%   ORIGINAL: h4/hreal/HRAT__LT__TOTAL
% 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/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/hrat/HRAT__ADD__TOTAL: !i h. h = i \/ (?d. h = h4/hrat/hrat__add i d) \/ (?d. i = h4/hrat/hrat__add h d)
% Assm: h4/hreal/hrat__lt0: !y x. h4/hreal/hrat__lt x y <=> (?d. y = h4/hrat/hrat__add x d)
% Goal: !y x. x = y \/ h4/hreal/hrat__lt x y \/ h4/hreal/hrat__lt y x
%   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_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_hrats_HRATu_u_ADDu_u_TOTAL]: !i h. h = i \/ (?d. h = h4/hrat/hrat__add i d) \/ (?d. i = h4/hrat/hrat__add h d)
% Assm [h4s_hreals_hratu_u_lt0]: !y x. h4/hreal/hrat__lt x y <=> (?d. y = h4/hrat/hrat__add x d)
% Goal: !y x. x = y \/ h4/hreal/hrat__lt x y \/ h4/hreal/hrat__lt y x
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_Q253681,TV_Q253677]: ![V_f, V_g]: (![V_x]: s(TV_Q253677,happ(s(t_fun(TV_Q253681,TV_Q253677),V_f),s(TV_Q253681,V_x))) = s(TV_Q253677,happ(s(t_fun(TV_Q253681,TV_Q253677),V_g),s(TV_Q253681,V_x))) => s(t_fun(TV_Q253681,TV_Q253677),V_f) = s(t_fun(TV_Q253681,TV_Q253677),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_hrats_HRATu_u_ADDu_u_TOTAL, axiom, ![V_i, V_h]: (s(t_h4s_hrats_hrat,V_h) = s(t_h4s_hrats_hrat,V_i) | (?[V_d]: s(t_h4s_hrats_hrat,V_h) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_i),s(t_h4s_hrats_hrat,V_d))) | ?[V_d]: s(t_h4s_hrats_hrat,V_i) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_d)))))).
fof(ah4s_hreals_hratu_u_lt0, axiom, ![V_y, V_x]: (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))) <=> ?[V_d]: s(t_h4s_hrats_hrat,V_y) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_d))))).
fof(ch4s_hreals_HRATu_u_LTu_u_TOTAL, conjecture, ![V_y, V_x]: (s(t_h4s_hrats_hrat,V_x) = s(t_h4s_hrats_hrat,V_y) | (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))) | p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_y),s(t_h4s_hrats_hrat,V_x))))))).
