# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(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,h4s_nums_0))),s(t_h4s_integers_int,X2))))=>(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,h4s_nums_0))),s(t_h4s_integers_int,X1))))=>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,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1)))))))),file('i/f/intExtension/INT__MUL__POS__SIGN', ch4s_intExtensions_INTu_u_MULu_u_POSu_u_SIGN)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/intExtension/INT__MUL__POS__SIGN', aHLu_FALSITY)).
fof(3, axiom,![X3]:![X4]:(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,h4s_nums_0))),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X3))))))<=>((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,h4s_nums_0))),s(t_h4s_integers_int,X4))))&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,h4s_nums_0))),s(t_h4s_integers_int,X3)))))|(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_integers_INTu_u_MULu_u_SIGNu_u_CASESu_c0)).
fof(8, axiom,![X9]:![X10]:((p(s(t_bool,X10))=>p(s(t_bool,X9)))=>((p(s(t_bool,X9))=>p(s(t_bool,X10)))=>s(t_bool,X10)=s(t_bool,X9))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(31, axiom,![X14]:(s(t_bool,f)=s(t_bool,X14)<=>~(p(s(t_bool,X14)))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(52, axiom,![X12]:![X7]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X12))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X12))))|s(t_h4s_integers_int,X7)=s(t_h4s_integers_int,X12))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_integers_INTu_u_LEu_u_LT)).
fof(64, axiom,![X7]: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,X7),s(t_h4s_integers_int,X7)))))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_integers_INTu_u_LEu_u_SQUARE)).
fof(65, axiom,![X7]: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,X7)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_integers_INTu_u_MULu_u_LZERO)).
fof(66, axiom,![X12]:![X7]: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,X7),s(t_h4s_integers_int,X12)))))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X12))))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_integers_INTu_u_NEGu_u_RMUL)).
fof(71, axiom,![X7]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X7)))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_integers_INTu_u_LEu_u_REFL)).
fof(72, axiom,![X26]:(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,X26))))=>?[X23]:s(t_h4s_integers_int,X26)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X23)))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_integers_NUMu_u_POSINTu_u_EXISTS)).
fof(74, axiom,![X23]:![X24]: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,X24))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X23)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X24),s(t_h4s_nums_num,X23))),file('i/f/intExtension/INT__MUL__POS__SIGN', ah4s_integers_INTu_u_LE)).
# SZS output end CNFRefutation
