%   ORIGINAL: h4/rat/RAT__AINV__AINV
% 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/quotient/QUOTIENT__def: !rep abs R. h4/quotient/QUOTIENT R abs rep <=> (!a. abs (rep a) = a) /\ (!a. R (rep a) (rep a)) /\ (!r s. R r s <=> R r r /\ R s s /\ abs r = abs s)
% Assm: h4/frac/FRAC__AINV__AINV: !f1. h4/frac/frac__ainv (h4/frac/frac__ainv f1) = f1
% Assm: h4/rat/rat__QUOTIENT: h4/quotient/QUOTIENT h4/rat/rat__equiv h4/rat/abs__rat h4/rat/rep__rat
% Assm: h4/rat/rat__ainv__def: !r1. h4/rat/rat__ainv r1 = h4/rat/abs__rat (h4/frac/frac__ainv (h4/rat/rep__rat r1))
% Assm: h4/rat/RAT__AINV__CONG: !x. h4/rat/abs__rat (h4/frac/frac__ainv (h4/rat/rep__rat (h4/rat/abs__rat x))) = h4/rat/abs__rat (h4/frac/frac__ainv x)
% Goal: !r1. h4/rat/rat__ainv (h4/rat/rat__ainv r1) = r1
%   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_quotients_QUOTIENTu_u_def]: !rep abs R. h4/quotient/QUOTIENT R abs rep <=> (!a. happ abs (happ rep a) = a) /\ (!a. happ (happ R (happ rep a)) (happ rep a)) /\ (!r s. happ (happ R r) s <=> happ (happ R r) r /\ happ (happ R s) s /\ happ abs r = happ abs s)
% Assm [h4s_fracs_FRACu_u_AINVu_u_AINV]: !f1. h4/frac/frac__ainv (h4/frac/frac__ainv f1) = f1
% Assm [h4s_rats_ratu_u_QUOTIENT]: h4/quotient/QUOTIENT h4/rat/rat__equiv h4/rat/abs__rat h4/rat/rep__rat
% Assm [h4s_rats_ratu_u_ainvu_u_def]: !r1. h4/rat/rat__ainv r1 = happ h4/rat/abs__rat (h4/frac/frac__ainv (happ h4/rat/rep__rat r1))
% Assm [h4s_rats_RATu_u_AINVu_u_CONG]: !x. happ h4/rat/abs__rat (h4/frac/frac__ainv (happ h4/rat/rep__rat (happ h4/rat/abs__rat x))) = happ h4/rat/abs__rat (h4/frac/frac__ainv x)
% Goal: !r1. h4/rat/rat__ainv (h4/rat/rat__ainv r1) = r1
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_Q92995,TV_Q92991]: ![V_f, V_g]: (![V_x]: s(TV_Q92991,happ(s(t_fun(TV_Q92995,TV_Q92991),V_f),s(TV_Q92995,V_x))) = s(TV_Q92991,happ(s(t_fun(TV_Q92995,TV_Q92991),V_g),s(TV_Q92995,V_x))) => s(t_fun(TV_Q92995,TV_Q92991),V_f) = s(t_fun(TV_Q92995,TV_Q92991),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_quotients_QUOTIENTu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![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) & (![V_a]: 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_R),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_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a)))))) & ![V_r, V_s]: (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_R),s(TV_u_27a,V_r))),s(TV_u_27a,V_s)))) <=> (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_R),s(TV_u_27a,V_r))),s(TV_u_27a,V_r)))) & (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_R),s(TV_u_27a,V_s))),s(TV_u_27a,V_s)))) & s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_r))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_s)))))))))).
fof(ah4s_fracs_FRACu_u_AINVu_u_AINV, axiom, ![V_f1]: s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,V_f1))))) = s(t_h4s_fracs_frac,V_f1)).
fof(ah4s_rats_ratu_u_QUOTIENT, axiom, p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_fracs_frac,t_fun(t_h4s_fracs_frac,t_bool)),h4s_rats_ratu_u_equiv),s(t_fun(t_h4s_fracs_frac,t_h4s_rats_rat),h4s_rats_absu_u_rat),s(t_fun(t_h4s_rats_rat,t_h4s_fracs_frac),h4s_rats_repu_u_rat))))).
fof(ah4s_rats_ratu_u_ainvu_u_def, axiom, ![V_r1]: s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_r1))) = s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_fracs_frac,t_h4s_rats_rat),h4s_rats_absu_u_rat),s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,happ(s(t_fun(t_h4s_rats_rat,t_h4s_fracs_frac),h4s_rats_repu_u_rat),s(t_h4s_rats_rat,V_r1)))))))).
fof(ah4s_rats_RATu_u_AINVu_u_CONG, axiom, ![V_x]: s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_fracs_frac,t_h4s_rats_rat),h4s_rats_absu_u_rat),s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,happ(s(t_fun(t_h4s_rats_rat,t_h4s_fracs_frac),h4s_rats_repu_u_rat),s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_fracs_frac,t_h4s_rats_rat),h4s_rats_absu_u_rat),s(t_h4s_fracs_frac,V_x))))))))) = s(t_h4s_rats_rat,happ(s(t_fun(t_h4s_fracs_frac,t_h4s_rats_rat),h4s_rats_absu_u_rat),s(t_h4s_fracs_frac,h4s_fracs_fracu_u_ainv(s(t_h4s_fracs_frac,V_x)))))).
fof(ch4s_rats_RATu_u_AINVu_u_AINV, conjecture, ![V_r1]: s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,h4s_rats_ratu_u_ainv(s(t_h4s_rats_rat,V_r1))))) = s(t_h4s_rats_rat,V_r1)).
