TSTP Solution File: SEU226+3 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU226+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_sat --cores 0 -t %d %s

% Computer : n021.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 18:32:40 EDT 2022

% Result   : Theorem 1.42s 0.54s
% Output   : Refutation 1.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   55 (  10 unt;   0 def)
%            Number of atoms       :  318 (  53 equ)
%            Maximal formula atoms :   20 (   5 avg)
%            Number of connectives :  404 ( 141   ~; 140   |;  93   &)
%                                         (  17 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   7 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-3 aty)
%            Number of variables   :  153 ( 125   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f401,plain,
    $false,
    inference(subsumption_resolution,[],[f397,f142]) ).

fof(f142,plain,
    ~ subset(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( function(sK8)
    & relation(sK8)
    & ~ subset(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8])],[f49,f89]) ).

fof(f89,plain,
    ( ? [X0,X1] :
        ( function(X1)
        & relation(X1)
        & ~ subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) )
   => ( function(sK8)
      & relation(sK8)
      & ~ subset(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7) ) ),
    introduced(choice_axiom,[]) ).

fof(f49,plain,
    ? [X0,X1] :
      ( function(X1)
      & relation(X1)
      & ~ subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
    inference(flattening,[],[f48]) ).

fof(f48,plain,
    ? [X0,X1] :
      ( ~ subset(relation_image(X1,relation_inverse_image(X1,X0)),X0)
      & function(X1)
      & relation(X1) ),
    inference(ennf_transformation,[],[f27]) ).

fof(f27,negated_conjecture,
    ~ ! [X0,X1] :
        ( ( function(X1)
          & relation(X1) )
       => subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
    inference(negated_conjecture,[],[f26]) ).

fof(f26,conjecture,
    ! [X0,X1] :
      ( ( function(X1)
        & relation(X1) )
     => subset(relation_image(X1,relation_inverse_image(X1,X0)),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_funct_1) ).

fof(f397,plain,
    subset(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7),
    inference(resolution,[],[f392,f135]) ).

fof(f135,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( in(sK4(X0,X1),X0)
          & ~ in(sK4(X0,X1),X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f82,f83]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X0)
          & ~ in(X2,X1) )
     => ( in(sK4(X0,X1),X0)
        & ~ in(sK4(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f82,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f81]) ).

fof(f81,plain,
    ! [X1,X0] :
      ( ( subset(X1,X0)
        | ? [X2] :
            ( in(X2,X1)
            & ~ in(X2,X0) ) )
      & ( ! [X2] :
            ( ~ in(X2,X1)
            | in(X2,X0) )
        | ~ subset(X1,X0) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X1,X0] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( ~ in(X2,X1)
          | in(X2,X0) ) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1] :
      ( subset(X1,X0)
    <=> ! [X2] :
          ( in(X2,X1)
         => in(X2,X0) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X1,X0] :
      ( ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) )
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f392,plain,
    in(sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7),sK7),
    inference(backward_demodulation,[],[f333,f389]) ).

fof(f389,plain,
    apply(sK8,sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7))) = sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7),
    inference(subsumption_resolution,[],[f388,f143]) ).

fof(f143,plain,
    relation(sK8),
    inference(cnf_transformation,[],[f90]) ).

fof(f388,plain,
    ( apply(sK8,sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7))) = sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7)
    | ~ relation(sK8) ),
    inference(subsumption_resolution,[],[f381,f144]) ).

fof(f144,plain,
    function(sK8),
    inference(cnf_transformation,[],[f90]) ).

fof(f381,plain,
    ( apply(sK8,sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7))) = sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7)
    | ~ function(sK8)
    | ~ relation(sK8) ),
    inference(resolution,[],[f184,f233]) ).

fof(f233,plain,
    in(sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7),relation_image(sK8,relation_inverse_image(sK8,sK7))),
    inference(resolution,[],[f136,f142]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK4(X0,X1),X0) ),
    inference(cnf_transformation,[],[f84]) ).

fof(f184,plain,
    ! [X2,X0,X6] :
      ( ~ in(X6,relation_image(X0,X2))
      | apply(X0,sK15(X0,X2,X6)) = X6
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(equality_resolution,[],[f165]) ).

fof(f165,plain,
    ! [X2,X0,X1,X6] :
      ( ~ function(X0)
      | apply(X0,sK15(X0,X2,X6)) = X6
      | ~ in(X6,X1)
      | relation_image(X0,X2) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0] :
      ( ~ function(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X2) = X1
            | ( ( ~ in(sK13(X0,X1,X2),X1)
                | ! [X4] :
                    ( ~ in(X4,X2)
                    | apply(X0,X4) != sK13(X0,X1,X2)
                    | ~ in(X4,relation_dom(X0)) ) )
              & ( in(sK13(X0,X1,X2),X1)
                | ( in(sK14(X0,X1,X2),X2)
                  & sK13(X0,X1,X2) = apply(X0,sK14(X0,X1,X2))
                  & in(sK14(X0,X1,X2),relation_dom(X0)) ) ) ) )
          & ( ! [X6] :
                ( ( ( in(sK15(X0,X2,X6),X2)
                    & apply(X0,sK15(X0,X2,X6)) = X6
                    & in(sK15(X0,X2,X6),relation_dom(X0)) )
                  | ~ in(X6,X1) )
                & ( in(X6,X1)
                  | ! [X8] :
                      ( ~ in(X8,X2)
                      | apply(X0,X8) != X6
                      | ~ in(X8,relation_dom(X0)) ) ) )
            | relation_image(X0,X2) != X1 ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15])],[f104,f107,f106,f105]) ).

fof(f105,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ! [X4] :
                ( ~ in(X4,X2)
                | apply(X0,X4) != X3
                | ~ in(X4,relation_dom(X0)) ) )
          & ( in(X3,X1)
            | ? [X5] :
                ( in(X5,X2)
                & apply(X0,X5) = X3
                & in(X5,relation_dom(X0)) ) ) )
     => ( ( ~ in(sK13(X0,X1,X2),X1)
          | ! [X4] :
              ( ~ in(X4,X2)
              | apply(X0,X4) != sK13(X0,X1,X2)
              | ~ in(X4,relation_dom(X0)) ) )
        & ( in(sK13(X0,X1,X2),X1)
          | ? [X5] :
              ( in(X5,X2)
              & sK13(X0,X1,X2) = apply(X0,X5)
              & in(X5,relation_dom(X0)) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f106,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( in(X5,X2)
          & sK13(X0,X1,X2) = apply(X0,X5)
          & in(X5,relation_dom(X0)) )
     => ( in(sK14(X0,X1,X2),X2)
        & sK13(X0,X1,X2) = apply(X0,sK14(X0,X1,X2))
        & in(sK14(X0,X1,X2),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0,X2,X6] :
      ( ? [X7] :
          ( in(X7,X2)
          & apply(X0,X7) = X6
          & in(X7,relation_dom(X0)) )
     => ( in(sK15(X0,X2,X6),X2)
        & apply(X0,sK15(X0,X2,X6)) = X6
        & in(sK15(X0,X2,X6),relation_dom(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f104,plain,
    ! [X0] :
      ( ~ function(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X2) = X1
            | ? [X3] :
                ( ( ~ in(X3,X1)
                  | ! [X4] :
                      ( ~ in(X4,X2)
                      | apply(X0,X4) != X3
                      | ~ in(X4,relation_dom(X0)) ) )
                & ( in(X3,X1)
                  | ? [X5] :
                      ( in(X5,X2)
                      & apply(X0,X5) = X3
                      & in(X5,relation_dom(X0)) ) ) ) )
          & ( ! [X6] :
                ( ( ? [X7] :
                      ( in(X7,X2)
                      & apply(X0,X7) = X6
                      & in(X7,relation_dom(X0)) )
                  | ~ in(X6,X1) )
                & ( in(X6,X1)
                  | ! [X8] :
                      ( ~ in(X8,X2)
                      | apply(X0,X8) != X6
                      | ~ in(X8,relation_dom(X0)) ) ) )
            | relation_image(X0,X2) != X1 ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ~ function(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X2) = X1
            | ? [X3] :
                ( ( ~ in(X3,X1)
                  | ! [X4] :
                      ( ~ in(X4,X2)
                      | apply(X0,X4) != X3
                      | ~ in(X4,relation_dom(X0)) ) )
                & ( in(X3,X1)
                  | ? [X4] :
                      ( in(X4,X2)
                      & apply(X0,X4) = X3
                      & in(X4,relation_dom(X0)) ) ) ) )
          & ( ! [X3] :
                ( ( ? [X4] :
                      ( in(X4,X2)
                      & apply(X0,X4) = X3
                      & in(X4,relation_dom(X0)) )
                  | ~ in(X3,X1) )
                & ( in(X3,X1)
                  | ! [X4] :
                      ( ~ in(X4,X2)
                      | apply(X0,X4) != X3
                      | ~ in(X4,relation_dom(X0)) ) ) )
            | relation_image(X0,X2) != X1 ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0] :
      ( ~ function(X0)
      | ! [X1,X2] :
          ( relation_image(X0,X2) = X1
        <=> ! [X3] :
              ( ? [X4] :
                  ( in(X4,X2)
                  & apply(X0,X4) = X3
                  & in(X4,relation_dom(X0)) )
            <=> in(X3,X1) ) )
      | ~ relation(X0) ),
    inference(flattening,[],[f50]) ).

fof(f50,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( relation_image(X0,X2) = X1
        <=> ! [X3] :
              ( ? [X4] :
                  ( in(X4,X2)
                  & apply(X0,X4) = X3
                  & in(X4,relation_dom(X0)) )
            <=> in(X3,X1) ) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( relation_image(X0,X2) = X1
        <=> ! [X3] :
              ( ? [X4] :
                  ( in(X4,X2)
                  & apply(X0,X4) = X3
                  & in(X4,relation_dom(X0)) )
            <=> in(X3,X1) ) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X2,X1] :
          ( ! [X3] :
              ( ? [X4] :
                  ( apply(X0,X4) = X3
                  & in(X4,relation_dom(X0))
                  & in(X4,X1) )
            <=> in(X3,X2) )
        <=> relation_image(X0,X1) = X2 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).

fof(f333,plain,
    in(apply(sK8,sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7))),sK7),
    inference(subsumption_resolution,[],[f332,f143]) ).

fof(f332,plain,
    ( ~ relation(sK8)
    | in(apply(sK8,sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7))),sK7) ),
    inference(subsumption_resolution,[],[f327,f144]) ).

fof(f327,plain,
    ( ~ function(sK8)
    | ~ relation(sK8)
    | in(apply(sK8,sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7))),sK7) ),
    inference(resolution,[],[f282,f182]) ).

fof(f182,plain,
    ! [X3,X0,X1] :
      ( ~ in(X3,relation_inverse_image(X0,X1))
      | ~ relation(X0)
      | in(apply(X0,X3),X1)
      | ~ function(X0) ),
    inference(equality_resolution,[],[f160]) ).

fof(f160,plain,
    ! [X2,X3,X0,X1] :
      ( in(apply(X0,X3),X1)
      | ~ in(X3,X2)
      | relation_inverse_image(X0,X1) != X2
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [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
            | ( ( ~ in(sK12(X0,X1,X2),relation_dom(X0))
                | ~ in(apply(X0,sK12(X0,X1,X2)),X1)
                | ~ in(sK12(X0,X1,X2),X2) )
              & ( ( in(sK12(X0,X1,X2),relation_dom(X0))
                  & in(apply(X0,sK12(X0,X1,X2)),X1) )
                | in(sK12(X0,X1,X2),X2) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f100,f101]) ).

fof(f101,plain,
    ! [X0,X1,X2] :
      ( ? [X4] :
          ( ( ~ in(X4,relation_dom(X0))
            | ~ in(apply(X0,X4),X1)
            | ~ in(X4,X2) )
          & ( ( in(X4,relation_dom(X0))
              & in(apply(X0,X4),X1) )
            | in(X4,X2) ) )
     => ( ( ~ in(sK12(X0,X1,X2),relation_dom(X0))
          | ~ in(apply(X0,sK12(X0,X1,X2)),X1)
          | ~ in(sK12(X0,X1,X2),X2) )
        & ( ( in(sK12(X0,X1,X2),relation_dom(X0))
            & in(apply(X0,sK12(X0,X1,X2)),X1) )
          | in(sK12(X0,X1,X2),X2) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [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
            | ? [X4] :
                ( ( ~ in(X4,relation_dom(X0))
                  | ~ in(apply(X0,X4),X1)
                  | ~ in(X4,X2) )
                & ( ( in(X4,relation_dom(X0))
                    & in(apply(X0,X4),X1) )
                  | in(X4,X2) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(rectify,[],[f99]) ).

fof(f99,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [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,[],[f98]) ).

fof(f98,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [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,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ! [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,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ( in(X3,relation_dom(X0))
                & in(apply(X0,X3),X1) ) )
        <=> relation_inverse_image(X0,X1) = X2 )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ! [X1,X2] :
          ( ! [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(f282,plain,
    in(sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7)),relation_inverse_image(sK8,sK7)),
    inference(subsumption_resolution,[],[f281,f144]) ).

fof(f281,plain,
    ( in(sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7)),relation_inverse_image(sK8,sK7))
    | ~ function(sK8) ),
    inference(subsumption_resolution,[],[f277,f143]) ).

fof(f277,plain,
    ( ~ relation(sK8)
    | ~ function(sK8)
    | in(sK15(sK8,relation_inverse_image(sK8,sK7),sK4(relation_image(sK8,relation_inverse_image(sK8,sK7)),sK7)),relation_inverse_image(sK8,sK7)) ),
    inference(resolution,[],[f183,f233]) ).

fof(f183,plain,
    ! [X2,X0,X6] :
      ( ~ in(X6,relation_image(X0,X2))
      | ~ function(X0)
      | ~ relation(X0)
      | in(sK15(X0,X2,X6),X2) ),
    inference(equality_resolution,[],[f166]) ).

fof(f166,plain,
    ! [X2,X0,X1,X6] :
      ( ~ function(X0)
      | in(sK15(X0,X2,X6),X2)
      | ~ in(X6,X1)
      | relation_image(X0,X2) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f108]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SEU226+3 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n021.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 14:49:26 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (32359)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51  % (32368)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51  % (32357)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 1.27/0.51  % (32376)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.27/0.51  % (32360)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 1.27/0.52  % (32363)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.27/0.52  % (32356)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.27/0.52  % (32363)Instruction limit reached!
% 1.27/0.52  % (32363)------------------------------
% 1.27/0.52  % (32363)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.27/0.52  % (32363)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.27/0.52  % (32363)Termination reason: Unknown
% 1.27/0.52  % (32363)Termination phase: Preprocessing 3
% 1.27/0.52  
% 1.27/0.52  % (32363)Memory used [KB]: 895
% 1.27/0.52  % (32363)Time elapsed: 0.003 s
% 1.27/0.52  % (32363)Instructions burned: 2 (million)
% 1.27/0.52  % (32363)------------------------------
% 1.27/0.52  % (32363)------------------------------
% 1.27/0.52  % (32355)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.27/0.52  % (32379)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.27/0.53  % (32378)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 1.27/0.53  % (32356)Refutation not found, incomplete strategy% (32356)------------------------------
% 1.27/0.53  % (32356)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.53  % (32373)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.42/0.53  % (32370)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.42/0.53  % (32362)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.42/0.53  % (32374)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.42/0.53  % (32358)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.42/0.53  % (32362)Instruction limit reached!
% 1.42/0.53  % (32362)------------------------------
% 1.42/0.53  % (32362)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.53  % (32362)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.53  % (32362)Termination reason: Unknown
% 1.42/0.53  % (32362)Termination phase: Saturation
% 1.42/0.53  
% 1.42/0.53  % (32362)Memory used [KB]: 5500
% 1.42/0.53  % (32362)Time elapsed: 0.134 s
% 1.42/0.53  % (32362)Instructions burned: 7 (million)
% 1.42/0.53  % (32362)------------------------------
% 1.42/0.53  % (32362)------------------------------
% 1.42/0.53  % (32383)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.42/0.53  % (32365)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.42/0.53  % (32366)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.42/0.53  % (32356)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.53  % (32356)Termination reason: Refutation not found, incomplete strategy
% 1.42/0.53  
% 1.42/0.53  % (32356)Memory used [KB]: 5500
% 1.42/0.53  % (32356)Time elapsed: 0.121 s
% 1.42/0.53  % (32356)Instructions burned: 4 (million)
% 1.42/0.53  % (32356)------------------------------
% 1.42/0.53  % (32356)------------------------------
% 1.42/0.54  % (32372)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.42/0.54  % (32375)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.42/0.54  TRYING [1]
% 1.42/0.54  TRYING [2]
% 1.42/0.54  % (32376)First to succeed.
% 1.42/0.54  % (32361)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.42/0.54  % (32377)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.42/0.54  % (32376)Refutation found. Thanks to Tanya!
% 1.42/0.54  % SZS status Theorem for theBenchmark
% 1.42/0.54  % SZS output start Proof for theBenchmark
% See solution above
% 1.42/0.54  % (32376)------------------------------
% 1.42/0.54  % (32376)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.42/0.54  % (32376)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.42/0.54  % (32376)Termination reason: Refutation
% 1.42/0.54  
% 1.42/0.54  % (32376)Memory used [KB]: 5756
% 1.42/0.54  % (32376)Time elapsed: 0.149 s
% 1.42/0.54  % (32376)Instructions burned: 12 (million)
% 1.42/0.54  % (32376)------------------------------
% 1.42/0.54  % (32376)------------------------------
% 1.42/0.54  % (32354)Success in time 0.191 s
%------------------------------------------------------------------------------