%   ORIGINAL: h4/machine__ieee/fp32__nchotomy
% 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/machine__ieee/float__to__fp32__fp32__to__float: !x. h4/machine__ieee/float__to__fp32 (h4/machine__ieee/fp32__to__float x) = x
% Goal: !x. ?y. x = h4/machine__ieee/float__to__fp32 y
%   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_machineu_u_ieees_floatu_u_tou_u_fp32u_u_fp32u_u_tou_u_float]: !x. h4/machine__ieee/float__to__fp32 (h4/machine__ieee/fp32__to__float x) = x
% Goal: !x. ?y. x = h4/machine__ieee/float__to__fp32 y
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_Q346638,TV_Q346634]: ![V_f, V_g]: (![V_x]: s(TV_Q346634,happ(s(t_fun(TV_Q346638,TV_Q346634),V_f),s(TV_Q346638,V_x))) = s(TV_Q346634,happ(s(t_fun(TV_Q346638,TV_Q346634),V_g),s(TV_Q346638,V_x))) => s(t_fun(TV_Q346638,TV_Q346634),V_f) = s(t_fun(TV_Q346638,TV_Q346634),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_machineu_u_ieees_floatu_u_tou_u_fp32u_u_fp32u_u_tou_u_float, axiom, ![V_x]: 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_fcps_bit0(t_h4s_ones_one)))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp32(s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),h4s_machineu_u_ieees_fp32u_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_fcps_bit0(t_h4s_ones_one)))))),V_x))))) = 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_fcps_bit0(t_h4s_ones_one)))))),V_x)).
fof(ch4s_machineu_u_ieees_fp32u_u_nchotomy, conjecture, ![V_x]: ?[V_y]: 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_fcps_bit0(t_h4s_ones_one)))))),V_x) = 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_fcps_bit0(t_h4s_ones_one)))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp32(s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),V_y)))).
