%   ORIGINAL: h4/words/WORD__LO__word__0_c1
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/words/WORD__NOT__LOWER: !b a. ~h4/words/word__lo a b <=> h4/words/word__ls b a
% Assm: h4/words/WORD__NOT__LOWER__EQUAL: !b a. ~h4/words/word__ls a b <=> h4/words/word__lo b a
% Assm: h4/words/WORD__0__LS: !w. h4/words/word__ls (h4/words/n2w h4/num/0) w
% Assm: h4/words/WORD__LS__word__0: !n. h4/words/word__ls n (h4/words/n2w h4/num/0) <=> n = h4/words/n2w h4/num/0
% Goal: !n. ~h4/words/word__lo n (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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_wordss_WORDu_u_NOTu_u_LOWER]: !b a. ~h4/words/word__lo a b <=> h4/words/word__ls b a
% Assm [h4s_wordss_WORDu_u_NOTu_u_LOWERu_u_EQUAL]: !b a. ~h4/words/word__ls a b <=> h4/words/word__lo b a
% Assm [h4s_wordss_WORDu_u_0u_u_LS]: !w. h4/words/word__ls (h4/words/n2w h4/num/0) w
% Assm [h4s_wordss_WORDu_u_LSu_u_wordu_u_0]: !n. h4/words/word__ls n (h4/words/n2w h4/num/0) <=> n = h4/words/n2w h4/num/0
% Goal: !n. ~h4/words/word__lo n (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_Q128264,TV_Q128260]: ![V_f, V_g]: (![V_x]: s(TV_Q128260,happ(s(t_fun(TV_Q128264,TV_Q128260),V_f),s(TV_Q128264,V_x))) = s(TV_Q128260,happ(s(t_fun(TV_Q128264,TV_Q128260),V_g),s(TV_Q128264,V_x))) => s(t_fun(TV_Q128264,TV_Q128260),V_f) = s(t_fun(TV_Q128264,TV_Q128260),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> 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_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_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_WORDu_u_NOTu_u_LOWER, axiom, ![TV_u_27a]: ![V_b, V_a]: (~ (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_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))).
fof(ah4s_wordss_WORDu_u_NOTu_u_LOWERu_u_EQUAL, axiom, ![TV_u_27a]: ![V_b, V_a]: (~ (p(s(t_bool,h4s_wordss_wordu_u_ls(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_b),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))).
fof(ah4s_wordss_WORDu_u_0u_u_LS, axiom, ![TV_u_27a]: ![V_w]: p(s(t_bool,h4s_wordss_wordu_u_ls(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_w))))).
fof(ah4s_wordss_WORDu_u_LSu_u_wordu_u_0, axiom, ![TV_u_27a]: ![V_n]: (p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_n),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_n) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))).
fof(ch4s_wordss_WORDu_u_LOu_u_wordu_u_0u_c1, conjecture, ![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)))))))).
