# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))<=>((s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,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))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MODEQ__THM', ch4s_arithmetics_MODEQu_u_THM)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MODEQ__THM', aHLu_FALSITY)).
fof(23, axiom,![X1]:![X2]:![X3]:(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,X3),s(t_h4s_nums_num,X2))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__THM', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(24, axiom,![X1]:(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__THM', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(25, axiom,![X2]:![X3]:(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))<=>s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,X2)),file('i/f/arithmetic/MODEQ__THM', ah4s_arithmetics_MODEQu_u_0u_u_CONG)).
fof(26, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)|s(t_bool,X6)=s(t_bool,f)),file('i/f/arithmetic/MODEQ__THM', aHLu_BOOLu_CASES)).
fof(27, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MODEQ__THM', aHLu_TRUTH)).
fof(29, axiom,![X6]:(s(t_bool,X6)=s(t_bool,t)<=>p(s(t_bool,X6))),file('i/f/arithmetic/MODEQ__THM', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
