# 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,X2))))=>p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__MOD', ch4s_arithmetics_MODEQu_u_MOD)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MODEQ__MOD', aHLu_TRUTH)).
fof(6, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)<=>p(s(t_bool,X3))),file('i/f/arithmetic/MODEQ__MOD', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>![X11]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X2)))),file('i/f/arithmetic/MODEQ__MOD', ah4s_arithmetics_MODu_u_MOD)).
fof(11, axiom,![X2]:![X12]:![X13]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X12))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X12),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MODEQ__MOD', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(12, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/MODEQ__MOD', aHLu_BOOLu_CASES)).
fof(13, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MODEQ__MOD', aHLu_FALSITY)).
# SZS output end CNFRefutation
