%   ORIGINAL: h4/integer/INT__MUL__REDUCE_c1
% 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/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/integer/INT__MUL__LZERO: !x. h4/integer/int__mul (h4/integer/int__of__num h4/num/0) x = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__MUL__RZERO: !x. h4/integer/int__mul x (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Assm: h4/integer/INT__NEG__LMUL: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm: h4/integer/INT__NEG__RMUL: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul x (h4/integer/int__neg y)
% Assm: h4/integer/INT__NEGNEG: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm: h4/integer/INT__MUL: !n m. h4/integer/int__mul (h4/integer/int__of__num m) (h4/integer/int__of__num n) = h4/integer/int__of__num (h4/arithmetic/_2A m n)
% Goal: !p. h4/integer/int__mul (h4/integer/int__of__num h4/num/0) p = h4/integer/int__of__num h4/num/0
%   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_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_integers_INTu_u_MULu_u_LZERO]: !x. h4/integer/int__mul (h4/integer/int__of__num h4/num/0) x = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_MULu_u_RZERO]: !x. h4/integer/int__mul x (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Assm [h4s_integers_INTu_u_NEGu_u_LMUL]: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul (h4/integer/int__neg x) y
% Assm [h4s_integers_INTu_u_NEGu_u_RMUL]: !y x. h4/integer/int__neg (h4/integer/int__mul x y) = h4/integer/int__mul x (h4/integer/int__neg y)
% Assm [h4s_integers_INTu_u_NEGNEG]: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm [h4s_integers_INTu_u_MUL]: !n m. h4/integer/int__mul (h4/integer/int__of__num m) (h4/integer/int__of__num n) = h4/integer/int__of__num (h4/arithmetic/_2A m n)
% Goal: !p. h4/integer/int__mul (h4/integer/int__of__num h4/num/0) p = h4/integer/int__of__num h4/num/0
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_Q8803,TV_Q8799]: ![V_f, V_g]: (![V_x]: s(TV_Q8799,happ(s(t_fun(TV_Q8803,TV_Q8799),V_f),s(TV_Q8803,V_x))) = s(TV_Q8799,happ(s(t_fun(TV_Q8803,TV_Q8799),V_g),s(TV_Q8803,V_x))) => s(t_fun(TV_Q8803,TV_Q8799),V_f) = s(t_fun(TV_Q8803,TV_Q8799),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_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_integers_INTu_u_MULu_u_LZERO, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_x))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_MULu_u_RZERO, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integers_INTu_u_NEGu_u_LMUL, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))),s(t_h4s_integers_int,V_y)))).
fof(ah4s_integers_INTu_u_NEGu_u_RMUL, axiom, ![V_y, V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))))) = s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_y)))))).
fof(ah4s_integers_INTu_u_NEGNEG, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integers_INTu_u_MUL, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ch4s_integers_INTu_u_MULu_u_REDUCEu_c1, conjecture, ![V_p]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_integers_int,V_p))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
