%------------------------------------------------------------------------------
% File     : LAT381+3 : TPTP v9.0.0. Released v4.0.0.
% Domain   : Lattice Theory
% Problem  : Tarski-Knaster fixed point theorem 01, 02 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_01.02 [Pas08]

% Status   : Theorem
% Rating   : 0.06 v8.2.0, 0.08 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.00 v6.2.0, 0.04 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.05 v5.1.0, 0.19 v5.0.0, 0.21 v4.1.0, 0.26 v4.0.1, 0.61 v4.0.0
% Syntax   : Number of formulae    :   17 (   2 unt;   6 def)
%            Number of atoms       :   86 (   2 equ)
%            Maximal formula atoms :   22 (   5 avg)
%            Number of connectives :   70 (   1   ~;   2   |;  28   &)
%                                         (   6 <=>;  33  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   7 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   12 (  10 usr;   1 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   40 (  39   !;   1   ?)
% 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(m__725,hypothesis,
    aSet0(xT) ).

fof(m__725_01,hypothesis,
    ( aSet0(xS)
    & ! [W0] :
        ( aElementOf0(W0,xS)
       => aElementOf0(W0,xT) )
    & aSubsetOf0(xS,xT) ) ).

fof(m__744,hypothesis,
    ( aElementOf0(xu,xT)
    & aElementOf0(xu,xT)
    & ! [W0] :
        ( aElementOf0(W0,xS)
       => sdtlseqdt0(W0,xu) )
    & aUpperBoundOfIn0(xu,xS,xT)
    & ! [W0] :
        ( ( ( aElementOf0(W0,xT)
            & ! [W1] :
                ( aElementOf0(W1,xS)
               => sdtlseqdt0(W1,W0) ) )
          | aUpperBoundOfIn0(W0,xS,xT) )
       => sdtlseqdt0(xu,W0) )
    & aSupremumOfIn0(xu,xS,xT)
    & aElementOf0(xv,xT)
    & aElementOf0(xv,xT)
    & ! [W0] :
        ( aElementOf0(W0,xS)
       => sdtlseqdt0(W0,xv) )
    & aUpperBoundOfIn0(xv,xS,xT)
    & ! [W0] :
        ( ( ( aElementOf0(W0,xT)
            & ! [W1] :
                ( aElementOf0(W1,xS)
               => sdtlseqdt0(W1,W0) ) )
          | aUpperBoundOfIn0(W0,xS,xT) )
       => sdtlseqdt0(xv,W0) )
    & aSupremumOfIn0(xv,xS,xT) ) ).

fof(m__,conjecture,
    xu = xv ).

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