# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),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,h4s_integers_intu_u_add(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X2))))))),file('i/f/int_arith/le__move__all__right', ch4s_intu_u_ariths_leu_u_moveu_u_allu_u_right)).
fof(2, axiom,![X3]:![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1))))),s(t_h4s_integers_int,X3)))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X1))))),file('i/f/int_arith/le__move__all__right', ah4s_integers_INTu_u_LTu_u_ADDNEG2)).
fof(7, axiom,![X3]:![X1]:![X2]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))),s(t_h4s_integers_int,X3)))=s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X2))))))),file('i/f/int_arith/le__move__all__right', ah4s_intu_u_ariths_ltu_u_moveu_u_leftu_u_right)).
fof(16, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/int_arith/le__move__all__right', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(29, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))<=>~(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X2)))))),file('i/f/int_arith/le__move__all__right', ah4s_integers_intu_u_le0)).
fof(45, axiom,![X1]:![X2]:(p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))<=>(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))|s(t_h4s_integers_int,X2)=s(t_h4s_integers_int,X1))),file('i/f/int_arith/le__move__all__right', ah4s_integers_INTu_u_LEu_u_LT)).
fof(46, axiom,![X2]: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,X2)))=s(t_h4s_integers_int,X2),file('i/f/int_arith/le__move__all__right', ah4s_integers_INTu_u_ADDu_u_LID)).
fof(49, axiom,![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X2)))))=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/le__move__all__right', ah4s_integers_INTu_u_ADDu_u_RINV)).
fof(51, axiom,![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),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),file('i/f/int_arith/le__move__all__right', ah4s_integers_INTu_u_ADDu_u_RID)).
fof(55, axiom,![X15]:![X16]:(p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X15))))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X16))))))<=>(~(s(t_h4s_nums_num,X15)=s(t_h4s_nums_num,h4s_nums_0))|~(s(t_h4s_nums_num,X16)=s(t_h4s_nums_num,h4s_nums_0)))),file('i/f/int_arith/le__move__all__right', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c2)).
fof(61, axiom,s(t_h4s_integers_int,h4s_integers_intu_u_neg(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_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/int_arith/le__move__all__right', ah4s_integers_INTu_u_NEGu_u_0)).
fof(64, axiom,![X15]:![X16]: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,X15))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,X16)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,X16))),file('i/f/int_arith/le__move__all__right', ah4s_integers_INTu_u_LTu_u_CALCULATEu_c0)).
fof(66, axiom,![X15]:~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_nums_0))))),file('i/f/int_arith/le__move__all__right', ah4s_primu_u_recs_NOTu_u_LESSu_u_0)).
fof(67, axiom,![X15]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X15))),s(t_h4s_nums_num,h4s_nums_0)))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X15),s(t_h4s_nums_num,h4s_arithmetics_zero))),file('i/f/int_arith/le__move__all__right', ah4s_numerals_numeralu_u_distribu_c27)).
fof(68, axiom,![X15]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,X15)))),file('i/f/int_arith/le__move__all__right', ah4s_arithmetics_ZEROu_u_LESSu_u_EQ)).
fof(69, axiom,![X15]:s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,X15)))))=s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,X15))),file('i/f/int_arith/le__move__all__right', ah4s_numerals_numeralu_u_distribu_c21)).
fof(70, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/le__move__all__right', aHLu_FALSITY)).
fof(75, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/int_arith/le__move__all__right', ah4s_bools_EQu_u_CLAUSESu_c2)).
# SZS output end CNFRefutation
