%   ORIGINAL: h4/HolSmt/r255
% 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/words/WORD__NEG__1: h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/words/word__T
% Assm: h4/words/WORD__OR__CLAUSES_c0: !a. h4/words/word__or h4/words/word__T a = h4/words/word__T
% Assm: h4/words/WORD__OR__CLAUSES_c1: !a. h4/words/word__or a h4/words/word__T = h4/words/word__T
% Assm: h4/words/WORD__OR__CLAUSES_c2: !a. h4/words/word__or (h4/words/n2w h4/num/0) a = a
% Assm: h4/words/WORD__OR__CLAUSES_c3: !a. h4/words/word__or a (h4/words/n2w h4/num/0) = a
% Assm: h4/words/WORD__OR__CLAUSES_c4: !a. h4/words/word__or a a = a
% Goal: !x. h4/words/word__or (h4/words/n2w 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_wordss_WORDu_u_NEGu_u_1]: h4/words/word__2comp (h4/words/n2w (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) = h4/words/word__T
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c0]: !a. h4/words/word__or h4/words/word__T a = h4/words/word__T
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c1]: !a. h4/words/word__or a h4/words/word__T = h4/words/word__T
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c2]: !a. h4/words/word__or (h4/words/n2w h4/num/0) a = a
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c3]: !a. h4/words/word__or a (h4/words/n2w h4/num/0) = a
% Assm [h4s_wordss_WORDu_u_ORu_u_CLAUSESu_c4]: !a. h4/words/word__or a a = a
% Goal: !x. h4/words/word__or (h4/words/n2w 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_Q342134,TV_Q342130]: ![V_f, V_g]: (![V_x]: s(TV_Q342130,happ(s(t_fun(TV_Q342134,TV_Q342130),V_f),s(TV_Q342134,V_x))) = s(TV_Q342130,happ(s(t_fun(TV_Q342134,TV_Q342130),V_g),s(TV_Q342134,V_x))) => s(t_fun(TV_Q342134,TV_Q342130),V_f) = s(t_fun(TV_Q342134,TV_Q342130),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_wordss_WORDu_u_NEGu_u_1, axiom, ![TV_u_27a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(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_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t)).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t)).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_t)).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c2, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c3, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ah4s_wordss_WORDu_u_ORu_u_CLAUSESu_c4, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)).
fof(ch4s_HolSmts_r255, conjecture, ![TV_u_27a]: ![V_x]: s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_or(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x))) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_x)).
