TSTP Solution File: RNG070+2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : RNG070+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n009.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 : Tue Apr 30 14:51:20 EDT 2024

% Result   : Theorem 0.15s 0.34s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   30
% Syntax   : Number of formulae    :  114 (  30 unt;   0 def)
%            Number of atoms       :  266 (  67 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  227 (  75   ~;  85   |;  41   &)
%                                         (  17 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   22 (  20 usr;  13 prp; 0-2 aty)
%            Number of functors    :   22 (  22 usr;  15 con; 0-2 aty)
%            Number of variables   :   51 (  51   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f722,plain,
    $false,
    inference(avatar_sat_refutation,[],[f256,f269,f278,f313,f319,f321,f481,f484,f493,f496,f701,f708,f721]) ).

fof(f721,plain,
    spl5_12,
    inference(avatar_contradiction_clause,[],[f720]) ).

fof(f720,plain,
    ( $false
    | spl5_12 ),
    inference(subsumption_resolution,[],[f719,f177]) ).

fof(f177,plain,
    aScalar0(xR),
    inference(cnf_transformation,[],[f52]) ).

fof(f52,axiom,
    ( xR = sdtasdt0(xC,xG)
    & aScalar0(xR) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1892) ).

fof(f719,plain,
    ( ~ aScalar0(xR)
    | spl5_12 ),
    inference(subsumption_resolution,[],[f718,f175]) ).

fof(f175,plain,
    aScalar0(xS),
    inference(cnf_transformation,[],[f54]) ).

fof(f54,axiom,
    ( xS = sdtasdt0(xF,xD)
    & aScalar0(xS) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1930) ).

fof(f718,plain,
    ( ~ aScalar0(xS)
    | ~ aScalar0(xR)
    | spl5_12 ),
    inference(resolution,[],[f700,f217]) ).

fof(f217,plain,
    ! [X0,X1] :
      ( aScalar0(sdtpldt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( aScalar0(sdtpldt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1] :
      ( aScalar0(sdtpldt0(X0,X1))
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => aScalar0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSumSc) ).

fof(f700,plain,
    ( ~ aScalar0(sdtpldt0(xR,xS))
    | spl5_12 ),
    inference(avatar_component_clause,[],[f698]) ).

fof(f698,plain,
    ( spl5_12
  <=> aScalar0(sdtpldt0(xR,xS)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).

fof(f708,plain,
    spl5_11,
    inference(avatar_contradiction_clause,[],[f707]) ).

fof(f707,plain,
    ( $false
    | spl5_11 ),
    inference(subsumption_resolution,[],[f706,f179]) ).

fof(f179,plain,
    aScalar0(xP),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,axiom,
    ( xP = sdtasdt0(xE,xH)
    & aScalar0(xP) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1911) ).

fof(f706,plain,
    ( ~ aScalar0(xP)
    | spl5_11 ),
    inference(duplicate_literal_removal,[],[f705]) ).

fof(f705,plain,
    ( ~ aScalar0(xP)
    | ~ aScalar0(xP)
    | spl5_11 ),
    inference(resolution,[],[f696,f217]) ).

fof(f696,plain,
    ( ~ aScalar0(sdtpldt0(xP,xP))
    | spl5_11 ),
    inference(avatar_component_clause,[],[f694]) ).

fof(f694,plain,
    ( spl5_11
  <=> aScalar0(sdtpldt0(xP,xP)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).

fof(f701,plain,
    ( ~ spl5_11
    | ~ spl5_12 ),
    inference(avatar_split_clause,[],[f679,f698,f694]) ).

fof(f679,plain,
    ( ~ aScalar0(sdtpldt0(xR,xS))
    | ~ aScalar0(sdtpldt0(xP,xP)) ),
    inference(subsumption_resolution,[],[f673,f143]) ).

fof(f143,plain,
    ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,axiom,
    ~ sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2590) ).

fof(f673,plain,
    ( sdtlseqdt0(sdtpldt0(xP,xP),sdtpldt0(xR,xS))
    | ~ aScalar0(sdtpldt0(xR,xS))
    | ~ aScalar0(sdtpldt0(xP,xP)) ),
    inference(resolution,[],[f222,f139]) ).

fof(f139,plain,
    ~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
    inference(flattening,[],[f62]) ).

fof(f62,negated_conjecture,
    ~ sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
    inference(negated_conjecture,[],[f61]) ).

fof(f61,conjecture,
    sdtlseqdt0(sdtpldt0(xR,xS),sdtpldt0(xP,xP)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).

fof(f222,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(cnf_transformation,[],[f106]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(flattening,[],[f105]) ).

fof(f105,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aScalar0(X1)
      | ~ aScalar0(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1] :
      ( ( aScalar0(X1)
        & aScalar0(X0) )
     => ( sdtlseqdt0(X1,X0)
        | sdtlseqdt0(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETot) ).

fof(f496,plain,
    spl5_9,
    inference(avatar_contradiction_clause,[],[f495]) ).

fof(f495,plain,
    ( $false
    | spl5_9 ),
    inference(subsumption_resolution,[],[f494,f147]) ).

fof(f147,plain,
    aVector0(xq),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ( xq = sziznziztdt0(xt)
    & ! [X0] :
        ( sdtlbdtrb0(xq,X0) = sdtlbdtrb0(xt,X0)
        | ~ aNaturalNumber0(X0) )
    & aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(xq))
    & aVector0(xq) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,axiom,
    ( xq = sziznziztdt0(xt)
    & ! [X0] :
        ( aNaturalNumber0(X0)
       => sdtlbdtrb0(xq,X0) = sdtlbdtrb0(xt,X0) )
    & aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(xq))
    & aVector0(xq) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1726) ).

fof(f494,plain,
    ( ~ aVector0(xq)
    | spl5_9 ),
    inference(resolution,[],[f488,f187]) ).

fof(f187,plain,
    ! [X0] :
      ( aNaturalNumber0(aDimensionOf0(X0))
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0] :
      ( aNaturalNumber0(aDimensionOf0(X0))
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0] :
      ( aVector0(X0)
     => aNaturalNumber0(aDimensionOf0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDimNat) ).

fof(f488,plain,
    ( ~ aNaturalNumber0(aDimensionOf0(xq))
    | spl5_9 ),
    inference(avatar_component_clause,[],[f486]) ).

fof(f486,plain,
    ( spl5_9
  <=> aNaturalNumber0(aDimensionOf0(xq)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).

fof(f493,plain,
    ( ~ spl5_9
    | spl5_10 ),
    inference(avatar_split_clause,[],[f246,f490,f486]) ).

fof(f490,plain,
    ( spl5_10
  <=> iLess0(aDimensionOf0(xq),aDimensionOf0(xs)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).

fof(f246,plain,
    ( iLess0(aDimensionOf0(xq),aDimensionOf0(xs))
    | ~ aNaturalNumber0(aDimensionOf0(xq)) ),
    inference(superposition,[],[f184,f241]) ).

fof(f241,plain,
    aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(xq)),
    inference(forward_demodulation,[],[f148,f141]) ).

fof(f141,plain,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    aDimensionOf0(xs) = aDimensionOf0(xt),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678_01) ).

fof(f148,plain,
    aDimensionOf0(xt) = szszuzczcdt0(aDimensionOf0(xq)),
    inference(cnf_transformation,[],[f69]) ).

fof(f184,plain,
    ! [X0] :
      ( iLess0(X0,szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0] :
      ( iLess0(X0,szszuzczcdt0(X0))
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => iLess0(X0,szszuzczcdt0(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).

fof(f484,plain,
    spl5_7,
    inference(avatar_contradiction_clause,[],[f483]) ).

fof(f483,plain,
    ( $false
    | spl5_7 ),
    inference(subsumption_resolution,[],[f482,f151]) ).

fof(f151,plain,
    aVector0(xp),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ( xp = sziznziztdt0(xs)
    & ! [X0] :
        ( sdtlbdtrb0(xp,X0) = sdtlbdtrb0(xs,X0)
        | ~ aNaturalNumber0(X0) )
    & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(xp))
    & aVector0(xp) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ( xp = sziznziztdt0(xs)
    & ! [X0] :
        ( aNaturalNumber0(X0)
       => sdtlbdtrb0(xp,X0) = sdtlbdtrb0(xs,X0) )
    & aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(xp))
    & aVector0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1709) ).

fof(f482,plain,
    ( ~ aVector0(xp)
    | spl5_7 ),
    inference(resolution,[],[f476,f187]) ).

fof(f476,plain,
    ( ~ aNaturalNumber0(aDimensionOf0(xp))
    | spl5_7 ),
    inference(avatar_component_clause,[],[f474]) ).

fof(f474,plain,
    ( spl5_7
  <=> aNaturalNumber0(aDimensionOf0(xp)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

fof(f481,plain,
    ( ~ spl5_7
    | spl5_8 ),
    inference(avatar_split_clause,[],[f245,f478,f474]) ).

fof(f478,plain,
    ( spl5_8
  <=> iLess0(aDimensionOf0(xp),aDimensionOf0(xs)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

fof(f245,plain,
    ( iLess0(aDimensionOf0(xp),aDimensionOf0(xs))
    | ~ aNaturalNumber0(aDimensionOf0(xp)) ),
    inference(superposition,[],[f184,f152]) ).

fof(f152,plain,
    aDimensionOf0(xs) = szszuzczcdt0(aDimensionOf0(xp)),
    inference(cnf_transformation,[],[f70]) ).

fof(f321,plain,
    spl5_3,
    inference(avatar_contradiction_clause,[],[f320]) ).

fof(f320,plain,
    ( $false
    | spl5_3 ),
    inference(subsumption_resolution,[],[f316,f140]) ).

fof(f140,plain,
    sz00 != aDimensionOf0(xs),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    sz00 != aDimensionOf0(xs),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1692) ).

fof(f316,plain,
    ( sz00 = aDimensionOf0(xs)
    | spl5_3 ),
    inference(superposition,[],[f141,f310]) ).

fof(f310,plain,
    ( sz00 = aDimensionOf0(xt)
    | spl5_3 ),
    inference(subsumption_resolution,[],[f308,f156]) ).

fof(f156,plain,
    aVector0(xt),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    ( aVector0(xt)
    & aVector0(xs) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1678) ).

fof(f308,plain,
    ( sz00 = aDimensionOf0(xt)
    | ~ aVector0(xt)
    | spl5_3 ),
    inference(resolution,[],[f196,f264]) ).

fof(f264,plain,
    ( ~ sP1(xt)
    | spl5_3 ),
    inference(avatar_component_clause,[],[f262]) ).

fof(f262,plain,
    ( spl5_3
  <=> sP1(xt) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f196,plain,
    ! [X0] :
      ( sP1(X0)
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(cnf_transformation,[],[f127]) ).

fof(f127,plain,
    ! [X0] :
      ( sP1(X0)
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(definition_folding,[],[f78,f126,f125]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
    <=> ( ! [X2] :
            ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
            | ~ aNaturalNumber0(X2) )
        & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
        & aVector0(X1) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f126,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> sP0(X0,X1) )
      | ~ sP1(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).

fof(f78,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
                | ~ aNaturalNumber0(X2) )
            & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
            & aVector0(X1) ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(flattening,[],[f77]) ).

fof(f77,plain,
    ! [X0] :
      ( ! [X1] :
          ( sziznziztdt0(X0) = X1
        <=> ( ! [X2] :
                ( sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2)
                | ~ aNaturalNumber0(X2) )
            & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
            & aVector0(X1) ) )
      | sz00 = aDimensionOf0(X0)
      | ~ aVector0(X0) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0] :
      ( aVector0(X0)
     => ( sz00 != aDimensionOf0(X0)
       => ! [X1] :
            ( sziznziztdt0(X0) = X1
          <=> ( ! [X2] :
                  ( aNaturalNumber0(X2)
                 => sdtlbdtrb0(X1,X2) = sdtlbdtrb0(X0,X2) )
              & aDimensionOf0(X0) = szszuzczcdt0(aDimensionOf0(X1))
              & aVector0(X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefInit) ).

fof(f319,plain,
    spl5_3,
    inference(avatar_contradiction_clause,[],[f318]) ).

fof(f318,plain,
    ( $false
    | spl5_3 ),
    inference(subsumption_resolution,[],[f315,f140]) ).

fof(f315,plain,
    ( sz00 = aDimensionOf0(xs)
    | spl5_3 ),
    inference(superposition,[],[f310,f141]) ).

fof(f313,plain,
    spl5_5,
    inference(avatar_contradiction_clause,[],[f312]) ).

fof(f312,plain,
    ( $false
    | spl5_5 ),
    inference(subsumption_resolution,[],[f311,f155]) ).

fof(f155,plain,
    aVector0(xs),
    inference(cnf_transformation,[],[f38]) ).

fof(f311,plain,
    ( ~ aVector0(xs)
    | spl5_5 ),
    inference(subsumption_resolution,[],[f309,f140]) ).

fof(f309,plain,
    ( sz00 = aDimensionOf0(xs)
    | ~ aVector0(xs)
    | spl5_5 ),
    inference(resolution,[],[f196,f273]) ).

fof(f273,plain,
    ( ~ sP1(xs)
    | spl5_5 ),
    inference(avatar_component_clause,[],[f271]) ).

fof(f271,plain,
    ( spl5_5
  <=> sP1(xs) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f278,plain,
    ( ~ spl5_5
    | spl5_6 ),
    inference(avatar_split_clause,[],[f260,f275,f271]) ).

fof(f275,plain,
    ( spl5_6
  <=> sP0(xs,xp) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

fof(f260,plain,
    ( sP0(xs,xp)
    | ~ sP1(xs) ),
    inference(superposition,[],[f237,f154]) ).

fof(f154,plain,
    xp = sziznziztdt0(xs),
    inference(cnf_transformation,[],[f70]) ).

fof(f237,plain,
    ! [X0] :
      ( sP0(X0,sziznziztdt0(X0))
      | ~ sP1(X0) ),
    inference(equality_resolution,[],[f189]) ).

fof(f189,plain,
    ! [X0,X1] :
      ( sP0(X0,X1)
      | sziznziztdt0(X0) != X1
      | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( sziznziztdt0(X0) = X1
            | ~ sP0(X0,X1) )
          & ( sP0(X0,X1)
            | sziznziztdt0(X0) != X1 ) )
      | ~ sP1(X0) ),
    inference(nnf_transformation,[],[f126]) ).

fof(f269,plain,
    ( ~ spl5_3
    | spl5_4 ),
    inference(avatar_split_clause,[],[f259,f266,f262]) ).

fof(f266,plain,
    ( spl5_4
  <=> sP0(xt,xq) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f259,plain,
    ( sP0(xt,xq)
    | ~ sP1(xt) ),
    inference(superposition,[],[f237,f150]) ).

fof(f150,plain,
    xq = sziznziztdt0(xt),
    inference(cnf_transformation,[],[f69]) ).

fof(f256,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f207,f253,f250]) ).

fof(f250,plain,
    ( spl5_1
  <=> ! [X0] : ~ sP2(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f253,plain,
    ( spl5_2
  <=> sz0z00 = smndt0(sz0z00) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f207,plain,
    ! [X0] :
      ( sz0z00 = smndt0(sz0z00)
      | ~ sP2(X0) ),
    inference(cnf_transformation,[],[f136]) ).

fof(f136,plain,
    ! [X0] :
      ( ( sz0z00 = smndt0(sz0z00)
        & smndt0(smndt0(X0)) = X0
        & sz0z00 = sdtpldt0(smndt0(X0),X0)
        & sz0z00 = sdtpldt0(X0,smndt0(X0))
        & sz0z00 = sdtasdt0(sz0z00,X0)
        & sz0z00 = sdtasdt0(X0,sz0z00)
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 )
      | ~ sP2(X0) ),
    inference(nnf_transformation,[],[f128]) ).

fof(f128,plain,
    ! [X0] :
      ( ( sz0z00 = smndt0(sz0z00)
        & smndt0(smndt0(X0)) = X0
        & sz0z00 = sdtpldt0(smndt0(X0),X0)
        & sz0z00 = sdtpldt0(X0,smndt0(X0))
        & sz0z00 = sdtasdt0(sz0z00,X0)
        & sz0z00 = sdtasdt0(X0,sz0z00)
        & sdtpldt0(sz0z00,X0) = X0
        & sdtpldt0(X0,sz0z00) = X0 )
      | ~ sP2(X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem    : RNG070+2 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30  % Computer : n009.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Tue Apr 30 02:02:41 EDT 2024
% 0.10/0.30  % CPUTime    : 
% 0.10/0.31  % (31273)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32  % (31276)WARNING: value z3 for option sas not known
% 0.15/0.32  % (31277)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.32  % (31280)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.32  % (31279)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.32  % (31278)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.32  % (31274)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.32  % (31275)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.32  % (31276)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [1]
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [2]
% 0.15/0.34  TRYING [3]
% 0.15/0.34  TRYING [3]
% 0.15/0.34  % (31276)First to succeed.
% 0.15/0.34  % (31279)Also succeeded, but the first one will report.
% 0.15/0.34  % (31276)Refutation found. Thanks to Tanya!
% 0.15/0.34  % SZS status Theorem for theBenchmark
% 0.15/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.35  % (31276)------------------------------
% 0.15/0.35  % (31276)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.35  % (31276)Termination reason: Refutation
% 0.15/0.35  
% 0.15/0.35  % (31276)Memory used [KB]: 1161
% 0.15/0.35  % (31276)Time elapsed: 0.022 s
% 0.15/0.35  % (31276)Instructions burned: 38 (million)
% 0.15/0.35  % (31276)------------------------------
% 0.15/0.35  % (31276)------------------------------
% 0.15/0.35  % (31273)Success in time 0.039 s
%------------------------------------------------------------------------------