# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/integer/INT__LE__DOUBLE', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__LE__DOUBLE', 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/integer/INT__LE__DOUBLE', aHLu_BOOLu_CASES)).
fof(8, axiom,![X6]: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,h4s_nums_0))),s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,X6),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_ADDu_u_LID)).
fof(11, axiom,![X7]:![X6]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7))))<=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X6)))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_intu_u_le0)).
fof(12, axiom,![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,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,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X6))))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_LEu_u_NEGTOTAL)).
fof(16, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/integer/INT__LE__DOUBLE', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(17, axiom,![X8]:![X7]:![X6]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X8)))))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X8))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_LTu_u_LADD)).
fof(21, axiom,![X6]: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,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X6)))))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_NEGu_u_GT0)).
fof(37, axiom,![X10]:![X6]:s(X10,happ(s(t_fun(X10,X10),h4s_combins_i),s(X10,X6)))=s(X10,X6),file('i/f/integer/INT__LE__DOUBLE', ah4s_combins_Iu_u_THM)).
fof(39, axiom,![X7]:![X6]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7))))|s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,X7))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_LEu_u_LT)).
fof(43, axiom,![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,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X6)))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_LEu_u_SQUARE)).
fof(57, axiom,![X6]: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,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X6)))))=s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_NEGu_u_GE0)).
fof(58, axiom,![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(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)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_MULu_u_LZERO)).
fof(59, axiom,![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_SUBu_u_REFL)).
fof(63, axiom,![X7]:![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7)))=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X6))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_ADDu_u_COMM)).
fof(68, axiom,![X8]:![X7]:![X6]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X7),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,X8)))))))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X8))),s(t_h4s_integers_int,X6))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_LTu_u_ADDNEG)).
fof(79, axiom,![X8]:![X7]:![X6]:((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7))))&p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X8)))))=>p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X8))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_LEu_u_TRANS)).
fof(80, 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/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_0)).
fof(86, axiom,![X7]:![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7)))=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,X7))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_intu_u_sub0)).
fof(87, axiom,![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X6)))))=s(t_h4s_integers_int,X6),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_NEGNEG)).
fof(92, axiom,![X7]:![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7)))))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X7))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_NEGu_u_RMUL)).
fof(99, axiom,![X7]:![X6]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X7))),s(t_h4s_integers_int,X7)))=s(t_h4s_integers_int,X6),file('i/f/integer/INT__LE__DOUBLE', ah4s_integers_INTu_u_SUBu_u_ADD)).
fof(111, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/integer/INT__LE__DOUBLE', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(112, axiom,![X10]:![X35]:(~(![X6]:p(s(t_bool,happ(s(t_fun(X10,t_bool),X35),s(X10,X6)))))<=>?[X6]:~(p(s(t_bool,happ(s(t_fun(X10,t_bool),X35),s(X10,X6)))))),file('i/f/integer/INT__LE__DOUBLE', ah4s_bools_NOTu_u_FORALLu_u_THM)).
fof(133, conjecture,![X6]: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,h4s_integers_intu_u_add(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X6)))))=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))),file('i/f/integer/INT__LE__DOUBLE', ch4s_integers_INTu_u_LEu_u_DOUBLE)).
# SZS output end CNFRefutation
