# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0))=>s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))),file('i/f/integer/INT__MOD', ch4s_integers_INTu_u_MOD)).
fof(23, axiom,![X1]:![X2]:(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))<=>s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,X1)),file('i/f/integer/INT__MOD', ah4s_integers_INTu_u_INJ)).
fof(24, axiom,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/integer/INT__MOD', ah4s_integers_INTu_u_ADD)).
fof(25, axiom,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X1))))),file('i/f/integer/INT__MOD', ah4s_integers_INTu_u_MUL)).
fof(26, axiom,![X1]:![X2]:(~(s(t_h4s_nums_num,X2)=s(t_h4s_nums_num,h4s_nums_0))=>s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X1))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X2)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))),file('i/f/integer/INT__MOD', ah4s_integers_INTu_u_DIV)).
fof(27, axiom,![X17]:![X18]:(~(s(t_h4s_integers_int,X17)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>s(t_h4s_integers_int,h4s_integers_intu_u_mod(s(t_h4s_integers_int,X18),s(t_h4s_integers_int,X17)))=s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X18),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,h4s_integers_intu_u_div(s(t_h4s_integers_int,X18),s(t_h4s_integers_int,X17))),s(t_h4s_integers_int,X17)))))),file('i/f/integer/INT__MOD', ah4s_integers_intu_u_mod0)).
fof(28, 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))))=>![X19]:(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,h4s_arithmetics_div(s(t_h4s_nums_num,X19),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,X19),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,X19),s(t_h4s_nums_num,X1))),s(t_h4s_nums_num,X1)))))),file('i/f/integer/INT__MOD', ah4s_arithmetics_DIVISION)).
fof(29, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),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,X2))),file('i/f/integer/INT__MOD', ah4s_arithmetics_ADDu_u_COMM)).
fof(30, axiom,![X1]:(~(s(t_h4s_nums_num,X1)=s(t_h4s_nums_num,h4s_nums_0))<=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X1))))),file('i/f/integer/INT__MOD', ah4s_arithmetics_NOTu_u_ZEROu_u_LTu_u_ZERO)).
fof(31, axiom,![X1]:![X2]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X2),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,X2))),file('i/f/integer/INT__MOD', ah4s_arithmetics_MULTu_u_COMM)).
fof(32, axiom,![X20]:![X7]:![X8]:(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X7)))=s(t_h4s_integers_int,X20)<=>s(t_h4s_integers_int,X8)=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X7)))),file('i/f/integer/INT__MOD', ah4s_integers_INTu_u_EQu_u_SUBu_u_RADD)).
# SZS output end CNFRefutation
