%   ORIGINAL: h4/integer/INT__GT__REDUCE_c9
% 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/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/integer/int__gt0: !y x. h4/integer/int__gt x y <=> h4/integer/int__lt y x
% Assm: h4/integer/INT__LT__REDUCE_c0: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c1: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n))) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c2: h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num h4/num/0) <=> F
% Assm: h4/integer/INT__LT__REDUCE_c3: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) <=> F
% Assm: h4/integer/INT__LT__REDUCE_c4: !n. h4/integer/int__lt (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__of__num h4/num/0) <=> F
% Assm: h4/integer/INT__LT__REDUCE_c5: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c6: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c7: !n m. h4/integer/int__lt (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) <=> h4/prim__rec/_3C n m
% Assm: h4/integer/INT__LT__REDUCE_c8: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c9: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) <=> T
% Assm: h4/integer/INT__LT__REDUCE_c10: !n m. h4/integer/int__lt (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) <=> F
% Assm: h4/integer/INT__LT__REDUCE_c11: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) <=> h4/prim__rec/_3C m n
% Goal: !n m. h4/integer/int__gt (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))) <=> T
%   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_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_integers_intu_u_gt0]: !y x. h4/integer/int__gt x y <=> h4/integer/int__lt y x
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c0]: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n))) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c1]: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n))) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c2]: h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__of__num h4/num/0) <=> F
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c3]: !n. h4/integer/int__lt (h4/integer/int__of__num h4/num/0) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) <=> F
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c4]: !n. h4/integer/int__lt (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__of__num h4/num/0) <=> F
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c5]: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c6]: !n. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))) (h4/integer/int__of__num h4/num/0) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c7]: !n m. h4/integer/int__lt (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) <=> h4/prim__rec/_3C n m
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c8]: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 n)))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c9]: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))) (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) <=> T
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c10]: !n m. h4/integer/int__lt (h4/integer/int__of__num (h4/arithmetic/NUMERAL n)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) <=> F
% Assm [h4s_integers_INTu_u_LTu_u_REDUCEu_c11]: !n m. h4/integer/int__lt (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL n))) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL m))) <=> h4/prim__rec/_3C m n
% Goal: !n m. h4/integer/int__gt (h4/integer/int__of__num (h4/arithmetic/NUMERAL m)) (h4/integer/int__neg (h4/integer/int__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)))) <=> T
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_Q11452,TV_Q11448]: ![V_f, V_g]: (![V_x]: s(TV_Q11448,happ(s(t_fun(TV_Q11452,TV_Q11448),V_f),s(TV_Q11452,V_x))) = s(TV_Q11448,happ(s(t_fun(TV_Q11452,TV_Q11448),V_g),s(TV_Q11452,V_x))) => s(t_fun(TV_Q11452,TV_Q11448),V_f) = s(t_fun(TV_Q11452,TV_Q11448),V_g))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_integers_intu_u_gt0, axiom, ![V_y, V_x]: s(t_bool,h4s_integers_intu_u_gt(s(t_h4s_integers_int,V_x),s(t_h4s_integers_int,V_y))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,V_y),s(t_h4s_integers_int,V_x)))).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c0, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))))))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c1, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c2, axiom, s(t_bool,h4s_integers_intu_u_lt(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))))) = s(t_bool,f)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c3, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(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_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))))))))) = s(t_bool,f)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c4, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(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_nums_0))))) = s(t_bool,f)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c5, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(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_nums_0))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c6, axiom, ![V_n]: s(t_bool,h4s_integers_intu_u_lt(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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(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_nums_0))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c7, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(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_numeral(s(t_h4s_nums_num,V_m))))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c8, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(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_numeral(s(t_h4s_nums_num,V_m))))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c9, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(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_numeral(s(t_h4s_nums_num,V_m))))))) = s(t_bool,t)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c10, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(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_numeral(s(t_h4s_nums_num,V_m))))))))) = s(t_bool,f)).
fof(ah4s_integers_INTu_u_LTu_u_REDUCEu_c11, axiom, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_lt(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_numeral(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_numeral(s(t_h4s_nums_num,V_m))))))))) = s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))).
fof(ch4s_integers_INTu_u_GTu_u_REDUCEu_c9, conjecture, ![V_n, V_m]: s(t_bool,h4s_integers_intu_u_gt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(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_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))))))))))) = s(t_bool,t)).
