TSTP Solution File: NUM471+2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : NUM471+2 : 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 : 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 : Thu Aug 31 12:09:49 EDT 2023

% Result   : Theorem 6.48s 1.40s
% Output   : Refutation 6.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   77 (  17 unt;   0 def)
%            Number of atoms       :  294 (  92 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  373 ( 156   ~; 155   |;  46   &)
%                                         (   3 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   99 (;  91   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f32949,plain,
    $false,
    inference(unit_resulting_resolution,[],[f124,f123,f13013,f32942,f474]) ).

fof(f474,plain,
    ! [X3,X4] :
      ( ~ sdtlseqdt0(sdtpldt0(X3,X4),X3)
      | sdtpldt0(X3,X4) = X3
      | ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4) ),
    inference(subsumption_resolution,[],[f471,f145]) ).

fof(f145,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1] :
      ( aNaturalNumber0(sdtpldt0(X0,X1))
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f54]) ).

fof(f54,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.8dUtbXOjax/Vampire---4.8_26783',mSortsB) ).

fof(f471,plain,
    ! [X3,X4] :
      ( sdtpldt0(X3,X4) = X3
      | ~ sdtlseqdt0(sdtpldt0(X3,X4),X3)
      | ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(sdtpldt0(X3,X4))
      | ~ aNaturalNumber0(X4) ),
    inference(duplicate_literal_removal,[],[f451]) ).

fof(f451,plain,
    ! [X3,X4] :
      ( sdtpldt0(X3,X4) = X3
      | ~ sdtlseqdt0(sdtpldt0(X3,X4),X3)
      | ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(sdtpldt0(X3,X4))
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X3) ),
    inference(resolution,[],[f165,f200]) ).

fof(f200,plain,
    ! [X2,X0] :
      ( sdtlseqdt0(X0,sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X0) ),
    inference(subsumption_resolution,[],[f194,f145]) ).

fof(f194,plain,
    ! [X2,X0] :
      ( sdtlseqdt0(X0,sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(sdtpldt0(X0,X2))
      | ~ aNaturalNumber0(X0) ),
    inference(equality_resolution,[],[f171]) ).

fof(f171,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(X0,X1)
      | sdtpldt0(X0,X2) != X1
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f112]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ( sdtpldt0(X0,sK3(X0,X1)) = X1
            & aNaturalNumber0(sK3(X0,X1)) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f110,f111]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( sdtpldt0(X0,X3) = X1
          & aNaturalNumber0(X3) )
     => ( sdtpldt0(X0,sK3(X0,X1)) = X1
        & aNaturalNumber0(sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X3] :
              ( sdtpldt0(X0,X3) = X1
              & aNaturalNumber0(X3) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(rectify,[],[f109]) ).

fof(f109,plain,
    ! [X0,X1] :
      ( ( ( sdtlseqdt0(X0,X1)
          | ! [X2] :
              ( sdtpldt0(X0,X2) != X1
              | ~ aNaturalNumber0(X2) ) )
        & ( ? [X2] :
              ( sdtpldt0(X0,X2) = X1
              & aNaturalNumber0(X2) )
          | ~ sdtlseqdt0(X0,X1) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(nnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) )
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( sdtlseqdt0(X0,X1)
      <=> ? [X2] :
            ( sdtpldt0(X0,X2) = X1
            & aNaturalNumber0(X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',mDefLE) ).

fof(f165,plain,
    ! [X0,X1] :
      ( ~ sdtlseqdt0(X1,X0)
      | X0 = X1
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ sdtlseqdt0(X1,X0)
      | ~ sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & sdtlseqdt0(X0,X1) )
       => X0 = X1 ) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',mLEAsym) ).

fof(f32942,plain,
    sdtlseqdt0(sdtpldt0(xm,xn),xm),
    inference(subsumption_resolution,[],[f32941,f119]) ).

fof(f119,plain,
    aNaturalNumber0(xq),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    ( xq = sdtsldt0(sdtpldt0(xm,xn),xl)
    & sdtpldt0(xm,xn) = sdtasdt0(xl,xq)
    & aNaturalNumber0(xq) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',m__1379) ).

fof(f32941,plain,
    ( sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | ~ aNaturalNumber0(xq) ),
    inference(subsumption_resolution,[],[f32940,f204]) ).

fof(f204,plain,
    xp != xq,
    inference(subsumption_resolution,[],[f203,f116]) ).

fof(f116,plain,
    aNaturalNumber0(xp),
    inference(cnf_transformation,[],[f37]) ).

fof(f37,axiom,
    ( xp = sdtsldt0(xm,xl)
    & xm = sdtasdt0(xl,xp)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',m__1360) ).

fof(f203,plain,
    ( xp != xq
    | ~ aNaturalNumber0(xp) ),
    inference(subsumption_resolution,[],[f202,f131]) ).

fof(f131,plain,
    aNaturalNumber0(sz00),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',mSortsC) ).

fof(f202,plain,
    ( xp != xq
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(xp) ),
    inference(superposition,[],[f113,f137]) ).

fof(f137,plain,
    ! [X0] :
      ( sdtpldt0(X0,sz00) = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 )
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sdtpldt0(sz00,X0) = X0
        & sdtpldt0(X0,sz00) = X0 ) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',m_AddZero) ).

fof(f113,plain,
    ! [X0] :
      ( xq != sdtpldt0(xp,X0)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f45]) ).

fof(f45,plain,
    ( ~ sdtlseqdt0(xp,xq)
    & ! [X0] :
        ( xq != sdtpldt0(xp,X0)
        | ~ aNaturalNumber0(X0) ) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f40,negated_conjecture,
    ~ ( sdtlseqdt0(xp,xq)
      | ? [X0] :
          ( xq = sdtpldt0(xp,X0)
          & aNaturalNumber0(X0) ) ),
    inference(negated_conjecture,[],[f39]) ).

fof(f39,conjecture,
    ( sdtlseqdt0(xp,xq)
    | ? [X0] :
        ( xq = sdtpldt0(xp,X0)
        & aNaturalNumber0(X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',m__) ).

fof(f32940,plain,
    ( sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | xp = xq
    | ~ aNaturalNumber0(xq) ),
    inference(subsumption_resolution,[],[f32919,f247]) ).

fof(f247,plain,
    sdtlseqdt0(xq,xp),
    inference(subsumption_resolution,[],[f246,f119]) ).

fof(f246,plain,
    ( sdtlseqdt0(xq,xp)
    | ~ aNaturalNumber0(xq) ),
    inference(subsumption_resolution,[],[f243,f116]) ).

fof(f243,plain,
    ( sdtlseqdt0(xq,xp)
    | ~ aNaturalNumber0(xp)
    | ~ aNaturalNumber0(xq) ),
    inference(resolution,[],[f150,f114]) ).

fof(f114,plain,
    ~ sdtlseqdt0(xp,xq),
    inference(cnf_transformation,[],[f45]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( sdtlseqdt0(X1,X0)
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X1,X0)
        & X0 != X1 )
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( ( sdtlseqdt0(X1,X0)
        & X0 != X1 )
      | sdtlseqdt0(X0,X1)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X0)
          & X0 != X1 )
        | sdtlseqdt0(X0,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',mLETotal) ).

fof(f32919,plain,
    ( sdtlseqdt0(sdtpldt0(xm,xn),xm)
    | ~ sdtlseqdt0(xq,xp)
    | xp = xq
    | ~ aNaturalNumber0(xq) ),
    inference(superposition,[],[f10426,f120]) ).

fof(f120,plain,
    sdtpldt0(xm,xn) = sdtasdt0(xl,xq),
    inference(cnf_transformation,[],[f38]) ).

fof(f10426,plain,
    ! [X26] :
      ( sdtlseqdt0(sdtasdt0(xl,X26),xm)
      | ~ sdtlseqdt0(X26,xp)
      | xp = X26
      | ~ aNaturalNumber0(X26) ),
    inference(subsumption_resolution,[],[f10425,f122]) ).

fof(f122,plain,
    aNaturalNumber0(xl),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xl) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',m__1324) ).

fof(f10425,plain,
    ! [X26] :
      ( sdtlseqdt0(sdtasdt0(xl,X26),xm)
      | ~ sdtlseqdt0(X26,xp)
      | xp = X26
      | ~ aNaturalNumber0(X26)
      | ~ aNaturalNumber0(xl) ),
    inference(subsumption_resolution,[],[f10424,f116]) ).

fof(f10424,plain,
    ! [X26] :
      ( sdtlseqdt0(sdtasdt0(xl,X26),xm)
      | ~ sdtlseqdt0(X26,xp)
      | xp = X26
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(X26)
      | ~ aNaturalNumber0(xl) ),
    inference(subsumption_resolution,[],[f10363,f115]) ).

fof(f115,plain,
    sz00 != xl,
    inference(cnf_transformation,[],[f36]) ).

fof(f36,axiom,
    sz00 != xl,
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',m__1347) ).

fof(f10363,plain,
    ! [X26] :
      ( sdtlseqdt0(sdtasdt0(xl,X26),xm)
      | ~ sdtlseqdt0(X26,xp)
      | xp = X26
      | sz00 = xl
      | ~ aNaturalNumber0(xp)
      | ~ aNaturalNumber0(X26)
      | ~ aNaturalNumber0(xl) ),
    inference(superposition,[],[f177,f117]) ).

fof(f117,plain,
    xm = sdtasdt0(xl,xp),
    inference(cnf_transformation,[],[f37]) ).

fof(f177,plain,
    ! [X2,X0,X1] :
      ( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
      | ~ sdtlseqdt0(X1,X2)
      | X1 = X2
      | sz00 = X0
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,plain,
    ! [X0,X1,X2] :
      ( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
        & sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
        & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
      | ~ sdtlseqdt0(X1,X2)
      | X1 = X2
      | sz00 = X0
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1,X2] :
      ( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
        & sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
        & sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
        & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
      | ~ sdtlseqdt0(X1,X2)
      | X1 = X2
      | sz00 = X0
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1,X2] :
      ( ( aNaturalNumber0(X2)
        & aNaturalNumber0(X1)
        & aNaturalNumber0(X0) )
     => ( ( sdtlseqdt0(X1,X2)
          & X1 != X2
          & sz00 != X0 )
       => ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
          & sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
          & sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
          & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',mMonMul) ).

fof(f13013,plain,
    xm != sdtpldt0(xm,xn),
    inference(subsumption_resolution,[],[f13012,f119]) ).

fof(f13012,plain,
    ( xm != sdtpldt0(xm,xn)
    | ~ aNaturalNumber0(xq) ),
    inference(subsumption_resolution,[],[f13000,f204]) ).

fof(f13000,plain,
    ( xm != sdtpldt0(xm,xn)
    | xp = xq
    | ~ aNaturalNumber0(xq) ),
    inference(superposition,[],[f5581,f120]) ).

fof(f5581,plain,
    ! [X24] :
      ( xm != sdtasdt0(xl,X24)
      | xp = X24
      | ~ aNaturalNumber0(X24) ),
    inference(subsumption_resolution,[],[f5580,f122]) ).

fof(f5580,plain,
    ! [X24] :
      ( xm != sdtasdt0(xl,X24)
      | xp = X24
      | ~ aNaturalNumber0(X24)
      | ~ aNaturalNumber0(xl) ),
    inference(subsumption_resolution,[],[f5579,f115]) ).

fof(f5579,plain,
    ! [X24] :
      ( xm != sdtasdt0(xl,X24)
      | xp = X24
      | ~ aNaturalNumber0(X24)
      | sz00 = xl
      | ~ aNaturalNumber0(xl) ),
    inference(subsumption_resolution,[],[f5538,f116]) ).

fof(f5538,plain,
    ! [X24] :
      ( xm != sdtasdt0(xl,X24)
      | xp = X24
      | ~ aNaturalNumber0(X24)
      | ~ aNaturalNumber0(xp)
      | sz00 = xl
      | ~ aNaturalNumber0(xl) ),
    inference(superposition,[],[f143,f117]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
      | X1 = X2
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X1)
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( X1 = X2
          | ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
            & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
          | ~ aNaturalNumber0(X2)
          | ~ aNaturalNumber0(X1) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ! [X0] :
      ( ! [X1,X2] :
          ( X1 = X2
          | ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
            & sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
          | ~ aNaturalNumber0(X2)
          | ~ aNaturalNumber0(X1) )
      | sz00 = X0
      | ~ aNaturalNumber0(X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0] :
      ( aNaturalNumber0(X0)
     => ( sz00 != X0
       => ! [X1,X2] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X1) )
           => ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
                | sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
             => X1 = X2 ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783',mMulCanc) ).

fof(f123,plain,
    aNaturalNumber0(xm),
    inference(cnf_transformation,[],[f34]) ).

fof(f124,plain,
    aNaturalNumber0(xn),
    inference(cnf_transformation,[],[f34]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : NUM471+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15  % Command    : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36  % Computer : n022.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit   : 300
% 0.16/0.36  % WCLimit    : 300
% 0.16/0.36  % DateTime   : Fri Aug 25 08:17:40 EDT 2023
% 0.16/0.36  % CPUTime    : 
% 0.16/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.16/0.36  Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.8dUtbXOjax/Vampire---4.8_26783
% 0.16/0.36  % (26956)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42  % (26959)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)
% 0.22/0.42  % (26961)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)
% 0.22/0.42  % (26963)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)
% 0.22/0.42  % (26962)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)
% 0.22/0.42  % (26960)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)
% 0.22/0.42  % (26958)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)
% 0.22/0.42  % (26964)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)
% 6.48/1.40  % (26958)First to succeed.
% 6.48/1.40  % (26958)Refutation found. Thanks to Tanya!
% 6.48/1.40  % SZS status Theorem for Vampire---4
% 6.48/1.40  % SZS output start Proof for Vampire---4
% See solution above
% 6.48/1.41  % (26958)------------------------------
% 6.48/1.41  % (26958)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 6.48/1.41  % (26958)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 6.48/1.41  % (26958)Termination reason: Refutation
% 6.48/1.41  
% 6.48/1.41  % (26958)Memory used [KB]: 10618
% 6.48/1.41  % (26958)Time elapsed: 0.976 s
% 6.48/1.41  % (26958)------------------------------
% 6.48/1.41  % (26958)------------------------------
% 6.48/1.41  % (26956)Success in time 1.032 s
% 6.48/1.41  % Vampire---4.8 exiting
%------------------------------------------------------------------------------