# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MOD__LESS', ch4s_arithmetics_MODu_u_LESS)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MOD__LESS', aHLu_FALSITY)).
fof(18, 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))))=>![X13]:(s(t_h4s_nums_num,X13)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MOD__LESS', ah4s_arithmetics_DIVISION)).
fof(19, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/MOD__LESS', aHLu_BOOLu_CASES)).
fof(20, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MOD__LESS', aHLu_TRUTH)).
fof(22, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/arithmetic/MOD__LESS', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
