%   ORIGINAL: h4/binary__ieee/rounding__distinct_c5
% 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/numeral/numeral__distrib_c19: !n m. h4/arithmetic/NUMERAL n = h4/arithmetic/NUMERAL m <=> n = m
% Assm: h4/numeral/numeral__eq_c5: !n m. h4/arithmetic/BIT2 n = h4/arithmetic/BIT1 m <=> F
% Assm: h4/binary__ieee/rounding2num__thm_c2: h4/binary__ieee/rounding2num h4/binary__ieee/roundTowardNegative = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm: h4/binary__ieee/rounding2num__thm_c3: h4/binary__ieee/rounding2num h4/binary__ieee/roundTowardZero = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/binary__ieee/rounding__EQ__rounding: !a_27 a. a = a_27 <=> h4/binary__ieee/rounding2num a = h4/binary__ieee/rounding2num a_27
% Goal: ~(h4/binary__ieee/roundTowardNegative = h4/binary__ieee/roundTowardZero)
%   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_numerals_numeralu_u_distribu_c19]: !n m. h4/arithmetic/NUMERAL n = h4/arithmetic/NUMERAL m <=> n = m
% Assm [h4s_numerals_numeralu_u_equ_c5]: !n m. h4/arithmetic/BIT2 n = h4/arithmetic/BIT1 m <=> F
% Assm [h4s_binaryu_u_ieees_rounding2numu_u_thmu_c2]: h4/binary__ieee/rounding2num h4/binary__ieee/roundTowardNegative = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm [h4s_binaryu_u_ieees_rounding2numu_u_thmu_c3]: h4/binary__ieee/rounding2num h4/binary__ieee/roundTowardZero = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_binaryu_u_ieees_roundingu_u_EQu_u_rounding]: !a_27 a. a = a_27 <=> h4/binary__ieee/rounding2num a = h4/binary__ieee/rounding2num a_27
% Goal: ~(h4/binary__ieee/roundTowardNegative = h4/binary__ieee/roundTowardZero)
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_Q102460,TV_Q102456]: ![V_f, V_g]: (![V_x]: s(TV_Q102456,happ(s(t_fun(TV_Q102460,TV_Q102456),V_f),s(TV_Q102460,V_x))) = s(TV_Q102456,happ(s(t_fun(TV_Q102460,TV_Q102456),V_g),s(TV_Q102460,V_x))) => s(t_fun(TV_Q102460,TV_Q102456),V_f) = s(t_fun(TV_Q102460,TV_Q102456),V_g))).
fof(ah4s_numerals_numeralu_u_distribu_c19, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
fof(ah4s_numerals_numeralu_u_equ_c5, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))) <=> p(s(t_bool,f)))).
fof(ah4s_binaryu_u_ieees_rounding2numu_u_thmu_c2, axiom, s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_roundtowardnegative))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_binaryu_u_ieees_rounding2numu_u_thmu_c3, axiom, s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_roundtowardzero))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))).
fof(ah4s_binaryu_u_ieees_roundingu_u_EQu_u_rounding, axiom, ![V_au_27, V_a]: (s(t_h4s_binaryu_u_ieees_rounding,V_a) = s(t_h4s_binaryu_u_ieees_rounding,V_au_27) <=> s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,V_a))) = s(t_h4s_nums_num,h4s_binaryu_u_ieees_rounding2num(s(t_h4s_binaryu_u_ieees_rounding,V_au_27))))).
fof(ch4s_binaryu_u_ieees_roundingu_u_distinctu_c5, conjecture, ~ (s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_roundtowardnegative) = s(t_h4s_binaryu_u_ieees_rounding,h4s_binaryu_u_ieees_roundtowardzero))).
