SET007 Axioms: SET007+928.ax


%------------------------------------------------------------------------------
% File     : SET007+928 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : On the Calculus of Binary Arithmetics, Part II
% 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    : binari_6 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   87 (   0 unit)
%            Number of atoms       :  281 (  95 equality)
%            Maximal formula depth :    8 (   5 average)
%            Number of connectives :  194 (   0 ~  ;   0  |;   8  &)
%                                         (   0 <=>; 186 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    2 (   0 propositional; 1-2 arity)
%            Number of functors    :   10 (   2 constant; 0-2 arity)
%            Number of variables   :  186 (   0 singleton; 186 !;   0 ?)
%            Maximal term depth    :    6 (   2 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_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => k1_bvfunc_1(k8_margrel1,A) = A ) )).

fof(t2_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => k1_bvfunc_1(k7_margrel1,A) = k8_margrel1 ) )).

fof(t3_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ( k1_bvfunc_1(A,A) = k8_margrel1
        & k9_margrel1(k1_bvfunc_1(A,A)) = k7_margrel1 ) ) )).

fof(t4_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k9_margrel1(k1_bvfunc_1(A,B)) = k10_margrel1(A,k9_margrel1(B)) ) ) )).

fof(t5_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ( k1_bvfunc_1(A,k9_margrel1(A)) = k9_margrel1(A)
        & k9_margrel1(k1_bvfunc_1(A,k9_margrel1(A))) = A ) ) )).

fof(t6_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => k1_bvfunc_1(k9_margrel1(A),A) = A ) )).

fof(t7_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => k2_bvfunc_1(k8_margrel1,A) = A ) )).

fof(t8_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => k2_bvfunc_1(k7_margrel1,A) = k9_margrel1(A) ) )).

fof(t9_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ( k2_bvfunc_1(A,A) = k8_margrel1
        & k9_margrel1(k2_bvfunc_1(A,A)) = k7_margrel1 ) ) )).

fof(t10_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => k2_bvfunc_1(k9_margrel1(A),A) = k7_margrel1 ) )).

fof(t11_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k10_margrel1(A,k2_bvfunc_1(B,C)) = k10_margrel1(k10_margrel1(A,k1_binarith(k9_margrel1(B),C)),k1_binarith(k9_margrel1(C),B)) ) ) ) )).

fof(t12_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k10_margrel1(A,k1_binari_5(B,C)) = k1_binarith(k10_margrel1(A,k9_margrel1(B)),k10_margrel1(A,k9_margrel1(C))) ) ) ) )).

fof(t13_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k10_margrel1(A,k3_binari_5(B,C)) = k10_margrel1(k10_margrel1(A,k9_margrel1(B)),k9_margrel1(C)) ) ) ) )).

fof(t14_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k10_margrel1(A,B)) = k10_margrel1(A,B) ) ) )).

fof(t15_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k1_binarith(A,B)) = k1_binarith(A,k10_margrel1(A,B)) ) ) )).

fof(t16_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k2_binarith(A,B)) = k10_margrel1(A,k9_margrel1(B)) ) ) )).

fof(t17_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k1_bvfunc_1(A,B)) = k10_margrel1(A,B) ) ) )).

fof(t18_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k2_bvfunc_1(A,B)) = k10_margrel1(A,B) ) ) )).

fof(t19_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k1_binari_5(A,B)) = k10_margrel1(A,k9_margrel1(B)) ) ) )).

fof(t20_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k3_binari_5(A,B)) = k7_margrel1 ) ) )).

fof(t21_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k1_binarith(A,k2_binarith(B,C)) = k1_binarith(k1_binarith(A,k10_margrel1(k9_margrel1(B),C)),k10_margrel1(B,k9_margrel1(C))) ) ) ) )).

fof(t22_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k1_binarith(A,k2_bvfunc_1(B,C)) = k10_margrel1(k1_binarith(k1_binarith(A,k9_margrel1(B)),C),k1_binarith(k1_binarith(A,k9_margrel1(C)),B)) ) ) ) )).

fof(t23_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k1_binarith(A,k1_binari_5(B,C)) = k1_binarith(k1_binarith(A,k9_margrel1(B)),k9_margrel1(C)) ) ) ) )).

fof(t24_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => ( k1_binarith(A,k3_binari_5(B,C)) = k10_margrel1(k1_binarith(A,k9_margrel1(B)),k1_binarith(A,k9_margrel1(C)))
                & k1_binarith(A,k3_binari_5(B,C)) = k10_margrel1(k1_bvfunc_1(B,A),k1_bvfunc_1(C,A)) ) ) ) ) )).

fof(t25_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binarith(A,k1_binarith(A,B)) = k1_binarith(A,B) ) ) )).

fof(t26_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binarith(A,k1_bvfunc_1(A,B)) = k8_margrel1 ) ) )).

fof(t27_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binarith(A,k2_bvfunc_1(A,B)) = k1_bvfunc_1(B,A) ) ) )).

fof(t28_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binarith(A,k1_binari_5(A,B)) = k8_margrel1 ) ) )).

fof(t29_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binarith(A,k3_binari_5(A,B)) = k1_bvfunc_1(B,A) ) ) )).

fof(t30_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k1_bvfunc_1(A,k2_binarith(B,C)) = k1_binarith(k1_binarith(k9_margrel1(A),k10_margrel1(k9_margrel1(B),C)),k10_margrel1(B,k9_margrel1(C))) ) ) ) )).

fof(t31_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k1_bvfunc_1(A,k2_bvfunc_1(B,C)) = k10_margrel1(k1_binarith(k1_binarith(k9_margrel1(A),k9_margrel1(B)),C),k1_binarith(k1_binarith(k9_margrel1(A),B),k9_margrel1(C))) ) ) ) )).

fof(t32_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k1_bvfunc_1(A,k1_binari_5(B,C)) = k1_binarith(k1_binarith(k9_margrel1(A),k9_margrel1(B)),k9_margrel1(C)) ) ) ) )).

fof(t33_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => ( k1_bvfunc_1(A,k3_binari_5(B,C)) = k10_margrel1(k1_binarith(k9_margrel1(A),k9_margrel1(B)),k1_binarith(k9_margrel1(A),k9_margrel1(C)))
                & k1_bvfunc_1(A,k3_binari_5(B,C)) = k10_margrel1(k1_bvfunc_1(A,k9_margrel1(B)),k1_bvfunc_1(A,k9_margrel1(C))) ) ) ) ) )).

fof(t34_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,k10_margrel1(A,B)) = k1_bvfunc_1(A,B) ) ) )).

fof(t35_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,k1_binarith(A,B)) = k8_margrel1 ) ) )).

fof(t36_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,k2_binarith(A,B)) = k1_binarith(k9_margrel1(A),k9_margrel1(B)) ) ) )).

fof(t37_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,k1_bvfunc_1(A,B)) = k1_bvfunc_1(A,B) ) ) )).

fof(t38_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ( k1_bvfunc_1(A,k2_bvfunc_1(A,B)) = k1_bvfunc_1(A,B)
            & k1_bvfunc_1(A,k2_bvfunc_1(A,B)) = k1_bvfunc_1(A,k1_bvfunc_1(A,B)) ) ) ) )).

fof(t39_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,k1_binari_5(A,B)) = k9_margrel1(k10_margrel1(A,B)) ) ) )).

fof(t40_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_bvfunc_1(A,k3_binari_5(A,B)) = k9_margrel1(A) ) ) )).

fof(t41_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => ( k1_binari_5(A,k1_bvfunc_1(B,C)) = k10_margrel1(k1_binarith(k9_margrel1(A),B),k1_binarith(k9_margrel1(A),k9_margrel1(C)))
                & k1_binari_5(A,k1_bvfunc_1(B,C)) = k10_margrel1(k1_bvfunc_1(A,B),k1_bvfunc_1(A,k9_margrel1(C))) ) ) ) ) )).

fof(t42_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k1_binari_5(A,k2_bvfunc_1(B,C)) = k9_margrel1(k10_margrel1(k10_margrel1(A,k1_binarith(k9_margrel1(B),C)),k1_binarith(k9_margrel1(C),B))) ) ) ) )).

fof(t43_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => ( k1_binari_5(A,k1_binari_5(B,C)) = k10_margrel1(k1_binarith(k9_margrel1(A),B),k1_binarith(k9_margrel1(A),C))
                & k1_binari_5(A,k1_binari_5(B,C)) = k10_margrel1(k1_bvfunc_1(A,B),k1_bvfunc_1(A,C)) ) ) ) ) )).

fof(t44_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k1_binari_5(A,k3_binari_5(B,C)) = k1_binarith(k1_binarith(k9_margrel1(A),B),C) ) ) ) )).

fof(t45_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binari_5(A,k10_margrel1(A,B)) = k9_margrel1(k10_margrel1(A,B)) ) ) )).

fof(t46_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binari_5(A,k2_binarith(A,B)) = k1_bvfunc_1(A,B) ) ) )).

fof(t47_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binari_5(A,k1_bvfunc_1(A,B)) = k9_margrel1(k10_margrel1(A,B)) ) ) )).

fof(t48_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binari_5(A,k2_bvfunc_1(A,B)) = k9_margrel1(k10_margrel1(A,B)) ) ) )).

fof(t49_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binari_5(A,k1_binari_5(A,B)) = k1_bvfunc_1(A,B) ) ) )).

fof(t50_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binari_5(A,k3_binari_5(A,B)) = k8_margrel1 ) ) )).

fof(t51_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k3_binari_5(A,k2_binarith(B,C)) = k9_margrel1(k1_binarith(k1_binarith(A,k10_margrel1(k9_margrel1(B),C)),k10_margrel1(B,k9_margrel1(C)))) ) ) ) )).

fof(t52_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k3_binari_5(A,k2_bvfunc_1(B,C)) = k9_margrel1(k10_margrel1(k1_binarith(k1_binarith(A,k9_margrel1(B)),C),k1_binarith(k1_binarith(A,k9_margrel1(C)),B))) ) ) ) )).

fof(t53_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k3_binari_5(A,k1_binari_5(B,C)) = k10_margrel1(k10_margrel1(k9_margrel1(A),B),C) ) ) ) )).

fof(t54_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k3_binari_5(A,k3_binari_5(B,C)) = k1_binarith(k10_margrel1(k9_margrel1(A),B),k10_margrel1(k9_margrel1(A),C)) ) ) ) )).

fof(t55_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k3_binari_5(A,k10_margrel1(A,B)) = k9_margrel1(A) ) ) )).

fof(t56_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k3_binari_5(A,k1_binarith(A,B)) = k10_margrel1(k9_margrel1(A),k9_margrel1(B)) ) ) )).

fof(t57_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k3_binari_5(A,k2_binarith(A,B)) = k10_margrel1(k9_margrel1(A),k9_margrel1(B)) ) ) )).

fof(t58_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k3_binari_5(A,k1_bvfunc_1(A,B)) = k7_margrel1 ) ) )).

fof(t59_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k3_binari_5(A,k2_bvfunc_1(A,B)) = k10_margrel1(k9_margrel1(A),B) ) ) )).

fof(t60_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k3_binari_5(A,k1_binari_5(A,B)) = k7_margrel1 ) ) )).

fof(t61_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k3_binari_5(A,k3_binari_5(A,B)) = k10_margrel1(k9_margrel1(A),B) ) ) )).

fof(t62_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k2_binarith(A,k10_margrel1(B,C)) = k10_margrel1(k1_binarith(A,k10_margrel1(B,C)),k1_binarith(k9_margrel1(A),k9_margrel1(k10_margrel1(B,C)))) ) ) ) )).

fof(t63_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(A,k10_margrel1(A,B)) = k10_margrel1(A,k9_margrel1(B)) ) ) )).

fof(t64_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(A,k1_binarith(A,B)) = k10_margrel1(k9_margrel1(A),B) ) ) )).

fof(t65_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(k9_margrel1(A),k2_binarith(A,B)) = k10_margrel1(k9_margrel1(A),B) ) ) )).

fof(t66_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k9_margrel1(k2_binarith(A,B))) = k10_margrel1(A,B) ) ) )).

fof(t67_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(A,k2_binarith(A,B)) = B ) ) )).

fof(t68_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k9_margrel1(k1_bvfunc_1(A,B))) = k10_margrel1(A,k9_margrel1(B)) ) ) )).

fof(t69_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(A,k1_bvfunc_1(A,B)) = k1_binarith(k9_margrel1(A),k9_margrel1(B)) ) ) )).

fof(t70_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(k9_margrel1(A),k2_bvfunc_1(A,B)) = k10_margrel1(k9_margrel1(A),k9_margrel1(B)) ) ) )).

fof(t71_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(A,k9_margrel1(k2_bvfunc_1(A,B))) = k10_margrel1(A,k9_margrel1(B)) ) ) )).

fof(t72_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(A,k2_bvfunc_1(A,B)) = k9_margrel1(B) ) ) )).

fof(t73_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(A,k1_binari_5(A,B)) = k1_bvfunc_1(A,B) ) ) )).

fof(t74_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(A,k3_binari_5(A,B)) = k1_bvfunc_1(B,A) ) ) )).

fof(t75_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(k9_margrel1(A),k1_bvfunc_1(A,B)) = k1_binarith(k9_margrel1(A),k10_margrel1(k9_margrel1(A),B)) ) ) )).

fof(t76_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => ! [C] :
              ( v2_margrel1(C)
             => k10_margrel1(k9_margrel1(A),k2_bvfunc_1(B,C)) = k10_margrel1(k10_margrel1(k9_margrel1(A),k1_binarith(k9_margrel1(B),C)),k1_binarith(k9_margrel1(C),B)) ) ) ) )).

fof(t77_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(k9_margrel1(A),k2_bvfunc_1(A,B)) = k10_margrel1(k10_margrel1(k9_margrel1(A),k9_margrel1(B)),k1_binarith(k9_margrel1(A),B)) ) ) )).

fof(t78_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(k9_margrel1(A),k1_binari_5(A,B)) = k1_binarith(k9_margrel1(A),k10_margrel1(k9_margrel1(A),k9_margrel1(B))) ) ) )).

fof(t79_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k10_margrel1(k9_margrel1(A),k3_binari_5(A,B)) = k10_margrel1(k9_margrel1(A),k9_margrel1(B)) ) ) )).

fof(t80_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binarith(k9_margrel1(A),k1_bvfunc_1(A,B)) = k1_binarith(k9_margrel1(A),B) ) ) )).

fof(t81_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binarith(k9_margrel1(A),k2_bvfunc_1(A,B)) = k1_binarith(k9_margrel1(A),B) ) ) )).

fof(t82_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k1_binarith(k9_margrel1(A),k1_binari_5(A,B)) = k1_binarith(k9_margrel1(A),k9_margrel1(B)) ) ) )).

fof(t83_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(k9_margrel1(A),k1_bvfunc_1(A,B)) = k10_margrel1(A,B) ) ) )).

fof(t84_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(k9_margrel1(A),k1_bvfunc_1(B,A)) = k1_binarith(k10_margrel1(A,k1_binarith(A,k9_margrel1(B))),k10_margrel1(k9_margrel1(A),B)) ) ) )).

fof(t85_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k9_margrel1(k1_bvfunc_1(A,B)) = k10_margrel1(A,k9_margrel1(B)) ) ) )).

fof(t86_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k9_margrel1(k2_bvfunc_1(A,B)) = k1_binarith(k10_margrel1(A,k9_margrel1(B)),k10_margrel1(B,k9_margrel1(A))) ) ) )).

fof(t87_binari_6,axiom,(
    ! [A] :
      ( v2_margrel1(A)
     => ! [B] :
          ( v2_margrel1(B)
         => k2_binarith(k9_margrel1(A),k2_bvfunc_1(A,B)) = B ) ) )).
%------------------------------------------------------------------------------