# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/numeral/numeral__lte_c3', ch4s_numerals_numeralu_u_lteu_c3)).
fof(5, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/numeral/numeral__lte_c3', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(31, axiom,![X1]:![X2]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))))),file('i/f/numeral/numeral__lte_c3', ah4s_arithmetics_NOTu_u_LESS)).
fof(33, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),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/numeral/numeral__lte_c3', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(38, axiom,![X2]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X2)))),file('i/f/numeral/numeral__lte_c3', ah4s_arithmetics_LESSu_u_EQu_u_REFL)).
fof(44, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__lte_c3', ah4s_arithmetics_ALTu_u_ZERO)).
fof(52, axiom,![X1]:(s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))<=>p(s(t_bool,f))),file('i/f/numeral/numeral__lte_c3', ah4s_numerals_numeralu_u_equ_c0)).
fof(59, axiom,![X1]:![X2]: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_bit1(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),file('i/f/numeral/numeral__lte_c3', ah4s_numerals_numeralu_u_ltu_c3)).
fof(63, axiom,![X2]:(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,X2)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))),file('i/f/numeral/numeral__lte_c3', ah4s_arithmetics_LESSu_u_0u_u_CASES)).
fof(67, axiom,~(p(s(t_bool,f))),file('i/f/numeral/numeral__lte_c3', aHLu_FALSITY)).
fof(68, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/numeral/numeral__lte_c3', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(79, 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_bit1(s(t_h4s_nums_num,X1)))))=s(t_bool,t),file('i/f/numeral/numeral__lte_c3', ah4s_numerals_numeralu_u_ltu_c0)).
# SZS output end CNFRefutation
