# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X3))),s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X2)))))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))),file('i/f/words/word__add__n2w', ch4s_wordss_wordu_u_addu_u_n2w)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/words/word__add__n2w', aHLu_TRUTH)).
fof(8, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/words/word__add__n2w', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(11, axiom,![X1]:![X12]:![X13]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_add(s(t_h4s_fcps_cart(t_bool,X1),X13),s(t_h4s_fcps_cart(t_bool,X1),X12)))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X13))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X12))))))),file('i/f/words/word__add__n2w', ah4s_wordss_wordu_u_addu_u_def)).
fof(12, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))),file('i/f/words/word__add__n2w', ah4s_wordss_w2nu_u_n2w)).
fof(13, axiom,![X1]:![X2]:s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value)))))))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X2))),file('i/f/words/word__add__n2w', ah4s_wordss_n2wu_u_mod)).
fof(14, axiom,![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>![X14]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X2))))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X2)))),file('i/f/words/word__add__n2w', ah4s_arithmetics_MODu_u_PLUS)).
fof(15, 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/word__add__n2w', ah4s_wordss_ZEROu_u_LTu_u_dimword)).
# SZS output end CNFRefutation
