%   ORIGINAL: h4/gcd/GCD__ADD__R
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/LESS__EQ__ADD: !n m. h4/arithmetic/_3C_3D m (h4/arithmetic/_2B m n)
% Assm: h4/arithmetic/ADD__SUB: !c a. h4/arithmetic/_2D (h4/arithmetic/_2B a c) c = a
% Assm: h4/gcd/IS__GCD__UNIQUE: !d c b a. h4/gcd/is__gcd a b c /\ h4/gcd/is__gcd a b d ==> c = d
% Assm: h4/gcd/IS__GCD__MINUS__R: !c b a. h4/arithmetic/_3C_3D a b /\ h4/gcd/is__gcd a (h4/arithmetic/_2D b a) c ==> h4/gcd/is__gcd a b c
% Assm: h4/gcd/GCD__IS__GCD: !b a. h4/gcd/is__gcd a b (h4/gcd/gcd a b)
% Goal: !b a. h4/gcd/gcd a (h4/arithmetic/_2B a b) = h4/gcd/gcd a b
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_ADD]: !n m. h4/arithmetic/_3C_3D m (h4/arithmetic/_2B m n)
% Assm [h4s_arithmetics_ADDu_u_SUB]: !c a. h4/arithmetic/_2D (h4/arithmetic/_2B a c) c = a
% Assm [h4s_gcds_ISu_u_GCDu_u_UNIQUE]: !d c b a. h4/gcd/is__gcd a b c /\ h4/gcd/is__gcd a b d ==> c = d
% Assm [h4s_gcds_ISu_u_GCDu_u_MINUSu_u_R]: !c b a. h4/arithmetic/_3C_3D a b /\ h4/gcd/is__gcd a (h4/arithmetic/_2D b a) c ==> h4/gcd/is__gcd a b c
% Assm [h4s_gcds_GCDu_u_ISu_u_GCD]: !b a. h4/gcd/is__gcd a b (h4/gcd/gcd a b)
% Goal: !b a. h4/gcd/gcd a (h4/arithmetic/_2B a b) = h4/gcd/gcd a b
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q331292,TV_Q331288]: ![V_f, V_g]: (![V_x]: s(TV_Q331288,happ(s(t_fun(TV_Q331292,TV_Q331288),V_f),s(TV_Q331292,V_x))) = s(TV_Q331288,happ(s(t_fun(TV_Q331292,TV_Q331288),V_g),s(TV_Q331292,V_x))) => s(t_fun(TV_Q331292,TV_Q331288),V_f) = s(t_fun(TV_Q331292,TV_Q331288),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_ADD, axiom, ![V_n, V_m]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_arithmetics_ADDu_u_SUB, axiom, ![V_c, V_a]: s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_c))),s(t_h4s_nums_num,V_c))) = s(t_h4s_nums_num,V_a)).
fof(ah4s_gcds_ISu_u_GCDu_u_UNIQUE, axiom, ![V_d, V_c, V_b, V_a]: ((p(s(t_bool,h4s_gcds_isu_u_gcd(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_c)))) & p(s(t_bool,h4s_gcds_isu_u_gcd(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_d))))) => s(t_h4s_nums_num,V_c) = s(t_h4s_nums_num,V_d))).
fof(ah4s_gcds_ISu_u_GCDu_u_MINUSu_u_R, axiom, ![V_c, V_b, V_a]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b)))) & p(s(t_bool,h4s_gcds_isu_u_gcd(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,V_c))))) => p(s(t_bool,h4s_gcds_isu_u_gcd(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,V_c)))))).
fof(ah4s_gcds_GCDu_u_ISu_u_GCD, axiom, ![V_b, V_a]: p(s(t_bool,h4s_gcds_isu_u_gcd(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b),s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b))))))).
fof(ch4s_gcds_GCDu_u_ADDu_u_R, conjecture, ![V_b, V_a]: s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b))))) = s(t_h4s_nums_num,h4s_gcds_gcd(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b)))).
