%   ORIGINAL: h4/bit/BITS__MUL
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/MOD__TIMES2: !n. h4/prim__rec/_3C h4/num/0 n ==> (!j k. h4/arithmetic/MOD (h4/arithmetic/_2A (h4/arithmetic/MOD j n) (h4/arithmetic/MOD k n)) n = h4/arithmetic/MOD (h4/arithmetic/_2A j k) n)
% Assm: h4/bit/ZERO__LT__TWOEXP: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)
% Assm: h4/bit/BITS__ZERO3: !n h. h4/bit/BITS h h4/num/0 n = h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/num/SUC h))
% Goal: !h b a. h4/bit/BITS h h4/num/0 (h4/arithmetic/_2A (h4/bit/BITS h h4/num/0 a) (h4/bit/BITS h h4/num/0 b)) = h4/bit/BITS h h4/num/0 (h4/arithmetic/_2A 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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_MODu_u_TIMES2]: !n. h4/prim__rec/_3C h4/num/0 n ==> (!j k. h4/arithmetic/MOD (h4/arithmetic/_2A (h4/arithmetic/MOD j n) (h4/arithmetic/MOD k n)) n = h4/arithmetic/MOD (h4/arithmetic/_2A j k) n)
% Assm [h4s_bits_ZEROu_u_LTu_u_TWOEXP]: !n. h4/prim__rec/_3C h4/num/0 (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) n)
% Assm [h4s_bits_BITSu_u_ZERO3]: !n h. h4/bit/BITS h h4/num/0 n = h4/arithmetic/MOD n (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/num/SUC h))
% Goal: !h b a. h4/bit/BITS h h4/num/0 (h4/arithmetic/_2A (h4/bit/BITS h h4/num/0 a) (h4/bit/BITS h h4/num/0 b)) = h4/bit/BITS h h4/num/0 (h4/arithmetic/_2A 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_Q201890,TV_Q201886]: ![V_f, V_g]: (![V_x]: s(TV_Q201886,happ(s(t_fun(TV_Q201890,TV_Q201886),V_f),s(TV_Q201890,V_x))) = s(TV_Q201886,happ(s(t_fun(TV_Q201890,TV_Q201886),V_g),s(TV_Q201890,V_x))) => s(t_fun(TV_Q201890,TV_Q201886),V_f) = s(t_fun(TV_Q201890,TV_Q201886),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,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_arithmetics_MODu_u_TIMES2, axiom, ![V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n)))) => ![V_j, V_k]: s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_j),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_n))))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_j),s(t_h4s_nums_num,V_k))),s(t_h4s_nums_num,V_n))))).
fof(ah4s_bits_ZEROu_u_LTu_u_TWOEXP, axiom, ![V_n]: p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_bits_BITSu_u_ZERO3, axiom, ![V_n, V_h]: s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_h)))))))).
fof(ch4s_bits_BITSu_u_MUL, conjecture, ![V_h, V_b, V_a]: s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_a))),s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_b))))))) = s(t_h4s_nums_num,h4s_bits_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,V_b)))))).
