TSTP Solution File: RNG111+4 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : RNG111+4 : TPTP v8.1.0. Released v4.0.0.
% 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 : n016.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 18:15:53 EDT 2022

% Result   : Theorem 1.52s 0.61s
% Output   : Refutation 1.52s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   60 (  10 unt;   3 typ;   0 def)
%            Number of atoms       :  459 ( 150 equ)
%            Maximal formula atoms :   36 (   8 avg)
%            Number of connectives :  607 ( 205   ~; 153   |; 225   &)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    4 (   0 usr;   3 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   2 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;  10 con; 0-2 aty)
%            Number of variables   :  202 (  97   !; 105   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_19,type,
    sQ52_eqProxy: ( $int * $int ) > $o ).

tff(pred_def_20,type,
    sQ53_eqProxy: ( $rat * $rat ) > $o ).

tff(pred_def_21,type,
    sQ54_eqProxy: ( $real * $real ) > $o ).

fof(f1630,plain,
    $false,
    inference(subsumption_resolution,[],[f1629,f1094]) ).

fof(f1094,plain,
    aElementOf0(sK20,xI),
    inference(subsumption_resolution,[],[f531,f1066]) ).

fof(f1066,plain,
    sP2,
    inference(subsumption_resolution,[],[f1065,f493]) ).

fof(f493,plain,
    aElementOf0(sK23,xI),
    inference(literal_reordering,[],[f294]) ).

fof(f294,plain,
    aElementOf0(sK23,xI),
    inference(cnf_transformation,[],[f169]) ).

fof(f169,plain,
    ( ! [X1] :
        ( sz00 = X1
        | sP3(X1)
        | ( ! [X2,X3] :
              ( ~ aElementOf0(X2,slsdtgt0(xa))
              | ~ aElementOf0(X3,slsdtgt0(xb))
              | sdtpldt0(X2,X3) != X1 )
          & ~ aElementOf0(X1,xI) ) )
    & ! [X4] :
        ( sP2
        | ( ~ aElementOf0(X4,xI)
          & ! [X5,X6] :
              ( sdtpldt0(X5,X6) != X4
              | ~ aElementOf0(X6,slsdtgt0(xb))
              | ~ aElementOf0(X5,slsdtgt0(xa)) ) )
        | ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK23))
        | sz00 = X4 )
    & sz00 != sK23
    & aElementOf0(sK23,xI)
    & sdtpldt0(sK25,sK24) = sK23
    & aElementOf0(sK24,slsdtgt0(xb))
    & aElementOf0(sK25,slsdtgt0(xa)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25])],[f166,f168,f167]) ).

fof(f167,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( sz00 = X1
            | sP3(X1)
            | ( ! [X2,X3] :
                  ( ~ aElementOf0(X2,slsdtgt0(xa))
                  | ~ aElementOf0(X3,slsdtgt0(xb))
                  | sdtpldt0(X2,X3) != X1 )
              & ~ aElementOf0(X1,xI) ) )
        & ! [X4] :
            ( sP2
            | ( ~ aElementOf0(X4,xI)
              & ! [X5,X6] :
                  ( sdtpldt0(X5,X6) != X4
                  | ~ aElementOf0(X6,slsdtgt0(xb))
                  | ~ aElementOf0(X5,slsdtgt0(xa)) ) )
            | ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X0))
            | sz00 = X4 )
        & sz00 != X0
        & aElementOf0(X0,xI)
        & ? [X7,X8] :
            ( sdtpldt0(X8,X7) = X0
            & aElementOf0(X7,slsdtgt0(xb))
            & aElementOf0(X8,slsdtgt0(xa)) ) )
   => ( ! [X1] :
          ( sz00 = X1
          | sP3(X1)
          | ( ! [X2,X3] :
                ( ~ aElementOf0(X2,slsdtgt0(xa))
                | ~ aElementOf0(X3,slsdtgt0(xb))
                | sdtpldt0(X2,X3) != X1 )
            & ~ aElementOf0(X1,xI) ) )
      & ! [X4] :
          ( sP2
          | ( ~ aElementOf0(X4,xI)
            & ! [X5,X6] :
                ( sdtpldt0(X5,X6) != X4
                | ~ aElementOf0(X6,slsdtgt0(xb))
                | ~ aElementOf0(X5,slsdtgt0(xa)) ) )
          | ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK23))
          | sz00 = X4 )
      & sz00 != sK23
      & aElementOf0(sK23,xI)
      & ? [X8,X7] :
          ( sK23 = sdtpldt0(X8,X7)
          & aElementOf0(X7,slsdtgt0(xb))
          & aElementOf0(X8,slsdtgt0(xa)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f168,plain,
    ( ? [X8,X7] :
        ( sK23 = sdtpldt0(X8,X7)
        & aElementOf0(X7,slsdtgt0(xb))
        & aElementOf0(X8,slsdtgt0(xa)) )
   => ( sdtpldt0(sK25,sK24) = sK23
      & aElementOf0(sK24,slsdtgt0(xb))
      & aElementOf0(sK25,slsdtgt0(xa)) ) ),
    introduced(choice_axiom,[]) ).

fof(f166,plain,
    ? [X0] :
      ( ! [X1] :
          ( sz00 = X1
          | sP3(X1)
          | ( ! [X2,X3] :
                ( ~ aElementOf0(X2,slsdtgt0(xa))
                | ~ aElementOf0(X3,slsdtgt0(xb))
                | sdtpldt0(X2,X3) != X1 )
            & ~ aElementOf0(X1,xI) ) )
      & ! [X4] :
          ( sP2
          | ( ~ aElementOf0(X4,xI)
            & ! [X5,X6] :
                ( sdtpldt0(X5,X6) != X4
                | ~ aElementOf0(X6,slsdtgt0(xb))
                | ~ aElementOf0(X5,slsdtgt0(xa)) ) )
          | ~ iLess0(sbrdtbr0(X4),sbrdtbr0(X0))
          | sz00 = X4 )
      & sz00 != X0
      & aElementOf0(X0,xI)
      & ? [X7,X8] :
          ( sdtpldt0(X8,X7) = X0
          & aElementOf0(X7,slsdtgt0(xb))
          & aElementOf0(X8,slsdtgt0(xa)) ) ),
    inference(rectify,[],[f127]) ).

fof(f127,plain,
    ? [X0] :
      ( ! [X12] :
          ( sz00 = X12
          | sP3(X12)
          | ( ! [X13,X14] :
                ( ~ aElementOf0(X13,slsdtgt0(xa))
                | ~ aElementOf0(X14,slsdtgt0(xb))
                | sdtpldt0(X13,X14) != X12 )
            & ~ aElementOf0(X12,xI) ) )
      & ! [X3] :
          ( sP2
          | ( ~ aElementOf0(X3,xI)
            & ! [X5,X4] :
                ( sdtpldt0(X5,X4) != X3
                | ~ aElementOf0(X4,slsdtgt0(xb))
                | ~ aElementOf0(X5,slsdtgt0(xa)) ) )
          | ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
          | sz00 = X3 )
      & sz00 != X0
      & aElementOf0(X0,xI)
      & ? [X1,X2] :
          ( sdtpldt0(X2,X1) = X0
          & aElementOf0(X1,slsdtgt0(xb))
          & aElementOf0(X2,slsdtgt0(xa)) ) ),
    inference(definition_folding,[],[f103,f126,f125]) ).

fof(f125,plain,
    ( ? [X6] :
        ( ! [X7] :
            ( ( ~ aElementOf0(X7,xI)
              & ! [X9,X8] :
                  ( ~ aElementOf0(X8,slsdtgt0(xa))
                  | ~ aElementOf0(X9,slsdtgt0(xb))
                  | sdtpldt0(X8,X9) != X7 ) )
            | sz00 = X7
            | ~ iLess0(sbrdtbr0(X7),sbrdtbr0(X6)) )
        & aElementOf0(X6,xI)
        & sz00 != X6
        & ? [X10,X11] :
            ( sdtpldt0(X10,X11) = X6
            & aElementOf0(X10,slsdtgt0(xa))
            & aElementOf0(X11,slsdtgt0(xb)) ) )
    | ~ sP2 ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

fof(f126,plain,
    ! [X12] :
      ( ? [X15] :
          ( ? [X17,X16] :
              ( sdtpldt0(X17,X16) = X15
              & aElementOf0(X16,slsdtgt0(xb))
              & aElementOf0(X17,slsdtgt0(xa)) )
          & aElementOf0(X15,xI)
          & sz00 != X15
          & iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) )
      | ~ sP3(X12) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).

fof(f103,plain,
    ? [X0] :
      ( ! [X12] :
          ( sz00 = X12
          | ? [X15] :
              ( ? [X17,X16] :
                  ( sdtpldt0(X17,X16) = X15
                  & aElementOf0(X16,slsdtgt0(xb))
                  & aElementOf0(X17,slsdtgt0(xa)) )
              & aElementOf0(X15,xI)
              & sz00 != X15
              & iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) )
          | ( ! [X13,X14] :
                ( ~ aElementOf0(X13,slsdtgt0(xa))
                | ~ aElementOf0(X14,slsdtgt0(xb))
                | sdtpldt0(X13,X14) != X12 )
            & ~ aElementOf0(X12,xI) ) )
      & ! [X3] :
          ( ? [X6] :
              ( ! [X7] :
                  ( ( ~ aElementOf0(X7,xI)
                    & ! [X9,X8] :
                        ( ~ aElementOf0(X8,slsdtgt0(xa))
                        | ~ aElementOf0(X9,slsdtgt0(xb))
                        | sdtpldt0(X8,X9) != X7 ) )
                  | sz00 = X7
                  | ~ iLess0(sbrdtbr0(X7),sbrdtbr0(X6)) )
              & aElementOf0(X6,xI)
              & sz00 != X6
              & ? [X10,X11] :
                  ( sdtpldt0(X10,X11) = X6
                  & aElementOf0(X10,slsdtgt0(xa))
                  & aElementOf0(X11,slsdtgt0(xb)) ) )
          | ( ~ aElementOf0(X3,xI)
            & ! [X5,X4] :
                ( sdtpldt0(X5,X4) != X3
                | ~ aElementOf0(X4,slsdtgt0(xb))
                | ~ aElementOf0(X5,slsdtgt0(xa)) ) )
          | ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
          | sz00 = X3 )
      & sz00 != X0
      & aElementOf0(X0,xI)
      & ? [X1,X2] :
          ( sdtpldt0(X2,X1) = X0
          & aElementOf0(X1,slsdtgt0(xb))
          & aElementOf0(X2,slsdtgt0(xa)) ) ),
    inference(flattening,[],[f102]) ).

fof(f102,plain,
    ? [X0] :
      ( ! [X12] :
          ( ? [X15] :
              ( iLess0(sbrdtbr0(X15),sbrdtbr0(X12))
              & aElementOf0(X15,xI)
              & sz00 != X15
              & ? [X17,X16] :
                  ( sdtpldt0(X17,X16) = X15
                  & aElementOf0(X16,slsdtgt0(xb))
                  & aElementOf0(X17,slsdtgt0(xa)) ) )
          | sz00 = X12
          | ( ! [X13,X14] :
                ( ~ aElementOf0(X13,slsdtgt0(xa))
                | ~ aElementOf0(X14,slsdtgt0(xb))
                | sdtpldt0(X13,X14) != X12 )
            & ~ aElementOf0(X12,xI) ) )
      & ! [X3] :
          ( ? [X6] :
              ( ! [X7] :
                  ( ~ iLess0(sbrdtbr0(X7),sbrdtbr0(X6))
                  | ( ~ aElementOf0(X7,xI)
                    & ! [X9,X8] :
                        ( ~ aElementOf0(X8,slsdtgt0(xa))
                        | ~ aElementOf0(X9,slsdtgt0(xb))
                        | sdtpldt0(X8,X9) != X7 ) )
                  | sz00 = X7 )
              & ? [X10,X11] :
                  ( sdtpldt0(X10,X11) = X6
                  & aElementOf0(X10,slsdtgt0(xa))
                  & aElementOf0(X11,slsdtgt0(xb)) )
              & aElementOf0(X6,xI)
              & sz00 != X6 )
          | ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
          | ( ~ aElementOf0(X3,xI)
            & ! [X5,X4] :
                ( sdtpldt0(X5,X4) != X3
                | ~ aElementOf0(X4,slsdtgt0(xb))
                | ~ aElementOf0(X5,slsdtgt0(xa)) ) )
          | sz00 = X3 )
      & ? [X1,X2] :
          ( sdtpldt0(X2,X1) = X0
          & aElementOf0(X1,slsdtgt0(xb))
          & aElementOf0(X2,slsdtgt0(xa)) )
      & sz00 != X0
      & aElementOf0(X0,xI) ),
    inference(ennf_transformation,[],[f62]) ).

fof(f62,plain,
    ~ ! [X0] :
        ( ( ? [X1,X2] :
              ( sdtpldt0(X2,X1) = X0
              & aElementOf0(X1,slsdtgt0(xb))
              & aElementOf0(X2,slsdtgt0(xa)) )
          & sz00 != X0
          & aElementOf0(X0,xI) )
       => ( ! [X3] :
              ( ( ( ? [X5,X4] :
                      ( sdtpldt0(X5,X4) = X3
                      & aElementOf0(X4,slsdtgt0(xb))
                      & aElementOf0(X5,slsdtgt0(xa)) )
                  | aElementOf0(X3,xI) )
                & sz00 != X3 )
             => ( iLess0(sbrdtbr0(X3),sbrdtbr0(X0))
               => ? [X6] :
                    ( ! [X7] :
                        ( ( ( aElementOf0(X7,xI)
                            | ? [X9,X8] :
                                ( aElementOf0(X9,slsdtgt0(xb))
                                & sdtpldt0(X8,X9) = X7
                                & aElementOf0(X8,slsdtgt0(xa)) ) )
                          & sz00 != X7 )
                       => ~ iLess0(sbrdtbr0(X7),sbrdtbr0(X6)) )
                    & ? [X10,X11] :
                        ( sdtpldt0(X10,X11) = X6
                        & aElementOf0(X10,slsdtgt0(xa))
                        & aElementOf0(X11,slsdtgt0(xb)) )
                    & aElementOf0(X6,xI)
                    & sz00 != X6 ) ) )
         => ? [X12] :
              ( ! [X15] :
                  ( ( aElementOf0(X15,xI)
                    & sz00 != X15
                    & ? [X17,X16] :
                        ( sdtpldt0(X17,X16) = X15
                        & aElementOf0(X16,slsdtgt0(xb))
                        & aElementOf0(X17,slsdtgt0(xa)) ) )
                 => ~ iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) )
              & sz00 != X12
              & ( ? [X14,X13] :
                    ( aElementOf0(X13,slsdtgt0(xa))
                    & sdtpldt0(X13,X14) = X12
                    & aElementOf0(X14,slsdtgt0(xb)) )
                | aElementOf0(X12,xI) ) ) ) ),
    inference(rectify,[],[f46]) ).

fof(f46,negated_conjecture,
    ~ ! [X0] :
        ( ( ? [X2,X1] :
              ( aElementOf0(X1,slsdtgt0(xa))
              & aElementOf0(X2,slsdtgt0(xb))
              & sdtpldt0(X1,X2) = X0 )
          & sz00 != X0
          & aElementOf0(X0,xI) )
       => ( ! [X1] :
              ( ( ( aElementOf0(X1,xI)
                  | ? [X3,X2] :
                      ( sdtpldt0(X2,X3) = X1
                      & aElementOf0(X2,slsdtgt0(xa))
                      & aElementOf0(X3,slsdtgt0(xb)) ) )
                & sz00 != X1 )
             => ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
               => ? [X2] :
                    ( aElementOf0(X2,xI)
                    & ! [X3] :
                        ( ( ( ? [X4,X5] :
                                ( sdtpldt0(X4,X5) = X3
                                & aElementOf0(X5,slsdtgt0(xb))
                                & aElementOf0(X4,slsdtgt0(xa)) )
                            | aElementOf0(X3,xI) )
                          & sz00 != X3 )
                       => ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
                    & sz00 != X2
                    & ? [X3,X4] :
                        ( aElementOf0(X3,slsdtgt0(xa))
                        & sdtpldt0(X3,X4) = X2
                        & aElementOf0(X4,slsdtgt0(xb)) ) ) ) )
         => ? [X1] :
              ( sz00 != X1
              & ( aElementOf0(X1,xI)
                | ? [X2,X3] :
                    ( sdtpldt0(X2,X3) = X1
                    & aElementOf0(X3,slsdtgt0(xb))
                    & aElementOf0(X2,slsdtgt0(xa)) ) )
              & ! [X2] :
                  ( ( ? [X4,X3] :
                        ( aElementOf0(X4,slsdtgt0(xb))
                        & aElementOf0(X3,slsdtgt0(xa))
                        & sdtpldt0(X3,X4) = X2 )
                    & aElementOf0(X2,xI)
                    & sz00 != X2 )
                 => ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ) ),
    inference(negated_conjecture,[],[f45]) ).

fof(f45,conjecture,
    ! [X0] :
      ( ( ? [X2,X1] :
            ( aElementOf0(X1,slsdtgt0(xa))
            & aElementOf0(X2,slsdtgt0(xb))
            & sdtpldt0(X1,X2) = X0 )
        & sz00 != X0
        & aElementOf0(X0,xI) )
     => ( ! [X1] :
            ( ( ( aElementOf0(X1,xI)
                | ? [X3,X2] :
                    ( sdtpldt0(X2,X3) = X1
                    & aElementOf0(X2,slsdtgt0(xa))
                    & aElementOf0(X3,slsdtgt0(xb)) ) )
              & sz00 != X1 )
           => ( iLess0(sbrdtbr0(X1),sbrdtbr0(X0))
             => ? [X2] :
                  ( aElementOf0(X2,xI)
                  & ! [X3] :
                      ( ( ( ? [X4,X5] :
                              ( sdtpldt0(X4,X5) = X3
                              & aElementOf0(X5,slsdtgt0(xb))
                              & aElementOf0(X4,slsdtgt0(xa)) )
                          | aElementOf0(X3,xI) )
                        & sz00 != X3 )
                     => ~ iLess0(sbrdtbr0(X3),sbrdtbr0(X2)) )
                  & sz00 != X2
                  & ? [X3,X4] :
                      ( aElementOf0(X3,slsdtgt0(xa))
                      & sdtpldt0(X3,X4) = X2
                      & aElementOf0(X4,slsdtgt0(xb)) ) ) ) )
       => ? [X1] :
            ( sz00 != X1
            & ( aElementOf0(X1,xI)
              | ? [X2,X3] :
                  ( sdtpldt0(X2,X3) = X1
                  & aElementOf0(X3,slsdtgt0(xb))
                  & aElementOf0(X2,slsdtgt0(xa)) ) )
            & ! [X2] :
                ( ( ? [X4,X3] :
                      ( aElementOf0(X4,slsdtgt0(xb))
                      & aElementOf0(X3,slsdtgt0(xa))
                      & sdtpldt0(X3,X4) = X2 )
                  & aElementOf0(X2,xI)
                  & sz00 != X2 )
               => ~ iLess0(sbrdtbr0(X2),sbrdtbr0(X1)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).

fof(f1065,plain,
    ( sP2
    | ~ aElementOf0(sK23,xI) ),
    inference(subsumption_resolution,[],[f1064,f574]) ).

fof(f574,plain,
    sz00 != sK23,
    inference(literal_reordering,[],[f295]) ).

fof(f295,plain,
    sz00 != sK23,
    inference(cnf_transformation,[],[f169]) ).

fof(f1064,plain,
    ( sz00 = sK23
    | sP2
    | ~ aElementOf0(sK23,xI) ),
    inference(resolution,[],[f1063,f473]) ).

fof(f473,plain,
    ! [X1] :
      ( sP3(X1)
      | sz00 = X1
      | ~ aElementOf0(X1,xI) ),
    inference(literal_reordering,[],[f298]) ).

fof(f298,plain,
    ! [X1] :
      ( sP3(X1)
      | sz00 = X1
      | ~ aElementOf0(X1,xI) ),
    inference(cnf_transformation,[],[f169]) ).

fof(f1063,plain,
    ( ~ sP3(sK23)
    | sP2 ),
    inference(subsumption_resolution,[],[f1062,f448]) ).

fof(f448,plain,
    ! [X0] :
      ( ~ sP3(X0)
      | aElementOf0(sK17(X0),xI) ),
    inference(literal_reordering,[],[f280]) ).

fof(f280,plain,
    ! [X0] :
      ( ~ sP3(X0)
      | aElementOf0(sK17(X0),xI) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f160,plain,
    ! [X0] :
      ( ( sdtpldt0(sK18(X0),sK19(X0)) = sK17(X0)
        & aElementOf0(sK19(X0),slsdtgt0(xb))
        & aElementOf0(sK18(X0),slsdtgt0(xa))
        & aElementOf0(sK17(X0),xI)
        & sz00 != sK17(X0)
        & iLess0(sbrdtbr0(sK17(X0)),sbrdtbr0(X0)) )
      | ~ sP3(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18,sK19])],[f157,f159,f158]) ).

fof(f158,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2,X3] :
              ( sdtpldt0(X2,X3) = X1
              & aElementOf0(X3,slsdtgt0(xb))
              & aElementOf0(X2,slsdtgt0(xa)) )
          & aElementOf0(X1,xI)
          & sz00 != X1
          & iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
     => ( ? [X3,X2] :
            ( sdtpldt0(X2,X3) = sK17(X0)
            & aElementOf0(X3,slsdtgt0(xb))
            & aElementOf0(X2,slsdtgt0(xa)) )
        & aElementOf0(sK17(X0),xI)
        & sz00 != sK17(X0)
        & iLess0(sbrdtbr0(sK17(X0)),sbrdtbr0(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f159,plain,
    ! [X0] :
      ( ? [X3,X2] :
          ( sdtpldt0(X2,X3) = sK17(X0)
          & aElementOf0(X3,slsdtgt0(xb))
          & aElementOf0(X2,slsdtgt0(xa)) )
     => ( sdtpldt0(sK18(X0),sK19(X0)) = sK17(X0)
        & aElementOf0(sK19(X0),slsdtgt0(xb))
        & aElementOf0(sK18(X0),slsdtgt0(xa)) ) ),
    introduced(choice_axiom,[]) ).

fof(f157,plain,
    ! [X0] :
      ( ? [X1] :
          ( ? [X2,X3] :
              ( sdtpldt0(X2,X3) = X1
              & aElementOf0(X3,slsdtgt0(xb))
              & aElementOf0(X2,slsdtgt0(xa)) )
          & aElementOf0(X1,xI)
          & sz00 != X1
          & iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
      | ~ sP3(X0) ),
    inference(rectify,[],[f156]) ).

fof(f156,plain,
    ! [X12] :
      ( ? [X15] :
          ( ? [X17,X16] :
              ( sdtpldt0(X17,X16) = X15
              & aElementOf0(X16,slsdtgt0(xb))
              & aElementOf0(X17,slsdtgt0(xa)) )
          & aElementOf0(X15,xI)
          & sz00 != X15
          & iLess0(sbrdtbr0(X15),sbrdtbr0(X12)) )
      | ~ sP3(X12) ),
    inference(nnf_transformation,[],[f126]) ).

fof(f1062,plain,
    ( ~ aElementOf0(sK17(sK23),xI)
    | sP2
    | ~ sP3(sK23) ),
    inference(subsumption_resolution,[],[f1061,f430]) ).

fof(f430,plain,
    ! [X0] :
      ( sz00 != sK17(X0)
      | ~ sP3(X0) ),
    inference(literal_reordering,[],[f279]) ).

fof(f279,plain,
    ! [X0] :
      ( sz00 != sK17(X0)
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f1061,plain,
    ( sP2
    | ~ sP3(sK23)
    | sz00 = sK17(sK23)
    | ~ aElementOf0(sK17(sK23),xI) ),
    inference(resolution,[],[f577,f479]) ).

fof(f479,plain,
    ! [X4] :
      ( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK23))
      | ~ aElementOf0(X4,xI)
      | sz00 = X4
      | sP2 ),
    inference(literal_reordering,[],[f297]) ).

fof(f297,plain,
    ! [X4] :
      ( ~ iLess0(sbrdtbr0(X4),sbrdtbr0(sK23))
      | sz00 = X4
      | sP2
      | ~ aElementOf0(X4,xI) ),
    inference(cnf_transformation,[],[f169]) ).

fof(f577,plain,
    ! [X0] :
      ( iLess0(sbrdtbr0(sK17(X0)),sbrdtbr0(X0))
      | ~ sP3(X0) ),
    inference(literal_reordering,[],[f278]) ).

fof(f278,plain,
    ! [X0] :
      ( iLess0(sbrdtbr0(sK17(X0)),sbrdtbr0(X0))
      | ~ sP3(X0) ),
    inference(cnf_transformation,[],[f160]) ).

fof(f531,plain,
    ( ~ sP2
    | aElementOf0(sK20,xI) ),
    inference(literal_reordering,[],[f288]) ).

fof(f288,plain,
    ( ~ sP2
    | aElementOf0(sK20,xI) ),
    inference(cnf_transformation,[],[f165]) ).

fof(f165,plain,
    ( ( ! [X1] :
          ( ( ~ aElementOf0(X1,xI)
            & ! [X2,X3] :
                ( ~ aElementOf0(X3,slsdtgt0(xa))
                | ~ aElementOf0(X2,slsdtgt0(xb))
                | sdtpldt0(X3,X2) != X1 ) )
          | sz00 = X1
          | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20)) )
      & aElementOf0(sK20,xI)
      & sz00 != sK20
      & sdtpldt0(sK21,sK22) = sK20
      & aElementOf0(sK21,slsdtgt0(xa))
      & aElementOf0(sK22,slsdtgt0(xb)) )
    | ~ sP2 ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f162,f164,f163]) ).

fof(f163,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( ( ~ aElementOf0(X1,xI)
              & ! [X2,X3] :
                  ( ~ aElementOf0(X3,slsdtgt0(xa))
                  | ~ aElementOf0(X2,slsdtgt0(xb))
                  | sdtpldt0(X3,X2) != X1 ) )
            | sz00 = X1
            | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
        & aElementOf0(X0,xI)
        & sz00 != X0
        & ? [X4,X5] :
            ( sdtpldt0(X4,X5) = X0
            & aElementOf0(X4,slsdtgt0(xa))
            & aElementOf0(X5,slsdtgt0(xb)) ) )
   => ( ! [X1] :
          ( ( ~ aElementOf0(X1,xI)
            & ! [X2,X3] :
                ( ~ aElementOf0(X3,slsdtgt0(xa))
                | ~ aElementOf0(X2,slsdtgt0(xb))
                | sdtpldt0(X3,X2) != X1 ) )
          | sz00 = X1
          | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20)) )
      & aElementOf0(sK20,xI)
      & sz00 != sK20
      & ? [X5,X4] :
          ( sdtpldt0(X4,X5) = sK20
          & aElementOf0(X4,slsdtgt0(xa))
          & aElementOf0(X5,slsdtgt0(xb)) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f164,plain,
    ( ? [X5,X4] :
        ( sdtpldt0(X4,X5) = sK20
        & aElementOf0(X4,slsdtgt0(xa))
        & aElementOf0(X5,slsdtgt0(xb)) )
   => ( sdtpldt0(sK21,sK22) = sK20
      & aElementOf0(sK21,slsdtgt0(xa))
      & aElementOf0(sK22,slsdtgt0(xb)) ) ),
    introduced(choice_axiom,[]) ).

fof(f162,plain,
    ( ? [X0] :
        ( ! [X1] :
            ( ( ~ aElementOf0(X1,xI)
              & ! [X2,X3] :
                  ( ~ aElementOf0(X3,slsdtgt0(xa))
                  | ~ aElementOf0(X2,slsdtgt0(xb))
                  | sdtpldt0(X3,X2) != X1 ) )
            | sz00 = X1
            | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(X0)) )
        & aElementOf0(X0,xI)
        & sz00 != X0
        & ? [X4,X5] :
            ( sdtpldt0(X4,X5) = X0
            & aElementOf0(X4,slsdtgt0(xa))
            & aElementOf0(X5,slsdtgt0(xb)) ) )
    | ~ sP2 ),
    inference(rectify,[],[f161]) ).

fof(f161,plain,
    ( ? [X6] :
        ( ! [X7] :
            ( ( ~ aElementOf0(X7,xI)
              & ! [X9,X8] :
                  ( ~ aElementOf0(X8,slsdtgt0(xa))
                  | ~ aElementOf0(X9,slsdtgt0(xb))
                  | sdtpldt0(X8,X9) != X7 ) )
            | sz00 = X7
            | ~ iLess0(sbrdtbr0(X7),sbrdtbr0(X6)) )
        & aElementOf0(X6,xI)
        & sz00 != X6
        & ? [X10,X11] :
            ( sdtpldt0(X10,X11) = X6
            & aElementOf0(X10,slsdtgt0(xa))
            & aElementOf0(X11,slsdtgt0(xb)) ) )
    | ~ sP2 ),
    inference(nnf_transformation,[],[f125]) ).

fof(f1629,plain,
    ~ aElementOf0(sK20,xI),
    inference(subsumption_resolution,[],[f1628,f1093]) ).

fof(f1093,plain,
    sz00 != sK20,
    inference(subsumption_resolution,[],[f572,f1066]) ).

fof(f572,plain,
    ( ~ sP2
    | sz00 != sK20 ),
    inference(literal_reordering,[],[f287]) ).

fof(f287,plain,
    ( ~ sP2
    | sz00 != sK20 ),
    inference(cnf_transformation,[],[f165]) ).

fof(f1628,plain,
    ( sz00 = sK20
    | ~ aElementOf0(sK20,xI) ),
    inference(resolution,[],[f1620,f473]) ).

fof(f1620,plain,
    ~ sP3(sK20),
    inference(subsumption_resolution,[],[f1619,f448]) ).

fof(f1619,plain,
    ( ~ aElementOf0(sK17(sK20),xI)
    | ~ sP3(sK20) ),
    inference(subsumption_resolution,[],[f1618,f430]) ).

fof(f1618,plain,
    ( sz00 = sK17(sK20)
    | ~ aElementOf0(sK17(sK20),xI)
    | ~ sP3(sK20) ),
    inference(resolution,[],[f1616,f577]) ).

fof(f1616,plain,
    ! [X1] :
      ( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20))
      | ~ aElementOf0(X1,xI)
      | sz00 = X1 ),
    inference(subsumption_resolution,[],[f461,f1066]) ).

fof(f461,plain,
    ! [X1] :
      ( ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20))
      | sz00 = X1
      | ~ aElementOf0(X1,xI)
      | ~ sP2 ),
    inference(literal_reordering,[],[f290]) ).

fof(f290,plain,
    ! [X1] :
      ( ~ sP2
      | ~ aElementOf0(X1,xI)
      | sz00 = X1
      | ~ iLess0(sbrdtbr0(X1),sbrdtbr0(sK20)) ),
    inference(cnf_transformation,[],[f165]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : RNG111+4 : TPTP v8.1.0. Released v4.0.0.
% 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
% 0.14/0.34  % Computer : n016.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 30 12:33:46 EDT 2022
% 0.14/0.34  % CPUTime    : 
% 0.21/0.51  % (8039)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.51  % (8051)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)
% 0.21/0.51  % (8050)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.51  % (8040)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)
% 0.21/0.51  % (8043)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)
% 0.21/0.51  % (8031)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)
% 0.21/0.52  % (8029)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)
% 0.21/0.52  % (8032)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  % (8035)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  % (8041)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.53  % (8057)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.53  % (8054)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.53  % (8052)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)
% 1.40/0.53  % (8053)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.40/0.53  % (8030)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)
% 1.40/0.53  % (8034)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)
% 1.40/0.53  % (8042)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.40/0.53  % (8045)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)
% 1.40/0.53  % (8033)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.40/0.53  % (8049)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)
% 1.40/0.54  % (8058)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)
% 1.40/0.54  % (8055)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)
% 1.40/0.54  % (8044)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)
% 1.40/0.54  % (8046)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.40/0.54  % (8056)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)
% 1.40/0.54  % (8047)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.40/0.54  % (8036)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.40/0.54  % (8037)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.40/0.55  % (8038)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)
% 1.52/0.55  % (8036)Instruction limit reached!
% 1.52/0.55  % (8036)------------------------------
% 1.52/0.55  % (8036)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.55  % (8048)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)
% 1.52/0.55  % (8037)Instruction limit reached!
% 1.52/0.55  % (8037)------------------------------
% 1.52/0.55  % (8037)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.55  % (8037)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.55  % (8037)Termination reason: Unknown
% 1.52/0.55  % (8037)Termination phase: Preprocessing 3
% 1.52/0.55  
% 1.52/0.55  % (8037)Memory used [KB]: 1023
% 1.52/0.55  % (8037)Time elapsed: 0.004 s
% 1.52/0.55  % (8037)Instructions burned: 3 (million)
% 1.52/0.55  % (8037)------------------------------
% 1.52/0.55  % (8037)------------------------------
% 1.52/0.56  TRYING [1]
% 1.52/0.56  TRYING [2]
% 1.52/0.56  % (8030)Refutation not found, incomplete strategy% (8030)------------------------------
% 1.52/0.56  % (8030)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.56  % (8030)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.56  % (8030)Termination reason: Refutation not found, incomplete strategy
% 1.52/0.56  TRYING [1]
% 1.52/0.56  TRYING [2]
% 1.52/0.57  % (8036)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.57  % (8036)Termination reason: Unknown
% 1.52/0.57  % (8036)Termination phase: Saturation
% 1.52/0.57  
% 1.52/0.57  % (8036)Memory used [KB]: 5756
% 1.52/0.57  % (8036)Time elapsed: 0.005 s
% 1.52/0.57  % (8036)Instructions burned: 9 (million)
% 1.52/0.57  % (8036)------------------------------
% 1.52/0.57  % (8036)------------------------------
% 1.52/0.57  TRYING [1]
% 1.52/0.58  
% 1.52/0.58  % (8030)Memory used [KB]: 6140
% 1.52/0.58  % (8030)Time elapsed: 0.161 s
% 1.52/0.58  % (8030)Instructions burned: 24 (million)
% 1.52/0.58  % (8030)------------------------------
% 1.52/0.58  % (8030)------------------------------
% 1.52/0.58  % (8031)Instruction limit reached!
% 1.52/0.58  % (8031)------------------------------
% 1.52/0.58  % (8031)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.58  % (8031)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.58  % (8031)Termination reason: Unknown
% 1.52/0.58  % (8031)Termination phase: Saturation
% 1.52/0.58  
% 1.52/0.58  % (8031)Memory used [KB]: 1663
% 1.52/0.58  % (8031)Time elapsed: 0.158 s
% 1.52/0.58  % (8031)Instructions burned: 38 (million)
% 1.52/0.58  % (8031)------------------------------
% 1.52/0.58  % (8031)------------------------------
% 1.52/0.58  TRYING [2]
% 1.52/0.59  TRYING [3]
% 1.52/0.59  % (8035)Instruction limit reached!
% 1.52/0.59  % (8035)------------------------------
% 1.52/0.59  % (8035)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.59  % (8035)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.59  % (8035)Termination reason: Unknown
% 1.52/0.59  % (8035)Termination phase: Finite model building constraint generation
% 1.52/0.59  
% 1.52/0.59  % (8035)Memory used [KB]: 7675
% 1.52/0.59  % (8035)Time elapsed: 0.129 s
% 1.52/0.59  % (8035)Instructions burned: 51 (million)
% 1.52/0.59  % (8035)------------------------------
% 1.52/0.59  % (8035)------------------------------
% 1.52/0.60  TRYING [3]
% 1.52/0.60  % (8043)First to succeed.
% 1.52/0.61  % (8039)Instruction limit reached!
% 1.52/0.61  % (8039)------------------------------
% 1.52/0.61  % (8039)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.61  % (8034)Instruction limit reached!
% 1.52/0.61  % (8034)------------------------------
% 1.52/0.61  % (8034)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.61  % (8043)Refutation found. Thanks to Tanya!
% 1.52/0.61  % SZS status Theorem for theBenchmark
% 1.52/0.61  % SZS output start Proof for theBenchmark
% See solution above
% 1.52/0.61  % (8043)------------------------------
% 1.52/0.61  % (8043)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.61  % (8043)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.61  % (8043)Termination reason: Refutation
% 1.52/0.61  
% 1.52/0.61  % (8043)Memory used [KB]: 6908
% 1.52/0.61  % (8043)Time elapsed: 0.040 s
% 1.52/0.61  % (8043)Instructions burned: 47 (million)
% 1.52/0.61  % (8043)------------------------------
% 1.52/0.61  % (8043)------------------------------
% 1.52/0.61  % (8028)Success in time 0.259 s
%------------------------------------------------------------------------------