TSTP Solution File: SEU051+1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SEU051+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 : n017.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 18:26:27 EDT 2022

% Result   : Theorem 1.65s 0.59s
% Output   : Refutation 1.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   79 (  18 unt;   0 def)
%            Number of atoms       :  425 (  69 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  537 ( 191   ~; 185   |; 122   &)
%                                         (  19 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   7 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-3 aty)
%            Number of functors    :   13 (  13 usr;   3 con; 0-3 aty)
%            Number of variables   :  238 ( 201   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f287,plain,
    $false,
    inference(subsumption_resolution,[],[f286,f165]) ).

fof(f165,plain,
    ~ in(sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),relation_image(sK2,sK4)),
    inference(unit_resulting_resolution,[],[f102,f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ~ in(sK6(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ( ~ in(sK6(X0,X1),X1)
          & in(sK6(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f70,f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ in(X3,X1)
          & in(X3,X0) )
     => ( ~ in(sK6(X0,X1),X1)
        & in(sK6(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X3] :
            ( ~ in(X3,X1)
            & in(X3,X0) ) ) ),
    inference(rectify,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) )
    <=> subset(X0,X1) ),
    inference(ennf_transformation,[],[f6]) ).

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

fof(f102,plain,
    ~ subset(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),
    inference(cnf_transformation,[],[f66]) ).

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

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

fof(f64,plain,
    ? [X0,X1,X2] :
      ( relation(X0)
      & function(X0)
      & ~ subset(relation_image(relation_rng_restriction(X1,X0),X2),relation_image(X0,X2)) ),
    inference(rectify,[],[f48]) ).

fof(f48,plain,
    ? [X2,X1,X0] :
      ( relation(X2)
      & function(X2)
      & ~ subset(relation_image(relation_rng_restriction(X1,X2),X0),relation_image(X2,X0)) ),
    inference(flattening,[],[f47]) ).

fof(f47,plain,
    ? [X0,X1,X2] :
      ( ~ subset(relation_image(relation_rng_restriction(X1,X2),X0),relation_image(X2,X0))
      & relation(X2)
      & function(X2) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ~ ! [X0,X1,X2] :
        ( ( relation(X2)
          & function(X2) )
       => subset(relation_image(relation_rng_restriction(X1,X2),X0),relation_image(X2,X0)) ),
    inference(rectify,[],[f28]) ).

fof(f28,negated_conjecture,
    ~ ! [X1,X0,X2] :
        ( ( relation(X2)
          & function(X2) )
       => subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
    inference(negated_conjecture,[],[f27]) ).

fof(f27,conjecture,
    ! [X1,X0,X2] :
      ( ( relation(X2)
        & function(X2) )
     => subset(relation_image(relation_rng_restriction(X0,X2),X1),relation_image(X2,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t120_funct_1) ).

fof(f286,plain,
    in(sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),relation_image(sK2,sK4)),
    inference(forward_demodulation,[],[f280,f223]) ).

fof(f223,plain,
    sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)) = apply(sK2,sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))),
    inference(forward_demodulation,[],[f222,f181]) ).

fof(f181,plain,
    apply(relation_rng_restriction(sK3,sK2),sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))) = sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),
    inference(unit_resulting_resolution,[],[f151,f152,f163,f148]) ).

fof(f148,plain,
    ! [X2,X3,X0] :
      ( ~ in(X3,relation_image(X0,X2))
      | ~ relation(X0)
      | ~ function(X0)
      | apply(X0,sK10(X0,X2,X3)) = X3 ),
    inference(equality_resolution,[],[f132]) ).

fof(f132,plain,
    ! [X2,X3,X0,X1] :
      ( apply(X0,sK10(X0,X2,X3)) = X3
      | ~ in(X3,X1)
      | relation_image(X0,X2) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [X3] :
                ( ( ( in(sK10(X0,X2,X3),relation_dom(X0))
                    & in(sK10(X0,X2,X3),X2)
                    & apply(X0,sK10(X0,X2,X3)) = X3 )
                  | ~ in(X3,X1) )
                & ( in(X3,X1)
                  | ! [X5] :
                      ( ~ in(X5,relation_dom(X0))
                      | ~ in(X5,X2)
                      | apply(X0,X5) != X3 ) ) )
            | relation_image(X0,X2) != X1 )
          & ( relation_image(X0,X2) = X1
            | ( ( ~ in(sK11(X0,X1,X2),X1)
                | ! [X7] :
                    ( ~ in(X7,relation_dom(X0))
                    | ~ in(X7,X2)
                    | apply(X0,X7) != sK11(X0,X1,X2) ) )
              & ( in(sK11(X0,X1,X2),X1)
                | ( in(sK12(X0,X1,X2),relation_dom(X0))
                  & in(sK12(X0,X1,X2),X2)
                  & sK11(X0,X1,X2) = apply(X0,sK12(X0,X1,X2)) ) ) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12])],[f84,f87,f86,f85]) ).

fof(f85,plain,
    ! [X0,X2,X3] :
      ( ? [X4] :
          ( in(X4,relation_dom(X0))
          & in(X4,X2)
          & apply(X0,X4) = X3 )
     => ( in(sK10(X0,X2,X3),relation_dom(X0))
        & in(sK10(X0,X2,X3),X2)
        & apply(X0,sK10(X0,X2,X3)) = X3 ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0,X1,X2] :
      ( ? [X6] :
          ( ( ~ in(X6,X1)
            | ! [X7] :
                ( ~ in(X7,relation_dom(X0))
                | ~ in(X7,X2)
                | apply(X0,X7) != X6 ) )
          & ( in(X6,X1)
            | ? [X8] :
                ( in(X8,relation_dom(X0))
                & in(X8,X2)
                & apply(X0,X8) = X6 ) ) )
     => ( ( ~ in(sK11(X0,X1,X2),X1)
          | ! [X7] :
              ( ~ in(X7,relation_dom(X0))
              | ~ in(X7,X2)
              | apply(X0,X7) != sK11(X0,X1,X2) ) )
        & ( in(sK11(X0,X1,X2),X1)
          | ? [X8] :
              ( in(X8,relation_dom(X0))
              & in(X8,X2)
              & sK11(X0,X1,X2) = apply(X0,X8) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ? [X8] :
          ( in(X8,relation_dom(X0))
          & in(X8,X2)
          & sK11(X0,X1,X2) = apply(X0,X8) )
     => ( in(sK12(X0,X1,X2),relation_dom(X0))
        & in(sK12(X0,X1,X2),X2)
        & sK11(X0,X1,X2) = apply(X0,sK12(X0,X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f84,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [X3] :
                ( ( ? [X4] :
                      ( in(X4,relation_dom(X0))
                      & in(X4,X2)
                      & apply(X0,X4) = X3 )
                  | ~ in(X3,X1) )
                & ( in(X3,X1)
                  | ! [X5] :
                      ( ~ in(X5,relation_dom(X0))
                      | ~ in(X5,X2)
                      | apply(X0,X5) != X3 ) ) )
            | relation_image(X0,X2) != X1 )
          & ( relation_image(X0,X2) = X1
            | ? [X6] :
                ( ( ~ in(X6,X1)
                  | ! [X7] :
                      ( ~ in(X7,relation_dom(X0))
                      | ~ in(X7,X2)
                      | apply(X0,X7) != X6 ) )
                & ( in(X6,X1)
                  | ? [X8] :
                      ( in(X8,relation_dom(X0))
                      & in(X8,X2)
                      & apply(X0,X8) = X6 ) ) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(rectify,[],[f83]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ( ! [X3] :
                ( ( ? [X4] :
                      ( in(X4,relation_dom(X0))
                      & in(X4,X1)
                      & apply(X0,X4) = X3 )
                  | ~ in(X3,X2) )
                & ( in(X3,X2)
                  | ! [X4] :
                      ( ~ in(X4,relation_dom(X0))
                      | ~ in(X4,X1)
                      | apply(X0,X4) != X3 ) ) )
            | relation_image(X0,X1) != X2 )
          & ( relation_image(X0,X1) = X2
            | ? [X3] :
                ( ( ~ in(X3,X2)
                  | ! [X4] :
                      ( ~ in(X4,relation_dom(X0))
                      | ~ in(X4,X1)
                      | apply(X0,X4) != X3 ) )
                & ( in(X3,X2)
                  | ? [X4] :
                      ( in(X4,relation_dom(X0))
                      & in(X4,X1)
                      & apply(X0,X4) = X3 ) ) ) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ! [X3] :
              ( ? [X4] :
                  ( in(X4,relation_dom(X0))
                  & in(X4,X1)
                  & apply(X0,X4) = X3 )
            <=> in(X3,X2) )
        <=> relation_image(X0,X1) = X2 )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(flattening,[],[f49]) ).

fof(f49,plain,
    ! [X0] :
      ( ! [X2,X1] :
          ( ! [X3] :
              ( ? [X4] :
                  ( in(X4,relation_dom(X0))
                  & in(X4,X1)
                  & apply(X0,X4) = X3 )
            <=> in(X3,X2) )
        <=> relation_image(X0,X1) = X2 )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X2,X1] :
          ( ! [X3] :
              ( ? [X4] :
                  ( in(X4,relation_dom(X0))
                  & in(X4,X1)
                  & apply(X0,X4) = X3 )
            <=> in(X3,X2) )
        <=> relation_image(X0,X1) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).

fof(f163,plain,
    in(sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)),relation_image(relation_rng_restriction(sK3,sK2),sK4)),
    inference(unit_resulting_resolution,[],[f102,f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( in(sK6(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f152,plain,
    ! [X0] : function(relation_rng_restriction(X0,sK2)),
    inference(unit_resulting_resolution,[],[f103,f104,f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( function(relation_rng_restriction(X0,X1))
      | ~ function(X1)
      | ~ relation(X1) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ~ relation(X1)
      | ( function(relation_rng_restriction(X0,X1))
        & relation(relation_rng_restriction(X0,X1)) )
      | ~ function(X1) ),
    inference(rectify,[],[f52]) ).

fof(f52,plain,
    ! [X1,X0] :
      ( ~ relation(X0)
      | ( function(relation_rng_restriction(X1,X0))
        & relation(relation_rng_restriction(X1,X0)) )
      | ~ function(X0) ),
    inference(flattening,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( ( function(relation_rng_restriction(X1,X0))
        & relation(relation_rng_restriction(X1,X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1] :
      ( ( function(X0)
        & relation(X0) )
     => ( function(relation_rng_restriction(X1,X0))
        & relation(relation_rng_restriction(X1,X0)) ) ),
    inference(rectify,[],[f13]) ).

fof(f13,axiom,
    ! [X1,X0] :
      ( ( relation(X1)
        & function(X1) )
     => ( function(relation_rng_restriction(X0,X1))
        & relation(relation_rng_restriction(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc5_funct_1) ).

fof(f104,plain,
    relation(sK2),
    inference(cnf_transformation,[],[f66]) ).

fof(f103,plain,
    function(sK2),
    inference(cnf_transformation,[],[f66]) ).

fof(f151,plain,
    ! [X0] : relation(relation_rng_restriction(X0,sK2)),
    inference(unit_resulting_resolution,[],[f103,f104,f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( relation(relation_rng_restriction(X0,X1))
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f222,plain,
    apply(relation_rng_restriction(sK3,sK2),sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))) = apply(sK2,sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))),
    inference(unit_resulting_resolution,[],[f182,f200,f115]) ).

fof(f115,plain,
    ! [X2,X0,X1,X6] :
      ( ~ sP0(X0,X1,X2)
      | ~ in(X6,relation_dom(X2))
      | apply(X2,X6) = apply(X0,X6) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ( ( ~ in(sK8(X0,X1,X2),relation_dom(X0))
            | ~ in(apply(X0,sK8(X0,X1,X2)),X1)
            | ~ in(sK8(X0,X1,X2),relation_dom(X2)) )
          & ( ( in(sK8(X0,X1,X2),relation_dom(X0))
              & in(apply(X0,sK8(X0,X1,X2)),X1) )
            | in(sK8(X0,X1,X2),relation_dom(X2)) ) )
        | ( apply(X2,sK9(X0,X2)) != apply(X0,sK9(X0,X2))
          & in(sK9(X0,X2),relation_dom(X2)) ) )
      & ( ( ! [X5] :
              ( ( in(X5,relation_dom(X2))
                | ~ in(X5,relation_dom(X0))
                | ~ in(apply(X0,X5),X1) )
              & ( ( in(X5,relation_dom(X0))
                  & in(apply(X0,X5),X1) )
                | ~ in(X5,relation_dom(X2)) ) )
          & ! [X6] :
              ( apply(X2,X6) = apply(X0,X6)
              | ~ in(X6,relation_dom(X2)) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f79,f81,f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,relation_dom(X0))
            | ~ in(apply(X0,X3),X1)
            | ~ in(X3,relation_dom(X2)) )
          & ( ( in(X3,relation_dom(X0))
              & in(apply(X0,X3),X1) )
            | in(X3,relation_dom(X2)) ) )
     => ( ( ~ in(sK8(X0,X1,X2),relation_dom(X0))
          | ~ in(apply(X0,sK8(X0,X1,X2)),X1)
          | ~ in(sK8(X0,X1,X2),relation_dom(X2)) )
        & ( ( in(sK8(X0,X1,X2),relation_dom(X0))
            & in(apply(X0,sK8(X0,X1,X2)),X1) )
          | in(sK8(X0,X1,X2),relation_dom(X2)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f81,plain,
    ! [X0,X2] :
      ( ? [X4] :
          ( apply(X0,X4) != apply(X2,X4)
          & in(X4,relation_dom(X2)) )
     => ( apply(X2,sK9(X0,X2)) != apply(X0,sK9(X0,X2))
        & in(sK9(X0,X2),relation_dom(X2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( ( sP0(X0,X1,X2)
        | ? [X3] :
            ( ( ~ in(X3,relation_dom(X0))
              | ~ in(apply(X0,X3),X1)
              | ~ in(X3,relation_dom(X2)) )
            & ( ( in(X3,relation_dom(X0))
                & in(apply(X0,X3),X1) )
              | in(X3,relation_dom(X2)) ) )
        | ? [X4] :
            ( apply(X0,X4) != apply(X2,X4)
            & in(X4,relation_dom(X2)) ) )
      & ( ( ! [X5] :
              ( ( in(X5,relation_dom(X2))
                | ~ in(X5,relation_dom(X0))
                | ~ in(apply(X0,X5),X1) )
              & ( ( in(X5,relation_dom(X0))
                  & in(apply(X0,X5),X1) )
                | ~ in(X5,relation_dom(X2)) ) )
          & ! [X6] :
              ( apply(X2,X6) = apply(X0,X6)
              | ~ in(X6,relation_dom(X2)) ) )
        | ~ sP0(X0,X1,X2) ) ),
    inference(rectify,[],[f78]) ).

fof(f78,plain,
    ! [X2,X1,X0] :
      ( ( sP0(X2,X1,X0)
        | ? [X3] :
            ( ( ~ in(X3,relation_dom(X2))
              | ~ in(apply(X2,X3),X1)
              | ~ in(X3,relation_dom(X0)) )
            & ( ( in(X3,relation_dom(X2))
                & in(apply(X2,X3),X1) )
              | in(X3,relation_dom(X0)) ) )
        | ? [X4] :
            ( apply(X0,X4) != apply(X2,X4)
            & in(X4,relation_dom(X0)) ) )
      & ( ( ! [X3] :
              ( ( in(X3,relation_dom(X0))
                | ~ in(X3,relation_dom(X2))
                | ~ in(apply(X2,X3),X1) )
              & ( ( in(X3,relation_dom(X2))
                  & in(apply(X2,X3),X1) )
                | ~ in(X3,relation_dom(X0)) ) )
          & ! [X4] :
              ( apply(X0,X4) = apply(X2,X4)
              | ~ in(X4,relation_dom(X0)) ) )
        | ~ sP0(X2,X1,X0) ) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ! [X2,X1,X0] :
      ( ( sP0(X2,X1,X0)
        | ? [X3] :
            ( ( ~ in(X3,relation_dom(X2))
              | ~ in(apply(X2,X3),X1)
              | ~ in(X3,relation_dom(X0)) )
            & ( ( in(X3,relation_dom(X2))
                & in(apply(X2,X3),X1) )
              | in(X3,relation_dom(X0)) ) )
        | ? [X4] :
            ( apply(X0,X4) != apply(X2,X4)
            & in(X4,relation_dom(X0)) ) )
      & ( ( ! [X3] :
              ( ( in(X3,relation_dom(X0))
                | ~ in(X3,relation_dom(X2))
                | ~ in(apply(X2,X3),X1) )
              & ( ( in(X3,relation_dom(X2))
                  & in(apply(X2,X3),X1) )
                | ~ in(X3,relation_dom(X0)) ) )
          & ! [X4] :
              ( apply(X0,X4) = apply(X2,X4)
              | ~ in(X4,relation_dom(X0)) ) )
        | ~ sP0(X2,X1,X0) ) ),
    inference(nnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X2,X1,X0] :
      ( sP0(X2,X1,X0)
    <=> ( ! [X3] :
            ( in(X3,relation_dom(X0))
          <=> ( in(X3,relation_dom(X2))
              & in(apply(X2,X3),X1) ) )
        & ! [X4] :
            ( apply(X0,X4) = apply(X2,X4)
            | ~ in(X4,relation_dom(X0)) ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f200,plain,
    ! [X0] : sP0(sK2,X0,relation_rng_restriction(X0,sK2)),
    inference(unit_resulting_resolution,[],[f169,f145]) ).

fof(f145,plain,
    ! [X2,X1] :
      ( ~ sP1(relation_rng_restriction(X2,X1),X1,X2)
      | sP0(X1,X2,relation_rng_restriction(X2,X1)) ),
    inference(equality_resolution,[],[f114]) ).

fof(f114,plain,
    ! [X2,X0,X1] :
      ( sP0(X1,X2,X0)
      | relation_rng_restriction(X2,X1) != X0
      | ~ sP1(X0,X1,X2) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ( ( sP0(X1,X2,X0)
          | relation_rng_restriction(X2,X1) != X0 )
        & ( relation_rng_restriction(X2,X1) = X0
          | ~ sP0(X1,X2,X0) ) )
      | ~ sP1(X0,X1,X2) ),
    inference(rectify,[],[f75]) ).

fof(f75,plain,
    ! [X0,X2,X1] :
      ( ( ( sP0(X2,X1,X0)
          | relation_rng_restriction(X1,X2) != X0 )
        & ( relation_rng_restriction(X1,X2) = X0
          | ~ sP0(X2,X1,X0) ) )
      | ~ sP1(X0,X2,X1) ),
    inference(nnf_transformation,[],[f61]) ).

fof(f61,plain,
    ! [X0,X2,X1] :
      ( ( sP0(X2,X1,X0)
      <=> relation_rng_restriction(X1,X2) = X0 )
      | ~ sP1(X0,X2,X1) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f169,plain,
    ! [X0,X1] : sP1(relation_rng_restriction(X0,sK2),sK2,X1),
    inference(unit_resulting_resolution,[],[f103,f104,f151,f152,f125]) ).

fof(f125,plain,
    ! [X2,X0,X1] :
      ( sP1(X0,X2,X1)
      | ~ function(X0)
      | ~ relation(X2)
      | ~ relation(X0)
      | ~ function(X2) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ! [X2] :
          ( ~ relation(X2)
          | ~ function(X2)
          | sP1(X0,X2,X1) )
      | ~ relation(X0) ),
    inference(definition_folding,[],[f56,f61,f60]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( ~ function(X0)
      | ! [X2] :
          ( ~ relation(X2)
          | ~ function(X2)
          | ( ( ! [X3] :
                  ( in(X3,relation_dom(X0))
                <=> ( in(X3,relation_dom(X2))
                    & in(apply(X2,X3),X1) ) )
              & ! [X4] :
                  ( apply(X0,X4) = apply(X2,X4)
                  | ~ in(X4,relation_dom(X0)) ) )
          <=> relation_rng_restriction(X1,X2) = X0 ) )
      | ~ relation(X0) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X1,X0] :
      ( ! [X2] :
          ( ( ( ! [X3] :
                  ( in(X3,relation_dom(X0))
                <=> ( in(X3,relation_dom(X2))
                    & in(apply(X2,X3),X1) ) )
              & ! [X4] :
                  ( apply(X0,X4) = apply(X2,X4)
                  | ~ in(X4,relation_dom(X0)) ) )
          <=> relation_rng_restriction(X1,X2) = X0 )
          | ~ function(X2)
          | ~ relation(X2) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X1,X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( relation_rng_restriction(X1,X2) = X0
          <=> ( ! [X4] :
                  ( in(X4,relation_dom(X0))
                 => apply(X0,X4) = apply(X2,X4) )
              & ! [X3] :
                  ( in(X3,relation_dom(X0))
                <=> ( in(X3,relation_dom(X2))
                    & in(apply(X2,X3),X1) ) ) ) ) ) ),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X1,X0] :
      ( ( relation(X1)
        & function(X1) )
     => ! [X2] :
          ( ( function(X2)
            & relation(X2) )
         => ( ( ! [X3] :
                  ( ( in(X3,relation_dom(X2))
                    & in(apply(X2,X3),X0) )
                <=> in(X3,relation_dom(X1)) )
              & ! [X3] :
                  ( in(X3,relation_dom(X1))
                 => apply(X2,X3) = apply(X1,X3) ) )
          <=> relation_rng_restriction(X0,X2) = X1 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t85_funct_1) ).

fof(f182,plain,
    in(sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4))),relation_dom(relation_rng_restriction(sK3,sK2))),
    inference(unit_resulting_resolution,[],[f152,f151,f163,f146]) ).

fof(f146,plain,
    ! [X2,X3,X0] :
      ( in(sK10(X0,X2,X3),relation_dom(X0))
      | ~ in(X3,relation_image(X0,X2))
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(equality_resolution,[],[f134]) ).

fof(f134,plain,
    ! [X2,X3,X0,X1] :
      ( in(sK10(X0,X2,X3),relation_dom(X0))
      | ~ in(X3,X1)
      | relation_image(X0,X2) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f280,plain,
    in(apply(sK2,sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4)))),relation_image(sK2,sK4)),
    inference(unit_resulting_resolution,[],[f103,f104,f180,f221,f150]) ).

fof(f150,plain,
    ! [X2,X0,X5] :
      ( in(apply(X0,X5),relation_image(X0,X2))
      | ~ in(X5,X2)
      | ~ function(X0)
      | ~ relation(X0)
      | ~ in(X5,relation_dom(X0)) ),
    inference(equality_resolution,[],[f149]) ).

fof(f149,plain,
    ! [X2,X0,X1,X5] :
      ( in(apply(X0,X5),X1)
      | ~ in(X5,relation_dom(X0))
      | ~ in(X5,X2)
      | relation_image(X0,X2) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f131]) ).

fof(f131,plain,
    ! [X2,X3,X0,X1,X5] :
      ( in(X3,X1)
      | ~ in(X5,relation_dom(X0))
      | ~ in(X5,X2)
      | apply(X0,X5) != X3
      | relation_image(X0,X2) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f221,plain,
    in(sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4))),relation_dom(sK2)),
    inference(unit_resulting_resolution,[],[f182,f200,f117]) ).

fof(f117,plain,
    ! [X2,X0,X1,X5] :
      ( ~ sP0(X0,X1,X2)
      | in(X5,relation_dom(X0))
      | ~ in(X5,relation_dom(X2)) ),
    inference(cnf_transformation,[],[f82]) ).

fof(f180,plain,
    in(sK10(relation_rng_restriction(sK3,sK2),sK4,sK6(relation_image(relation_rng_restriction(sK3,sK2),sK4),relation_image(sK2,sK4))),sK4),
    inference(unit_resulting_resolution,[],[f151,f152,f163,f147]) ).

fof(f147,plain,
    ! [X2,X3,X0] :
      ( in(sK10(X0,X2,X3),X2)
      | ~ relation(X0)
      | ~ function(X0)
      | ~ in(X3,relation_image(X0,X2)) ),
    inference(equality_resolution,[],[f133]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1] :
      ( in(sK10(X0,X2,X3),X2)
      | ~ in(X3,X1)
      | relation_image(X0,X2) != X1
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU051+1 : 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 : n017.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 14:04:50 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 1.39/0.55  % (20718)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)
% 1.39/0.56  % (20723)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)
% 1.39/0.56  % (20715)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)
% 1.39/0.56  % (20735)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)
% 1.65/0.57  % (20723)Instruction limit reached!
% 1.65/0.57  % (20723)------------------------------
% 1.65/0.57  % (20723)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.57  % (20726)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)
% 1.65/0.57  % (20723)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.57  % (20723)Termination reason: Unknown
% 1.65/0.57  % (20723)Termination phase: Saturation
% 1.65/0.57  
% 1.65/0.57  % (20723)Memory used [KB]: 6140
% 1.65/0.57  % (20723)Time elapsed: 0.139 s
% 1.65/0.57  % (20723)Instructions burned: 7 (million)
% 1.65/0.57  % (20723)------------------------------
% 1.65/0.57  % (20723)------------------------------
% 1.65/0.58  % (20736)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)
% 1.65/0.58  % (20732)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)
% 1.65/0.58  % (20726)Instruction limit reached!
% 1.65/0.58  % (20726)------------------------------
% 1.65/0.58  % (20726)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.58  % (20726)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.58  % (20726)Termination reason: Unknown
% 1.65/0.58  % (20726)Termination phase: Property scanning
% 1.65/0.58  
% 1.65/0.58  % (20726)Memory used [KB]: 1535
% 1.65/0.58  % (20726)Time elapsed: 0.005 s
% 1.65/0.58  % (20726)Instructions burned: 3 (million)
% 1.65/0.58  % (20726)------------------------------
% 1.65/0.58  % (20726)------------------------------
% 1.65/0.58  % (20732)Refutation not found, incomplete strategy% (20732)------------------------------
% 1.65/0.58  % (20732)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.58  % (20732)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.58  % (20732)Termination reason: Refutation not found, incomplete strategy
% 1.65/0.58  
% 1.65/0.58  % (20732)Memory used [KB]: 6012
% 1.65/0.58  % (20732)Time elapsed: 0.155 s
% 1.65/0.58  % (20732)Instructions burned: 4 (million)
% 1.65/0.58  % (20732)------------------------------
% 1.65/0.58  % (20732)------------------------------
% 1.65/0.58  % (20715)First to succeed.
% 1.65/0.59  % (20722)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)
% 1.65/0.59  % (20720)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)
% 1.65/0.59  % (20716)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)
% 1.65/0.59  % (20717)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)
% 1.65/0.59  % (20715)Refutation found. Thanks to Tanya!
% 1.65/0.59  % SZS status Theorem for theBenchmark
% 1.65/0.59  % SZS output start Proof for theBenchmark
% See solution above
% 1.65/0.59  % (20715)------------------------------
% 1.65/0.59  % (20715)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.65/0.59  % (20715)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.65/0.59  % (20715)Termination reason: Refutation
% 1.65/0.59  
% 1.65/0.59  % (20715)Memory used [KB]: 6396
% 1.65/0.59  % (20715)Time elapsed: 0.160 s
% 1.65/0.59  % (20715)Instructions burned: 16 (million)
% 1.65/0.59  % (20715)------------------------------
% 1.65/0.59  % (20715)------------------------------
% 1.65/0.59  % (20711)Success in time 0.238 s
%------------------------------------------------------------------------------