# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:?[X3]:(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,X3)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value))))))),file('i/f/words/ranged__word__nchotomy', ch4s_wordss_rangedu_u_wordu_u_nchotomy)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/words/ranged__word__nchotomy', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/words/ranged__word__nchotomy', aHLu_FALSITY)).
fof(6, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/words/ranged__word__nchotomy', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(7, axiom,![X5]:![X6]:(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,X6),s(t_h4s_nums_num,X5)))=s(t_h4s_nums_num,X6)<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X5)))))),file('i/f/words/ranged__word__nchotomy', ah4s_arithmetics_Xu_u_MODu_u_Yu_u_EQu_u_X)).
fof(8, 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/ranged__word__nchotomy', ah4s_wordss_ZEROu_u_LTu_u_dimword)).
fof(10, axiom,![X1]:![X2]:?[X3]: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,X3))),file('i/f/words/ranged__word__nchotomy', ah4s_wordss_wordu_u_nchotomy)).
fof(11, axiom,![X1]:![X3]:![X7]:(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X7)))=s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_n2w(s(t_h4s_nums_num,X3)))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X7),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,X3),s(t_h4s_nums_num,h4s_wordss_dimword(s(t_h4s_bools_itself(X1),h4s_bools_theu_u_value)))))),file('i/f/words/ranged__word__nchotomy', ah4s_wordss_n2wu_u_11)).
fof(12, axiom,![X3]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3))))=>![X8]:(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X3)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X3))),s(t_h4s_nums_num,X3)))))),file('i/f/words/ranged__word__nchotomy', ah4s_arithmetics_DIVISION)).
fof(13, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/words/ranged__word__nchotomy', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
