%   ORIGINAL: h4/words/WORD__LOWER__REFL
% 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/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> 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__LOWER__OR__EQ: !b a. h4/words/word__ls a b <=> h4/words/word__lo a b \/ a = b
% Goal: !a. ~h4/words/word__lo a a
%   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_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> 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_LOWERu_u_ORu_u_EQ]: !b a. h4/words/word__ls a b <=> h4/words/word__lo a b \/ a = b
% Goal: !a. ~h4/words/word__lo a a
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_Q127653,TV_Q127649]: ![V_f, V_g]: (![V_x]: s(TV_Q127649,happ(s(t_fun(TV_Q127653,TV_Q127649),V_f),s(TV_Q127653,V_x))) = s(TV_Q127649,happ(s(t_fun(TV_Q127653,TV_Q127649),V_g),s(TV_Q127653,V_x))) => s(t_fun(TV_Q127653,TV_Q127649),V_f) = s(t_fun(TV_Q127653,TV_Q127649),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> 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_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_LOWERu_u_ORu_u_EQ, 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_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))) | 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(ch4s_wordss_WORDu_u_LOWERu_u_REFL, conjecture, ![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_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a)))))).
