# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![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))))=>p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/arithmetic/MODEQ__0', ch4s_arithmetics_MODEQu_u_0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MODEQ__0', aHLu_TRUTH)).
fof(6, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)<=>p(s(t_bool,X2))),file('i/f/arithmetic/MODEQ__0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, 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))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_ZEROu_u_MOD)).
fof(11, axiom,![X1]:![X11]:![X12]:(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_arithmetics_modeq(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X11))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(12, 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))))=>(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_DIVMODu_u_ID)).
fof(13, axiom,![X2]:(s(t_bool,X2)=s(t_bool,t)|s(t_bool,X2)=s(t_bool,f)),file('i/f/arithmetic/MODEQ__0', aHLu_BOOLu_CASES)).
fof(14, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MODEQ__0', aHLu_FALSITY)).
# SZS output end CNFRefutation
