TSTP Solution File: NUM474+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM474+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s

% Computer : n005.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 : Thu Aug 31 12:09:51 EDT 2023

% Result   : Theorem 0.21s 0.56s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   17
% Syntax   : Number of formulae    :  110 (  30 unt;   0 def)
%            Number of atoms       :  327 ( 110 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  383 ( 166   ~; 172   |;  28   &)
%                                         (   9 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   4 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :   89 (;  89   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f5417,plain,
    $false,
    inference(avatar_sat_refutation,[],[f2187,f2194,f3561,f4978]) ).

fof(f4978,plain,
    ( ~ spl2_2
    | ~ spl2_3 ),
    inference(avatar_contradiction_clause,[],[f4977]) ).

fof(f4977,plain,
    ( $false
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(subsumption_resolution,[],[f4976,f2174]) ).

fof(f2174,plain,
    sdtpldt0(xm,xn) != sdtpldt0(xm,sdtasdt0(xl,xr)),
    inference(backward_demodulation,[],[f111,f2173]) ).

fof(f2173,plain,
    xm = sdtasdt0(xl,xp),
    inference(forward_demodulation,[],[f2170,f115]) ).

fof(f115,plain,
    xp = sdtsldt0(xm,xl),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    xp = sdtsldt0(xm,xl),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',m__1360) ).

fof(f2170,plain,
    xm = sdtasdt0(xl,sdtsldt0(xm,xl)),
    inference(unit_resulting_resolution,[],[f117,f118,f112,f120,f182]) ).

fof(f182,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f154]) ).

fof(f154,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,X2) = X1
      | sdtsldt0(X1,X0) != X2
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f102,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtsldt0(X1,X0) = X2
            | sdtasdt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtsldt0(X1,X0) != X2 ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f101]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtsldt0(X1,X0) = X2
            | sdtasdt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtsldt0(X1,X0) != X2 ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtsldt0(X1,X0) = X2
        <=> ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtsldt0(X1,X0) = X2
        <=> ( sdtasdt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( doDivides0(X0,X1)
          & sz00 != X0 )
       => ! [X2] :
            ( sdtsldt0(X1,X0) = X2
          <=> ( sdtasdt0(X0,X2) = X1
              & aNaturalNumber0(X2) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',mDefQuot) ).

fof(f120,plain,
    doDivides0(xl,xm),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,axiom,
    ( doDivides0(xl,sdtpldt0(xm,xn))
    & doDivides0(xl,xm) ),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',m__1324_04) ).

fof(f112,plain,
    sz00 != xl,
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    sz00 != xl,
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',m__1347) ).

fof(f118,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xl) ),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',m__1324) ).

fof(f117,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[],[f34]) ).

fof(f111,plain,
    sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
    inference(flattening,[],[f42]) ).

fof(f42,negated_conjecture,
    sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) != sdtpldt0(sdtasdt0(xl,xp),xn),
    inference(negated_conjecture,[],[f41]) ).

fof(f41,conjecture,
    sdtpldt0(sdtasdt0(xl,xp),sdtasdt0(xl,xr)) = sdtpldt0(sdtasdt0(xl,xp),xn),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',m__) ).

fof(f4976,plain,
    ( sdtpldt0(xm,xn) = sdtpldt0(xm,sdtasdt0(xl,xr))
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f4754,f4975]) ).

fof(f4975,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xq,xl)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(forward_demodulation,[],[f4954,f4958]) ).

fof(f4958,plain,
    ( sdtpldt0(xm,xn) = sdtpldt0(sdtasdt0(xl,xr),xm)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(forward_demodulation,[],[f4938,f3565]) ).

fof(f3565,plain,
    sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
    inference(subsumption_resolution,[],[f3564,f117]) ).

fof(f3564,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
    | ~ aNaturalNumber0(xl) ),
    inference(subsumption_resolution,[],[f3563,f1163]) ).

fof(f1163,plain,
    aNaturalNumber0(sdtpldt0(xm,xn)),
    inference(unit_resulting_resolution,[],[f118,f119,f136]) ).

fof(f136,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => aNaturalNumber0(sdtpldt0(X0,X1)) ),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',mSortsB) ).

fof(f119,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f34]) ).

fof(f3563,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl) ),
    inference(subsumption_resolution,[],[f3562,f112]) ).

fof(f3562,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
    | sz00 = xl
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl) ),
    inference(subsumption_resolution,[],[f3555,f121]) ).

fof(f121,plain,
    doDivides0(xl,sdtpldt0(xm,xn)),
    inference(cnf_transformation,[],[f35]) ).

fof(f3555,plain,
    ( sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | sz00 = xl
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[],[f182,f116]) ).

fof(f116,plain,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    xq = sdtsldt0(sdtpldt0(xm,xn),xl),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',m__1379) ).

fof(f4938,plain,
    ( sdtpldt0(sdtasdt0(xl,xr),xm) = sdtasdt0(xl,xq)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f4362,f4927]) ).

fof(f4927,plain,
    ( xq = sdtpldt0(xr,xp)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(forward_demodulation,[],[f3617,f2193]) ).

fof(f2193,plain,
    ( xq = sdtpldt0(xp,xr)
    | ~ spl2_3 ),
    inference(avatar_component_clause,[],[f2191]) ).

fof(f2191,plain,
    ( spl2_3
  <=> xq = sdtpldt0(xp,xr) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

fof(f3617,plain,
    ( sdtpldt0(xp,xr) = sdtpldt0(xr,xp)
    | ~ spl2_2 ),
    inference(unit_resulting_resolution,[],[f2172,f2186,f138]) ).

fof(f138,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',mAddComm) ).

fof(f2186,plain,
    ( aNaturalNumber0(xr)
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f2184]) ).

fof(f2184,plain,
    ( spl2_2
  <=> aNaturalNumber0(xr) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

fof(f2172,plain,
    aNaturalNumber0(xp),
    inference(forward_demodulation,[],[f2171,f115]) ).

fof(f2171,plain,
    aNaturalNumber0(sdtsldt0(xm,xl)),
    inference(unit_resulting_resolution,[],[f117,f118,f112,f120,f183]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtsldt0(X1,X0))
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f153]) ).

fof(f153,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtsldt0(X1,X0) != X2
      | ~ doDivides0(X0,X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f102]) ).

fof(f4362,plain,
    ( sdtpldt0(sdtasdt0(xl,xr),xm) = sdtasdt0(xl,sdtpldt0(xr,xp))
    | ~ spl2_2 ),
    inference(forward_demodulation,[],[f4019,f2173]) ).

fof(f4019,plain,
    ( sdtasdt0(xl,sdtpldt0(xr,xp)) = sdtpldt0(sdtasdt0(xl,xr),sdtasdt0(xl,xp))
    | ~ spl2_2 ),
    inference(unit_resulting_resolution,[],[f117,f2172,f2186,f165]) ).

fof(f165,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1,X2] :
      ( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',mAMDistr) ).

fof(f4954,plain,
    ( sdtpldt0(sdtasdt0(xl,xr),xm) = sdtasdt0(xq,xl)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f4759,f4927]) ).

fof(f4759,plain,
    ( sdtpldt0(sdtasdt0(xl,xr),xm) = sdtasdt0(sdtpldt0(xr,xp),xl)
    | ~ spl2_2 ),
    inference(backward_demodulation,[],[f4274,f3628]) ).

fof(f3628,plain,
    ( sdtasdt0(xl,xr) = sdtasdt0(xr,xl)
    | ~ spl2_2 ),
    inference(unit_resulting_resolution,[],[f117,f2186,f139]) ).

fof(f139,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',mMulComm) ).

fof(f4274,plain,
    ( sdtasdt0(sdtpldt0(xr,xp),xl) = sdtpldt0(sdtasdt0(xr,xl),xm)
    | ~ spl2_2 ),
    inference(forward_demodulation,[],[f4166,f3092]) ).

fof(f3092,plain,
    xm = sdtasdt0(xp,xl),
    inference(forward_demodulation,[],[f2246,f2173]) ).

fof(f2246,plain,
    sdtasdt0(xl,xp) = sdtasdt0(xp,xl),
    inference(unit_resulting_resolution,[],[f117,f2172,f139]) ).

fof(f4166,plain,
    ( sdtasdt0(sdtpldt0(xr,xp),xl) = sdtpldt0(sdtasdt0(xr,xl),sdtasdt0(xp,xl))
    | ~ spl2_2 ),
    inference(unit_resulting_resolution,[],[f117,f2172,f2186,f166]) ).

fof(f166,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f4754,plain,
    ( sdtpldt0(xm,sdtasdt0(xl,xr)) = sdtasdt0(xq,xl)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(backward_demodulation,[],[f4243,f3628]) ).

fof(f4243,plain,
    ( sdtpldt0(xm,sdtasdt0(xr,xl)) = sdtasdt0(xq,xl)
    | ~ spl2_2
    | ~ spl2_3 ),
    inference(forward_demodulation,[],[f4242,f2193]) ).

fof(f4242,plain,
    ( sdtasdt0(sdtpldt0(xp,xr),xl) = sdtpldt0(xm,sdtasdt0(xr,xl))
    | ~ spl2_2 ),
    inference(forward_demodulation,[],[f4215,f3092]) ).

fof(f4215,plain,
    ( sdtasdt0(sdtpldt0(xp,xr),xl) = sdtpldt0(sdtasdt0(xp,xl),sdtasdt0(xr,xl))
    | ~ spl2_2 ),
    inference(unit_resulting_resolution,[],[f117,f2172,f2186,f166]) ).

fof(f3561,plain,
    spl2_1,
    inference(avatar_contradiction_clause,[],[f3560]) ).

fof(f3560,plain,
    ( $false
    | spl2_1 ),
    inference(subsumption_resolution,[],[f3559,f117]) ).

fof(f3559,plain,
    ( ~ aNaturalNumber0(xl)
    | spl2_1 ),
    inference(subsumption_resolution,[],[f3558,f1163]) ).

fof(f3558,plain,
    ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | spl2_1 ),
    inference(subsumption_resolution,[],[f3557,f112]) ).

fof(f3557,plain,
    ( sz00 = xl
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | spl2_1 ),
    inference(subsumption_resolution,[],[f3556,f121]) ).

fof(f3556,plain,
    ( ~ doDivides0(xl,sdtpldt0(xm,xn))
    | sz00 = xl
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl)
    | spl2_1 ),
    inference(subsumption_resolution,[],[f3554,f2182]) ).

fof(f2182,plain,
    ( ~ aNaturalNumber0(xq)
    | spl2_1 ),
    inference(avatar_component_clause,[],[f2180]) ).

fof(f2180,plain,
    ( spl2_1
  <=> aNaturalNumber0(xq) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

fof(f3554,plain,
    ( aNaturalNumber0(xq)
    | ~ doDivides0(xl,sdtpldt0(xm,xn))
    | sz00 = xl
    | ~ aNaturalNumber0(sdtpldt0(xm,xn))
    | ~ aNaturalNumber0(xl) ),
    inference(superposition,[],[f183,f116]) ).

fof(f2194,plain,
    ( ~ spl2_1
    | spl2_3 ),
    inference(avatar_split_clause,[],[f2189,f2191,f2180]) ).

fof(f2189,plain,
    ( xq = sdtpldt0(xp,xr)
    | ~ aNaturalNumber0(xq) ),
    inference(subsumption_resolution,[],[f2188,f2172]) ).

fof(f2188,plain,
    ( xq = sdtpldt0(xp,xr)
    | ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp) ),
    inference(subsumption_resolution,[],[f2176,f113]) ).

fof(f113,plain,
    sdtlseqdt0(xp,xq),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,axiom,
    sdtlseqdt0(xp,xq),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',m__1395) ).

fof(f2176,plain,
    ( xq = sdtpldt0(xp,xr)
    | ~ sdtlseqdt0(xp,xq)
    | ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[],[f179,f114]) ).

fof(f114,plain,
    xr = sdtmndt0(xq,xp),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    xr = sdtmndt0(xq,xp),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',m__1422) ).

fof(f179,plain,
    ! [X0,X1] :
      ( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f144]) ).

fof(f144,plain,
    ! [X2,X0,X1] :
      ( sdtpldt0(X0,X2) = X1
      | sdtmndt0(X1,X0) != X2
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f100,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X1,X0) = X2
            | sdtpldt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtmndt0(X1,X0) != X2 ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( sdtmndt0(X1,X0) = X2
            | sdtpldt0(X0,X2) != X1
            | ~ aNaturalNumber0(X2) )
          & ( ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
            | sdtmndt0(X1,X0) != X2 ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( sdtmndt0(X1,X0) = X2
        <=> ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtlseqdt0(X0,X1)
       => ! [X2] :
            ( sdtmndt0(X1,X0) = X2
          <=> ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416',mDefDiff) ).

fof(f2187,plain,
    ( ~ spl2_1
    | spl2_2 ),
    inference(avatar_split_clause,[],[f2178,f2184,f2180]) ).

fof(f2178,plain,
    ( aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xq) ),
    inference(subsumption_resolution,[],[f2177,f2172]) ).

fof(f2177,plain,
    ( aNaturalNumber0(xr)
    | ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp) ),
    inference(subsumption_resolution,[],[f2175,f113]) ).

fof(f2175,plain,
    ( aNaturalNumber0(xr)
    | ~ sdtlseqdt0(xp,xq)
    | ~ aNaturalNumber0(xq)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[],[f180,f114]) ).

fof(f180,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtmndt0(X1,X0))
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f143]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( aNaturalNumber0(X2)
      | sdtmndt0(X1,X0) != X2
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f100]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : NUM474+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35  % Computer : n005.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Fri Aug 25 08:28:38 EDT 2023
% 0.15/0.35  % CPUTime    : 
% 0.15/0.35  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.35  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.uBNh6Gn4kr/Vampire---4.8_11416
% 0.15/0.36  % (11523)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42  % (11530)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.21/0.42  % (11524)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.21/0.42  % (11529)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.21/0.42  % (11528)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.42  % (11526)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.21/0.42  % (11527)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.21/0.44  % (11525)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.21/0.55  % (11527)First to succeed.
% 0.21/0.56  % (11527)Refutation found. Thanks to Tanya!
% 0.21/0.56  % SZS status Theorem for Vampire---4
% 0.21/0.56  % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.56  % (11527)------------------------------
% 0.21/0.56  % (11527)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.56  % (11527)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.56  % (11527)Termination reason: Refutation
% 0.21/0.56  
% 0.21/0.56  % (11527)Memory used [KB]: 8443
% 0.21/0.56  % (11527)Time elapsed: 0.138 s
% 0.21/0.56  % (11527)------------------------------
% 0.21/0.56  % (11527)------------------------------
% 0.21/0.56  % (11523)Success in time 0.197 s
% 0.21/0.56  % Vampire---4.8 exiting
%------------------------------------------------------------------------------