# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))<=>s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/numeral/numeral__distrib_c30', ch4s_numerals_numeralu_u_distribu_c30)).
fof(4, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/numeral/numeral__distrib_c30', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(37, axiom,![X20]:(s(t_h4s_nums_num,X20)=s(t_h4s_nums_num,h4s_nums_0)|?[X1]:s(t_h4s_nums_num,X20)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))),file('i/f/numeral/numeral__distrib_c30', ah4s_arithmetics_numu_u_CASES)).
fof(38, axiom,![X1]:~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/numeral/numeral__distrib_c30', ah4s_arithmetics_NOTu_u_SUCu_u_LESSu_u_EQu_u_0)).
fof(64, axiom,![X5]:(s(t_bool,X5)=s(t_bool,f)<=>~(p(s(t_bool,X5)))),file('i/f/numeral/numeral__distrib_c30', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(70, axiom,![X1]:![X20]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X20)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X1))),file('i/f/numeral/numeral__distrib_c30', ah4s_arithmetics_GREATERu_u_EQ)).
fof(71, axiom,![X1]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,t),file('i/f/numeral/numeral__distrib_c30', ah4s_numerals_numeralu_u_distribu_c29)).
fof(72, axiom,![X1]:![X20]:(~(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X1)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,X1))))),file('i/f/numeral/numeral__distrib_c30', ah4s_arithmetics_NOTu_u_GREATERu_u_EQ)).
# SZS output end CNFRefutation
