# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', aHLu_BOOLu_CASES)).
fof(6, axiom,![X8]:s(t_h4s_integers_int,h4s_integeru_u_words_uintu_u_max(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_wordss_uintu_u_max(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_integeru_u_words_UINTu_u_MAX0)).
fof(12, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(13, axiom,![X11]:![X12]: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,X11))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(20, axiom,![X11]:![X12]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,X11))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_arithmetics_LESSu_u_EQ)).
fof(21, axiom,![X1]:((p(s(t_bool,X1))=>p(s(t_bool,f)))<=>s(t_bool,X1)=s(t_bool,f)),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(22, axiom,![X11]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_numerals_numeralu_u_distribu_c27)).
fof(24, axiom,![X11]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X11))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(25, axiom,![X11]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X11)))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(31, axiom,![X8]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_wordss_intu_u_min(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value))),s(t_h4s_nums_num,h4s_wordss_uintu_u_max(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value)))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_wordss_BOUNDu_u_ORDERu_c1)).
fof(33, axiom,![X11]:![X12]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_arithmetics_NOTu_u_LESS)).
fof(34, axiom,![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X12)))=s(t_h4s_nums_num,X12),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(40, axiom,![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X11),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_numerals_numeralu_u_distribu_c1)).
fof(53, axiom,![X11]:![X12]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X12)))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12))))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_numerals_numeralu_u_distribu_c2)).
fof(60, axiom,![X11]:![X12]:(~(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,X11))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))),s(t_h4s_nums_num,X11))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X11))),s(t_h4s_nums_num,X12)))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(66, axiom,![X8]:p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integeru_u_words_intu_u_min(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value))),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/INT__ZERO__LT__UINT__MAX', ah4s_integeru_u_words_INTu_u_ZEROu_u_LTu_u_INTu_u_MIN)).
fof(74, axiom,![X11]:![X12]:(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,X11)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X12)))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(75, axiom,![X8]:s(t_h4s_integers_int,h4s_integeru_u_words_intu_u_min(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value)))=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_intu_u_min(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value))))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_integeru_u_words_INTu_u_MIN0)).
fof(76, axiom,![X11]:![X12]:(p(s(t_bool,h4s_integers_intu_u_lt(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,X11))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X12))))))<=>(~(s(t_h4s_nums_num,X11)=s(t_h4s_nums_num,h4s_nums_0))|~(s(t_h4s_nums_num,X12)=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c2)).
fof(79, axiom,![X6]:~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X6))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_integers_INTu_u_LTu_u_REFL)).
fof(81, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(127, axiom,![X8]:![X4]:s(t_h4s_nums_num,h4s_lists_listu_u_size(s(t_fun(X8,t_h4s_nums_num),X4),s(t_h4s_lists_list(X8),h4s_lists_nil)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_lists_listu_u_sizeu_u_defu_c0)).
fof(132, axiom,![X11]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,X11),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ah4s_numerals_numeralu_u_addu_c1)).
fof(133, conjecture,![X8]:p(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,h4s_nums_0))),s(t_h4s_integers_int,h4s_integeru_u_words_uintu_u_max(s(t_h4s_bools_itself(X8),h4s_bools_theu_u_value)))))),file('i/f/integer_word/INT__ZERO__LT__UINT__MAX', ch4s_integeru_u_words_INTu_u_ZEROu_u_LTu_u_UINTu_u_MAX)).
# SZS output end CNFRefutation
