# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1)))=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2))),file('i/f/hrat/TRAT__ADD__SYM__EQ', ch4s_hrats_TRATu_u_ADDu_u_SYMu_u_EQ)).
fof(6, axiom,![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/hrat/TRAT__ADD__SYM__EQ', ah4s_arithmetics_ADDu_u_SYM)).
fof(7, axiom,![X10]:![X11]:s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X11),s(t_h4s_nums_num,X10)))=s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,X10),s(t_h4s_nums_num,X11))),file('i/f/hrat/TRAT__ADD__SYM__EQ', ah4s_arithmetics_MULTu_u_SYM)).
fof(8, axiom,![X12]:![X6]:![X13]:![X7]:s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_hrats_tratu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X6))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,X13),s(t_h4s_nums_num,X12)))))=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X7))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))))),s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X13))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6))))))))),s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X6))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X12))))))))),file('i/f/hrat/TRAT__ADD__SYM__EQ', ah4s_hrats_tratu_u_add0)).
fof(9, axiom,![X4]:![X5]:![X7]:s(t_h4s_pairs_prod(X4,X5),h4s_pairs_u_2c(s(X4,h4s_pairs_fst(s(t_h4s_pairs_prod(X4,X5),X7))),s(X5,h4s_pairs_snd(s(t_h4s_pairs_prod(X4,X5),X7)))))=s(t_h4s_pairs_prod(X4,X5),X7),file('i/f/hrat/TRAT__ADD__SYM__EQ', ah4s_pairs_PAIR)).
# SZS output end CNFRefutation
