# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/integer/INT__REM__EQ0', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/integer/INT__REM__EQ0', 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__REM__EQ0', aHLu_BOOLu_CASES)).
fof(22, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/integer/INT__REM__EQ0', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(23, axiom,![X1]:(s(t_bool,X1)=s(t_bool,f)<=>~(p(s(t_bool,X1)))),file('i/f/integer/INT__REM__EQ0', ah4s_bools_EQu_u_CLAUSESu_c3)).
fof(30, axiom,![X7]:![X8]:![X17]:(p(s(t_bool,h4s_bools_cond(s(t_bool,X17),s(t_bool,X8),s(t_bool,X7))))<=>((~(p(s(t_bool,X17)))|p(s(t_bool,X8)))&(p(s(t_bool,X17))|p(s(t_bool,X7))))),file('i/f/integer/INT__REM__EQ0', ah4s_bools_CONDu_u_EXPAND)).
fof(46, axiom,![X6]: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_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))))=s(t_h4s_integers_int,X6),file('i/f/integer/INT__REM__EQ0', ah4s_integers_INTu_u_ADDu_u_RID)).
fof(47, axiom,![X6]:p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X6)))),file('i/f/integer/INT__REM__EQ0', ah4s_integers_INTu_u_LEu_u_REFL)).
fof(48, axiom,![X11]:![X6]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X11))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X6),s(t_h4s_integers_int,X11))))|s(t_h4s_integers_int,X6)=s(t_h4s_integers_int,X11))),file('i/f/integer/INT__REM__EQ0', ah4s_integers_INTu_u_LEu_u_LT)).
fof(49, 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,h4s_integers_abs(s(t_h4s_integers_int,X20)))))),file('i/f/integer/INT__REM__EQ0', ah4s_integers_INTu_u_ABSu_u_POS)).
fof(50, axiom,![X21]: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,X21)))))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X21))),file('i/f/integer/INT__REM__EQ0', ah4s_integers_INTu_u_ABSu_u_NUM)).
fof(51, axiom,![X20]:(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X20)))=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)=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__EQ0', ah4s_integers_INTu_u_ABSu_u_EQ0)).
fof(52, axiom,![X19]:(~(s(t_h4s_integers_int,X19)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>![X20]:(s(t_h4s_integers_int,X20)=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,h4s_integers_intu_u_quot(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19))),s(t_h4s_integers_int,X19))),s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19)))))&(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,X20))),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_rem(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19))))),s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19))),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,h4s_integers_abs(s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19))))),s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X19))))))))),file('i/f/integer/INT__REM__EQ0', ah4s_integers_INTu_u_REMQUOT)).
fof(53, axiom,![X18]:![X19]:![X20]:((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X18))),s(t_h4s_integers_int,h4s_integers_abs(s(t_h4s_integers_int,X19))))))&(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,X20))),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,X18))),s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X18),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))))))&?[X22]:s(t_h4s_integers_int,X20)=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,X22),s(t_h4s_integers_int,X19))),s(t_h4s_integers_int,X18)))))=>s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19)))=s(t_h4s_integers_int,X18)),file('i/f/integer/INT__REM__EQ0', ah4s_integers_INTu_u_REMu_u_UNIQUE)).
fof(54, conjecture,![X19]:(~(s(t_h4s_integers_int,X19)=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))=>![X20]:(s(t_h4s_integers_int,h4s_integers_intu_u_rem(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))<=>?[X22]:s(t_h4s_integers_int,X20)=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X22),s(t_h4s_integers_int,X19))))),file('i/f/integer/INT__REM__EQ0', ch4s_integers_INTu_u_REMu_u_EQ0)).
# SZS output end CNFRefutation
