# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MOD__SUC', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MOD__SUC', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/arithmetic/MOD__SUC', aHLu_BOOLu_CASES)).
fof(21, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/arithmetic/MOD__SUC', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(22, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/arithmetic/MOD__SUC', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(39, axiom,![X19]:![X20]:s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X19))))),file('i/f/arithmetic/MOD__SUC', ah4s_arithmetics_ADDu_u_SUC)).
fof(41, axiom,![X19]:![X20]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))))&~(s(t_h4s_nums_num,X19)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20)))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,X19))))),file('i/f/arithmetic/MOD__SUC', ah4s_arithmetics_LESSu_u_NOTu_u_SUC)).
fof(42, axiom,![X19]:![X20]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X19))),file('i/f/arithmetic/MOD__SUC', ah4s_arithmetics_MULTu_u_CLAUSESu_c4)).
fof(43, axiom,![X19]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X19))))=>![X21]:(s(t_h4s_nums_num,X21)=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,X21),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X19)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X19)))))),file('i/f/arithmetic/MOD__SUC', ah4s_arithmetics_DIVISION)).
fof(44, axiom,![X16]:![X19]:![X21]:(?[X17]:(s(t_h4s_nums_num,X21)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X17),s(t_h4s_nums_num,X19))),s(t_h4s_nums_num,X16)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X16),s(t_h4s_nums_num,X19)))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X19)))=s(t_h4s_nums_num,X16)),file('i/f/arithmetic/MOD__SUC', ah4s_arithmetics_MODu_u_UNIQUE)).
fof(46, conjecture,![X10]:![X6]:((p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X10))))&~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X10))))),s(t_h4s_nums_num,X10)))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6))),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,X10)))))),file('i/f/arithmetic/MOD__SUC', ch4s_arithmetics_MODu_u_SUC)).
# SZS output end CNFRefutation
