TSTP Solution File: SEU227+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU227+1 : TPTP v8.1.0. Released v3.3.0.
% 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 : n023.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 2.21s 0.66s
% Output   : Refutation 2.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   72 (  10 unt;   0 def)
%            Number of atoms       :  344 (  32 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  422 ( 150   ~; 150   |;  83   &)
%                                         (  18 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   5 con; 0-3 aty)
%            Number of variables   :  231 ( 179   !;  52   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1009,plain,
    $false,
    inference(subsumption_resolution,[],[f1008,f224]) ).

fof(f224,plain,
    ~ subset(sK12,sF25),
    inference(definition_folding,[],[f181,f223,f222]) ).

fof(f222,plain,
    sF24 = relation_image(sK11,sK12),
    introduced(function_definition,[]) ).

fof(f223,plain,
    sF25 = relation_inverse_image(sK11,sF24),
    introduced(function_definition,[]) ).

fof(f181,plain,
    ~ subset(sK12,relation_inverse_image(sK11,relation_image(sK11,sK12))),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ( subset(sK12,relation_dom(sK11))
    & ~ subset(sK12,relation_inverse_image(sK11,relation_image(sK11,sK12)))
    & relation(sK11) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f117,f118]) ).

fof(f118,plain,
    ( ? [X0,X1] :
        ( subset(X1,relation_dom(X0))
        & ~ subset(X1,relation_inverse_image(X0,relation_image(X0,X1)))
        & relation(X0) )
   => ( subset(sK12,relation_dom(sK11))
      & ~ subset(sK12,relation_inverse_image(sK11,relation_image(sK11,sK12)))
      & relation(sK11) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ? [X0,X1] :
      ( subset(X1,relation_dom(X0))
      & ~ subset(X1,relation_inverse_image(X0,relation_image(X0,X1)))
      & relation(X0) ),
    inference(rectify,[],[f79]) ).

fof(f79,plain,
    ? [X1,X0] :
      ( subset(X0,relation_dom(X1))
      & ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
      & relation(X1) ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ? [X0,X1] :
      ( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
      & subset(X0,relation_dom(X1))
      & relation(X1) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,negated_conjecture,
    ~ ! [X0,X1] :
        ( relation(X1)
       => ( subset(X0,relation_dom(X1))
         => subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
    inference(negated_conjecture,[],[f41]) ).

fof(f41,conjecture,
    ! [X0,X1] :
      ( relation(X1)
     => ( subset(X0,relation_dom(X1))
       => subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).

fof(f1008,plain,
    subset(sK12,sF25),
    inference(duplicate_literal_removal,[],[f1007]) ).

fof(f1007,plain,
    ( subset(sK12,sF25)
    | subset(sK12,sF25) ),
    inference(resolution,[],[f779,f153]) ).

fof(f153,plain,
    ! [X0,X1] :
      ( in(sK4(X0,X1),X1)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ( subset(X1,X0)
        | ( ~ in(sK4(X0,X1),X0)
          & in(sK4(X0,X1),X1) ) )
      & ( ! [X3] :
            ( in(X3,X0)
            | ~ in(X3,X1) )
        | ~ subset(X1,X0) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f98,f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ in(X2,X0)
          & in(X2,X1) )
     => ( ~ in(sK4(X0,X1),X0)
        & in(sK4(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f98,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,[],[f97]) ).

fof(f97,plain,
    ! [X1,X0] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ in(X2,X1)
            & in(X2,X0) ) )
      & ( ! [X2] :
            ( in(X2,X1)
            | ~ in(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X1)
          | ~ in(X2,X0) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X1,X0] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).

fof(f779,plain,
    ! [X16] :
      ( ~ in(sK4(sF25,X16),sK12)
      | subset(X16,sF25) ),
    inference(resolution,[],[f698,f154]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ~ in(sK4(X0,X1),X0)
      | subset(X1,X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f698,plain,
    ! [X0] :
      ( in(X0,sF25)
      | ~ in(X0,sK12) ),
    inference(forward_demodulation,[],[f697,f223]) ).

fof(f697,plain,
    ! [X0] :
      ( in(X0,relation_inverse_image(sK11,sF24))
      | ~ in(X0,sK12) ),
    inference(subsumption_resolution,[],[f692,f288]) ).

fof(f288,plain,
    ! [X4] :
      ( ~ in(X4,sK12)
      | in(X4,sF23) ),
    inference(resolution,[],[f152,f221]) ).

fof(f221,plain,
    subset(sK12,sF23),
    inference(definition_folding,[],[f182,f220]) ).

fof(f220,plain,
    relation_dom(sK11) = sF23,
    introduced(function_definition,[]) ).

fof(f182,plain,
    subset(sK12,relation_dom(sK11)),
    inference(cnf_transformation,[],[f119]) ).

fof(f152,plain,
    ! [X3,X0,X1] :
      ( ~ subset(X1,X0)
      | ~ in(X3,X1)
      | in(X3,X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f692,plain,
    ! [X0] :
      ( in(X0,relation_inverse_image(sK11,sF24))
      | ~ in(X0,sK12)
      | ~ in(X0,sF23) ),
    inference(resolution,[],[f654,f399]) ).

fof(f399,plain,
    ! [X0,X1] :
      ( ~ in(sK0(sK11,X0),X1)
      | ~ in(X0,sF23)
      | in(X0,relation_inverse_image(sK11,X1)) ),
    inference(subsumption_resolution,[],[f392,f180]) ).

fof(f180,plain,
    relation(sK11),
    inference(cnf_transformation,[],[f119]) ).

fof(f392,plain,
    ! [X0,X1] :
      ( ~ in(X0,sF23)
      | ~ relation(sK11)
      | ~ in(sK0(sK11,X0),X1)
      | in(X0,relation_inverse_image(sK11,X1)) ),
    inference(resolution,[],[f319,f219]) ).

fof(f219,plain,
    ! [X2,X3,X0,X5] :
      ( ~ in(ordered_pair(X3,X5),X0)
      | in(X3,relation_inverse_image(X0,X2))
      | ~ relation(X0)
      | ~ in(X5,X2) ),
    inference(equality_resolution,[],[f201]) ).

fof(f201,plain,
    ! [X2,X3,X0,X1,X5] :
      ( in(X3,X1)
      | ~ in(X5,X2)
      | ~ in(ordered_pair(X3,X5),X0)
      | relation_inverse_image(X0,X2) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [X3] :
                ( ( ( in(sK15(X0,X2,X3),X2)
                    & in(ordered_pair(X3,sK15(X0,X2,X3)),X0) )
                  | ~ in(X3,X1) )
                & ( in(X3,X1)
                  | ! [X5] :
                      ( ~ in(X5,X2)
                      | ~ in(ordered_pair(X3,X5),X0) ) ) )
            | relation_inverse_image(X0,X2) != X1 )
          & ( relation_inverse_image(X0,X2) = X1
            | ( ( ~ in(sK16(X0,X1,X2),X1)
                | ! [X7] :
                    ( ~ in(X7,X2)
                    | ~ in(ordered_pair(sK16(X0,X1,X2),X7),X0) ) )
              & ( in(sK16(X0,X1,X2),X1)
                | ( in(sK17(X0,X1,X2),X2)
                  & in(ordered_pair(sK16(X0,X1,X2),sK17(X0,X1,X2)),X0) ) ) ) ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f126,f129,f128,f127]) ).

fof(f127,plain,
    ! [X0,X2,X3] :
      ( ? [X4] :
          ( in(X4,X2)
          & in(ordered_pair(X3,X4),X0) )
     => ( in(sK15(X0,X2,X3),X2)
        & in(ordered_pair(X3,sK15(X0,X2,X3)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ! [X0,X1,X2] :
      ( ? [X6] :
          ( ( ~ in(X6,X1)
            | ! [X7] :
                ( ~ in(X7,X2)
                | ~ in(ordered_pair(X6,X7),X0) ) )
          & ( in(X6,X1)
            | ? [X8] :
                ( in(X8,X2)
                & in(ordered_pair(X6,X8),X0) ) ) )
     => ( ( ~ in(sK16(X0,X1,X2),X1)
          | ! [X7] :
              ( ~ in(X7,X2)
              | ~ in(ordered_pair(sK16(X0,X1,X2),X7),X0) ) )
        & ( in(sK16(X0,X1,X2),X1)
          | ? [X8] :
              ( in(X8,X2)
              & in(ordered_pair(sK16(X0,X1,X2),X8),X0) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ! [X0,X1,X2] :
      ( ? [X8] :
          ( in(X8,X2)
          & in(ordered_pair(sK16(X0,X1,X2),X8),X0) )
     => ( in(sK17(X0,X1,X2),X2)
        & in(ordered_pair(sK16(X0,X1,X2),sK17(X0,X1,X2)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [X3] :
                ( ( ? [X4] :
                      ( in(X4,X2)
                      & in(ordered_pair(X3,X4),X0) )
                  | ~ in(X3,X1) )
                & ( in(X3,X1)
                  | ! [X5] :
                      ( ~ in(X5,X2)
                      | ~ in(ordered_pair(X3,X5),X0) ) ) )
            | relation_inverse_image(X0,X2) != X1 )
          & ( relation_inverse_image(X0,X2) = X1
            | ? [X6] :
                ( ( ~ in(X6,X1)
                  | ! [X7] :
                      ( ~ in(X7,X2)
                      | ~ in(ordered_pair(X6,X7),X0) ) )
                & ( in(X6,X1)
                  | ? [X8] :
                      ( in(X8,X2)
                      & in(ordered_pair(X6,X8),X0) ) ) ) ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f125]) ).

fof(f125,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ( ! [X3] :
                ( ( ? [X4] :
                      ( in(X4,X2)
                      & in(ordered_pair(X3,X4),X0) )
                  | ~ in(X3,X1) )
                & ( in(X3,X1)
                  | ! [X4] :
                      ( ~ in(X4,X2)
                      | ~ in(ordered_pair(X3,X4),X0) ) ) )
            | relation_inverse_image(X0,X2) != X1 )
          & ( relation_inverse_image(X0,X2) = X1
            | ? [X3] :
                ( ( ~ in(X3,X1)
                  | ! [X4] :
                      ( ~ in(X4,X2)
                      | ~ in(ordered_pair(X3,X4),X0) ) )
                & ( in(X3,X1)
                  | ? [X4] :
                      ( in(X4,X2)
                      & in(ordered_pair(X3,X4),X0) ) ) ) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( ! [X3] :
              ( ? [X4] :
                  ( in(X4,X2)
                  & in(ordered_pair(X3,X4),X0) )
            <=> in(X3,X1) )
        <=> relation_inverse_image(X0,X2) = X1 )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( relation(X0)
     => ! [X1,X2] :
          ( ! [X3] :
              ( ? [X4] :
                  ( in(X4,X2)
                  & in(ordered_pair(X3,X4),X0) )
            <=> in(X3,X1) )
        <=> relation_inverse_image(X0,X2) = X1 ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(ordered_pair(X3,X4),X0)
                  & in(X4,X1) ) )
        <=> relation_inverse_image(X0,X1) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).

fof(f319,plain,
    ! [X0] :
      ( in(ordered_pair(X0,sK0(sK11,X0)),sK11)
      | ~ in(X0,sF23) ),
    inference(subsumption_resolution,[],[f316,f180]) ).

fof(f316,plain,
    ! [X0] :
      ( ~ in(X0,sF23)
      | in(ordered_pair(X0,sK0(sK11,X0)),sK11)
      | ~ relation(sK11) ),
    inference(superposition,[],[f212,f220]) ).

fof(f212,plain,
    ! [X2,X0] :
      ( ~ in(X2,relation_dom(X0))
      | ~ relation(X0)
      | in(ordered_pair(X2,sK0(X0,X2)),X0) ),
    inference(equality_resolution,[],[f146]) ).

fof(f146,plain,
    ! [X2,X0,X1] :
      ( in(ordered_pair(X2,sK0(X0,X2)),X0)
      | ~ in(X2,X1)
      | relation_dom(X0) != X1
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( in(ordered_pair(X2,sK0(X0,X2)),X0)
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X4] : ~ in(ordered_pair(X2,X4),X0) ) )
            | relation_dom(X0) != X1 )
          & ( relation_dom(X0) = X1
            | ( ( ~ in(sK1(X0,X1),X1)
                | ! [X6] : ~ in(ordered_pair(sK1(X0,X1),X6),X0) )
              & ( in(sK1(X0,X1),X1)
                | in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) ) ) ) )
      | ~ relation(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f89,f92,f91,f90]) ).

fof(f90,plain,
    ! [X0,X2] :
      ( ? [X3] : in(ordered_pair(X2,X3),X0)
     => in(ordered_pair(X2,sK0(X0,X2)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ! [X0,X1] :
      ( ? [X5] :
          ( ( ~ in(X5,X1)
            | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
          & ( in(X5,X1)
            | ? [X7] : in(ordered_pair(X5,X7),X0) ) )
     => ( ( ~ in(sK1(X0,X1),X1)
          | ! [X6] : ~ in(ordered_pair(sK1(X0,X1),X6),X0) )
        & ( in(sK1(X0,X1),X1)
          | ? [X7] : in(ordered_pair(sK1(X0,X1),X7),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( ? [X7] : in(ordered_pair(sK1(X0,X1),X7),X0)
     => in(ordered_pair(sK1(X0,X1),sK2(X0,X1)),X0) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X4] : ~ in(ordered_pair(X2,X4),X0) ) )
            | relation_dom(X0) != X1 )
          & ( relation_dom(X0) = X1
            | ? [X5] :
                ( ( ~ in(X5,X1)
                  | ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
                & ( in(X5,X1)
                  | ? [X7] : in(ordered_pair(X5,X7),X0) ) ) ) )
      | ~ relation(X0) ),
    inference(rectify,[],[f88]) ).

fof(f88,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ! [X2] :
                ( ( ? [X3] : in(ordered_pair(X2,X3),X0)
                  | ~ in(X2,X1) )
                & ( in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) ) )
            | relation_dom(X0) != X1 )
          & ( relation_dom(X0) = X1
            | ? [X2] :
                ( ( ~ in(X2,X1)
                  | ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
                & ( in(X2,X1)
                  | ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ? [X3] : in(ordered_pair(X2,X3),X0)
            <=> in(X2,X1) )
        <=> relation_dom(X0) = X1 )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X1] :
          ( ! [X2] :
              ( ? [X3] : in(ordered_pair(X2,X3),X0)
            <=> in(X2,X1) )
        <=> relation_dom(X0) = X1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

fof(f654,plain,
    ! [X0] :
      ( in(sK0(sK11,X0),sF24)
      | ~ in(X0,sK12) ),
    inference(subsumption_resolution,[],[f652,f288]) ).

fof(f652,plain,
    ! [X0] :
      ( in(sK0(sK11,X0),sF24)
      | ~ in(X0,sK12)
      | ~ in(X0,sF23) ),
    inference(superposition,[],[f400,f222]) ).

fof(f400,plain,
    ! [X2,X3] :
      ( in(sK0(sK11,X2),relation_image(sK11,X3))
      | ~ in(X2,X3)
      | ~ in(X2,sF23) ),
    inference(subsumption_resolution,[],[f393,f180]) ).

fof(f393,plain,
    ! [X2,X3] :
      ( ~ relation(sK11)
      | ~ in(X2,X3)
      | ~ in(X2,sF23)
      | in(sK0(sK11,X2),relation_image(sK11,X3)) ),
    inference(resolution,[],[f319,f216]) ).

fof(f216,plain,
    ! [X2,X0,X8,X6] :
      ( ~ in(ordered_pair(X8,X6),X0)
      | ~ relation(X0)
      | in(X6,relation_image(X0,X2))
      | ~ in(X8,X2) ),
    inference(equality_resolution,[],[f172]) ).

fof(f172,plain,
    ! [X2,X0,X1,X8,X6] :
      ( ~ relation(X0)
      | in(X6,X1)
      | ~ in(X8,X2)
      | ~ in(ordered_pair(X8,X6),X0)
      | relation_image(X0,X2) != X1 ),
    inference(cnf_transformation,[],[f115]) ).

fof(f115,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X2) = X1
            | ( ( ~ in(sK8(X0,X1,X2),X1)
                | ! [X4] :
                    ( ~ in(X4,X2)
                    | ~ in(ordered_pair(X4,sK8(X0,X1,X2)),X0) ) )
              & ( in(sK8(X0,X1,X2),X1)
                | ( in(sK9(X0,X1,X2),X2)
                  & in(ordered_pair(sK9(X0,X1,X2),sK8(X0,X1,X2)),X0) ) ) ) )
          & ( ! [X6] :
                ( ( ( in(sK10(X0,X2,X6),X2)
                    & in(ordered_pair(sK10(X0,X2,X6),X6),X0) )
                  | ~ in(X6,X1) )
                & ( in(X6,X1)
                  | ! [X8] :
                      ( ~ in(X8,X2)
                      | ~ in(ordered_pair(X8,X6),X0) ) ) )
            | relation_image(X0,X2) != X1 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10])],[f111,f114,f113,f112]) ).

fof(f112,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(X3,X1)
            | ! [X4] :
                ( ~ in(X4,X2)
                | ~ in(ordered_pair(X4,X3),X0) ) )
          & ( in(X3,X1)
            | ? [X5] :
                ( in(X5,X2)
                & in(ordered_pair(X5,X3),X0) ) ) )
     => ( ( ~ in(sK8(X0,X1,X2),X1)
          | ! [X4] :
              ( ~ in(X4,X2)
              | ~ in(ordered_pair(X4,sK8(X0,X1,X2)),X0) ) )
        & ( in(sK8(X0,X1,X2),X1)
          | ? [X5] :
              ( in(X5,X2)
              & in(ordered_pair(X5,sK8(X0,X1,X2)),X0) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f113,plain,
    ! [X0,X1,X2] :
      ( ? [X5] :
          ( in(X5,X2)
          & in(ordered_pair(X5,sK8(X0,X1,X2)),X0) )
     => ( in(sK9(X0,X1,X2),X2)
        & in(ordered_pair(sK9(X0,X1,X2),sK8(X0,X1,X2)),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ! [X0,X2,X6] :
      ( ? [X7] :
          ( in(X7,X2)
          & in(ordered_pair(X7,X6),X0) )
     => ( in(sK10(X0,X2,X6),X2)
        & in(ordered_pair(sK10(X0,X2,X6),X6),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X2) = X1
            | ? [X3] :
                ( ( ~ in(X3,X1)
                  | ! [X4] :
                      ( ~ in(X4,X2)
                      | ~ in(ordered_pair(X4,X3),X0) ) )
                & ( in(X3,X1)
                  | ? [X5] :
                      ( in(X5,X2)
                      & in(ordered_pair(X5,X3),X0) ) ) ) )
          & ( ! [X6] :
                ( ( ? [X7] :
                      ( in(X7,X2)
                      & in(ordered_pair(X7,X6),X0) )
                  | ~ in(X6,X1) )
                & ( in(X6,X1)
                  | ! [X8] :
                      ( ~ in(X8,X2)
                      | ~ in(ordered_pair(X8,X6),X0) ) ) )
            | relation_image(X0,X2) != X1 ) ) ),
    inference(rectify,[],[f110]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( ( relation_image(X0,X2) = X1
            | ? [X3] :
                ( ( ~ in(X3,X1)
                  | ! [X4] :
                      ( ~ in(X4,X2)
                      | ~ in(ordered_pair(X4,X3),X0) ) )
                & ( in(X3,X1)
                  | ? [X4] :
                      ( in(X4,X2)
                      & in(ordered_pair(X4,X3),X0) ) ) ) )
          & ( ! [X3] :
                ( ( ? [X4] :
                      ( in(X4,X2)
                      & in(ordered_pair(X4,X3),X0) )
                  | ~ in(X3,X1) )
                & ( in(X3,X1)
                  | ! [X4] :
                      ( ~ in(X4,X2)
                      | ~ in(ordered_pair(X4,X3),X0) ) ) )
            | relation_image(X0,X2) != X1 ) ) ),
    inference(nnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ! [X1,X2] :
          ( relation_image(X0,X2) = X1
        <=> ! [X3] :
              ( ? [X4] :
                  ( in(X4,X2)
                  & in(ordered_pair(X4,X3),X0) )
            <=> in(X3,X1) ) ) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( relation(X0)
     => ! [X1,X2] :
          ( relation_image(X0,X2) = X1
        <=> ! [X3] :
              ( ? [X4] :
                  ( in(X4,X2)
                  & in(ordered_pair(X4,X3),X0) )
            <=> in(X3,X1) ) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( relation(X0)
     => ! [X2,X1] :
          ( ! [X3] :
              ( in(X3,X2)
            <=> ? [X4] :
                  ( in(ordered_pair(X4,X3),X0)
                  & in(X4,X1) ) )
        <=> relation_image(X0,X1) = X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SEU227+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.15/0.36  % Computer : n023.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Tue Aug 30 15:14:05 EDT 2022
% 0.15/0.36  % CPUTime    : 
% 0.21/0.51  % (11565)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)
% 0.21/0.51  % (11555)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)
% 0.21/0.52  % (11552)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)
% 0.21/0.52  % (11557)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.52  % (11558)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)
% 0.21/0.52  % (11566)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.21/0.53  % (11564)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.21/0.53  TRYING [1]
% 0.21/0.53  % (11570)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.53  % (11562)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.54  TRYING [2]
% 0.21/0.54  % (11557)Instruction limit reached!
% 0.21/0.54  % (11557)------------------------------
% 0.21/0.54  % (11557)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54  % (11557)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54  % (11557)Termination reason: Unknown
% 0.21/0.54  % (11557)Termination phase: Clausification
% 0.21/0.54  
% 0.21/0.54  % (11557)Memory used [KB]: 1023
% 0.21/0.54  % (11557)Time elapsed: 0.005 s
% 0.21/0.54  % (11557)Instructions burned: 3 (million)
% 0.21/0.54  % (11557)------------------------------
% 0.21/0.54  % (11557)------------------------------
% 0.21/0.54  % (11574)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.54  % (11573)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.54  % (11572)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)
% 0.21/0.54  TRYING [1]
% 0.21/0.56  TRYING [3]
% 0.21/0.56  TRYING [2]
% 0.21/0.57  TRYING [3]
% 0.21/0.58  % (11561)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.59  % (11578)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.21/0.59  % (11555)Instruction limit reached!
% 0.21/0.59  % (11555)------------------------------
% 0.21/0.59  % (11555)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.59  % (11569)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)
% 0.21/0.59  % (11553)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.60  % (11549)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)
% 0.21/0.60  % (11575)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)
% 0.21/0.60  % (11555)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.60  % (11555)Termination reason: Unknown
% 0.21/0.60  % (11555)Termination phase: Finite model building SAT solving
% 0.21/0.60  
% 0.21/0.60  % (11555)Memory used [KB]: 8187
% 0.21/0.60  % (11555)Time elapsed: 0.155 s
% 0.21/0.60  % (11555)Instructions burned: 52 (million)
% 0.21/0.60  % (11555)------------------------------
% 0.21/0.60  % (11555)------------------------------
% 0.21/0.61  % (11552)Instruction limit reached!
% 0.21/0.61  % (11552)------------------------------
% 0.21/0.61  % (11552)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.62  % (11552)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.62  % (11552)Termination reason: Unknown
% 0.21/0.62  % (11552)Termination phase: Saturation
% 0.21/0.62  
% 0.21/0.62  % (11552)Memory used [KB]: 6012
% 0.21/0.62  % (11552)Time elapsed: 0.185 s
% 0.21/0.62  % (11552)Instructions burned: 51 (million)
% 0.21/0.62  % (11552)------------------------------
% 0.21/0.62  % (11552)------------------------------
% 0.21/0.62  % (11566)Instruction limit reached!
% 0.21/0.62  % (11566)------------------------------
% 0.21/0.62  % (11566)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.62  % (11566)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.62  % (11566)Termination reason: Unknown
% 0.21/0.62  % (11566)Termination phase: Finite model building SAT solving
% 0.21/0.62  
% 0.21/0.62  % (11566)Memory used [KB]: 8187
% 0.21/0.62  % (11566)Time elapsed: 0.168 s
% 0.21/0.62  % (11566)Instructions burned: 59 (million)
% 0.21/0.62  % (11566)------------------------------
% 0.21/0.62  % (11566)------------------------------
% 0.21/0.63  % (11558)Instruction limit reached!
% 0.21/0.63  % (11558)------------------------------
% 0.21/0.63  % (11558)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.63  % (11560)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.63  % (11558)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.63  % (11558)Termination reason: Unknown
% 0.21/0.63  % (11558)Termination phase: Saturation
% 0.21/0.63  
% 0.21/0.63  % (11558)Memory used [KB]: 2174
% 0.21/0.63  % (11558)Time elapsed: 0.210 s
% 0.21/0.63  % (11558)Instructions burned: 51 (million)
% 0.21/0.63  % (11558)------------------------------
% 0.21/0.63  % (11558)------------------------------
% 0.21/0.63  % (11554)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)
% 0.21/0.63  TRYING [1]
% 0.21/0.63  TRYING [2]
% 0.21/0.64  % (11568)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)
% 1.80/0.64  % (11564)First to succeed.
% 1.80/0.64  % (11550)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)
% 1.80/0.64  % (11559)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 2.21/0.66  % (11567)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 2.21/0.66  % (11564)Refutation found. Thanks to Tanya!
% 2.21/0.66  % SZS status Theorem for theBenchmark
% 2.21/0.66  % SZS output start Proof for theBenchmark
% See solution above
% 2.21/0.66  % (11564)------------------------------
% 2.21/0.66  % (11564)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.21/0.66  % (11564)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.21/0.66  % (11564)Termination reason: Refutation
% 2.21/0.66  
% 2.21/0.66  % (11564)Memory used [KB]: 2302
% 2.21/0.66  % (11564)Time elapsed: 0.206 s
% 2.21/0.66  % (11564)Instructions burned: 65 (million)
% 2.21/0.66  % (11564)------------------------------
% 2.21/0.66  % (11564)------------------------------
% 2.21/0.66  % (11548)Success in time 0.291 s
%------------------------------------------------------------------------------