TSTP Solution File: SEU362+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU362+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 : n022.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 18:33:25 EDT 2022

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   77 (  22 unt;   0 def)
%            Number of atoms       :  314 (  36 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  339 ( 102   ~;  78   |; 123   &)
%                                         (   5 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-3 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :  140 (  92   !;  48   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f283,plain,
    $false,
    inference(subsumption_resolution,[],[f282,f228]) ).

fof(f228,plain,
    element(the_InternalRel(sK11),powerset(the_InternalRel(sK10))),
    inference(resolution,[],[f227,f141]) ).

fof(f141,plain,
    ! [X0,X1] :
      ( ~ subset(X0,X1)
      | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

fof(f227,plain,
    subset(the_InternalRel(sK11),the_InternalRel(sK10)),
    inference(subsumption_resolution,[],[f224,f158]) ).

fof(f158,plain,
    rel_str(sK10),
    inference(cnf_transformation,[],[f119]) ).

fof(f119,plain,
    ( subrelstr(sK11,sK10)
    & element(sK13,the_carrier(sK10))
    & element(sK14,the_carrier(sK11))
    & sK12 = sK14
    & related(sK11,sK14,sK15)
    & sK15 = sK13
    & element(sK15,the_carrier(sK11))
    & ~ related(sK10,sK12,sK13)
    & element(sK12,the_carrier(sK10))
    & rel_str(sK10) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,sK14,sK15])],[f64,f118,f117,f116,f115,f114,f113]) ).

fof(f113,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( subrelstr(X1,X0)
            & ? [X2] :
                ( ? [X3] :
                    ( element(X3,the_carrier(X0))
                    & ? [X4] :
                        ( element(X4,the_carrier(X1))
                        & ? [X5] :
                            ( X2 = X4
                            & related(X1,X4,X5)
                            & X3 = X5
                            & element(X5,the_carrier(X1))
                            & ~ related(X0,X2,X3) ) ) )
                & element(X2,the_carrier(X0)) ) )
        & rel_str(X0) )
   => ( ? [X1] :
          ( subrelstr(X1,sK10)
          & ? [X2] :
              ( ? [X3] :
                  ( element(X3,the_carrier(sK10))
                  & ? [X4] :
                      ( element(X4,the_carrier(X1))
                      & ? [X5] :
                          ( X2 = X4
                          & related(X1,X4,X5)
                          & X3 = X5
                          & element(X5,the_carrier(X1))
                          & ~ related(sK10,X2,X3) ) ) )
              & element(X2,the_carrier(sK10)) ) )
      & rel_str(sK10) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ( ? [X1] :
        ( subrelstr(X1,sK10)
        & ? [X2] :
            ( ? [X3] :
                ( element(X3,the_carrier(sK10))
                & ? [X4] :
                    ( element(X4,the_carrier(X1))
                    & ? [X5] :
                        ( X2 = X4
                        & related(X1,X4,X5)
                        & X3 = X5
                        & element(X5,the_carrier(X1))
                        & ~ related(sK10,X2,X3) ) ) )
            & element(X2,the_carrier(sK10)) ) )
   => ( subrelstr(sK11,sK10)
      & ? [X2] :
          ( ? [X3] :
              ( element(X3,the_carrier(sK10))
              & ? [X4] :
                  ( element(X4,the_carrier(sK11))
                  & ? [X5] :
                      ( X2 = X4
                      & related(sK11,X4,X5)
                      & X3 = X5
                      & element(X5,the_carrier(sK11))
                      & ~ related(sK10,X2,X3) ) ) )
          & element(X2,the_carrier(sK10)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( element(X3,the_carrier(sK10))
            & ? [X4] :
                ( element(X4,the_carrier(sK11))
                & ? [X5] :
                    ( X2 = X4
                    & related(sK11,X4,X5)
                    & X3 = X5
                    & element(X5,the_carrier(sK11))
                    & ~ related(sK10,X2,X3) ) ) )
        & element(X2,the_carrier(sK10)) )
   => ( ? [X3] :
          ( element(X3,the_carrier(sK10))
          & ? [X4] :
              ( element(X4,the_carrier(sK11))
              & ? [X5] :
                  ( sK12 = X4
                  & related(sK11,X4,X5)
                  & X3 = X5
                  & element(X5,the_carrier(sK11))
                  & ~ related(sK10,sK12,X3) ) ) )
      & element(sK12,the_carrier(sK10)) ) ),
    introduced(choice_axiom,[]) ).

fof(f116,plain,
    ( ? [X3] :
        ( element(X3,the_carrier(sK10))
        & ? [X4] :
            ( element(X4,the_carrier(sK11))
            & ? [X5] :
                ( sK12 = X4
                & related(sK11,X4,X5)
                & X3 = X5
                & element(X5,the_carrier(sK11))
                & ~ related(sK10,sK12,X3) ) ) )
   => ( element(sK13,the_carrier(sK10))
      & ? [X4] :
          ( element(X4,the_carrier(sK11))
          & ? [X5] :
              ( sK12 = X4
              & related(sK11,X4,X5)
              & sK13 = X5
              & element(X5,the_carrier(sK11))
              & ~ related(sK10,sK12,sK13) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f117,plain,
    ( ? [X4] :
        ( element(X4,the_carrier(sK11))
        & ? [X5] :
            ( sK12 = X4
            & related(sK11,X4,X5)
            & sK13 = X5
            & element(X5,the_carrier(sK11))
            & ~ related(sK10,sK12,sK13) ) )
   => ( element(sK14,the_carrier(sK11))
      & ? [X5] :
          ( sK12 = sK14
          & related(sK11,sK14,X5)
          & sK13 = X5
          & element(X5,the_carrier(sK11))
          & ~ related(sK10,sK12,sK13) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f118,plain,
    ( ? [X5] :
        ( sK12 = sK14
        & related(sK11,sK14,X5)
        & sK13 = X5
        & element(X5,the_carrier(sK11))
        & ~ related(sK10,sK12,sK13) )
   => ( sK12 = sK14
      & related(sK11,sK14,sK15)
      & sK15 = sK13
      & element(sK15,the_carrier(sK11))
      & ~ related(sK10,sK12,sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f64,plain,
    ? [X0] :
      ( ? [X1] :
          ( subrelstr(X1,X0)
          & ? [X2] :
              ( ? [X3] :
                  ( element(X3,the_carrier(X0))
                  & ? [X4] :
                      ( element(X4,the_carrier(X1))
                      & ? [X5] :
                          ( X2 = X4
                          & related(X1,X4,X5)
                          & X3 = X5
                          & element(X5,the_carrier(X1))
                          & ~ related(X0,X2,X3) ) ) )
              & element(X2,the_carrier(X0)) ) )
      & rel_str(X0) ),
    inference(flattening,[],[f63]) ).

fof(f63,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ? [X5] :
                          ( ~ related(X0,X2,X3)
                          & related(X1,X4,X5)
                          & X3 = X5
                          & X2 = X4
                          & element(X5,the_carrier(X1)) )
                      & element(X4,the_carrier(X1)) )
                  & element(X3,the_carrier(X0)) )
              & element(X2,the_carrier(X0)) )
          & subrelstr(X1,X0) )
      & rel_str(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,negated_conjecture,
    ~ ! [X0] :
        ( rel_str(X0)
       => ! [X1] :
            ( subrelstr(X1,X0)
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => ! [X3] :
                    ( element(X3,the_carrier(X0))
                   => ! [X4] :
                        ( element(X4,the_carrier(X1))
                       => ! [X5] :
                            ( element(X5,the_carrier(X1))
                           => ( ( related(X1,X4,X5)
                                & X3 = X5
                                & X2 = X4 )
                             => related(X0,X2,X3) ) ) ) ) ) ) ),
    inference(negated_conjecture,[],[f39]) ).

fof(f39,conjecture,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( subrelstr(X1,X0)
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ! [X3] :
                  ( element(X3,the_carrier(X0))
                 => ! [X4] :
                      ( element(X4,the_carrier(X1))
                     => ! [X5] :
                          ( element(X5,the_carrier(X1))
                         => ( ( related(X1,X4,X5)
                              & X3 = X5
                              & X2 = X4 )
                           => related(X0,X2,X3) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_yellow_0) ).

fof(f224,plain,
    ( subset(the_InternalRel(sK11),the_InternalRel(sK10))
    | ~ rel_str(sK10) ),
    inference(resolution,[],[f221,f167]) ).

fof(f167,plain,
    subrelstr(sK11,sK10),
    inference(cnf_transformation,[],[f119]) ).

fof(f221,plain,
    ! [X0,X1] :
      ( ~ subrelstr(X1,X0)
      | subset(the_InternalRel(X1),the_InternalRel(X0))
      | ~ rel_str(X0) ),
    inference(subsumption_resolution,[],[f148,f156]) ).

fof(f156,plain,
    ! [X0,X1] :
      ( ~ subrelstr(X1,X0)
      | ~ rel_str(X0)
      | rel_str(X1) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ~ rel_str(X0)
      | ! [X1] :
          ( ~ subrelstr(X1,X0)
          | rel_str(X1) ) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( subrelstr(X1,X0)
         => rel_str(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).

fof(f148,plain,
    ! [X0,X1] :
      ( ~ subrelstr(X1,X0)
      | ~ rel_str(X1)
      | ~ rel_str(X0)
      | subset(the_InternalRel(X1),the_InternalRel(X0)) ),
    inference(cnf_transformation,[],[f104]) ).

fof(f104,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ rel_str(X1)
          | ( ( subrelstr(X1,X0)
              | ~ subset(the_InternalRel(X1),the_InternalRel(X0))
              | ~ subset(the_carrier(X1),the_carrier(X0)) )
            & ( ( subset(the_InternalRel(X1),the_InternalRel(X0))
                & subset(the_carrier(X1),the_carrier(X0)) )
              | ~ subrelstr(X1,X0) ) ) )
      | ~ rel_str(X0) ),
    inference(flattening,[],[f103]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ rel_str(X1)
          | ( ( subrelstr(X1,X0)
              | ~ subset(the_InternalRel(X1),the_InternalRel(X0))
              | ~ subset(the_carrier(X1),the_carrier(X0)) )
            & ( ( subset(the_InternalRel(X1),the_InternalRel(X0))
                & subset(the_carrier(X1),the_carrier(X0)) )
              | ~ subrelstr(X1,X0) ) ) )
      | ~ rel_str(X0) ),
    inference(nnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ rel_str(X1)
          | ( subrelstr(X1,X0)
          <=> ( subset(the_InternalRel(X1),the_InternalRel(X0))
              & subset(the_carrier(X1),the_carrier(X0)) ) ) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( rel_str(X1)
         => ( subrelstr(X1,X0)
          <=> ( subset(the_InternalRel(X1),the_InternalRel(X0))
              & subset(the_carrier(X1),the_carrier(X0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_yellow_0) ).

fof(f282,plain,
    ~ element(the_InternalRel(sK11),powerset(the_InternalRel(sK10))),
    inference(resolution,[],[f281,f244]) ).

fof(f244,plain,
    ! [X0] :
      ( element(ordered_pair(sK14,sK13),X0)
      | ~ element(the_InternalRel(sK11),powerset(X0)) ),
    inference(resolution,[],[f242,f139]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( ~ in(X0,X2)
      | ~ element(X2,powerset(X1))
      | element(X0,X1) ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ~ element(X2,powerset(X1))
      | ~ in(X0,X2)
      | element(X0,X1) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X1,X0,X2] :
      ( element(X0,X1)
      | ~ in(X0,X2)
      | ~ element(X2,powerset(X1)) ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X1,X0,X2] :
      ( ( in(X0,X2)
        & element(X2,powerset(X1)) )
     => element(X0,X1) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X2,X1] :
      ( ( in(X0,X1)
        & element(X1,powerset(X2)) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

fof(f242,plain,
    in(ordered_pair(sK14,sK13),the_InternalRel(sK11)),
    inference(subsumption_resolution,[],[f241,f165]) ).

fof(f165,plain,
    element(sK14,the_carrier(sK11)),
    inference(cnf_transformation,[],[f119]) ).

fof(f241,plain,
    ( ~ element(sK14,the_carrier(sK11))
    | in(ordered_pair(sK14,sK13),the_InternalRel(sK11)) ),
    inference(subsumption_resolution,[],[f240,f196]) ).

fof(f196,plain,
    rel_str(sK11),
    inference(subsumption_resolution,[],[f193,f158]) ).

fof(f193,plain,
    ( rel_str(sK11)
    | ~ rel_str(sK10) ),
    inference(resolution,[],[f156,f167]) ).

fof(f240,plain,
    ( ~ rel_str(sK11)
    | in(ordered_pair(sK14,sK13),the_InternalRel(sK11))
    | ~ element(sK14,the_carrier(sK11)) ),
    inference(subsumption_resolution,[],[f239,f172]) ).

fof(f172,plain,
    element(sK13,the_carrier(sK11)),
    inference(definition_unfolding,[],[f161,f162]) ).

fof(f162,plain,
    sK15 = sK13,
    inference(cnf_transformation,[],[f119]) ).

fof(f161,plain,
    element(sK15,the_carrier(sK11)),
    inference(cnf_transformation,[],[f119]) ).

fof(f239,plain,
    ( in(ordered_pair(sK14,sK13),the_InternalRel(sK11))
    | ~ element(sK13,the_carrier(sK11))
    | ~ element(sK14,the_carrier(sK11))
    | ~ rel_str(sK11) ),
    inference(resolution,[],[f168,f171]) ).

fof(f171,plain,
    related(sK11,sK14,sK13),
    inference(definition_unfolding,[],[f163,f162]) ).

fof(f163,plain,
    related(sK11,sK14,sK15),
    inference(cnf_transformation,[],[f119]) ).

fof(f168,plain,
    ! [X2,X0,X1] :
      ( ~ related(X0,X1,X2)
      | ~ rel_str(X0)
      | in(ordered_pair(X1,X2),the_InternalRel(X0))
      | ~ element(X2,the_carrier(X0))
      | ~ element(X1,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f120]) ).

fof(f120,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | ! [X2] :
              ( ~ element(X2,the_carrier(X0))
              | ( ( related(X0,X1,X2)
                  | ~ in(ordered_pair(X1,X2),the_InternalRel(X0)) )
                & ( in(ordered_pair(X1,X2),the_InternalRel(X0))
                  | ~ related(X0,X1,X2) ) ) ) )
      | ~ rel_str(X0) ),
    inference(nnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ element(X1,the_carrier(X0))
          | ! [X2] :
              ( ~ element(X2,the_carrier(X0))
              | ( related(X0,X1,X2)
              <=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) )
      | ~ rel_str(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0] :
      ( rel_str(X0)
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( related(X0,X1,X2)
              <=> in(ordered_pair(X1,X2),the_InternalRel(X0)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).

fof(f281,plain,
    ~ element(ordered_pair(sK14,sK13),the_InternalRel(sK10)),
    inference(subsumption_resolution,[],[f278,f228]) ).

fof(f278,plain,
    ( ~ element(ordered_pair(sK14,sK13),the_InternalRel(sK10))
    | ~ element(the_InternalRel(sK11),powerset(the_InternalRel(sK10))) ),
    inference(resolution,[],[f276,f245]) ).

fof(f245,plain,
    ! [X1] :
      ( ~ empty(X1)
      | ~ element(the_InternalRel(sK11),powerset(X1)) ),
    inference(resolution,[],[f242,f152]) ).

fof(f152,plain,
    ! [X2,X0,X1] :
      ( ~ in(X1,X2)
      | ~ empty(X0)
      | ~ element(X2,powerset(X0)) ),
    inference(cnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X0)
      | ~ in(X1,X2)
      | ~ element(X2,powerset(X0)) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,plain,
    ! [X1,X2,X0] :
      ~ ( empty(X0)
        & in(X1,X2)
        & element(X2,powerset(X0)) ),
    inference(rectify,[],[f38]) ).

fof(f38,axiom,
    ! [X2,X0,X1] :
      ~ ( in(X0,X1)
        & empty(X2)
        & element(X1,powerset(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

fof(f276,plain,
    ( empty(the_InternalRel(sK10))
    | ~ element(ordered_pair(sK14,sK13),the_InternalRel(sK10)) ),
    inference(resolution,[],[f275,f151]) ).

fof(f151,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f108]) ).

fof(f108,plain,
    ! [X0,X1] :
      ( empty(X1)
      | ~ element(X0,X1)
      | in(X0,X1) ),
    inference(rectify,[],[f61]) ).

fof(f61,plain,
    ! [X1,X0] :
      ( empty(X0)
      | ~ element(X1,X0)
      | in(X1,X0) ),
    inference(flattening,[],[f60]) ).

fof(f60,plain,
    ! [X1,X0] :
      ( in(X1,X0)
      | empty(X0)
      | ~ element(X1,X0) ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X1,X0] :
      ( element(X1,X0)
     => ( in(X1,X0)
        | empty(X0) ) ),
    inference(rectify,[],[f35]) ).

fof(f35,axiom,
    ! [X1,X0] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f275,plain,
    ~ in(ordered_pair(sK14,sK13),the_InternalRel(sK10)),
    inference(subsumption_resolution,[],[f274,f166]) ).

fof(f166,plain,
    element(sK13,the_carrier(sK10)),
    inference(cnf_transformation,[],[f119]) ).

fof(f274,plain,
    ( ~ element(sK13,the_carrier(sK10))
    | ~ in(ordered_pair(sK14,sK13),the_InternalRel(sK10)) ),
    inference(subsumption_resolution,[],[f273,f158]) ).

fof(f273,plain,
    ( ~ in(ordered_pair(sK14,sK13),the_InternalRel(sK10))
    | ~ rel_str(sK10)
    | ~ element(sK13,the_carrier(sK10)) ),
    inference(subsumption_resolution,[],[f270,f174]) ).

fof(f174,plain,
    element(sK14,the_carrier(sK10)),
    inference(definition_unfolding,[],[f159,f164]) ).

fof(f164,plain,
    sK12 = sK14,
    inference(cnf_transformation,[],[f119]) ).

fof(f159,plain,
    element(sK12,the_carrier(sK10)),
    inference(cnf_transformation,[],[f119]) ).

fof(f270,plain,
    ( ~ element(sK14,the_carrier(sK10))
    | ~ in(ordered_pair(sK14,sK13),the_InternalRel(sK10))
    | ~ rel_str(sK10)
    | ~ element(sK13,the_carrier(sK10)) ),
    inference(resolution,[],[f169,f173]) ).

fof(f173,plain,
    ~ related(sK10,sK14,sK13),
    inference(definition_unfolding,[],[f160,f164]) ).

fof(f160,plain,
    ~ related(sK10,sK12,sK13),
    inference(cnf_transformation,[],[f119]) ).

fof(f169,plain,
    ! [X2,X0,X1] :
      ( related(X0,X1,X2)
      | ~ in(ordered_pair(X1,X2),the_InternalRel(X0))
      | ~ rel_str(X0)
      | ~ element(X1,the_carrier(X0))
      | ~ element(X2,the_carrier(X0)) ),
    inference(cnf_transformation,[],[f120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem    : SEU362+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.33  % Computer : n022.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Tue Aug 30 15:20:26 EDT 2022
% 0.13/0.33  % CPUTime    : 
% 0.19/0.48  % (24862)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.48  % (24877)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)
% 0.19/0.49  % (24878)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)
% 0.19/0.49  % (24869)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)
% 0.19/0.49  % (24870)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)
% 0.19/0.49  % (24860)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)
% 0.19/0.49  % (24861)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)
% 0.19/0.50  % (24859)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (24862)Instruction limit reached!
% 0.19/0.50  % (24862)------------------------------
% 0.19/0.50  % (24862)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (24857)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)
% 0.19/0.50  % (24862)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (24862)Termination reason: Unknown
% 0.19/0.50  % (24862)Termination phase: Saturation
% 0.19/0.50  
% 0.19/0.50  % (24862)Memory used [KB]: 5628
% 0.19/0.50  % (24862)Time elapsed: 0.108 s
% 0.19/0.50  % (24862)Instructions burned: 7 (million)
% 0.19/0.50  % (24862)------------------------------
% 0.19/0.50  % (24862)------------------------------
% 0.19/0.50  TRYING [1]
% 0.19/0.50  TRYING [2]
% 0.19/0.50  TRYING [3]
% 0.19/0.51  % (24877)First to succeed.
% 0.19/0.51  % (24877)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (24877)------------------------------
% 0.19/0.51  % (24877)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (24877)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (24877)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (24877)Memory used [KB]: 1151
% 0.19/0.51  % (24877)Time elapsed: 0.069 s
% 0.19/0.51  % (24877)Instructions burned: 9 (million)
% 0.19/0.51  % (24877)------------------------------
% 0.19/0.51  % (24877)------------------------------
% 0.19/0.51  % (24854)Success in time 0.168 s
%------------------------------------------------------------------------------