# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/intto/pos__pos__thm', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/intto/pos__pos__thm', 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/intto/pos__pos__thm', aHLu_BOOLu_CASES)).
fof(9, axiom,![X7]:![X12]:![X8]:![X13]:![X6]:![X14]:![X15]:((s(t_bool,X15)=s(t_bool,X14)&((p(s(t_bool,X14))=>s(X7,X6)=s(X7,X13))&(~(p(s(t_bool,X14)))=>s(X7,X8)=s(X7,X12))))=>s(X7,h4s_bools_cond(s(t_bool,X15),s(X7,X6),s(X7,X8)))=s(X7,h4s_bools_cond(s(t_bool,X14),s(X7,X13),s(X7,X12)))),file('i/f/intto/pos__pos__thm', ah4s_bools_CONDu_u_CONG)).
fof(10, axiom,![X16]:![X17]:(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,X16)))<=>s(t_h4s_nums_num,X17)=s(t_h4s_nums_num,X16)),file('i/f/intto/pos__pos__thm', ah4s_integers_INTu_u_INJ)).
fof(11, axiom,![X16]:![X17]:s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X16))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X17)))))=s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,X16))),s(t_h4s_nums_num,X17))),file('i/f/intto/pos__pos__thm', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(12, axiom,![X7]:![X8]:![X6]:![X18]:?[X19]:((p(s(t_bool,X19))<=>s(X7,X6)=s(X7,X8))&s(t_h4s_totos_cpn,happ(s(t_fun(X7,t_h4s_totos_cpn),happ(s(t_fun(X7,t_fun(X7,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(X7,t_fun(X7,t_bool)),X18))),s(X7,X6))),s(X7,X8)))=s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,X19),s(t_h4s_totos_cpn,h4s_totos_equal),s(t_h4s_totos_cpn,h4s_bools_cond(s(t_bool,happ(s(t_fun(X7,t_bool),happ(s(t_fun(X7,t_fun(X7,t_bool)),X18),s(X7,X6))),s(X7,X8))),s(t_h4s_totos_cpn,h4s_totos_less),s(t_h4s_totos_cpn,h4s_totos_greater)))))),file('i/f/intto/pos__pos__thm', ah4s_totos_TOu_u_ofu_u_LinearOrder0)).
fof(13, axiom,s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord)=s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))),file('i/f/intto/pos__pos__thm', ah4s_totos_numOrd0)).
fof(14, axiom,s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_inttos_intord)=s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_totos_tou_u_ofu_u_linearorder(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_bool)),h4s_integers_intu_u_lt))),file('i/f/intto/pos__pos__thm', ah4s_inttos_intOrd0)).
fof(15, conjecture,![X16]:![X17]:s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_integers_int,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_totos_cpn)),h4s_inttos_intord),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,X16)))))=s(t_h4s_totos_cpn,happ(s(t_fun(t_h4s_nums_num,t_h4s_totos_cpn),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_totos_cpn)),h4s_totos_numord),s(t_h4s_nums_num,X17))),s(t_h4s_nums_num,X16))),file('i/f/intto/pos__pos__thm', ch4s_inttos_posu_u_posu_u_thm)).
# SZS output end CNFRefutation
