# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:((p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))))&p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))=>p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__TRANS', ch4s_arithmetics_MODEQu_u_TRANS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MODEQ__TRANS', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MODEQ__TRANS', aHLu_FALSITY)).
fof(18, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/arithmetic/MODEQ__TRANS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(46, axiom,![X4]:![X21]:![X22]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X4))))=>(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X21))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X4))))),file('i/f/arithmetic/MODEQ__TRANS', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(47, axiom,![X4]:![X21]:![X22]:(p(s(t_bool,h4s_arithmetics_modeq(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X21))))<=>((s(t_h4s_nums_num,X4)=s(t_h4s_nums_num,h4s_nums_0)&s(t_h4s_nums_num,X22)=s(t_h4s_nums_num,X21))|(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X4))))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X4)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X4)))))),file('i/f/arithmetic/MODEQ__TRANS', ah4s_arithmetics_MODEQu_u_THM)).
fof(50, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/arithmetic/MODEQ__TRANS', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
