SET007 Axioms: SET007+765.ax


%------------------------------------------------------------------------------
% File     : SET007+765 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Basic Notions and Properties of Orthoposets
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : oposet_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  152 (  35 unit)
%            Number of atoms       :  800 (  21 equality)
%            Maximal formula depth :   26 (   6 average)
%            Number of connectives :  784 ( 136 ~  ;   0  |; 458  &)
%                                         (  24 <=>; 166 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   69 (   1 propositional; 0-3 arity)
%            Number of functors    :   20 (   4 constant; 0-4 arity)
%            Number of variables   :  154 (   0 singleton; 131 !;  23 ?)
%            Maximal term depth    :    4 (   1 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & v1_oposet_1(A) ) )).

fof(rc2_oposet_1,axiom,(
    ! [A] :
    ? [B] :
      ( m1_relset_1(B,A,A)
      & v1_relat_1(B)
      & v2_relat_2(B)
      & v5_relat_2(B)
      & v8_relat_2(B) ) )).

fof(fc1_oposet_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( ~ v3_struct_0(g1_oposet_1(A,B,C))
        & v1_oposet_1(g1_oposet_1(A,B,C)) ) ) )).

fof(rc3_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v1_oposet_1(A) ) )).

fof(rc4_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ? [B] :
          ( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
          & ~ v1_xboole_0(B)
          & v1_relat_1(B)
          & v1_funct_1(B)
          & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
          & v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
          & v2_oposet_1(B,u1_struct_0(A)) ) ) )).

fof(fc2_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1) )).

fof(fc3_oposet_1,axiom,
    ( ~ v3_struct_0(k4_oposet_1)
    & v1_oposet_1(k4_oposet_1) )).

fof(fc4_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1)
    & v3_oposet_1(k3_oposet_1) )).

fof(rc5_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v3_oposet_1(A) ) )).

fof(fc5_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v2_orders_2(k3_oposet_1)
    & v3_orders_2(k3_oposet_1)
    & v4_orders_2(k3_oposet_1)
    & v1_lattice3(k3_oposet_1)
    & v2_lattice3(k3_oposet_1)
    & v3_lattice3(k3_oposet_1)
    & v1_yellow_0(k3_oposet_1)
    & v2_yellow_0(k3_oposet_1)
    & v3_yellow_0(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1)
    & v3_oposet_1(k3_oposet_1) )).

fof(rc6_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v1_oposet_1(A) ) )).

fof(cc1_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_necklace(A) )
       => ( ~ v3_struct_0(A)
          & v5_oposet_1(A) ) ) ) )).

fof(fc6_oposet_1,axiom,
    ( ~ v3_struct_0(k4_oposet_1)
    & v3_necklace(k4_oposet_1)
    & v1_oposet_1(k4_oposet_1)
    & v5_oposet_1(k4_oposet_1) )).

fof(rc7_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v3_necklace(A)
      & v1_oposet_1(A)
      & v5_oposet_1(A) ) )).

fof(cc2_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v1_necklace(A) )
       => ( ~ v3_struct_0(A)
          & v6_oposet_1(A) ) ) ) )).

fof(rc8_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v1_necklace(A)
      & v1_oposet_1(A)
      & v6_oposet_1(A) ) )).

fof(cc3_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & v7_oposet_1(A) ) ) ) )).

fof(fc7_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v2_orders_2(k3_oposet_1)
    & v3_orders_2(k3_oposet_1)
    & v4_orders_2(k3_oposet_1)
    & v1_lattice3(k3_oposet_1)
    & v2_lattice3(k3_oposet_1)
    & v3_lattice3(k3_oposet_1)
    & v1_yellow_0(k3_oposet_1)
    & v2_yellow_0(k3_oposet_1)
    & v3_yellow_0(k3_oposet_1)
    & v1_necklace(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1)
    & v3_oposet_1(k3_oposet_1)
    & v6_oposet_1(k3_oposet_1)
    & v7_oposet_1(k3_oposet_1) )).

fof(rc9_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v4_orders_2(A)
      & v1_necklace(A)
      & v1_oposet_1(A)
      & v6_oposet_1(A)
      & v7_oposet_1(A) ) )).

fof(cc4_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v8_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_necklace(A) ) ) ) )).

fof(fc8_oposet_1,axiom,
    ( ~ v3_struct_0(k4_oposet_1)
    & v2_necklace(k4_oposet_1)
    & v3_necklace(k4_oposet_1)
    & v1_oposet_1(k4_oposet_1)
    & v5_oposet_1(k4_oposet_1)
    & v8_oposet_1(k4_oposet_1) )).

fof(rc10_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v2_necklace(A)
      & v1_oposet_1(A)
      & v8_oposet_1(A) ) )).

fof(cc5_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & v9_oposet_1(A) ) ) ) )).

fof(rc11_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_necklace(A)
      & v1_oposet_1(A)
      & v6_oposet_1(A)
      & v7_oposet_1(A)
      & v9_oposet_1(A) ) )).

fof(fc9_oposet_1,axiom,
    ( ~ v3_struct_0(k4_oposet_1)
    & v3_orders_2(k4_oposet_1)
    & v2_necklace(k4_oposet_1)
    & v3_necklace(k4_oposet_1)
    & v1_oposet_1(k4_oposet_1)
    & v5_oposet_1(k4_oposet_1)
    & v8_oposet_1(k4_oposet_1)
    & v9_oposet_1(k4_oposet_1) )).

fof(rc12_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v3_orders_2(A)
      & v2_necklace(A)
      & v3_necklace(A)
      & v1_oposet_1(A)
      & v5_oposet_1(A)
      & v8_oposet_1(A)
      & v9_oposet_1(A) ) )).

fof(cc6_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v6_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_necklace(A)
          & v6_oposet_1(A) ) ) ) )).

fof(cc7_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v7_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_orders_2(A)
          & v7_oposet_1(A) ) ) ) )).

fof(cc8_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v9_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v3_orders_2(A)
          & v9_oposet_1(A) ) ) ) )).

fof(cc9_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_necklace(A)
          & v9_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v3_orders_2(A)
          & v9_oposet_1(A) ) ) ) )).

fof(cc10_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_necklace(A)
          & v3_necklace(A) )
       => ( ~ v3_struct_0(A)
          & v2_necklace(A)
          & v8_oposet_1(A) ) ) ) )).

fof(cc11_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v11_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v10_oposet_1(A) ) ) ) )).

fof(fc10_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v2_orders_2(k3_oposet_1)
    & v3_orders_2(k3_oposet_1)
    & v4_orders_2(k3_oposet_1)
    & v1_lattice3(k3_oposet_1)
    & v2_lattice3(k3_oposet_1)
    & v3_lattice3(k3_oposet_1)
    & v1_yellow_0(k3_oposet_1)
    & v2_yellow_0(k3_oposet_1)
    & v3_yellow_0(k3_oposet_1)
    & v1_necklace(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1)
    & v3_oposet_1(k3_oposet_1)
    & v6_oposet_1(k3_oposet_1)
    & v7_oposet_1(k3_oposet_1)
    & v9_oposet_1(k3_oposet_1)
    & v10_oposet_1(k3_oposet_1)
    & v11_oposet_1(k3_oposet_1) )).

fof(rc13_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v1_oposet_1(A)
      & v3_oposet_1(A)
      & v10_oposet_1(A)
      & v11_oposet_1(A)
      & v12_oposet_1(A) ) )).

fof(fc11_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v2_orders_2(k3_oposet_1)
    & v3_orders_2(k3_oposet_1)
    & v4_orders_2(k3_oposet_1)
    & v1_lattice3(k3_oposet_1)
    & v2_lattice3(k3_oposet_1)
    & v3_lattice3(k3_oposet_1)
    & v1_yellow_0(k3_oposet_1)
    & v2_yellow_0(k3_oposet_1)
    & v3_yellow_0(k3_oposet_1)
    & v1_necklace(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1)
    & v3_oposet_1(k3_oposet_1)
    & v6_oposet_1(k3_oposet_1)
    & v7_oposet_1(k3_oposet_1)
    & v9_oposet_1(k3_oposet_1)
    & v10_oposet_1(k3_oposet_1)
    & v11_oposet_1(k3_oposet_1)
    & v12_oposet_1(k3_oposet_1) )).

fof(cc12_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v13_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v14_oposet_1(A) ) ) ) )).

fof(cc13_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v14_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v13_oposet_1(A) ) ) ) )).

fof(cc14_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v14_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v7_oposet_1(A)
          & v9_oposet_1(A) ) ) ) )).

fof(cc15_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A) )
       => ( ~ v3_struct_0(A)
          & v13_oposet_1(A)
          & v14_oposet_1(A) ) ) ) )).

fof(rc14_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_oposet_1(A)
      & v3_oposet_1(A)
      & v7_oposet_1(A)
      & v9_oposet_1(A)
      & v13_oposet_1(A)
      & v14_oposet_1(A)
      & v15_oposet_1(A) ) )).

fof(fc12_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v2_orders_2(k3_oposet_1)
    & v3_orders_2(k3_oposet_1)
    & v4_orders_2(k3_oposet_1)
    & v1_lattice3(k3_oposet_1)
    & v2_lattice3(k3_oposet_1)
    & v3_lattice3(k3_oposet_1)
    & v1_yellow_0(k3_oposet_1)
    & v2_yellow_0(k3_oposet_1)
    & v3_yellow_0(k3_oposet_1)
    & v1_necklace(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1)
    & v3_oposet_1(k3_oposet_1)
    & v6_oposet_1(k3_oposet_1)
    & v7_oposet_1(k3_oposet_1)
    & v9_oposet_1(k3_oposet_1)
    & v10_oposet_1(k3_oposet_1)
    & v11_oposet_1(k3_oposet_1)
    & v12_oposet_1(k3_oposet_1)
    & v13_oposet_1(k3_oposet_1)
    & v14_oposet_1(k3_oposet_1)
    & v15_oposet_1(k3_oposet_1) )).

fof(cc16_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v17_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v16_oposet_1(A) ) ) ) )).

fof(cc17_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v16_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v5_oposet_1(A) ) ) ) )).

fof(cc18_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_necklace(A)
          & v16_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v5_oposet_1(A)
          & v16_oposet_1(A)
          & v17_oposet_1(A) ) ) ) )).

fof(cc19_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v17_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v3_necklace(A)
          & v5_oposet_1(A) ) ) ) )).

fof(fc13_oposet_1,axiom,
    ( ~ v3_struct_0(k4_oposet_1)
    & v3_orders_2(k4_oposet_1)
    & v2_necklace(k4_oposet_1)
    & v3_necklace(k4_oposet_1)
    & v1_oposet_1(k4_oposet_1)
    & v5_oposet_1(k4_oposet_1)
    & v8_oposet_1(k4_oposet_1)
    & v9_oposet_1(k4_oposet_1)
    & v16_oposet_1(k4_oposet_1)
    & v17_oposet_1(k4_oposet_1) )).

fof(rc15_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v3_necklace(A)
      & v1_oposet_1(A)
      & v5_oposet_1(A)
      & v16_oposet_1(A)
      & v17_oposet_1(A) ) )).

fof(cc20_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( ( ~ v3_struct_0(A)
          & v14_oposet_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v7_oposet_1(A)
          & v9_oposet_1(A)
          & v13_oposet_1(A)
          & v14_oposet_1(A) ) ) ) )).

fof(fc14_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v2_orders_2(k3_oposet_1)
    & v3_orders_2(k3_oposet_1)
    & v4_orders_2(k3_oposet_1)
    & v1_lattice3(k3_oposet_1)
    & v2_lattice3(k3_oposet_1)
    & v3_lattice3(k3_oposet_1)
    & v1_yellow_0(k3_oposet_1)
    & v2_yellow_0(k3_oposet_1)
    & v3_yellow_0(k3_oposet_1)
    & v1_necklace(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1)
    & v3_oposet_1(k3_oposet_1)
    & v6_oposet_1(k3_oposet_1)
    & v7_oposet_1(k3_oposet_1)
    & v9_oposet_1(k3_oposet_1)
    & v10_oposet_1(k3_oposet_1)
    & v11_oposet_1(k3_oposet_1)
    & v12_oposet_1(k3_oposet_1)
    & v13_oposet_1(k3_oposet_1)
    & v14_oposet_1(k3_oposet_1)
    & v15_oposet_1(k3_oposet_1)
    & v19_oposet_1(k3_oposet_1) )).

fof(rc16_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v7_oposet_1(A)
      & v9_oposet_1(A)
      & v13_oposet_1(A)
      & v14_oposet_1(A)
      & v15_oposet_1(A)
      & v19_oposet_1(A) ) )).

fof(fc15_oposet_1,axiom,
    ( ~ v3_struct_0(k3_oposet_1)
    & v2_orders_2(k3_oposet_1)
    & v3_orders_2(k3_oposet_1)
    & v4_orders_2(k3_oposet_1)
    & v1_lattice3(k3_oposet_1)
    & v2_lattice3(k3_oposet_1)
    & v3_lattice3(k3_oposet_1)
    & v1_yellow_0(k3_oposet_1)
    & v2_yellow_0(k3_oposet_1)
    & v3_yellow_0(k3_oposet_1)
    & v1_necklace(k3_oposet_1)
    & v3_realset2(k3_oposet_1)
    & v1_oposet_1(k3_oposet_1)
    & v3_oposet_1(k3_oposet_1)
    & v6_oposet_1(k3_oposet_1)
    & v7_oposet_1(k3_oposet_1)
    & v9_oposet_1(k3_oposet_1)
    & v10_oposet_1(k3_oposet_1)
    & v11_oposet_1(k3_oposet_1)
    & v12_oposet_1(k3_oposet_1)
    & v13_oposet_1(k3_oposet_1)
    & v14_oposet_1(k3_oposet_1)
    & v15_oposet_1(k3_oposet_1)
    & v19_oposet_1(k3_oposet_1)
    & v20_oposet_1(k3_oposet_1)
    & v21_oposet_1(k3_oposet_1) )).

fof(rc17_oposet_1,axiom,(
    ? [A] :
      ( l1_oposet_1(A)
      & ~ v3_struct_0(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v7_oposet_1(A)
      & v9_oposet_1(A)
      & v13_oposet_1(A)
      & v14_oposet_1(A)
      & v20_oposet_1(A)
      & v21_oposet_1(A) ) )).

fof(d1_oposet_1,axiom,(
    ! [A,B] : k1_oposet_1(A,B) = k1_xboole_0 )).

fof(d2_oposet_1,axiom,(
    ! [A,B] : k2_oposet_1(A,B) = k2_zfmisc_1(A,B) )).

fof(t1_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => k3_relat_1(k6_partfun1(A)) = A ) )).

fof(t2_oposet_1,axiom,(
    $true )).

fof(t3_oposet_1,axiom,(
    k7_vectsp_2 = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) )).

fof(t4_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => ( k1_yellow_0(A,k2_struct_0(A,B,C)) = C
                  & k2_yellow_0(A,k2_struct_0(A,B,C)) = B ) ) ) ) ) )).

fof(t5_oposet_1,axiom,(
    $true )).

fof(t6_oposet_1,axiom,(
    ! [A,B] : k3_relat_1(k1_oposet_1(A,B)) = k1_xboole_0 )).

fof(t7_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ( r1_relat_2(B,A)
           => ( v1_relat_2(B)
              & k3_relat_1(B) = A ) ) ) ) )).

fof(t8_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ( r3_relat_2(B,A)
           => v3_relat_2(B) ) ) ) )).

fof(t9_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_relset_1(C,A,A)
             => ( ( v3_relat_2(C)
                  & r1_tarski(k3_relat_1(C),B) )
               => r3_relat_2(C,B) ) ) ) ) )).

fof(t10_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_relset_1(C,A,A)
             => ( ( v4_relat_2(C)
                  & r1_tarski(k3_relat_1(C),B) )
               => r4_relat_2(C,B) ) ) ) ) )).

fof(t11_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ( r4_relat_2(B,A)
           => v4_relat_2(B) ) ) ) )).

fof(t12_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_relset_1(C,A,A)
             => ( ( v8_relat_2(C)
                  & r1_tarski(k3_relat_1(C),B) )
               => r8_relat_2(C,B) ) ) ) ) )).

fof(t13_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ( r8_relat_2(B,A)
           => v8_relat_2(B) ) ) ) )).

fof(t14_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_relset_1(C,A,A)
             => ( ( v5_relat_2(C)
                  & r1_tarski(k3_relat_1(C),B) )
               => r5_relat_2(C,B) ) ) ) ) )).

fof(t15_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ( r5_relat_2(B,A)
           => v5_relat_2(B) ) ) ) )).

fof(t16_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( m2_relset_1(C,A,A)
             => ( ( v2_relat_2(C)
                  & r1_tarski(k3_relat_1(C),B) )
               => r2_relat_2(C,B) ) ) ) ) )).

fof(t17_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,A,A)
         => ( r2_relat_2(B,A)
           => v2_relat_2(B) ) ) ) )).

fof(d3_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ( v2_oposet_1(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,A)
               => k8_funct_2(A,A,B,k8_funct_2(A,A,B,C)) = C ) ) ) ) )).

fof(t18_oposet_1,axiom,(
    $true )).

fof(t19_oposet_1,axiom,(
    v2_oposet_1(k7_vectsp_2,k1_tarski(k1_xboole_0)) )).

fof(t20_oposet_1,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => v2_oposet_1(k6_partfun1(A),A) ) )).

fof(d4_oposet_1,axiom,(
    k3_oposet_1 = g1_oposet_1(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0)),k7_vectsp_2) )).

fof(d5_oposet_1,axiom,(
    k4_oposet_1 = g1_oposet_1(k1_tarski(k1_xboole_0),k1_oposet_1(k1_tarski(k1_xboole_0),k1_tarski(k1_xboole_0)),k7_vectsp_2) )).

fof(d6_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v3_oposet_1(A)
      <=> ? [B] :
            ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
            & B = u1_robbins1(A)
            & v2_oposet_1(B,u1_struct_0(A)) ) ) ) )).

fof(t21_oposet_1,axiom,(
    v3_oposet_1(k3_oposet_1) )).

fof(d7_oposet_1,axiom,(
    $true )).

fof(d8_oposet_1,axiom,(
    $true )).

fof(d9_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v4_oposet_1(A)
      <=> v1_relat_2(u1_orders_2(A)) ) ) )).

fof(t22_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v2_orders_2(A)
       => v4_oposet_1(A) ) ) )).

fof(t23_oposet_1,axiom,(
    v2_orders_2(k3_oposet_1) )).

fof(d10_oposet_1,axiom,(
    $true )).

fof(d11_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v5_oposet_1(A)
      <=> v2_relat_2(u1_orders_2(A)) ) ) )).

fof(d12_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v3_necklace(A)
      <=> r2_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).

fof(t24_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v3_necklace(A)
       => v5_oposet_1(A) ) ) )).

fof(t25_oposet_1,axiom,(
    v3_necklace(k4_oposet_1) )).

fof(d13_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v6_oposet_1(A)
      <=> ( v3_relat_2(u1_orders_2(A))
          & m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(t26_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v1_necklace(A)
       => v6_oposet_1(A) ) ) )).

fof(t27_oposet_1,axiom,(
    v1_necklace(k3_oposet_1) )).

fof(d14_oposet_1,axiom,(
    $true )).

fof(d15_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v7_oposet_1(A)
      <=> ( v4_relat_2(u1_orders_2(A))
          & m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(t28_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v4_orders_2(A)
       => v7_oposet_1(A) ) ) )).

fof(d16_oposet_1,axiom,(
    $true )).

fof(d17_oposet_1,axiom,(
    $true )).

fof(d18_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v8_oposet_1(A)
      <=> r5_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).

fof(t29_oposet_1,axiom,(
    $true )).

fof(t30_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v8_oposet_1(A)
       => v2_necklace(A) ) ) )).

fof(t31_oposet_1,axiom,(
    v8_oposet_1(k4_oposet_1) )).

fof(d19_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v9_oposet_1(A)
      <=> ( v8_relat_2(u1_orders_2(A))
          & m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ) ) )).

fof(t32_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v3_orders_2(A)
       => v9_oposet_1(A) ) ) )).

fof(t33_oposet_1,axiom,(
    $true )).

fof(t34_oposet_1,axiom,(
    v3_orders_2(k4_oposet_1) )).

fof(t35_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ( v6_oposet_1(A)
          & v9_oposet_1(A) )
       => v4_oposet_1(A) ) ) )).

fof(t36_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ( v5_oposet_1(A)
          & v9_oposet_1(A) )
       => v2_necklace(A) ) ) )).

fof(t37_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v2_necklace(A)
       => v5_oposet_1(A) ) ) )).

fof(t38_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ( v2_orders_2(A)
          & v6_oposet_1(A) )
       => v1_necklace(A) ) ) )).

fof(t39_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ( v2_orders_2(A)
          & v7_oposet_1(A) )
       => v4_orders_2(A) ) ) )).

fof(t40_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ( v2_orders_2(A)
          & v9_oposet_1(A) )
       => v3_orders_2(A) ) ) )).

fof(t41_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ( v3_necklace(A)
          & v9_oposet_1(A) )
       => v3_orders_2(A) ) ) )).

fof(t42_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ( v3_necklace(A)
          & v2_necklace(A) )
       => v8_oposet_1(A) ) ) )).

fof(d20_oposet_1,axiom,(
    $true )).

fof(d21_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v10_oposet_1(A)
      <=> ( v4_oposet_1(A)
          & v9_oposet_1(A) ) ) ) )).

fof(d22_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v11_oposet_1(A)
      <=> ( v2_orders_2(A)
          & v3_orders_2(A) ) ) ) )).

fof(t43_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v11_oposet_1(A)
       => v10_oposet_1(A) ) ) )).

fof(d23_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v12_oposet_1(A)
      <=> ( v3_oposet_1(A)
          & v11_oposet_1(A) ) ) ) )).

fof(d24_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v13_oposet_1(A)
      <=> ( v2_orders_2(A)
          & v7_oposet_1(A)
          & v9_oposet_1(A) ) ) ) )).

fof(d25_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v14_oposet_1(A)
      <=> ( v2_orders_2(A)
          & v4_orders_2(A)
          & v3_orders_2(A) ) ) ) )).

fof(t44_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v13_oposet_1(A)
      <=> v14_oposet_1(A) ) ) )).

fof(d26_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v15_oposet_1(A)
      <=> ( v3_oposet_1(A)
          & v14_oposet_1(A) ) ) ) )).

fof(d27_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v16_oposet_1(A)
      <=> ( v2_necklace(A)
          & v9_oposet_1(A) ) ) ) )).

fof(d28_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v17_oposet_1(A)
      <=> ( v8_oposet_1(A)
          & v3_orders_2(A) ) ) ) )).

fof(t45_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v17_oposet_1(A)
       => v16_oposet_1(A) ) ) )).

fof(t46_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v16_oposet_1(A)
       => v5_oposet_1(A) ) ) )).

fof(t47_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( ( v3_necklace(A)
          & v16_oposet_1(A) )
       => v17_oposet_1(A) ) ) )).

fof(t48_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v17_oposet_1(A)
       => v3_necklace(A) ) ) )).

fof(t49_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_oposet_1(A)
        & l1_oposet_1(A) )
     => ( v7_oposet_1(A)
       => v14_oposet_1(A) ) ) )).

fof(d29_oposet_1,axiom,(
    $true )).

fof(d30_oposet_1,axiom,(
    $true )).

fof(d31_oposet_1,axiom,(
    $true )).

fof(d32_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v18_oposet_1(B,A)
          <=> ? [C] :
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
                & C = B
                & v2_oposet_1(C,u1_struct_0(A))
                & v5_waybel_0(C,A,A) ) ) ) ) )).

fof(d33_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v19_oposet_1(A)
      <=> ? [B] :
            ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
            & B = u1_robbins1(A)
            & v18_oposet_1(B,A) ) ) ) )).

fof(t50_oposet_1,axiom,(
    $true )).

fof(t51_oposet_1,axiom,(
    v18_oposet_1(u1_robbins1(k3_oposet_1),k3_oposet_1) )).

fof(d34_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r1_oposet_1(A,B)
          <=> ( v18_oposet_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( r1_yellow_0(A,k2_struct_0(A,C,k1_waybel_0(A,A,B,C)))
                    & r2_yellow_0(A,k2_struct_0(A,C,k1_waybel_0(A,A,B,C))) ) ) ) ) ) ) )).

fof(d35_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v20_oposet_1(A)
      <=> ? [B] :
            ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
            & B = u1_robbins1(A)
            & r1_oposet_1(A,B) ) ) ) )).

fof(t52_oposet_1,axiom,(
    v20_oposet_1(k3_oposet_1) )).

fof(d36_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r2_oposet_1(A,B)
          <=> ( v18_oposet_1(B,A)
              & ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( r1_yellow_0(A,k2_struct_0(A,C,k1_waybel_0(A,A,B,C)))
                    & r2_yellow_0(A,k2_struct_0(A,C,k1_waybel_0(A,A,B,C)))
                    & r4_waybel_1(A,k1_yellow_0(A,k2_struct_0(A,C,k1_waybel_0(A,A,B,C))),u1_struct_0(A))
                    & r3_waybel_1(A,k2_yellow_0(A,k2_struct_0(A,C,k1_waybel_0(A,A,B,C))),u1_struct_0(A)) ) ) ) ) ) ) )).

fof(d37_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ( v21_oposet_1(A)
      <=> ? [B] :
            ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
            & B = u1_robbins1(A)
            & r2_oposet_1(A,B) ) ) ) )).

fof(t53_oposet_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_oposet_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r2_oposet_1(A,B)
           => r1_oposet_1(A,B) ) ) ) )).

fof(t54_oposet_1,axiom,(
    v21_oposet_1(k3_oposet_1) )).

fof(dt_l1_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( l1_orders_2(A)
        & l1_robbins1(A) ) ) )).

fof(existence_l1_oposet_1,axiom,(
    ? [A] : l1_oposet_1(A) )).

fof(abstractness_v1_oposet_1,axiom,(
    ! [A] :
      ( l1_oposet_1(A)
     => ( v1_oposet_1(A)
       => A = g1_oposet_1(u1_struct_0(A),u1_orders_2(A),u1_robbins1(A)) ) ) )).

fof(dt_k1_oposet_1,axiom,(
    ! [A,B] : m2_relset_1(k1_oposet_1(A,B),A,B) )).

fof(dt_k2_oposet_1,axiom,(
    ! [A,B] : m2_relset_1(k2_oposet_1(A,B),A,B) )).

fof(dt_k3_oposet_1,axiom,
    ( v1_oposet_1(k3_oposet_1)
    & l1_oposet_1(k3_oposet_1) )).

fof(dt_k4_oposet_1,axiom,
    ( v1_oposet_1(k4_oposet_1)
    & l1_oposet_1(k4_oposet_1) )).

fof(dt_g1_oposet_1,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v1_oposet_1(g1_oposet_1(A,B,C))
        & l1_oposet_1(g1_oposet_1(A,B,C)) ) ) )).

fof(free_g1_oposet_1,axiom,(
    ! [A,B,C] :
      ( ( m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ! [D,E,F] :
          ( g1_oposet_1(A,B,C) = g1_oposet_1(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).
%------------------------------------------------------------------------------