# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/int_arith/INT__NUM__FORALL', aHLu_TRUTH)).
fof(14, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(42, axiom,![X15]:(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,h4s_nums_0))),s(t_h4s_integers_int,X15))))=>?[X29]:s(t_h4s_integers_int,X15)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X29)))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_integers_NUMu_u_POSINTu_u_EXISTS)).
fof(62, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(82, axiom,![X29]:![X33]: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,X33))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X29)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X33),s(t_h4s_nums_num,X29))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_integers_INTu_u_LT)).
fof(85, axiom,![X29]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X29),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(125, axiom,![X18]:![X6]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X18))))<=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X18),s(t_h4s_integers_int,X6)))))),file('i/f/int_arith/INT__NUM__FORALL', ah4s_integers_intu_u_le0)).
fof(133, conjecture,![X8]:(![X29]:p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X8),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X29))))))<=>![X6]:(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,h4s_nums_0))),s(t_h4s_integers_int,X6))))=>p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X8),s(t_h4s_integers_int,X6)))))),file('i/f/int_arith/INT__NUM__FORALL', ch4s_intu_u_ariths_INTu_u_NUMu_u_FORALL)).
# SZS output end CNFRefutation
