# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_h4s_fcps_cart(t_bool,X1)),h4s_combins_o(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_fcps_cart(t_bool,X1)),h4s_wordss_wordu_u_fromu_u_decu_u_list),s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_h4s_lists_list(t_h4s_nums_num)),h4s_wordss_wordu_u_tou_u_decu_u_list)))=s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_h4s_fcps_cart(t_bool,X1)),h4s_combins_i),file('i/f/words/word__dec__list', ch4s_wordss_wordu_u_decu_u_list)).
fof(2, axiom,![X1]:![X2]:s(X1,happ(s(t_fun(X1,X1),h4s_combins_i),s(X1,X2)))=s(X1,X2),file('i/f/words/word__dec__list', ah4s_combins_Iu_u_THM)).
fof(3, axiom,![X3]:![X1]:![X4]:![X2]:![X5]:![X6]:s(X3,happ(s(t_fun(X4,X3),h4s_combins_o(s(t_fun(X1,X3),X6),s(t_fun(X4,X1),X5))),s(X4,X2)))=s(X3,happ(s(t_fun(X1,X3),X6),s(X1,happ(s(t_fun(X4,X1),X5),s(X4,X2))))),file('i/f/words/word__dec__list', ah4s_combins_ou_u_THM)).
fof(4, axiom,![X1]:s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_h4s_lists_list(t_h4s_nums_num)),h4s_wordss_wordu_u_tou_u_decu_u_list)=s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_h4s_lists_list(t_h4s_nums_num)),h4s_wordss_w2l(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),file('i/f/words/word__dec__list', ah4s_wordss_wordu_u_tou_u_decu_u_listu_u_def)).
fof(5, axiom,![X1]:s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_fcps_cart(t_bool,X1)),h4s_wordss_wordu_u_fromu_u_decu_u_list)=s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_fcps_cart(t_bool,X1)),h4s_wordss_l2w(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),file('i/f/words/word__dec__list', ah4s_wordss_wordu_u_fromu_u_decu_u_listu_u_def)).
fof(6, axiom,![X7]:![X8]:![X6]:![X5]:(![X2]:s(X8,happ(s(t_fun(X7,X8),X6),s(X7,X2)))=s(X8,happ(s(t_fun(X7,X8),X5),s(X7,X2)))=>s(t_fun(X7,X8),X6)=s(t_fun(X7,X8),X5)),file('i/f/words/word__dec__list', aHLu_EXT)).
fof(8, axiom,![X1]:![X9]:![X10]:(p(s(t_bool,h4s_primu_u_recs_u_3c(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,X10))))=>s(t_h4s_fcps_cart(t_bool,X1),happ(s(t_fun(t_h4s_lists_list(t_h4s_nums_num),t_h4s_fcps_cart(t_bool,X1)),h4s_wordss_l2w(s(t_h4s_nums_num,X10))),s(t_h4s_lists_list(t_h4s_nums_num),happ(s(t_fun(t_h4s_fcps_cart(t_bool,X1),t_h4s_lists_list(t_h4s_nums_num)),h4s_wordss_w2l(s(t_h4s_nums_num,X10))),s(t_h4s_fcps_cart(t_bool,X1),X9)))))=s(t_h4s_fcps_cart(t_bool,X1),X9)),file('i/f/words/word__dec__list', ah4s_wordss_l2wu_u_w2l)).
fof(9, axiom,![X11]:![X12]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X12)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))),file('i/f/words/word__dec__list', ah4s_numerals_numeralu_u_distribu_c22)).
fof(10, axiom,![X11]:![X12]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X12))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))))),file('i/f/words/word__dec__list', ah4s_numerals_numeralu_u_ltu_c5)).
fof(11, axiom,![X11]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/words/word__dec__list', ah4s_numerals_numeralu_u_ltu_c2)).
fof(13, axiom,~(p(s(t_bool,f))),file('i/f/words/word__dec__list', aHLu_FALSITY)).
fof(14, axiom,![X13]:(s(t_bool,X13)=s(t_bool,t)|s(t_bool,X13)=s(t_bool,f)),file('i/f/words/word__dec__list', aHLu_BOOLu_CASES)).
fof(16, axiom,p(s(t_bool,t)),file('i/f/words/word__dec__list', aHLu_TRUTH)).
# SZS output end CNFRefutation
