SET007 Axioms: SET007+928.ax
%------------------------------------------------------------------------------
% File : SET007+928 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 281 ( 95 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 194 ( 0 ~; 0 |; 8 &)
% ( 0 <=>; 186 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 186 ( 186 !; 0 ?)
% 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 ) ) ).
%------------------------------------------------------------------------------