# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![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,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))<=>~(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))=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,X2),s(t_h4s_nums_num,X1))))),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MOD__SUC__IFF', ch4s_arithmetics_MODu_u_SUCu_u_IFF)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MOD__SUC__IFF', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MOD__SUC__IFF', aHLu_FALSITY)).
fof(4, axiom,![X3]:(s(t_bool,X3)=s(t_bool,t)|s(t_bool,X3)=s(t_bool,f)),file('i/f/arithmetic/MOD__SUC__IFF', aHLu_BOOLu_CASES)).
fof(22, axiom,![X3]:(s(t_bool,X3)=s(t_bool,f)<=>~(p(s(t_bool,X3)))),file('i/f/arithmetic/MOD__SUC__IFF', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(36, axiom,![X13]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X13))))=>![X14]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,h4s_nums_0)),file('i/f/arithmetic/MOD__SUC__IFF', ah4s_arithmetics_MODu_u_EQu_u_0)).
fof(37, axiom,![X1]:![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_nums_suc(s(t_h4s_nums_num,X2)))=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,X2),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,h4s_nums_suc(s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/MOD__SUC__IFF', ah4s_arithmetics_MODu_u_SUC)).
fof(38, axiom,![X13]:~(s(t_h4s_nums_num,h4s_nums_0)=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13)))),file('i/f/arithmetic/MOD__SUC__IFF', ah4s_arithmetics_SUCu_u_NOT)).
# SZS output end CNFRefutation
