# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))))))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),file('i/f/numeral/numeral__div2_c1', ch4s_numerals_numeralu_u_div2u_c1)).
fof(3, axiom,![X4]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,X4),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(4, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1))),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_TIMES2)).
fof(5, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_div2(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_DIV2u_u_def)).
fof(8, axiom,![X1]:![X5]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X5))))))<=>~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1)))))),file('i/f/numeral/numeral__div2_c1', ah4s_numerals_numeralu_u_ltu_c5)).
fof(10, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_BIT10)).
fof(11, axiom,![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X5),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(12, axiom,![X1]:![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))))),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(13, axiom,![X6]:![X1]:![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X6)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X6))),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_ADDu_u_ASSOC)).
fof(14, axiom,![X1]:![X5]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X5),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X5))),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_MULTu_u_COMM)).
fof(15, 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,X1))))=>![X4]:![X7]:s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X1)))))),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_ADDu_u_DIVu_u_ADDu_u_DIV)).
fof(16, axiom,![X1]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,X1)))))=s(t_bool,t),file('i/f/numeral/numeral__div2_c1', ah4s_numerals_numeralu_u_ltu_c1)).
fof(18, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_ALTu_u_ZERO)).
fof(19, axiom,s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/numeral/numeral__div2_c1', ah4s_numerals_numeralu_u_sucu_c0)).
fof(20, axiom,![X1]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_zero)))=s(t_bool,f),file('i/f/numeral/numeral__div2_c1', ah4s_numerals_numeralu_u_ltu_c2)).
fof(21, axiom,![X7]:![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X1))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/numeral/numeral__div2_c1', ah4s_arithmetics_LESSu_u_DIVu_u_EQu_u_ZERO)).
fof(22, axiom,p(s(t_bool,t)),file('i/f/numeral/numeral__div2_c1', aHLu_TRUTH)).
fof(23, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/numeral/numeral__div2_c1', aHLu_BOOLu_CASES)).
fof(25, axiom,![X8]:(s(t_bool,t)=s(t_bool,X8)<=>p(s(t_bool,X8))),file('i/f/numeral/numeral__div2_c1', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(29, axiom,![X7]:![X9]:![X6]:((p(s(t_bool,X6))<=>s(t_bool,X9)=s(t_bool,X7))<=>((p(s(t_bool,X6))|(p(s(t_bool,X9))|p(s(t_bool,X7))))&((p(s(t_bool,X6))|(~(p(s(t_bool,X7)))|~(p(s(t_bool,X9)))))&((p(s(t_bool,X9))|(~(p(s(t_bool,X7)))|~(p(s(t_bool,X6)))))&(p(s(t_bool,X7))|(~(p(s(t_bool,X9)))|~(p(s(t_bool,X6))))))))),file('i/f/numeral/numeral__div2_c1', ah4s_sats_dcu_u_eq)).
# SZS output end CNFRefutation
