%------------------------------------------------------------------------------
% File     : LAT388+1 : TPTP v8.2.0. Released v4.0.0.
% Domain   : Lattice Theory
% Problem  : Tarski-Knaster fixed point theorem 03_01_05, 00 expansion
% Version  : Especial.
% English  :

% Refs     : [VLP07] Verchinine et al. (2007), System for Automated Deduction
%          : [Pas08] Paskevich (2008), Email to G. Sutcliffe
%          : [VL+08] Verchinine et al. (2008), On Correctness of Mathematic
% Source   : [Pas08]
% Names    : tarski_03_01_05.00 [Pas08]

% Status   : Theorem
% Rating   : 0.03 v8.1.0, 0.00 v6.1.0, 0.07 v6.0.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.00 v5.1.0, 0.05 v5.0.0, 0.12 v4.1.0, 0.17 v4.0.1, 0.61 v4.0.0
% Syntax   : Number of formulae    :   31 (   5 unt;  10 def)
%            Number of atoms       :  110 (   8 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   80 (   1   ~;   0   |;  26   &)
%                                         (  10 <=>;  43  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :   58 (  54   !;   4   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : Problem generated by the SAD system [VLP07]
%------------------------------------------------------------------------------
fof(mSetSort,axiom,
    ! [W0] :
      ( aSet0(W0)
     => $true ) ).

fof(mElmSort,axiom,
    ! [W0] :
      ( aElement0(W0)
     => $true ) ).

fof(mEOfElem,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aElementOf0(W1,W0)
         => aElement0(W1) ) ) ).

fof(mDefEmpty,definition,
    ! [W0] :
      ( aSet0(W0)
     => ( isEmpty0(W0)
      <=> ~ ? [W1] : aElementOf0(W1,W0) ) ) ).

fof(mDefSub,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
        <=> ( aSet0(W1)
            & ! [W2] :
                ( aElementOf0(W2,W1)
               => aElementOf0(W2,W0) ) ) ) ) ).

fof(mLessRel,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => ( sdtlseqdt0(W0,W1)
       => $true ) ) ).

fof(mARefl,axiom,
    ! [W0] :
      ( aElement0(W0)
     => sdtlseqdt0(W0,W0) ) ).

fof(mASymm,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aElement0(W1) )
     => ( ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W0) )
       => W0 = W1 ) ) ).

fof(mTrans,axiom,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aElement0(W1)
        & aElement0(W2) )
     => ( ( sdtlseqdt0(W0,W1)
          & sdtlseqdt0(W1,W2) )
       => sdtlseqdt0(W0,W2) ) ) ).

fof(mDefLB,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
         => ! [W2] :
              ( aLowerBoundOfIn0(W2,W1,W0)
            <=> ( aElementOf0(W2,W0)
                & ! [W3] :
                    ( aElementOf0(W3,W1)
                   => sdtlseqdt0(W2,W3) ) ) ) ) ) ).

fof(mDefUB,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
         => ! [W2] :
              ( aUpperBoundOfIn0(W2,W1,W0)
            <=> ( aElementOf0(W2,W0)
                & ! [W3] :
                    ( aElementOf0(W3,W1)
                   => sdtlseqdt0(W3,W2) ) ) ) ) ) ).

fof(mDefInf,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
         => ! [W2] :
              ( aInfimumOfIn0(W2,W1,W0)
            <=> ( aElementOf0(W2,W0)
                & aLowerBoundOfIn0(W2,W1,W0)
                & ! [W3] :
                    ( aLowerBoundOfIn0(W3,W1,W0)
                   => sdtlseqdt0(W3,W2) ) ) ) ) ) ).

fof(mDefSup,definition,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
         => ! [W2] :
              ( aSupremumOfIn0(W2,W1,W0)
            <=> ( aElementOf0(W2,W0)
                & aUpperBoundOfIn0(W2,W1,W0)
                & ! [W3] :
                    ( aUpperBoundOfIn0(W3,W1,W0)
                   => sdtlseqdt0(W2,W3) ) ) ) ) ) ).

fof(mSupUn,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
         => ! [W2,W3] :
              ( ( aSupremumOfIn0(W2,W1,W0)
                & aSupremumOfIn0(W3,W1,W0) )
             => W2 = W3 ) ) ) ).

fof(mInfUn,axiom,
    ! [W0] :
      ( aSet0(W0)
     => ! [W1] :
          ( aSubsetOf0(W1,W0)
         => ! [W2,W3] :
              ( ( aInfimumOfIn0(W2,W1,W0)
                & aInfimumOfIn0(W3,W1,W0) )
             => W2 = W3 ) ) ) ).

fof(mDefCLat,definition,
    ! [W0] :
      ( aCompleteLattice0(W0)
    <=> ( aSet0(W0)
        & ! [W1] :
            ( aSubsetOf0(W1,W0)
           => ? [W2] :
                ( aInfimumOfIn0(W2,W1,W0)
                & ? [W3] : aSupremumOfIn0(W3,W1,W0) ) ) ) ) ).

fof(mConMap,axiom,
    ! [W0] :
      ( aFunction0(W0)
     => $true ) ).

fof(mDomSort,axiom,
    ! [W0] :
      ( aFunction0(W0)
     => aSet0(szDzozmdt0(W0)) ) ).

fof(mRanSort,axiom,
    ! [W0] :
      ( aFunction0(W0)
     => aSet0(szRzazndt0(W0)) ) ).

fof(mDefDom,definition,
    ! [W0,W1] :
      ( ( aFunction0(W0)
        & aSet0(W1) )
     => ( isOn0(W0,W1)
      <=> ( szDzozmdt0(W0) = szRzazndt0(W0)
          & szRzazndt0(W0) = W1 ) ) ) ).

fof(mImgSort,axiom,
    ! [W0] :
      ( aFunction0(W0)
     => ! [W1] :
          ( aElementOf0(W1,szDzozmdt0(W0))
         => aElementOf0(sdtlpdtrp0(W0,W1),szRzazndt0(W0)) ) ) ).

fof(mDefFix,definition,
    ! [W0] :
      ( aFunction0(W0)
     => ! [W1] :
          ( aFixedPointOf0(W1,W0)
        <=> ( aElementOf0(W1,szDzozmdt0(W0))
            & sdtlpdtrp0(W0,W1) = W1 ) ) ) ).

fof(mDefMonot,definition,
    ! [W0] :
      ( aFunction0(W0)
     => ( isMonotone0(W0)
      <=> ! [W1,W2] :
            ( ( aElementOf0(W1,szDzozmdt0(W0))
              & aElementOf0(W2,szDzozmdt0(W0)) )
           => ( sdtlseqdt0(W1,W2)
             => sdtlseqdt0(sdtlpdtrp0(W0,W1),sdtlpdtrp0(W0,W2)) ) ) ) ) ).

fof(m__1123,hypothesis,
    ( aCompleteLattice0(xU)
    & aFunction0(xf)
    & isMonotone0(xf)
    & isOn0(xf,xU) ) ).

fof(m__1144,hypothesis,
    xS = cS1142(xf) ).

fof(m__1173,hypothesis,
    aSubsetOf0(xT,xS) ).

fof(m__1244,hypothesis,
    xP = cS1241(xU,xf,xT) ).

fof(m__1261,hypothesis,
    aInfimumOfIn0(xp,xP,xU) ).

fof(m__1299,hypothesis,
    ( aLowerBoundOfIn0(sdtlpdtrp0(xf,xp),xP,xU)
    & aUpperBoundOfIn0(sdtlpdtrp0(xf,xp),xT,xU) ) ).

fof(m__1330,hypothesis,
    ( aFixedPointOf0(xp,xf)
    & aSupremumOfIn0(xp,xT,xS) ) ).

fof(m__,conjecture,
    ? [W0] : aSupremumOfIn0(W0,xT,xS) ).

%------------------------------------------------------------------------------