# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:(?[X4]:(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))=>s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X1)),file('i/f/arithmetic/MOD__UNIQUE', ch4s_arithmetics_MODu_u_UNIQUE)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/arithmetic/MOD__UNIQUE', aHLu_TRUTH)).
fof(7, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)<=>p(s(t_bool,X5))),file('i/f/arithmetic/MOD__UNIQUE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(8, axiom,![X8]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X8),file('i/f/arithmetic/MOD__UNIQUE', ah4s_arithmetics_ADDu_u_CLAUSESu_c1)).
fof(9, axiom,![X2]:![X8]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X8))),file('i/f/arithmetic/MOD__UNIQUE', ah4s_arithmetics_ADDu_u_SYM)).
fof(10, axiom,![X9]:![X2]:![X8]:(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X9)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X9)))<=>s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X2)),file('i/f/arithmetic/MOD__UNIQUE', ah4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ)).
fof(11, axiom,![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/MOD__UNIQUE', ah4s_primu_u_recs_LESSu_u_0)).
fof(12, axiom,s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/MOD__UNIQUE', ah4s_arithmetics_ONE)).
fof(13, axiom,![X2]:![X8]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2)))))=s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X2))))),file('i/f/arithmetic/MOD__UNIQUE', ah4s_arithmetics_ADDu_u_CLAUSESu_c3)).
fof(14, axiom,![X2]:![X8]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X8))))=>?[X9]:s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))),file('i/f/arithmetic/MOD__UNIQUE', ah4s_arithmetics_LESSu_u_ADDu_u_1)).
fof(15, axiom,![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X2))))=>![X3]:(s(t_h4s_nums_num,X3)=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,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X2)))))),file('i/f/arithmetic/MOD__UNIQUE', ah4s_arithmetics_DIVISION)).
fof(16, axiom,![X4]:![X2]:![X3]:(?[X1]:(s(t_h4s_nums_num,X3)=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X4),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,X1)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X1),s(t_h4s_nums_num,X2)))))=>s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X3),s(t_h4s_nums_num,X2)))=s(t_h4s_nums_num,X4)),file('i/f/arithmetic/MOD__UNIQUE', ah4s_arithmetics_DIVu_u_UNIQUE)).
fof(17, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/arithmetic/MOD__UNIQUE', aHLu_BOOLu_CASES)).
fof(18, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/MOD__UNIQUE', aHLu_FALSITY)).
# SZS output end CNFRefutation
