%   ORIGINAL: h4/quotient/C__RSP
% 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/combin/C__THM: !y x f. h4/combin/C f x y = f y x
% Assm: h4/quotient/FUN__REL: !g f R2 R1. h4/quotient/_3D_3D_3D_3E R1 R2 f g <=> (!x y. R1 x y ==> R2 (f x) (g y))
% Goal: !rep1 abs1 R1. h4/quotient/QUOTIENT R1 abs1 rep1 ==> (!R2 abs2 rep2. h4/quotient/QUOTIENT R2 abs2 rep2 ==> (!R3 abs3 rep3. h4/quotient/QUOTIENT R3 abs3 rep3 ==> (!f1 f2 x1 x2 y1 y2. h4/quotient/_3D_3D_3D_3E R1 (h4/quotient/_3D_3D_3D_3E R2 R3) f1 f2 /\ R2 x1 x2 /\ R1 y1 y2 ==> R3 (h4/combin/C f1 x1 y1) (h4/combin/C f2 x2 y2))))
%   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_combins_Cu_u_THM]: !y x f. h4/combin/C f x y = happ (happ f y) x
% Assm [h4s_quotients_FUNu_u_REL]: !g f R2 R1. happ (happ (h4/quotient/_3D_3D_3D_3E R1 R2) f) g <=> (!x y. happ (happ R1 x) y ==> happ (happ R2 (happ f x)) (happ g y))
% Goal: !rep1 abs1 R1. h4/quotient/QUOTIENT R1 abs1 rep1 ==> (!R2 abs2 rep2. h4/quotient/QUOTIENT R2 abs2 rep2 ==> (!R3 abs3 rep3. h4/quotient/QUOTIENT R3 abs3 rep3 ==> (!f1 f2 x1 x2 y1 y2. happ (happ (h4/quotient/_3D_3D_3D_3E R1 (h4/quotient/_3D_3D_3D_3E R2 R3)) f1) f2 /\ happ (happ R2 x1) x2 /\ happ (happ R1 y1) y2 ==> happ (happ R3 (h4/combin/C f1 x1 y1)) (h4/combin/C f2 x2 y2))))
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_Q225983,TV_Q225979]: ![V_f, V_g]: (![V_x]: s(TV_Q225979,happ(s(t_fun(TV_Q225983,TV_Q225979),V_f),s(TV_Q225983,V_x))) = s(TV_Q225979,happ(s(t_fun(TV_Q225983,TV_Q225979),V_g),s(TV_Q225983,V_x))) => s(t_fun(TV_Q225983,TV_Q225979),V_f) = s(t_fun(TV_Q225983,TV_Q225979),V_g))).
fof(ah4s_combins_Cu_u_THM, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_combins_c(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27b,V_x),s(TV_u_27a,V_y))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_y))),s(TV_u_27b,V_x)))).
fof(ah4s_quotients_FUNu_u_REL, axiom, ![TV_u_27b,TV_u_27a]: ![V_g, V_f, V_R2, V_R1]: (p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2))),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(t_fun(TV_u_27a,TV_u_27b),V_g)))) <=> ![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_g),s(TV_u_27a,V_y))))))))).
fof(ch4s_quotients_Cu_u_RSP, conjecture, ![TV_u_27d,TV_u_27e,TV_u_27f,TV_u_27c,TV_u_27b,TV_u_27a]: ![V_rep1, V_abs1, V_R1]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(TV_u_27a,TV_u_27d),V_abs1),s(t_fun(TV_u_27d,TV_u_27a),V_rep1)))) => ![V_R2, V_abs2, V_rep2]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(t_fun(TV_u_27b,TV_u_27e),V_abs2),s(t_fun(TV_u_27e,TV_u_27b),V_rep2)))) => ![V_R3, V_abs3, V_rep3]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27c,t_fun(TV_u_27c,t_bool)),V_R3),s(t_fun(TV_u_27c,TV_u_27f),V_abs3),s(t_fun(TV_u_27f,TV_u_27c),V_rep3)))) => ![V_f1, V_f2, V_x1, V_x2, V_y1, V_y2]: ((p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(t_fun(t_fun(TV_u_27b,TV_u_27c),t_fun(t_fun(TV_u_27b,TV_u_27c),t_bool)),h4s_quotients_u_3du_3du_3du_3e(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(t_fun(TV_u_27c,t_fun(TV_u_27c,t_bool)),V_R3))))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f1))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f2)))) & (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R2),s(TV_u_27b,V_x1))),s(TV_u_27b,V_x2)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R1),s(TV_u_27a,V_y1))),s(TV_u_27a,V_y2)))))) => p(s(t_bool,happ(s(t_fun(TV_u_27c,t_bool),happ(s(t_fun(TV_u_27c,t_fun(TV_u_27c,t_bool)),V_R3),s(TV_u_27c,h4s_combins_c(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f1),s(TV_u_27b,V_x1),s(TV_u_27a,V_y1))))),s(TV_u_27c,h4s_combins_c(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f2),s(TV_u_27b,V_x2),s(TV_u_27a,V_y2))))))))))).
