%   ORIGINAL: h4/prelim/ordering__eq__dec_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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/numeral/numeral__distrib_c18: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c19: !n m. h4/arithmetic/NUMERAL n = h4/arithmetic/NUMERAL m <=> n = m
% Assm: h4/numeral/numeral__eq_c1: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__eq_c3: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__eq_c4: !n m. h4/arithmetic/BIT1 n = h4/arithmetic/BIT2 m <=> F
% Assm: h4/prelim/ordering2num__thm_c0: h4/prelim/ordering2num h4/prelim/LESS = h4/num/0
% Assm: h4/prelim/ordering2num__thm_c1: h4/prelim/ordering2num h4/prelim/EQUAL = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/prelim/ordering2num__thm_c2: h4/prelim/ordering2num h4/prelim/GREATER = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm: h4/prelim/ordering__EQ__ordering: !a_27 a. a = a_27 <=> h4/prelim/ordering2num a = h4/prelim/ordering2num a_27
% Goal: h4/prelim/LESS = h4/prelim/EQUAL <=> F
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_numerals_numeralu_u_distribu_c18]: !n. h4/num/0 = h4/arithmetic/NUMERAL n <=> n = h4/arithmetic/ZERO
% 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_c1]: !n. h4/arithmetic/BIT1 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_equ_c3]: !n. h4/arithmetic/BIT2 n = h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_equ_c4]: !n m. h4/arithmetic/BIT1 n = h4/arithmetic/BIT2 m <=> F
% Assm [h4s_prelims_ordering2numu_u_thmu_c0]: h4/prelim/ordering2num h4/prelim/LESS = h4/num/0
% Assm [h4s_prelims_ordering2numu_u_thmu_c1]: h4/prelim/ordering2num h4/prelim/EQUAL = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_prelims_ordering2numu_u_thmu_c2]: h4/prelim/ordering2num h4/prelim/GREATER = h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)
% Assm [h4s_prelims_orderingu_u_EQu_u_ordering]: !a_27 a. a = a_27 <=> h4/prelim/ordering2num a = h4/prelim/ordering2num a_27
% Goal: h4/prelim/LESS = h4/prelim/EQUAL <=> F
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_Q188898,TV_Q188894]: ![V_f, V_g]: (![V_x]: s(TV_Q188894,happ(s(t_fun(TV_Q188898,TV_Q188894),V_f),s(TV_Q188898,V_x))) = s(TV_Q188894,happ(s(t_fun(TV_Q188898,TV_Q188894),V_g),s(TV_Q188898,V_x))) => s(t_fun(TV_Q188898,TV_Q188894),V_f) = s(t_fun(TV_Q188898,TV_Q188894),V_g))).
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_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_numerals_numeralu_u_distribu_c18, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_arithmetics_zero))).
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_c1, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_equ_c3, axiom, ![V_n]: (s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_zero) <=> p(s(t_bool,f)))).
fof(ah4s_numerals_numeralu_u_equ_c4, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))) <=> p(s(t_bool,f)))).
fof(ah4s_prelims_ordering2numu_u_thmu_c0, axiom, s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,h4s_prelims_less))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_prelims_ordering2numu_u_thmu_c1, axiom, s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,h4s_prelims_equal))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_prelims_ordering2numu_u_thmu_c2, axiom, s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,h4s_prelims_greater))) = 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_prelims_orderingu_u_EQu_u_ordering, axiom, ![V_au_27, V_a]: (s(t_h4s_prelims_ordering,V_a) = s(t_h4s_prelims_ordering,V_au_27) <=> s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,V_a))) = s(t_h4s_nums_num,h4s_prelims_ordering2num(s(t_h4s_prelims_ordering,V_au_27))))).
fof(ch4s_prelims_orderingu_u_equ_u_decu_c1, conjecture, (s(t_h4s_prelims_ordering,h4s_prelims_less) = s(t_h4s_prelims_ordering,h4s_prelims_equal) <=> p(s(t_bool,f)))).
