%   ORIGINAL: h4/integerRing/int__rewrites_c8
% 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/integerRing/int__calculate_c0: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/_2B n m)
% Assm: h4/integerRing/int__calculate_c1: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__of__num m) = h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/integer/int__of__num (h4/arithmetic/_2D m n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D n m)))
% Assm: h4/integerRing/int__calculate_c2: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/_2D n m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D m n)))
% Assm: h4/integerRing/int__calculate_c3: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2B n m))
% Assm: h4/integerRing/int__calculate_c4: !n m. h4/integer/int__mul (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/_2A n m)
% Assm: h4/integerRing/int__calculate_c5: !n m. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__of__num m) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2A n m))
% Assm: h4/integerRing/int__calculate_c6: !n m. h4/integer/int__mul (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2A n m))
% Assm: h4/integerRing/int__calculate_c7: !n m. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/integer/int__of__num (h4/arithmetic/_2A n m)
% Assm: h4/integerRing/int__calculate_c8: !n m. h4/integer/int__of__num n = h4/integer/int__of__num m <=> n = m
% Assm: h4/integerRing/int__calculate_c9: !n m. h4/integer/int__of__num n = h4/integer/int__neg (h4/integer/int__of__num m) <=> n = h4/num/0 /\ m = h4/num/0
% Assm: h4/integerRing/int__calculate_c10: !n m. h4/integer/int__neg (h4/integer/int__of__num n) = h4/integer/int__of__num m <=> n = h4/num/0 /\ m = h4/num/0
% Assm: h4/integerRing/int__calculate_c11: !n m. h4/integer/int__neg (h4/integer/int__of__num n) = h4/integer/int__neg (h4/integer/int__of__num m) <=> n = m
% Assm: h4/integerRing/int__calculate_c12: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm: h4/integerRing/int__calculate_c13: h4/integer/int__neg (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Goal: !n m. h4/integer/int__of__num n = h4/integer/int__of__num m <=> n = m
%   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_integerRings_intu_u_calculateu_c0]: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/_2B n m)
% Assm [h4s_integerRings_intu_u_calculateu_c1]: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__of__num m) = h4/bool/COND (h4/arithmetic/_3C_3D n m) (h4/integer/int__of__num (h4/arithmetic/_2D m n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D n m)))
% Assm [h4s_integerRings_intu_u_calculateu_c2]: !n m. h4/integer/int__add (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/bool/COND (h4/arithmetic/_3C_3D m n) (h4/integer/int__of__num (h4/arithmetic/_2D n m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2D m n)))
% Assm [h4s_integerRings_intu_u_calculateu_c3]: !n m. h4/integer/int__add (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2B n m))
% Assm [h4s_integerRings_intu_u_calculateu_c4]: !n m. h4/integer/int__mul (h4/integer/int__of__num n) (h4/integer/int__of__num m) = h4/integer/int__of__num (h4/arithmetic/_2A n m)
% Assm [h4s_integerRings_intu_u_calculateu_c5]: !n m. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__of__num m) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2A n m))
% Assm [h4s_integerRings_intu_u_calculateu_c6]: !n m. h4/integer/int__mul (h4/integer/int__of__num n) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/_2A n m))
% Assm [h4s_integerRings_intu_u_calculateu_c7]: !n m. h4/integer/int__mul (h4/integer/int__neg (h4/integer/int__of__num n)) (h4/integer/int__neg (h4/integer/int__of__num m)) = h4/integer/int__of__num (h4/arithmetic/_2A n m)
% Assm [h4s_integerRings_intu_u_calculateu_c8]: !n m. h4/integer/int__of__num n = h4/integer/int__of__num m <=> n = m
% Assm [h4s_integerRings_intu_u_calculateu_c9]: !n m. h4/integer/int__of__num n = h4/integer/int__neg (h4/integer/int__of__num m) <=> n = h4/num/0 /\ m = h4/num/0
% Assm [h4s_integerRings_intu_u_calculateu_c10]: !n m. h4/integer/int__neg (h4/integer/int__of__num n) = h4/integer/int__of__num m <=> n = h4/num/0 /\ m = h4/num/0
% Assm [h4s_integerRings_intu_u_calculateu_c11]: !n m. h4/integer/int__neg (h4/integer/int__of__num n) = h4/integer/int__neg (h4/integer/int__of__num m) <=> n = m
% Assm [h4s_integerRings_intu_u_calculateu_c12]: !x. h4/integer/int__neg (h4/integer/int__neg x) = x
% Assm [h4s_integerRings_intu_u_calculateu_c13]: h4/integer/int__neg (h4/integer/int__of__num h4/num/0) = h4/integer/int__of__num h4/num/0
% Goal: !n m. h4/integer/int__of__num n = h4/integer/int__of__num m <=> n = m
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_Q167781,TV_Q167777]: ![V_f, V_g]: (![V_x]: s(TV_Q167777,happ(s(t_fun(TV_Q167781,TV_Q167777),V_f),s(TV_Q167781,V_x))) = s(TV_Q167777,happ(s(t_fun(TV_Q167781,TV_Q167777),V_g),s(TV_Q167781,V_x))) => s(t_fun(TV_Q167781,TV_Q167777),V_f) = s(t_fun(TV_Q167781,TV_Q167777),V_g))).
fof(ah4s_integerRings_intu_u_calculateu_c0, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_integerRings_intu_u_calculateu_c1, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))))).
fof(ah4s_integerRings_intu_u_calculateu_c2, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))))))).
fof(ah4s_integerRings_intu_u_calculateu_c3, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_integerRings_intu_u_calculateu_c4, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_integerRings_intu_u_calculateu_c5, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_integerRings_intu_u_calculateu_c6, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_integerRings_intu_u_calculateu_c7, axiom, ![V_n, V_m]: s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_integerRings_intu_u_calculateu_c8, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
fof(ah4s_integerRings_intu_u_calculateu_c9, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) <=> (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0) & s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integerRings_intu_u_calculateu_c10, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) <=> (s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,h4s_nums_0) & s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0)))).
fof(ah4s_integerRings_intu_u_calculateu_c11, axiom, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))))) = s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
fof(ah4s_integerRings_intu_u_calculateu_c12, axiom, ![V_x]: s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,V_x))))) = s(t_h4s_integers_int,V_x)).
fof(ah4s_integerRings_intu_u_calculateu_c13, axiom, s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ch4s_integerRings_intu_u_rewritesu_c8, conjecture, ![V_n, V_m]: (s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_n))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,V_m))) <=> s(t_h4s_nums_num,V_n) = s(t_h4s_nums_num,V_m))).
