# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))=s(t_bool,t),file('i/f/numeral/numeral__distrib_c26', ch4s_numerals_numeralu_u_distribu_c26)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/numeral/numeral__distrib_c26', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/numeral/numeral__distrib_c26', aHLu_FALSITY)).
fof(4, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/numeral/numeral__distrib_c26', aHLu_BOOLu_CASES)).
fof(25, axiom,![X2]:(s(t_bool,t)=s(t_bool,X2)<=>p(s(t_bool,X2))),file('i/f/numeral/numeral__distrib_c26', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(27, axiom,![X2]:(s(t_bool,f)=s(t_bool,X2)<=>~(p(s(t_bool,X2)))),file('i/f/numeral/numeral__distrib_c26', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(46, axiom,![X1]:![X20]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X1))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X1))))|s(t_h4s_nums_num,X20)=s(t_h4s_nums_num,X1))),file('i/f/numeral/numeral__distrib_c26', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(50, axiom,![X20]:(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,X20)|p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X20))))),file('i/f/numeral/numeral__distrib_c26', ah4s_arithmetics_LESSu_u_0u_u_CASES)).
fof(61, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/numeral/numeral__distrib_c26', ah4s_arithmetics_ALTu_u_ZERO)).
# SZS output end CNFRefutation
