# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/arithmetic/DIVMOD__ID', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/arithmetic/DIVMOD__ID', 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/DIVMOD__ID', aHLu_BOOLu_CASES)).
fof(6, 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/DIVMOD__ID', ah4s_arithmetics_ONE)).
fof(21, axiom,![X9]:![X7]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))))=>![X10]:s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X10)),file('i/f/arithmetic/DIVMOD__ID', ah4s_arithmetics_DIVu_u_MULT)).
fof(28, axiom,![X7]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/DIVMOD__ID', ah4s_arithmetics_MULTu_c0)).
fof(38, axiom,![X9]:![X7]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X9),s(t_h4s_nums_num,X7))))=>![X10]:s(t_h4s_nums_num,h4s_arithmetics_mod(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X9))),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,X9)),file('i/f/arithmetic/DIVMOD__ID', ah4s_arithmetics_MODu_u_MULT)).
fof(40, axiom,![X7]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X15))),file('i/f/arithmetic/DIVMOD__ID', ah4s_arithmetics_ADDu_u_SYM)).
fof(43, axiom,![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0)))=s(t_h4s_nums_num,X15),file('i/f/arithmetic/DIVMOD__ID', ah4s_arithmetics_ADDu_u_0)).
fof(74, axiom,s(t_h4s_nums_num,h4s_arithmetics_fact(s(t_h4s_nums_num,h4s_nums_0)))=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/DIVMOD__ID', ah4s_arithmetics_FACT0u_c0)).
fof(79, axiom,![X7]:![X15]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,X7))),file('i/f/arithmetic/DIVMOD__ID', ah4s_arithmetics_MULTu_u_CLAUSESu_c4)).
fof(87, axiom,s(t_h4s_nums_num,h4s_arithmetics_zero)=s(t_h4s_nums_num,h4s_nums_0),file('i/f/arithmetic/DIVMOD__ID', ah4s_arithmetics_ALTu_u_ZERO)).
fof(133, conjecture,![X7]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X7))))=>(s(t_h4s_nums_num,h4s_arithmetics_div(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X7)))=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_arithmetics_mod(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0))),file('i/f/arithmetic/DIVMOD__ID', ch4s_arithmetics_DIVMODu_u_ID)).
# SZS output end CNFRefutation
