# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:p(s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_fcps_cart(t_bool,X1),X2)))),file('i/f/words/WORD__0__LS', ch4s_wordss_WORDu_u_0u_u_LS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/words/WORD__0__LS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/words/WORD__0__LS', aHLu_FALSITY)).
fof(8, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/words/WORD__0__LS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X3]:((p(s(t_bool,X3))=>p(s(t_bool,f)))<=>s(t_bool,X3)=s(t_bool,f)),file('i/f/words/WORD__0__LS', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(11, axiom,![X6]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X6)))),file('i/f/words/WORD__0__LS', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(12, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/words/WORD__0__LS', aHLu_BOOLu_CASES)).
fof(13, axiom,![X1]:![X8]:![X9]:s(t_bool,h4s_wordss_wordu_u_ls(s(t_h4s_fcps_cart(t_bool,X1),X9),s(t_h4s_fcps_cart(t_bool,X1),X8)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X9))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X8))))),file('i/f/words/WORD__0__LS', ah4s_wordss_WORDu_u_LS)).
fof(14, axiom,![X1]:![X6]:s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X6)))))=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))))),file('i/f/words/WORD__0__LS', ah4s_wordss_w2nu_u_n2w)).
fof(15, axiom,![X6]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X6))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/words/WORD__0__LS', ah4s_arithmetics_ZEROu_u_MOD)).
fof(18, 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__0__LS', ah4s_wordss_ZEROu_u_LTu_u_dimword)).
fof(20, axiom,![X6]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X6))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/words/WORD__0__LS', ah4s_numerals_numeralu_u_lteu_c1)).
# SZS output end CNFRefutation
