# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/int_arith/HO__SUB__ELIM', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/HO__SUB__ELIM', aHLu_FALSITY)).
fof(6, axiom,![X7]:![X8]:s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X7)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_integers_INTu_u_LE)).
fof(8, axiom,![X7]:![X8]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X7)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_integers_INTu_u_LT)).
fof(9, axiom,![X7]:![X8]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))=>s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X7))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8)))))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_integers_INTu_u_SUB)).
fof(14, axiom,![X7]:![X8]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8))))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_arithmetics_NOTu_u_LESS)).
fof(16, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(34, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(79, axiom,![X10]:![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X10)))=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X10))))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_integers_intu_u_sub0)).
fof(104, axiom,![X7]:![X8]:(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7)))=s(t_h4s_nums_num,h4s_nums_0)<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_arithmetics_SUBu_u_EQu_u_0)).
fof(105, axiom,![X7]:![X8]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))|s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X7))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(119, axiom,![X7]:![X8]:(s(t_h4s_nums_num,X8)=s(t_h4s_nums_num,X7)<=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X8),s(t_h4s_nums_num,X7))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X7),s(t_h4s_nums_num,X8)))))),file('i/f/int_arith/HO__SUB__ELIM', ah4s_arithmetics_EQu_u_LESSu_u_EQ)).
fof(133, conjecture,![X17]:![X28]:![X21]:(p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X21),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,X28),s(t_h4s_nums_num,X17))))))))<=>((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X17))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X28))))))&p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X21),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,X28))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X17)))))))))))|(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X28))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X17))))))&p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X21),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))))),file('i/f/int_arith/HO__SUB__ELIM', ch4s_intu_u_ariths_HOu_u_SUBu_u_ELIM)).
# SZS output end CNFRefutation
