF18)
    | ~ relation(sK1) ),
    inference(subsumption_resolution,[],[f255,f126]) ).

fof(f255,plain,
    ( relation(sF18)
    | ~ function(sK1)
    | ~ relation(sK1) ),
    inference(superposition,[],[f146,f215]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : SEU221+3 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.36  % Computer : n016.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Thu Aug 24 01:25:23 EDT 2023
% 0.21/0.36  % CPUTime    : 
% 0.21/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.21/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.IV7ReKMQsI/Vampire---4.8_5356
% 0.21/0.37  % (5557)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (5563)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.42  % (5562)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.42  % (5559)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.43  % (5560)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.43  % (5564)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.43  % (5561)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.43  % (5558)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.21/0.44  % (5561)Refutation not found, incomplete strategy% (5561)------------------------------
% 0.21/0.44  % (5561)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.44  % (5561)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.44  % (5561)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.44  
% 0.21/0.44  % (5561)Memory used [KB]: 10362
% 0.21/0.44  % (5561)Time elapsed: 0.014 s
% 0.21/0.44  % (5561)------------------------------
% 0.21/0.44  % (5561)------------------------------
% 0.21/0.46  % (5562)First to succeed.
% 0.21/0.46  % (5562)Refutation found. Thanks to Tanya!
% 0.21/0.46  % SZS status Theorem for Vampire---4
% 0.21/0.46  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.46  % (5562)------------------------------
% 0.21/0.46  % (5562)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.46  % (5562)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.46  % (5562)Termination reason: Refutation
% 0.21/0.46  
% 0.21/0.46  % (5562)Memory used [KB]: 1791
% 0.21/0.46  % (5562)Time elapsed: 0.036 s
% 0.21/0.46  % (5562)------------------------------
% 0.21/0.46  % (5562)------------------------------
% 0.21/0.46  % (5557)Success in time 0.094 s
% 0.21/0.46  % Vampire---4.8 exiting
%------------------------------------------------------------------------------