%   ORIGINAL: h4/integerRing/int__rewrites_c33
% 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/numeral/iSUB__THM_c0: !x b. h4/numeral/iSUB b h4/arithmetic/ZERO x = h4/arithmetic/ZERO
% Assm: h4/numeral/iSUB__THM_c1: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm: h4/numeral/iSUB__THM_c2: !n. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO = h4/numeral/iDUB n
% Assm: h4/numeral/iSUB__THM_c3: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm: h4/numeral/iSUB__THM_c4: !n m. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)
% Assm: h4/numeral/iSUB__THM_c5: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)
% Assm: h4/numeral/iSUB__THM_c6: !n m. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) = h4/numeral/iDUB (h4/numeral/iSUB F n m)
% Assm: h4/numeral/iSUB__THM_c7: !n. h4/numeral/iSUB F (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO = h4/arithmetic/BIT1 n
% Assm: h4/numeral/iSUB__THM_c8: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)
% Assm: h4/numeral/iSUB__THM_c9: !n m. h4/numeral/iSUB F (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm: h4/numeral/iSUB__THM_c10: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT2 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm: h4/numeral/iSUB__THM_c11: !n m. h4/numeral/iSUB F (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT2 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)
% Goal: !n. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO = h4/numeral/iDUB n
%   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_numerals_iSUBu_u_THMu_c0]: !x b. h4/numeral/iSUB b h4/arithmetic/ZERO x = h4/arithmetic/ZERO
% Assm [h4s_numerals_iSUBu_u_THMu_c1]: !n. h4/numeral/iSUB T n h4/arithmetic/ZERO = n
% Assm [h4s_numerals_iSUBu_u_THMu_c2]: !n. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO = h4/numeral/iDUB n
% Assm [h4s_numerals_iSUBu_u_THMu_c3]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_iSUBu_u_THMu_c4]: !n m. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)
% Assm [h4s_numerals_iSUBu_u_THMu_c5]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)
% Assm [h4s_numerals_iSUBu_u_THMu_c6]: !n m. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT2 m) = h4/numeral/iDUB (h4/numeral/iSUB F n m)
% Assm [h4s_numerals_iSUBu_u_THMu_c7]: !n. h4/numeral/iSUB F (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO = h4/arithmetic/BIT1 n
% Assm [h4s_numerals_iSUBu_u_THMu_c8]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_iSUBu_u_THMu_c9]: !n m. h4/numeral/iSUB F (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_iSUBu_u_THMu_c10]: !n m. h4/numeral/iSUB T (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT2 m) = h4/numeral/iDUB (h4/numeral/iSUB T n m)
% Assm [h4s_numerals_iSUBu_u_THMu_c11]: !n m. h4/numeral/iSUB F (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT2 m) = h4/arithmetic/BIT1 (h4/numeral/iSUB F n m)
% Goal: !n. h4/numeral/iSUB F (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO = h4/numeral/iDUB n
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_Q168406,TV_Q168402]: ![V_f, V_g]: (![V_x]: s(TV_Q168402,happ(s(t_fun(TV_Q168406,TV_Q168402),V_f),s(TV_Q168406,V_x))) = s(TV_Q168402,happ(s(t_fun(TV_Q168406,TV_Q168402),V_g),s(TV_Q168406,V_x))) => s(t_fun(TV_Q168406,TV_Q168402),V_f) = s(t_fun(TV_Q168406,TV_Q168402),V_g))).
fof(ah4s_numerals_iSUBu_u_THMu_c0, axiom, ![V_x, V_b]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,V_b),s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_iSUBu_u_THMu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_iSUBu_u_THMu_c2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_iSUBu_u_THMu_c3, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c4, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c5, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c6, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c7, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))).
fof(ah4s_numerals_iSUBu_u_THMu_c8, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c9, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c10, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,t),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_numerals_iSUBu_u_THMu_c11, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ch4s_integerRings_intu_u_rewritesu_c33, conjecture, ![V_n]: s(t_h4s_nums_num,h4s_numerals_isub(s(t_bool,f),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_h4s_nums_num,h4s_numerals_idub(s(t_h4s_nums_num,V_n)))).
