# 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__EXISTS', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/INT__NUM__EXISTS', 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/int_arith/INT__NUM__EXISTS', aHLu_BOOLu_CASES)).
fof(7, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/int_arith/INT__NUM__EXISTS', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(31, axiom,![X20]:(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,X20))))=>?[X8]:s(t_h4s_integers_int,X20)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8)))),file('i/f/int_arith/INT__NUM__EXISTS', ah4s_integers_NUMu_u_POSINTu_u_EXISTS)).
fof(44, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/int_arith/INT__NUM__EXISTS', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(54, axiom,![X8]:![X28]: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,X28))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X28),s(t_h4s_nums_num,X8))),file('i/f/int_arith/INT__NUM__EXISTS', ah4s_integers_INTu_u_LE)).
fof(55, axiom,![X8]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X8)))),file('i/f/int_arith/INT__NUM__EXISTS', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(77, axiom,![X24]:![X6]:(~(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X24)))))<=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X24),s(t_h4s_integers_int,X6))))),file('i/f/int_arith/INT__NUM__EXISTS', ah4s_integers_INTu_u_NOTu_u_LE)).
fof(81, axiom,![X8]:![X28]:(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,X8)))<=>s(t_h4s_nums_num,X28)=s(t_h4s_nums_num,X8)),file('i/f/int_arith/INT__NUM__EXISTS', ah4s_integers_INTu_u_INJ)).
fof(99, axiom,![X6]:~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X6))))),file('i/f/int_arith/INT__NUM__EXISTS', ah4s_integers_INTu_u_LTu_u_REFL)).
fof(111, axiom,s(t_h4s_integers_int,h4s_integers_intu_u_0)=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/INT__NUM__EXISTS', ah4s_integers_INTu_u_0)).
fof(133, conjecture,![X7]:(?[X8]:p(s(t_bool,happ(s(t_fun(t_h4s_integers_int,t_bool),X7),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X8))))))<=>?[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),X7),s(t_h4s_integers_int,X6)))))),file('i/f/int_arith/INT__NUM__EXISTS', ch4s_intu_u_ariths_INTu_u_NUMu_u_EXISTS)).
# SZS output end CNFRefutation
