%   ORIGINAL: h4/words/word__msb__neg
% 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/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c3: !t. t \/ F <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/words/ZERO__LO__INT__MIN: h4/words/word__lo (h4/words/n2w h4/num/0) h4/words/word__L
% Assm: h4/words/WORD__MSB__INT__MIN__LS: !a. h4/words/word__msb a <=> h4/words/word__ls h4/words/word__L a
% Assm: h4/words/WORD__LT__LO: !b a. h4/words/word__lt a b <=> h4/words/word__ls h4/words/word__L a /\ (h4/words/word__lo b h4/words/word__L \/ h4/words/word__lo a b) \/ h4/words/word__lo a h4/words/word__L /\ h4/words/word__lo b h4/words/word__L /\ h4/words/word__lo a b
% Assm: h4/words/WORD__LO__word__0_c1: !n. ~h4/words/word__lo n (h4/words/n2w h4/num/0)
% Goal: !w. h4/words/word__msb w <=> h4/words/word__lt w (h4/words/n2w 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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c3]: !t. t \/ F <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_wordss_ZEROu_u_LOu_u_INTu_u_MIN]: h4/words/word__lo (h4/words/n2w h4/num/0) h4/words/word__L
% Assm [h4s_wordss_WORDu_u_MSBu_u_INTu_u_MINu_u_LS]: !a. h4/words/word__msb a <=> h4/words/word__ls h4/words/word__L a
% Assm [h4s_wordss_WORDu_u_LTu_u_LO]: !b a. h4/words/word__lt a b <=> h4/words/word__ls h4/words/word__L a /\ (h4/words/word__lo b h4/words/word__L \/ h4/words/word__lo a b) \/ h4/words/word__lo a h4/words/word__L /\ h4/words/word__lo b h4/words/word__L /\ h4/words/word__lo a b
% Assm [h4s_wordss_WORDu_u_LOu_u_wordu_u_0u_c1]: !n. ~h4/words/word__lo n (h4/words/n2w h4/num/0)
% Goal: !w. h4/words/word__msb w <=> h4/words/word__lt w (h4/words/n2w 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_Q128405,TV_Q128401]: ![V_f, V_g]: (![V_x]: s(TV_Q128401,happ(s(t_fun(TV_Q128405,TV_Q128401),V_f),s(TV_Q128405,V_x))) = s(TV_Q128401,happ(s(t_fun(TV_Q128405,TV_Q128401),V_g),s(TV_Q128405,V_x))) => s(t_fun(TV_Q128405,TV_Q128401),V_f) = s(t_fun(TV_Q128405,TV_Q128401),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,f))) <=> p(s(t_bool,V_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_wordss_ZEROu_u_LOu_u_INTu_u_MIN, axiom, ![TV_u_27a]: p(s(t_bool,h4s_wordss_wordu_u_lo(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),h4s_wordss_wordu_u_l))))).
fof(ah4s_wordss_WORDu_u_MSBu_u_INTu_u_MINu_u_LS, axiom, ![TV_u_27a]: ![V_a]: s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))) = s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))).
fof(ah4s_wordss_WORDu_u_LTu_u_LO, axiom, ![TV_u_27a]: ![V_b, V_a]: (p(s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) <=> ((p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_l),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))) & (p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_l)))) | p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))) | (p(s(t_bool,h4s_wordss_wordu_u_lo(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_l)))) & (p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_wordu_u_l)))) & p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))))))))).
fof(ah4s_wordss_WORDu_u_LOu_u_wordu_u_0u_c1, axiom, ![TV_u_27b]: ![V_n]: ~ (p(s(t_bool,h4s_wordss_wordu_u_lo(s(t_h4s_fcps_cart(t_bool,TV_u_27b),V_n),s(t_h4s_fcps_cart(t_bool,TV_u_27b),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))))))).
fof(ch4s_wordss_wordu_u_msbu_u_neg, conjecture, ![TV_u_27a]: ![V_w]: s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))) = s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))))).
