TSTP Solution File: SEU077+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU077+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_uns --cores 0 -t %d %s

% Computer : n013.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 18:26:35 EDT 2022

% Result   : Theorem 0.17s 0.56s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   62 (  15 unt;   0 def)
%            Number of atoms       :  330 (  50 equ)
%            Maximal formula atoms :   16 (   5 avg)
%            Number of connectives :  416 ( 148   ~; 144   |;  93   &)
%                                         (  15 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :  160 ( 127   !;  33   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f199,plain,
    $false,
    inference(subsumption_resolution,[],[f198,f137]) ).

fof(f137,plain,
    ~ in(sK7(sK2,sK3),sK2),
    inference(unit_resulting_resolution,[],[f99,f114]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ~ in(sK7(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ( ~ in(sK7(X0,X1),X0)
          & in(sK7(X0,X1),X1) ) )
      & ( ! [X3] :
            ( in(X3,X0)
            | ~ in(X3,X1) )
        | ~ subset(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f74,f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X0)
          & in(X2,X1) )
     => ( ~ in(sK7(X0,X1),X0)
        & in(sK7(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f74,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( ~ in(X2,X0)
            & in(X2,X1) ) )
      & ( ! [X3] :
            ( in(X3,X0)
            | ~ in(X3,X1) )
        | ~ subset(X1,X0) ) ),
    inference(rectify,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( ~ in(X2,X0)
            & in(X2,X1) ) )
      & ( ! [X2] :
            ( in(X2,X0)
            | ~ in(X2,X1) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( in(X2,X0)
          | ~ in(X2,X1) ) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f99,plain,
    ~ subset(sK3,sK2),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ( function(sK4)
    & subset(relation_inverse_image(sK4,sK3),relation_inverse_image(sK4,sK2))
    & ~ subset(sK3,sK2)
    & relation(sK4)
    & subset(sK3,relation_rng(sK4)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f64,f65]) ).

fof(f65,plain,
    ( ? [X0,X1,X2] :
        ( function(X2)
        & subset(relation_inverse_image(X2,X1),relation_inverse_image(X2,X0))
        & ~ subset(X1,X0)
        & relation(X2)
        & subset(X1,relation_rng(X2)) )
   => ( function(sK4)
      & subset(relation_inverse_image(sK4,sK3),relation_inverse_image(sK4,sK2))
      & ~ subset(sK3,sK2)
      & relation(sK4)
      & subset(sK3,relation_rng(sK4)) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ? [X0,X1,X2] :
      ( function(X2)
      & subset(relation_inverse_image(X2,X1),relation_inverse_image(X2,X0))
      & ~ subset(X1,X0)
      & relation(X2)
      & subset(X1,relation_rng(X2)) ),
    inference(rectify,[],[f47]) ).

fof(f47,plain,
    ? [X2,X1,X0] :
      ( function(X0)
      & subset(relation_inverse_image(X0,X1),relation_inverse_image(X0,X2))
      & ~ subset(X1,X2)
      & relation(X0)
      & subset(X1,relation_rng(X0)) ),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ? [X2,X1,X0] :
      ( ~ subset(X1,X2)
      & subset(X1,relation_rng(X0))
      & subset(relation_inverse_image(X0,X1),relation_inverse_image(X0,X2))
      & relation(X0)
      & function(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ~ ! [X2,X1,X0] :
        ( ( relation(X0)
          & function(X0) )
       => ( ( subset(X1,relation_rng(X0))
            & subset(relation_inverse_image(X0,X1),relation_inverse_image(X0,X2)) )
         => subset(X1,X2) ) ),
    inference(rectify,[],[f29]) ).

fof(f29,negated_conjecture,
    ~ ! [X2,X0,X1] :
        ( ( function(X2)
          & relation(X2) )
       => ( ( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
            & subset(X0,relation_rng(X2)) )
         => subset(X0,X1) ) ),
    inference(negated_conjecture,[],[f28]) ).

fof(f28,conjecture,
    ! [X2,X0,X1] :
      ( ( function(X2)
        & relation(X2) )
     => ( ( subset(relation_inverse_image(X2,X0),relation_inverse_image(X2,X1))
          & subset(X0,relation_rng(X2)) )
       => subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t158_funct_1) ).

fof(f198,plain,
    in(sK7(sK2,sK3),sK2),
    inference(forward_demodulation,[],[f196,f148]) ).

fof(f148,plain,
    sK7(sK2,sK3) = apply(sK4,sK9(sK4,sK7(sK2,sK3))),
    inference(unit_resulting_resolution,[],[f101,f98,f141,f131]) ).

fof(f131,plain,
    ! [X2,X0] :
      ( ~ in(X2,relation_rng(X0))
      | ~ relation(X0)
      | apply(X0,sK9(X0,X2)) = X2
      | ~ function(X0) ),
    inference(equality_resolution,[],[f122]) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | apply(X0,sK9(X0,X2)) = X2
      | ~ in(X2,X1)
      | relation_rng(X0) != X1 ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(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] :
                    ( sK10(X0,X1) != apply(X0,X6)
                    | ~ 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])],[f80,f83,f82,f81]) ).

fof(f81,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(f82,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] :
              ( sK10(X0,X1) != apply(X0,X6)
              | ~ 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(f83,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(f80,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(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,[],[f79]) ).

fof(f79,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(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,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ~ function(X0)
      | ! [X1] :
          ( ! [X2] :
              ( ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) )
            <=> in(X2,X1) )
        <=> relation_rng(X0) = X1 ) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ? [X3] :
                  ( apply(X0,X3) = X2
                  & in(X3,relation_dom(X0)) )
            <=> in(X2,X1) )
        <=> relation_rng(X0) = X1 )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( ( relation(X0)
        & function(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(f141,plain,
    in(sK7(sK2,sK3),relation_rng(sK4)),
    inference(unit_resulting_resolution,[],[f97,f135,f112]) ).

fof(f112,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X1,X0)
      | in(X3,X0)
      | ~ in(X3,X1) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f135,plain,
    in(sK7(sK2,sK3),sK3),
    inference(unit_resulting_resolution,[],[f99,f113]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( in(sK7(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f97,plain,
    subset(sK3,relation_rng(sK4)),
    inference(cnf_transformation,[],[f66]) ).

fof(f98,plain,
    relation(sK4),
    inference(cnf_transformation,[],[f66]) ).

fof(f101,plain,
    function(sK4),
    inference(cnf_transformation,[],[f66]) ).

fof(f196,plain,
    in(apply(sK4,sK9(sK4,sK7(sK2,sK3))),sK2),
    inference(unit_resulting_resolution,[],[f101,f98,f179,f130]) ).

fof(f130,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,relation_inverse_image(X0,X2))
      | in(apply(X0,X3),X2)
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(equality_resolution,[],[f93]) ).

fof(f93,plain,
    ! [X2,X3,X0,X1] :
      ( in(apply(X0,X3),X2)
      | ~ in(X3,X1)
      | relation_inverse_image(X0,X2) != X1
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [X3] :
                ( ( in(X3,X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(apply(X0,X3),X2) )
                & ( ( in(X3,relation_dom(X0))
                    & in(apply(X0,X3),X2) )
                  | ~ in(X3,X1) ) )
            | relation_inverse_image(X0,X2) != X1 )
          & ( relation_inverse_image(X0,X2) = X1
            | ( ( ~ in(sK1(X0,X1,X2),relation_dom(X0))
                | ~ in(apply(X0,sK1(X0,X1,X2)),X2)
                | ~ in(sK1(X0,X1,X2),X1) )
              & ( ( in(sK1(X0,X1,X2),relation_dom(X0))
                  & in(apply(X0,sK1(X0,X1,X2)),X2) )
                | in(sK1(X0,X1,X2),X1) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f61,f62]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,relation_dom(X0))
            | ~ in(apply(X0,X4),X2)
            | ~ in(X4,X1) )
          & ( ( in(X4,relation_dom(X0))
              & in(apply(X0,X4),X2) )
            | in(X4,X1) ) )
     => ( ( ~ in(sK1(X0,X1,X2),relation_dom(X0))
          | ~ in(apply(X0,sK1(X0,X1,X2)),X2)
          | ~ in(sK1(X0,X1,X2),X1) )
        & ( ( in(sK1(X0,X1,X2),relation_dom(X0))
            & in(apply(X0,sK1(X0,X1,X2)),X2) )
          | in(sK1(X0,X1,X2),X1) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f61,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [X3] :
                ( ( in(X3,X1)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(apply(X0,X3),X2) )
                & ( ( in(X3,relation_dom(X0))
                    & in(apply(X0,X3),X2) )
                  | ~ in(X3,X1) ) )
            | relation_inverse_image(X0,X2) != X1 )
          & ( relation_inverse_image(X0,X2) = X1
            | ? [X4] :
                ( ( ~ in(X4,relation_dom(X0))
                  | ~ in(apply(X0,X4),X2)
                  | ~ in(X4,X1) )
                & ( ( in(X4,relation_dom(X0))
                    & in(apply(X0,X4),X2) )
                  | in(X4,X1) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(rectify,[],[f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ( ! [X3] :
                ( ( in(X3,X2)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(apply(X0,X3),X1) )
                & ( ( in(X3,relation_dom(X0))
                    & in(apply(X0,X3),X1) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 )
          & ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(X3,relation_dom(X0))
                  | ~ in(apply(X0,X3),X1)
                  | ~ in(X3,X2) )
                & ( ( in(X3,relation_dom(X0))
                    & in(apply(X0,X3),X1) )
                  | in(X3,X2) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ( ! [X3] :
                ( ( in(X3,X2)
                  | ~ in(X3,relation_dom(X0))
                  | ~ in(apply(X0,X3),X1) )
                & ( ( in(X3,relation_dom(X0))
                    & in(apply(X0,X3),X1) )
                  | ~ in(X3,X2) ) )
            | relation_inverse_image(X0,X1) != X2 )
          & ( relation_inverse_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(X3,relation_dom(X0))
                  | ~ in(apply(X0,X3),X1)
                  | ~ in(X3,X2) )
                & ( ( in(X3,relation_dom(X0))
                    & in(apply(X0,X3),X1) )
                  | in(X3,X2) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(nnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ( in(X3,relation_dom(X0))
                & in(apply(X0,X3),X1) ) )
        <=> relation_inverse_image(X0,X1) = X2 )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ( in(X3,relation_dom(X0))
                & in(apply(X0,X3),X1) ) )
        <=> relation_inverse_image(X0,X1) = X2 )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( relation(X0)
        & function(X0) )
     => ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ( in(X3,relation_dom(X0))
                & in(apply(X0,X3),X1) ) )
        <=> relation_inverse_image(X0,X1) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).

fof(f179,plain,
    in(sK9(sK4,sK7(sK2,sK3)),relation_inverse_image(sK4,sK2)),
    inference(unit_resulting_resolution,[],[f100,f175,f112]) ).

fof(f175,plain,
    in(sK9(sK4,sK7(sK2,sK3)),relation_inverse_image(sK4,sK3)),
    inference(unit_resulting_resolution,[],[f135,f166]) ).

fof(f166,plain,
    ! [X1] :
      ( in(sK9(sK4,sK7(sK2,sK3)),relation_inverse_image(sK4,X1))
      | ~ in(sK7(sK2,sK3),X1) ),
    inference(subsumption_resolution,[],[f165,f101]) ).

fof(f165,plain,
    ! [X1] :
      ( ~ function(sK4)
      | in(sK9(sK4,sK7(sK2,sK3)),relation_inverse_image(sK4,X1))
      | ~ in(sK7(sK2,sK3),X1) ),
    inference(subsumption_resolution,[],[f164,f98]) ).

fof(f164,plain,
    ! [X1] :
      ( in(sK9(sK4,sK7(sK2,sK3)),relation_inverse_image(sK4,X1))
      | ~ relation(sK4)
      | ~ in(sK7(sK2,sK3),X1)
      | ~ function(sK4) ),
    inference(subsumption_resolution,[],[f160,f147]) ).

fof(f147,plain,
    in(sK9(sK4,sK7(sK2,sK3)),relation_dom(sK4)),
    inference(unit_resulting_resolution,[],[f98,f101,f141,f132]) ).

fof(f132,plain,
    ! [X2,X0] :
      ( in(sK9(X0,X2),relation_dom(X0))
      | ~ relation(X0)
      | ~ function(X0)
      | ~ in(X2,relation_rng(X0)) ),
    inference(equality_resolution,[],[f121]) ).

fof(f121,plain,
    ! [X2,X0,X1] :
      ( ~ relation(X0)
      | ~ function(X0)
      | in(sK9(X0,X2),relation_dom(X0))
      | ~ in(X2,X1)
      | relation_rng(X0) != X1 ),
    inference(cnf_transformation,[],[f84]) ).

fof(f160,plain,
    ! [X1] :
      ( ~ in(sK9(sK4,sK7(sK2,sK3)),relation_dom(sK4))
      | in(sK9(sK4,sK7(sK2,sK3)),relation_inverse_image(sK4,X1))
      | ~ in(sK7(sK2,sK3),X1)
      | ~ function(sK4)
      | ~ relation(sK4) ),
    inference(superposition,[],[f128,f148]) ).

fof(f128,plain,
    ! [X2,X3,X0] :
      ( ~ in(apply(X0,X3),X2)
      | in(X3,relation_inverse_image(X0,X2))
      | ~ function(X0)
      | ~ in(X3,relation_dom(X0))
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f95]) ).

fof(f95,plain,
    ! [X2,X3,X0,X1] :
      ( in(X3,X1)
      | ~ in(X3,relation_dom(X0))
      | ~ in(apply(X0,X3),X2)
      | relation_inverse_image(X0,X2) != X1
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f100,plain,
    subset(relation_inverse_image(sK4,sK3),relation_inverse_image(sK4,sK2)),
    inference(cnf_transformation,[],[f66]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SEU077+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.11/0.32  % Computer : n013.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Tue Aug 30 14:33:01 EDT 2022
% 0.11/0.32  % CPUTime    : 
% 0.17/0.47  % (10901)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 0.17/0.48  % (10900)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.17/0.49  % (10909)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.17/0.49  % (10916)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.17/0.50  % (10917)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.17/0.50  % (10908)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.17/0.51  % (10908)Instruction limit reached!
% 0.17/0.51  % (10908)------------------------------
% 0.17/0.51  % (10908)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.51  % (10899)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.17/0.52  % (10907)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.52  % (10908)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.52  % (10908)Termination reason: Unknown
% 0.17/0.52  % (10908)Termination phase: Saturation
% 0.17/0.52  
% 0.17/0.52  % (10908)Memory used [KB]: 6140
% 0.17/0.52  % (10908)Time elapsed: 0.124 s
% 0.17/0.52  % (10908)Instructions burned: 7 (million)
% 0.17/0.52  % (10908)------------------------------
% 0.17/0.52  % (10908)------------------------------
% 0.17/0.52  % (10907)Instruction limit reached!
% 0.17/0.52  % (10907)------------------------------
% 0.17/0.52  % (10907)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.52  % (10907)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.52  % (10907)Termination reason: Unknown
% 0.17/0.52  % (10907)Termination phase: Saturation
% 0.17/0.52  
% 0.17/0.52  % (10907)Memory used [KB]: 6012
% 0.17/0.52  % (10907)Time elapsed: 0.004 s
% 0.17/0.52  % (10907)Instructions burned: 3 (million)
% 0.17/0.52  % (10907)------------------------------
% 0.17/0.52  % (10907)------------------------------
% 0.17/0.52  % (10904)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.17/0.52  % (10903)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 0.17/0.52  % (10893)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.17/0.52  % (10922)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.17/0.53  % (10905)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)
% 0.17/0.54  % (10910)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.54  % (10895)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.17/0.54  % (10897)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.17/0.54  % (10896)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.17/0.54  % (10910)Instruction limit reached!
% 0.17/0.54  % (10910)------------------------------
% 0.17/0.54  % (10910)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.54  % (10910)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.54  % (10910)Termination reason: Unknown
% 0.17/0.54  % (10910)Termination phase: Property scanning
% 0.17/0.54  
% 0.17/0.54  % (10910)Memory used [KB]: 1535
% 0.17/0.54  % (10910)Time elapsed: 0.003 s
% 0.17/0.54  % (10910)Instructions burned: 3 (million)
% 0.17/0.54  % (10910)------------------------------
% 0.17/0.54  % (10910)------------------------------
% 0.17/0.54  % (10895)Instruction limit reached!
% 0.17/0.54  % (10895)------------------------------
% 0.17/0.54  % (10895)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.54  % (10895)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.54  % (10895)Termination reason: Unknown
% 0.17/0.54  % (10895)Termination phase: Property scanning
% 0.17/0.54  
% 0.17/0.54  % (10895)Memory used [KB]: 1535
% 0.17/0.54  % (10895)Time elapsed: 0.003 s
% 0.17/0.54  % (10895)Instructions burned: 3 (million)
% 0.17/0.54  % (10895)------------------------------
% 0.17/0.54  % (10895)------------------------------
% 0.17/0.54  % (10896)First to succeed.
% 0.17/0.54  % (10918)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 0.17/0.54  % (10904)Instruction limit reached!
% 0.17/0.54  % (10904)------------------------------
% 0.17/0.54  % (10904)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.54  % (10904)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.54  % (10904)Termination reason: Unknown
% 0.17/0.54  % (10904)Termination phase: Saturation
% 0.17/0.54  
% 0.17/0.54  % (10904)Memory used [KB]: 6140
% 0.17/0.54  % (10904)Time elapsed: 0.151 s
% 0.17/0.54  % (10904)Instructions burned: 7 (million)
% 0.17/0.54  % (10904)------------------------------
% 0.17/0.54  % (10904)------------------------------
% 0.17/0.54  % (10903)Instruction limit reached!
% 0.17/0.54  % (10903)------------------------------
% 0.17/0.54  % (10903)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.54  % (10903)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.54  % (10903)Termination reason: Unknown
% 0.17/0.54  % (10903)Termination phase: Saturation
% 0.17/0.54  
% 0.17/0.54  % (10903)Memory used [KB]: 6268
% 0.17/0.54  % (10903)Time elapsed: 0.155 s
% 0.17/0.54  % (10903)Instructions burned: 12 (million)
% 0.17/0.54  % (10903)------------------------------
% 0.17/0.54  % (10903)------------------------------
% 0.17/0.54  % (10915)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.17/0.54  % (10921)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)
% 0.17/0.55  % (10920)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.17/0.55  % (10919)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.17/0.55  % (10902)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.17/0.55  % (10911)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.17/0.55  % (10911)Instruction limit reached!
% 0.17/0.55  % (10911)------------------------------
% 0.17/0.55  % (10911)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.55  % (10911)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.55  % (10911)Termination reason: Unknown
% 0.17/0.55  % (10911)Termination phase: Preprocessing 3
% 0.17/0.55  
% 0.17/0.55  % (10911)Memory used [KB]: 1407
% 0.17/0.55  % (10911)Time elapsed: 0.003 s
% 0.17/0.55  % (10911)Instructions burned: 2 (million)
% 0.17/0.55  % (10911)------------------------------
% 0.17/0.55  % (10911)------------------------------
% 0.17/0.56  % (10912)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.17/0.56  % (10900)Instruction limit reached!
% 0.17/0.56  % (10900)------------------------------
% 0.17/0.56  % (10900)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.56  % (10896)Refutation found. Thanks to Tanya!
% 0.17/0.56  % SZS status Theorem for theBenchmark
% 0.17/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.56  % (10896)------------------------------
% 0.17/0.56  % (10896)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.56  % (10896)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.56  % (10896)Termination reason: Refutation
% 0.17/0.56  
% 0.17/0.56  % (10896)Memory used [KB]: 6012
% 0.17/0.56  % (10896)Time elapsed: 0.153 s
% 0.17/0.56  % (10896)Instructions burned: 5 (million)
% 0.17/0.56  % (10896)------------------------------
% 0.17/0.56  % (10896)------------------------------
% 0.17/0.56  % (10892)Success in time 0.227 s
%------------------------------------------------------------------------------