%   ORIGINAL: h4/hreal/HRAT__MEAN
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/hrat/HRAT__MUL__ASSOC: !j i h. h4/hrat/hrat__mul h (h4/hrat/hrat__mul i j) = h4/hrat/hrat__mul (h4/hrat/hrat__mul h i) j
% Assm: h4/hrat/HRAT__LDISTRIB: !j i h. h4/hrat/hrat__mul h (h4/hrat/hrat__add i j) = h4/hrat/hrat__add (h4/hrat/hrat__mul h i) (h4/hrat/hrat__mul h j)
% Assm: h4/hrat/HRAT__MUL__LINV: !h. h4/hrat/hrat__mul (h4/hrat/hrat__inv h) h = h4/hrat/hrat__1
% Assm: h4/hreal/HRAT__MUL__RID: !x. h4/hrat/hrat__mul x h4/hrat/hrat__1 = x
% Assm: h4/hreal/HRAT__LT__LADD: !z y x. h4/hreal/hrat__lt (h4/hrat/hrat__add z x) (h4/hrat/hrat__add z y) <=> h4/hreal/hrat__lt x y
% Assm: h4/hreal/HRAT__LT__RADD: !z y x. h4/hreal/hrat__lt (h4/hrat/hrat__add x z) (h4/hrat/hrat__add y z) <=> h4/hreal/hrat__lt x y
% Assm: h4/hreal/HRAT__LT__RMUL: !z y x. h4/hreal/hrat__lt (h4/hrat/hrat__mul x z) (h4/hrat/hrat__mul y z) <=> h4/hreal/hrat__lt x y
% Goal: !y x. h4/hreal/hrat__lt x y ==> (?z. h4/hreal/hrat__lt x z /\ h4/hreal/hrat__lt z 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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_hrats_HRATu_u_MULu_u_ASSOC]: !j i h. h4/hrat/hrat__mul h (h4/hrat/hrat__mul i j) = h4/hrat/hrat__mul (h4/hrat/hrat__mul h i) j
% Assm [h4s_hrats_HRATu_u_LDISTRIB]: !j i h. h4/hrat/hrat__mul h (h4/hrat/hrat__add i j) = h4/hrat/hrat__add (h4/hrat/hrat__mul h i) (h4/hrat/hrat__mul h j)
% Assm [h4s_hrats_HRATu_u_MULu_u_LINV]: !h. h4/hrat/hrat__mul (h4/hrat/hrat__inv h) h = h4/hrat/hrat__1
% Assm [h4s_hreals_HRATu_u_MULu_u_RID]: !x. h4/hrat/hrat__mul x h4/hrat/hrat__1 = x
% Assm [h4s_hreals_HRATu_u_LTu_u_LADD]: !z y x. h4/hreal/hrat__lt (h4/hrat/hrat__add z x) (h4/hrat/hrat__add z y) <=> h4/hreal/hrat__lt x y
% Assm [h4s_hreals_HRATu_u_LTu_u_RADD]: !z y x. h4/hreal/hrat__lt (h4/hrat/hrat__add x z) (h4/hrat/hrat__add y z) <=> h4/hreal/hrat__lt x y
% Assm [h4s_hreals_HRATu_u_LTu_u_RMUL]: !z y x. h4/hreal/hrat__lt (h4/hrat/hrat__mul x z) (h4/hrat/hrat__mul y z) <=> h4/hreal/hrat__lt x y
% Goal: !y x. h4/hreal/hrat__lt x y ==> (?z. h4/hreal/hrat__lt x z /\ h4/hreal/hrat__lt z 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_Q254331,TV_Q254327]: ![V_f, V_g]: (![V_x]: s(TV_Q254327,happ(s(t_fun(TV_Q254331,TV_Q254327),V_f),s(TV_Q254331,V_x))) = s(TV_Q254327,happ(s(t_fun(TV_Q254331,TV_Q254327),V_g),s(TV_Q254331,V_x))) => s(t_fun(TV_Q254331,TV_Q254327),V_f) = s(t_fun(TV_Q254331,TV_Q254327),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_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_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_hrats_HRATu_u_MULu_u_ASSOC, axiom, ![V_j, V_i, V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_i),s(t_h4s_hrats_hrat,V_j))))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_i))),s(t_h4s_hrats_hrat,V_j)))).
fof(ah4s_hrats_HRATu_u_LDISTRIB, axiom, ![V_j, V_i, V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(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_j))))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_i))),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_h),s(t_h4s_hrats_hrat,V_j)))))).
fof(ah4s_hrats_HRATu_u_MULu_u_LINV, axiom, ![V_h]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_inv(s(t_h4s_hrats_hrat,V_h))),s(t_h4s_hrats_hrat,V_h))) = s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1)).
fof(ah4s_hreals_HRATu_u_MULu_u_RID, axiom, ![V_x]: s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_1))) = s(t_h4s_hrats_hrat,V_x)).
fof(ah4s_hreals_HRATu_u_LTu_u_LADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_z),s(t_h4s_hrats_hrat,V_x))),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_z),s(t_h4s_hrats_hrat,V_y))))) = s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))).
fof(ah4s_hreals_HRATu_u_LTu_u_RADD, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_z))),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_add(s(t_h4s_hrats_hrat,V_y),s(t_h4s_hrats_hrat,V_z))))) = s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))).
fof(ah4s_hreals_HRATu_u_LTu_u_RMUL, axiom, ![V_z, V_y, V_x]: s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_z))),s(t_h4s_hrats_hrat,h4s_hrats_hratu_u_mul(s(t_h4s_hrats_hrat,V_y),s(t_h4s_hrats_hrat,V_z))))) = s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_y)))).
fof(ch4s_hreals_HRATu_u_MEAN, conjecture, ![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_z]: (p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_x),s(t_h4s_hrats_hrat,V_z)))) & p(s(t_bool,h4s_hreals_hratu_u_lt(s(t_h4s_hrats_hrat,V_z),s(t_h4s_hrats_hrat,V_y))))))).
