# 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,X2),s(t_h4s_nums_num,X1)))=s(t_h4s_nums_num,X2)<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1)))))),file('i/f/arithmetic/X__MOD__Y__EQ__X', ch4s_arithmetics_Xu_u_MODu_u_Yu_u_EQu_u_X)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/X__MOD__Y__EQ__X', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/X__MOD__Y__EQ__X', aHLu_FALSITY)).
fof(18, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(19, axiom,![X5]:(s(t_bool,X5)=s(t_bool,f)<=>~(p(s(t_bool,X5)))),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(38, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/arithmetic/X__MOD__Y__EQ__X', aHLu_BOOLu_CASES)).
fof(41, 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,X14)=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,X14),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X13)))))),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_arithmetics_DIVISION)).
fof(42, axiom,![X10]:![X13]:![X14]:(?[X11]:(s(t_h4s_nums_num,X14)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,X10)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X13)))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X14),s(t_h4s_nums_num,X13)))=s(t_h4s_nums_num,X10)),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_arithmetics_MODu_u_UNIQUE)).
fof(43, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,X15),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_arithmetics_ADDu_u_CLAUSESu_c0)).
fof(44, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/X__MOD__Y__EQ__X', ah4s_arithmetics_MULTu_u_CLAUSESu_c0)).
# SZS output end CNFRefutation
