# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X2)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),file('i/f/numeral/numeral__distrib_c31', ch4s_numerals_numeralu_u_distribu_c31)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/numeral/numeral__distrib_c31', aHLu_TRUTH)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/numeral/numeral__distrib_c31', aHLu_BOOLu_CASES)).
fof(7, axiom,![X4]:![X5]:((p(s(t_bool,X5))=>p(s(t_bool,X4)))=>((p(s(t_bool,X4))=>p(s(t_bool,X5)))=>s(t_bool,X5)=s(t_bool,X4))),file('i/f/numeral/numeral__distrib_c31', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(25, axiom,![X3]:(s(t_bool,t)=s(t_bool,X3)<=>p(s(t_bool,X3))),file('i/f/numeral/numeral__distrib_c31', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(27, axiom,![X3]:(s(t_bool,f)=s(t_bool,X3)<=>~(p(s(t_bool,X3)))),file('i/f/numeral/numeral__distrib_c31', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(46, 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__distrib_c31', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(49, axiom,![X1]:![X2]:(p(s(t_bool,h4s_arithmetics_u_3eu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))<=>(p(s(t_bool,h4s_arithmetics_u_3e(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__distrib_c31', ah4s_arithmetics_GREATERu_u_ORu_u_EQ)).
fof(50, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X7),file('i/f/numeral/numeral__distrib_c31', ah4s_arithmetics_NUMERALu_u_DEF)).
fof(52, axiom,![X1]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/numeral/numeral__distrib_c31', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(53, axiom,![X1]:![X2]:s(t_bool,h4s_arithmetics_u_3e(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))=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__distrib_c31', ah4s_arithmetics_GREATERu_u_DEF)).
fof(60, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__distrib_c31', ah4s_arithmetics_ALTu_u_ZERO)).
# SZS output end CNFRefutation
