# 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(46, axiom,![X22]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X22),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(48, axiom,![X22]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X22)))=s(t_h4s_nums_num,X22),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(50, axiom,![X1]:![X22]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X22))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_ADDu_u_COMM)).
fof(57, axiom,![X1]:![X25]:![X26]:(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,X26),s(t_h4s_nums_num,X25))))<=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X26),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X25),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_MODEQu_u_NONZEROu_u_MODEQUALITY)).
fof(73, axiom,![X22]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_MULTu_u_CLAUSESu_c1)).
fof(74, 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))))=>![X9]:(s(t_h4s_nums_num,X9)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X1)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_DIVISION)).
fof(76, axiom,![X24]:![X6]:![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8))))=>(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,X24)<=>(s(t_h4s_nums_num,X6)=s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X8)))&s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X8)))=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_MULTu_u_EQu_u_DIV)).
fof(77, axiom,![X11]:![X1]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_LESSu_u_DIVu_u_EQu_u_ZERO)).
fof(83, axiom,![X1]:![X22]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X22))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_MULTu_u_COMM)).
fof(91, axiom,![X1]:![X22]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X1)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X22),s(t_h4s_nums_num,X1))))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_MULTu_u_CLAUSESu_c5)).
fof(95, axiom,![X1]:s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),file('i/f/arithmetic/MODEQ__0', ah4s_arithmetics_BIT10)).
# SZS output end CNFRefutation
