# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1))),file('i/f/util_prob/LT__SUC', ch4s_utilu_u_probs_LTu_u_SUC)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/util_prob/LT__SUC', aHLu_FALSITY)).
fof(10, axiom,![X4]:((p(s(t_bool,X4))=>p(s(t_bool,f)))<=>s(t_bool,X4)=s(t_bool,f)),file('i/f/util_prob/LT__SUC', ah4s_bools_IMPu_u_Fu_u_EQu_u_F)).
fof(18, axiom,![X12]:![X13]:![X14]:((p(s(t_bool,X14))<=>s(t_bool,X13)=s(t_bool,X12))<=>((p(s(t_bool,X14))|(p(s(t_bool,X13))|p(s(t_bool,X12))))&((p(s(t_bool,X14))|(~(p(s(t_bool,X12)))|~(p(s(t_bool,X13)))))&((p(s(t_bool,X13))|(~(p(s(t_bool,X12)))|~(p(s(t_bool,X14)))))&(p(s(t_bool,X12))|(~(p(s(t_bool,X13)))|~(p(s(t_bool,X14))))))))),file('i/f/util_prob/LT__SUC', ah4s_sats_dcu_u_eq)).
fof(22, axiom,![X14]:![X15]:![X16]:((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14)))))=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X14))))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_LESSu_u_EQu_u_TRANS)).
fof(23, axiom,![X15]:![X16]:(s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,X15)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X16)))))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(24, axiom,![X15]:![X16]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X16))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_ADDu_u_SYM)).
fof(26, axiom,![X14]:![X15]:![X16]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X14)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X14))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(27, axiom,![X15]:![X16]:(~(s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,X15))<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,X15))))|p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X16)))))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_NOTu_u_NUMu_u_EQ)).
fof(28, axiom,![X15]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15)))=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,X15))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_SUCu_u_ONEu_u_ADD)).
fof(29, axiom,![X15]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/util_prob/LT__SUC', ah4s_numerals_numeralu_u_lteu_c1)).
fof(30, axiom,![X15]:![X16]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,X15))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_LESSu_u_EQ)).
fof(31, axiom,![X15]:![X16]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X16))))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_NOTu_u_LESS)).
fof(32, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/util_prob/LT__SUC', aHLu_BOOLu_CASES)).
fof(34, axiom,![X15]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(35, axiom,![X15]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/util_prob/LT__SUC', ah4s_numerals_numeralu_u_distribu_c27)).
fof(37, axiom,![X16]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X16)))=s(t_h4s_nums_num,X16),file('i/f/util_prob/LT__SUC', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(38, axiom,![X15]:![X16]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X16)))))=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,X15),s(t_h4s_nums_num,X16))))))),file('i/f/util_prob/LT__SUC', ah4s_numerals_numeralu_u_distribu_c2)).
fof(39, axiom,![X15]:s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X15)))))=s(t_h4s_nums_num,X15),file('i/f/util_prob/LT__SUC', ah4s_numerals_numeralu_u_addu_c0)).
fof(42, axiom,p(s(t_bool,t)),file('i/f/util_prob/LT__SUC', aHLu_TRUTH)).
fof(44, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/util_prob/LT__SUC', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
