%   ORIGINAL: h4/float/temonz
% 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/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/arithmetic/SUB__EQ__0: !n m. h4/arithmetic/_2D m n = h4/num/0 <=> h4/arithmetic/_3C_3D m n
% Assm: h4/numeral/numeral__distrib_c28: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/arithmetic/_3C_3D n m
% Assm: h4/numeral/numeral__lte_c0: !n. h4/arithmetic/_3C_3D h4/arithmetic/ZERO n <=> T
% Assm: h4/numeral/numeral__lte_c5: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) <=> ~h4/arithmetic/_3C_3D m n
% Assm: h4/numeral/numeral__pre_c1: h4/prim__rec/PRE (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__pre_c2: !n. h4/prim__rec/PRE (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 n)) = h4/arithmetic/BIT2 (h4/prim__rec/PRE (h4/arithmetic/BIT1 n))
% Assm: h4/numeral/numeral__pre_c3: !n. h4/prim__rec/PRE (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 n)) = h4/arithmetic/BIT2 (h4/arithmetic/BIT1 n)
% Assm: h4/numeral/numeral__texp__help_c0: !acc. h4/numeral/texp__help h4/arithmetic/ZERO acc = h4/arithmetic/BIT2 acc
% Assm: h4/numeral/numeral__texp__help_c1: !n acc. h4/numeral/texp__help (h4/arithmetic/BIT1 n) acc = h4/numeral/texp__help (h4/prim__rec/PRE (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT1 acc)
% Assm: h4/numeral/numeral__texp__help_c2: !n acc. h4/numeral/texp__help (h4/arithmetic/BIT2 n) acc = h4/numeral/texp__help (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 acc)
% Assm: h4/numeral/TWO__EXP__THM_c2: !n. h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = h4/arithmetic/NUMERAL (h4/numeral/texp__help (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO)
% Goal: ~(h4/arithmetic/_2D (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/num/0)
%   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_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_arithmetics_SUBu_u_EQu_u_0]: !n m. h4/arithmetic/_2D m n = h4/num/0 <=> h4/arithmetic/_3C_3D m n
% Assm [h4s_numerals_numeralu_u_distribu_c28]: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_numerals_numeralu_u_lteu_c0]: !n. h4/arithmetic/_3C_3D h4/arithmetic/ZERO n <=> T
% Assm [h4s_numerals_numeralu_u_lteu_c5]: !n m. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) (h4/arithmetic/BIT1 m) <=> ~h4/arithmetic/_3C_3D m n
% Assm [h4s_numerals_numeralu_u_preu_c1]: h4/prim__rec/PRE (h4/arithmetic/BIT1 h4/arithmetic/ZERO) = h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_preu_c2]: !n. h4/prim__rec/PRE (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 n)) = h4/arithmetic/BIT2 (h4/prim__rec/PRE (h4/arithmetic/BIT1 n))
% Assm [h4s_numerals_numeralu_u_preu_c3]: !n. h4/prim__rec/PRE (h4/arithmetic/BIT1 (h4/arithmetic/BIT2 n)) = h4/arithmetic/BIT2 (h4/arithmetic/BIT1 n)
% Assm [h4s_numerals_numeralu_u_texpu_u_helpu_c0]: !acc. h4/numeral/texp__help h4/arithmetic/ZERO acc = h4/arithmetic/BIT2 acc
% Assm [h4s_numerals_numeralu_u_texpu_u_helpu_c1]: !n acc. h4/numeral/texp__help (h4/arithmetic/BIT1 n) acc = h4/numeral/texp__help (h4/prim__rec/PRE (h4/arithmetic/BIT1 n)) (h4/arithmetic/BIT1 acc)
% Assm [h4s_numerals_numeralu_u_texpu_u_helpu_c2]: !n acc. h4/numeral/texp__help (h4/arithmetic/BIT2 n) acc = h4/numeral/texp__help (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 acc)
% Assm [h4s_numerals_TWOu_u_EXPu_u_THMu_c2]: !n. h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 n)) = h4/arithmetic/NUMERAL (h4/numeral/texp__help (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO)
% Goal: ~(h4/arithmetic/_2D (h4/arithmetic/EXP (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO)) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 (h4/arithmetic/BIT1 (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) = h4/num/0)
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_Q96113,TV_Q96109]: ![V_f, V_g]: (![V_x]: s(TV_Q96109,happ(s(t_fun(TV_Q96113,TV_Q96109),V_f),s(TV_Q96113,V_x))) = s(TV_Q96109,happ(s(t_fun(TV_Q96113,TV_Q96109),V_g),s(TV_Q96113,V_x))) => s(t_fun(TV_Q96113,TV_Q96109),V_f) = s(t_fun(TV_Q96113,TV_Q96109),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_arithmetics_SUBu_u_EQu_u_0, axiom, ![V_n, V_m]: (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_nums_num,h4s_nums_0) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_numeralu_u_distribu_c28, axiom, ![V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_numerals_numeralu_u_lteu_c0, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))) = s(t_bool,t)).
fof(ah4s_numerals_numeralu_u_lteu_c5, axiom, ![V_n, V_m]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(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)))))) <=> ~ (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))))).
fof(ah4s_numerals_numeralu_u_preu_c1, axiom, s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_arithmetics_zero)).
fof(ah4s_numerals_numeralu_u_preu_c2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(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,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))))))).
fof(ah4s_numerals_numeralu_u_preu_c3, axiom, ![V_n]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_bit1(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,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n)))))).
fof(ah4s_numerals_numeralu_u_texpu_u_helpu_c0, axiom, ![V_acc]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_acc))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_acc)))).
fof(ah4s_numerals_numeralu_u_texpu_u_helpu_c1, axiom, ![V_n, V_acc]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_acc))) = s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_primu_u_recs_pre(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_acc)))))).
fof(ah4s_numerals_numeralu_u_texpu_u_helpu_c2, axiom, ![V_n, V_acc]: s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_acc))) = s(t_h4s_nums_num,h4s_numerals_texpu_u_help(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_acc)))))).
fof(ah4s_numerals_TWOu_u_EXPu_u_THMu_c2, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),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_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_texpu_u_help(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ch4s_floats_temonz, conjecture, ~ (s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_arithmetics_exp(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))) = s(t_h4s_nums_num,h4s_nums_0))).
