SET007 Axioms: SET007+39.ax


%------------------------------------------------------------------------------
% File     : SET007+39 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Field Properties of Complex Numbers - Requirements
% 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    : arithm [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :    6 (   0 unit)
%            Number of atoms       :   12 (   6 equality)
%            Maximal formula depth :    3 (   3 average)
%            Number of connectives :    6 (   0 ~  ;   0  |;   0  &)
%                                         (   0 <=>;   6 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    2 (   0 propositional; 1-2 arity)
%            Number of functors    :    6 (   2 constant; 0-2 arity)
%            Number of variables   :    6 (   0 singleton;   6 !;   0 ?)
%            Maximal term depth    :    2 (   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(t1_arithm,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,np__0) = A ) )).

fof(t2_arithm,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,np__0) = np__0 ) )).

fof(t3_arithm,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(np__1,A) = A ) )).

fof(t4_arithm,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,np__0) = A ) )).

fof(t5_arithm,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(np__0,A) = np__0 ) )).

fof(t6_arithm,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,np__1) = A ) )).
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