# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MODEQ__SYM', aHLu_TRUTH)).
fof(6, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/arithmetic/MODEQ__SYM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/MODEQ__SYM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(26, axiom,![X15]:![X16]:![X17]:(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X16))))<=>((s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16))|(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X15)))))),file('i/f/arithmetic/MODEQ__SYM', ah4s_arithmetics_MODEQu_u_THM)).
fof(27, conjecture,![X18]:![X6]:![X15]:s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X18)))=s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X18),s(t_h4s_nums_num,X6))),file('i/f/arithmetic/MODEQ__SYM', ch4s_arithmetics_MODEQu_u_SYM)).
# SZS output end CNFRefutation
