%   ORIGINAL: h4/quotient/C__PRS
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/combin/C__THM: !y x f. h4/combin/C f x y = f y x
% Assm: h4/quotient/QUOTIENT__ABS__REP: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!a. abs (rep a) = a)
% Assm: h4/quotient/FUN__MAP__THM: !x h g f. h4/quotient/_2D_2D_3E f g h x = g (h (f x))
% 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 ==> (!f x y. h4/combin/C f x y = abs3 (h4/combin/C (h4/quotient/_2D_2D_3E abs1 (h4/quotient/_2D_2D_3E abs2 rep3) f) (rep2 x) (rep1 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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_combins_Cu_u_THM]: !y x f. h4/combin/C f x y = happ (happ f y) x
% Assm [h4s_quotients_QUOTIENTu_u_ABSu_u_REP]: !rep abs R. h4/quotient/QUOTIENT R abs rep ==> (!a. happ abs (happ rep a) = a)
% Assm [h4s_quotients_FUNu_u_MAPu_u_THM]: !x h g f. happ (happ (h4/quotient/_2D_2D_3E f g) h) x = happ g (happ h (happ f x))
% 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 ==> (!f x y. h4/combin/C f x y = happ abs3 (h4/combin/C (happ (h4/quotient/_2D_2D_3E abs1 (h4/quotient/_2D_2D_3E abs2 rep3)) f) (happ rep2 x) (happ rep1 y)))))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q225958,TV_Q225954]: ![V_f, V_g]: (![V_x]: s(TV_Q225954,happ(s(t_fun(TV_Q225958,TV_Q225954),V_f),s(TV_Q225958,V_x))) = s(TV_Q225954,happ(s(t_fun(TV_Q225958,TV_Q225954),V_g),s(TV_Q225958,V_x))) => s(t_fun(TV_Q225958,TV_Q225954),V_f) = s(t_fun(TV_Q225958,TV_Q225954),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
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_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_QUOTIENTu_u_ABSu_u_REP, axiom, ![TV_u_27a,TV_u_27b]: ![V_rep, V_abs, V_R]: (p(s(t_bool,h4s_quotients_quotient(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ![V_a]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))) = s(TV_u_27b,V_a))).
fof(ah4s_quotients_FUNu_u_MAPu_u_THM, axiom, ![TV_u_27d,TV_u_27b,TV_u_27c,TV_u_27a]: ![V_x, V_h, V_g, V_f]: s(TV_u_27d,happ(s(t_fun(TV_u_27a,TV_u_27d),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,TV_u_27d)),h4s_quotients_u_2du_2du_3e(s(t_fun(TV_u_27a,TV_u_27c),V_f),s(t_fun(TV_u_27b,TV_u_27d),V_g))),s(t_fun(TV_u_27c,TV_u_27b),V_h))),s(TV_u_27a,V_x))) = s(TV_u_27d,happ(s(t_fun(TV_u_27b,TV_u_27d),V_g),s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_h),s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_f),s(TV_u_27a,V_x)))))))).
fof(ch4s_quotients_Cu_u_PRS, conjecture, ![TV_u_27c,TV_u_27f,TV_u_27b,TV_u_27e,TV_u_27a,TV_u_27d]: ![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_f, V_x, V_y]: s(TV_u_27f,h4s_combins_c(s(t_fun(TV_u_27d,t_fun(TV_u_27e,TV_u_27f)),V_f),s(TV_u_27e,V_x),s(TV_u_27d,V_y))) = s(TV_u_27f,happ(s(t_fun(TV_u_27c,TV_u_27f),V_abs3),s(TV_u_27c,h4s_combins_c(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),happ(s(t_fun(t_fun(TV_u_27d,t_fun(TV_u_27e,TV_u_27f)),t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c))),h4s_quotients_u_2du_2du_3e(s(t_fun(TV_u_27a,TV_u_27d),V_abs1),s(t_fun(t_fun(TV_u_27e,TV_u_27f),t_fun(TV_u_27b,TV_u_27c)),h4s_quotients_u_2du_2du_3e(s(t_fun(TV_u_27b,TV_u_27e),V_abs2),s(t_fun(TV_u_27f,TV_u_27c),V_rep3))))),s(t_fun(TV_u_27d,t_fun(TV_u_27e,TV_u_27f)),V_f))),s(TV_u_27b,happ(s(t_fun(TV_u_27e,TV_u_27b),V_rep2),s(TV_u_27e,V_x))),s(TV_u_27a,happ(s(t_fun(TV_u_27d,TV_u_27a),V_rep1),s(TV_u_27d,V_y))))))))))).
