# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,X1),X2))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_bool,h4s_wordss_wordu_u_lt(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/integer_word/w2i__lt__0', ch4s_integeru_u_words_w2iu_u_ltu_u_0)).
fof(4, axiom,![X1]:![X2]:s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_bool,h4s_wordss_wordu_u_lt(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/integer_word/w2i__lt__0', ah4s_wordss_wordu_u_msbu_u_neg)).
fof(5, axiom,![X1]:![X5]:![X6]:s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,X1),X6),s(t_h4s_fcps_cart(t_bool,X1),X5)))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,X1),X6))),s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,X1),X5))))),file('i/f/integer_word/w2i__lt__0', ah4s_integeru_u_words_WORDu_u_LTi)).
fof(6, axiom,![X1]:![X5]:![X6]:(p(s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,X1),X6),s(t_h4s_fcps_cart(t_bool,X1),X5))))<=>((s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X6)))=s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X5)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X6))),s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X5)))))))|(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X6))))&~(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X5)))))))),file('i/f/integer_word/w2i__lt__0', ah4s_wordss_WORDu_u_LT)).
fof(29, axiom,![X18]:![X19]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X18))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X19)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X19))),file('i/f/integer_word/w2i__lt__0', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(32, axiom,![X18]:![X19]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X18))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X19)))))))=s(t_bool,f),file('i/f/integer_word/w2i__lt__0', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c3)).
fof(33, axiom,s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer_word/w2i__lt__0', ah4s_integers_INTu_u_NEGu_u_0)).
fof(34, axiom,![X1]:![X2]:![X18]:((~(p(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X2)))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,X1),X2))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X18)))))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X2))),s(t_h4s_nums_num,X18))))),file('i/f/integer_word/w2i__lt__0', ah4s_integeru_u_words_w2iu_u_w2nu_u_pos)).
fof(35, axiom,![X1]:![X2]:s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,X1),X2)))=s(t_h4s_integers_int,h4s_bools_cond(s(t_bool,h4s_wordss_wordu_u_msb(s(t_h4s_fcps_cart(t_bool,X1),X2))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),h4s_wordss_wordu_u_2comp(s(t_h4s_fcps_cart(t_bool,X1),X2))))))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_wordss_w2n(s(t_h4s_fcps_cart(t_bool,X1),X2))))))),file('i/f/integer_word/w2i__lt__0', ah4s_integeru_u_words_w2iu_u_def)).
fof(36, axiom,![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/integer_word/w2i__lt__0', ah4s_wordss_w2nu_u_equ_u_0)).
fof(40, axiom,~(p(s(t_bool,f))),file('i/f/integer_word/w2i__lt__0', aHLu_FALSITY)).
fof(41, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/integer_word/w2i__lt__0', aHLu_BOOLu_CASES)).
fof(51, axiom,(~(p(s(t_bool,t)))<=>p(s(t_bool,f))),file('i/f/integer_word/w2i__lt__0', ah4s_bools_NOTu_u_CLAUSESu_c1)).
fof(54, axiom,![X9]:(s(t_bool,f)=s(t_bool,X9)<=>~(p(s(t_bool,X9)))),file('i/f/integer_word/w2i__lt__0', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(56, axiom,~(s(t_bool,t)=s(t_bool,f)),file('i/f/integer_word/w2i__lt__0', ah4s_bools_BOOLu_u_EQu_u_DISTINCTu_c0)).
fof(60, axiom,![X1]:![X7]:![X8]:s(X1,h4s_bools_cond(s(t_bool,f),s(X1,X8),s(X1,X7)))=s(X1,X7),file('i/f/integer_word/w2i__lt__0', ah4s_bools_CONDu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
