# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_h4s_nums_num,h4s_nums_0)<=>s(t_h4s_fcps_cart(t_bool,X1),X2)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/words/w2n__eq__0', ch4s_wordss_w2nu_u_equ_u_0)).
fof(6, axiom,![X1]:![X2]:?[X5]:s(t_h4s_fcps_cart(t_bool,X1),X2)=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X5))),file('i/f/words/w2n__eq__0', ah4s_wordss_wordu_u_nchotomy)).
fof(7, axiom,![X1]:![X5]:![X6]:(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X6)))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X5)))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value)))))),file('i/f/words/w2n__eq__0', ah4s_wordss_n2wu_u_11)).
fof(8, axiom,![X1]:![X5]:s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X5)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))),file('i/f/words/w2n__eq__0', ah4s_wordss_w2nu_u_n2w)).
fof(9, axiom,![X5]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/words/w2n__eq__0', ah4s_arithmetics_ZEROu_u_MOD)).
fof(10, axiom,![X1]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value)))))),file('i/f/words/w2n__eq__0', ah4s_wordss_ZEROu_u_LTu_u_dimword)).
# SZS output end CNFRefutation
