# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(~(s(t_h4s_integers_int,X1)=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_rem(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X1)))=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__REM__ID', ch4s_integers_INTu_u_REMu_u_ID)).
fof(32, axiom,![X8]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X8),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,X8),file('i/f/integer/INT__REM__ID', ah4s_integers_INTu_u_ADDu_u_RID)).
fof(33, axiom,![X1]: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_abs(s(t_h4s_integers_int,X1)))))),file('i/f/integer/INT__REM__ID', ah4s_integers_INTu_u_ABSu_u_POS)).
fof(34, axiom,![X14]:s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X14))),file('i/f/integer/INT__REM__ID', ah4s_integers_INTu_u_ABSu_u_NUM)).
fof(35, axiom,![X1]:(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X1)))=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)=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__REM__ID', ah4s_integers_INTu_u_ABSu_u_EQ0)).
fof(36, axiom,![X12]:![X13]:![X1]:((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X12))),s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X13))))))&(p(s(t_bool,h4s_bools_cond(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))),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,X12))),s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))))&?[X15]:s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X15),s(t_h4s_integers_int,X13))),s(t_h4s_integers_int,X12)))))=>s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X13)))=s(t_h4s_integers_int,X12)),file('i/f/integer/INT__REM__ID', ah4s_integers_INTu_u_REMu_u_UNIQUE)).
fof(37, axiom,![X8]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X8)))),file('i/f/integer/INT__REM__ID', ah4s_integers_INTu_u_LEu_u_REFL)).
fof(38, axiom,![X7]:![X8]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X7))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X7))))|s(t_h4s_integers_int,X8)=s(t_h4s_integers_int,X7))),file('i/f/integer/INT__REM__ID', ah4s_integers_INTu_u_LEu_u_LT)).
fof(39, axiom,p(s(t_bool,t)),file('i/f/integer/INT__REM__ID', aHLu_TRUTH)).
fof(46, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/integer/INT__REM__ID', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(49, axiom,![X8]: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_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_integers_int,X8)))=s(t_h4s_integers_int,X8),file('i/f/integer/INT__REM__ID', ah4s_integers_INTu_u_MULu_u_LID)).
fof(50, axiom,![X6]:![X4]:![X16]:s(X6,h4s_bools_cond(s(t_bool,X16),s(X6,X4),s(X6,X4)))=s(X6,X4),file('i/f/integer/INT__REM__ID', ah4s_bools_CONDu_u_ID)).
# SZS output end CNFRefutation
