%   ORIGINAL: h4/words/WORD__LITERAL__MULT_c0
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/words/word__mul__n2w: !n m. h4/words/word__mul (h4/words/n2w m) (h4/words/n2w n) = h4/words/n2w (h4/arithmetic/_2A m n)
% Assm: h4/words/WORD__NEG__NEG: !w. h4/words/word__2comp (h4/words/word__2comp w) = w
% Assm: h4/words/WORD__NEG__LMUL: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul (h4/words/word__2comp v) w
% Assm: h4/words/WORD__NEG__RMUL: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul v (h4/words/word__2comp w)
% Goal: !n m. h4/words/word__mul (h4/words/n2w m) (h4/words/word__2comp (h4/words/n2w n)) = h4/words/word__2comp (h4/words/n2w (h4/arithmetic/_2A m n))
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_wordss_wordu_u_mulu_u_n2w]: !n m. h4/words/word__mul (h4/words/n2w m) (h4/words/n2w n) = h4/words/n2w (h4/arithmetic/_2A m n)
% Assm [h4s_wordss_WORDu_u_NEGu_u_NEG]: !w. h4/words/word__2comp (h4/words/word__2comp w) = w
% Assm [h4s_wordss_WORDu_u_NEGu_u_LMUL]: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul (h4/words/word__2comp v) w
% Assm [h4s_wordss_WORDu_u_NEGu_u_RMUL]: !w v. h4/words/word__2comp (h4/words/word__mul v w) = h4/words/word__mul v (h4/words/word__2comp w)
% Goal: !n m. h4/words/word__mul (h4/words/n2w m) (h4/words/word__2comp (h4/words/n2w n)) = h4/words/word__2comp (h4/words/n2w (h4/arithmetic/_2A m n))
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_Q123983,TV_Q123979]: ![V_f, V_g]: (![V_x]: s(TV_Q123979,happ(s(t_fun(TV_Q123983,TV_Q123979),V_f),s(TV_Q123983,V_x))) = s(TV_Q123979,happ(s(t_fun(TV_Q123983,TV_Q123979),V_g),s(TV_Q123983,V_x))) => s(t_fun(TV_Q123983,TV_Q123979),V_f) = s(t_fun(TV_Q123983,TV_Q123979),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_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_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_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_wordss_wordu_u_mulu_u_n2w, axiom, ![TV_u_27a]: ![V_n, V_m]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_wordss_WORDu_u_NEGu_u_NEG, axiom, ![TV_u_27a]: ![V_w]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)).
fof(ah4s_wordss_WORDu_u_NEGu_u_LMUL, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))).
fof(ah4s_wordss_WORDu_u_NEGu_u_RMUL, axiom, ![TV_u_27a]: ![V_w, V_v]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_v),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))))).
fof(ch4s_wordss_WORDu_u_LITERALu_u_MULTu_c0, conjecture, ![TV_u_27a]: ![V_n, V_m]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_mul(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_m))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,V_n))))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))).
