%   ORIGINAL: h4/HolSmt/r253
% 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/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/arithmetic/ADD__0: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm: h4/arithmetic/LESS__EQ__REFL: !m. h4/arithmetic/_3C_3D m m
% Assm: h4/arithmetic/SUB__RIGHT__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2D m n) p <=> h4/arithmetic/_3C_3D m (h4/arithmetic/_2B n p)
% Assm: h4/words/WORD__BITS__EXTRACT: !w l h. h4/words/word__bits h l w = h4/words/word__extract h l w
% Assm: h4/words/WORD__ALL__BITS: !w h. h4/arithmetic/_3C_3D (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) h ==> h4/words/word__bits h h4/num/0 w = w
% Assm: h4/words/dimindex__1: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Goal: !x. h4/words/word__extract h4/num/0 h4/num/0 x = x
%   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_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_arithmetics_ADDu_u_0]: !m. h4/arithmetic/_2B m h4/num/0 = m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_REFL]: !m. h4/arithmetic/_3C_3D m m
% Assm [h4s_arithmetics_SUBu_u_RIGHTu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2D m n) p <=> h4/arithmetic/_3C_3D m (h4/arithmetic/_2B n p)
% Assm [h4s_wordss_WORDu_u_BITSu_u_EXTRACT]: !w l h. h4/words/word__bits h l w = h4/words/word__extract h l w
% Assm [h4s_wordss_WORDu_u_ALLu_u_BITS]: !w h. h4/arithmetic/_3C_3D (h4/arithmetic/_2D (h4/fcp/dimindex h4/bool/the__value) (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) h ==> h4/words/word__bits h h4/num/0 w = w
% Assm [h4s_wordss_dimindexu_u_1]: h4/fcp/dimindex h4/bool/the__value = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Goal: !x. h4/words/word__extract h4/num/0 h4/num/0 x = x
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_Q342084,TV_Q342080]: ![V_f, V_g]: (![V_x]: s(TV_Q342080,happ(s(t_fun(TV_Q342084,TV_Q342080),V_f),s(TV_Q342084,V_x))) = s(TV_Q342080,happ(s(t_fun(TV_Q342084,TV_Q342080),V_g),s(TV_Q342084,V_x))) => s(t_fun(TV_Q342084,TV_Q342080),V_f) = s(t_fun(TV_Q342084,TV_Q342080),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_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_arithmetics_ADDu_u_0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_EQu_u_REFL, axiom, ![V_m]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_m))))).
fof(ah4s_arithmetics_SUBu_u_RIGHTu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(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,V_p))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_wordss_WORDu_u_BITSu_u_EXTRACT, axiom, ![TV_u_27a]: ![V_w, V_l, V_h]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,V_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w)))).
fof(ah4s_wordss_WORDu_u_ALLu_u_BITS, axiom, ![TV_u_27a]: ![V_w, V_h]: (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),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,V_h)))) => s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_bits(s(t_h4s_nums_num,V_h),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))).
fof(ah4s_wordss_dimindexu_u_1, axiom, s(t_h4s_nums_num,h4s_fcps_dimindex(s(t_h4s_bools_itself(t_h4s_ones_one),h4s_bools_theu_u_value))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ch4s_HolSmts_r253, conjecture, ![V_x]: s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),h4s_wordss_wordu_u_extract(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_x))) = s(t_h4s_fcps_cart(t_bool,t_h4s_ones_one),V_x)).
