%   ORIGINAL: h4/machine__ieee/fp16__mul__float__to__fp
% 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/machine__ieee/fp16__mul__def: !mode b a. h4/machine__ieee/fp16__mul mode a b = h4/machine__ieee/float__to__fp16 (h4/binary__ieee/float__mul mode (h4/machine__ieee/fp16__to__float a) (h4/machine__ieee/fp16__to__float b))
% Assm: h4/machine__ieee/fp16__to__float__float__to__fp16: !x. h4/machine__ieee/fp16__to__float (h4/machine__ieee/float__to__fp16 x) = x
% Goal: !mode b a. h4/machine__ieee/fp16__mul mode (h4/machine__ieee/float__to__fp16 a) (h4/machine__ieee/float__to__fp16 b) = h4/machine__ieee/float__to__fp16 (h4/binary__ieee/float__mul mode 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_machineu_u_ieees_fp16u_u_mulu_u_def]: !mode b a. h4/machine__ieee/fp16__mul mode a b = h4/machine__ieee/float__to__fp16 (h4/binary__ieee/float__mul mode (h4/machine__ieee/fp16__to__float a) (h4/machine__ieee/fp16__to__float b))
% Assm [h4s_machineu_u_ieees_fp16u_u_tou_u_floatu_u_floatu_u_tou_u_fp16]: !x. h4/machine__ieee/fp16__to__float (h4/machine__ieee/float__to__fp16 x) = x
% Goal: !mode b a. h4/machine__ieee/fp16__mul mode (h4/machine__ieee/float__to__fp16 a) (h4/machine__ieee/float__to__fp16 b) = h4/machine__ieee/float__to__fp16 (h4/binary__ieee/float__mul mode 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_Q346135,TV_Q346131]: ![V_f, V_g]: (![V_x]: s(TV_Q346131,happ(s(t_fun(TV_Q346135,TV_Q346131),V_f),s(TV_Q346135,V_x))) = s(TV_Q346131,happ(s(t_fun(TV_Q346135,TV_Q346131),V_g),s(TV_Q346135,V_x))) => s(t_fun(TV_Q346135,TV_Q346131),V_f) = s(t_fun(TV_Q346135,TV_Q346131),V_g))).
fof(ah4s_machineu_u_ieees_fp16u_u_mulu_u_def, axiom, ![V_mode, V_b, V_a]: s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_fp16u_u_mul(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),V_a),s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),V_b))) = s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp16(s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),h4s_binaryu_u_ieees_floatu_u_mul(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),h4s_machineu_u_ieees_fp16u_u_tou_u_float(s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),V_a))),s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),h4s_machineu_u_ieees_fp16u_u_tou_u_float(s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),V_b)))))))).
fof(ah4s_machineu_u_ieees_fp16u_u_tou_u_floatu_u_floatu_u_tou_u_fp16, axiom, ![V_x]: s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),h4s_machineu_u_ieees_fp16u_u_tou_u_float(s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp16(s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),V_x))))) = s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),V_x)).
fof(ch4s_machineu_u_ieees_fp16u_u_mulu_u_floatu_u_tou_u_fp, conjecture, ![V_mode, V_b, V_a]: s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_fp16u_u_mul(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp16(s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),V_a))),s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp16(s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),V_b))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp16(s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),h4s_binaryu_u_ieees_floatu_u_mul(s(t_h4s_binaryu_u_ieees_rounding,V_mode),s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),V_a),s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit0(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one))),V_b)))))).
