%   ORIGINAL: h4/machine__ieee/fp32__lessThan__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/fp32__lessThan__def: !b a. h4/machine__ieee/fp32__lessThan a b <=> h4/binary__ieee/float__less__than (h4/machine__ieee/fp32__to__float a) (h4/machine__ieee/fp32__to__float b)
% Assm: h4/machine__ieee/fp32__to__float__float__to__fp32: !x. h4/machine__ieee/fp32__to__float (h4/machine__ieee/float__to__fp32 x) = x
% Goal: !b a. h4/machine__ieee/fp32__lessThan (h4/machine__ieee/float__to__fp32 a) (h4/machine__ieee/float__to__fp32 b) <=> h4/binary__ieee/float__less__than 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_fp32u_u_lessThanu_u_def]: !b a. h4/machine__ieee/fp32__lessThan a b <=> h4/binary__ieee/float__less__than (h4/machine__ieee/fp32__to__float a) (h4/machine__ieee/fp32__to__float b)
% Assm [h4s_machineu_u_ieees_fp32u_u_tou_u_floatu_u_floatu_u_tou_u_fp32]: !x. h4/machine__ieee/fp32__to__float (h4/machine__ieee/float__to__fp32 x) = x
% Goal: !b a. h4/machine__ieee/fp32__lessThan (h4/machine__ieee/float__to__fp32 a) (h4/machine__ieee/float__to__fp32 b) <=> h4/binary__ieee/float__less__than 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_Q347564,TV_Q347560]: ![V_f, V_g]: (![V_x]: s(TV_Q347560,happ(s(t_fun(TV_Q347564,TV_Q347560),V_f),s(TV_Q347564,V_x))) = s(TV_Q347560,happ(s(t_fun(TV_Q347564,TV_Q347560),V_g),s(TV_Q347564,V_x))) => s(t_fun(TV_Q347564,TV_Q347560),V_f) = s(t_fun(TV_Q347564,TV_Q347560),V_g))).
fof(ah4s_machineu_u_ieees_fp32u_u_lessThanu_u_def, axiom, ![V_b, V_a]: s(t_bool,h4s_machineu_u_ieees_fp32u_u_lessthan(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_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_fcps_bit0(t_h4s_ones_one)))))),V_b))) = s(t_bool,h4s_binaryu_u_ieees_floatu_u_lessu_u_than(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_a))),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_b)))))).
fof(ah4s_machineu_u_ieees_fp32u_u_tou_u_floatu_u_floatu_u_tou_u_fp32, axiom, ![V_x]: 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)))))),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_x))))) = 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_x)).
fof(ch4s_machineu_u_ieees_fp32u_u_lessThanu_u_floatu_u_tou_u_fp, conjecture, ![V_b, V_a]: s(t_bool,h4s_machineu_u_ieees_fp32u_u_lessthan(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_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_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_b))))) = s(t_bool,h4s_binaryu_u_ieees_floatu_u_lessu_u_than(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_a),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_b)))).
