# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))&p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X3)))))))<=>?[X4]:(s(t_h4s_integers_int,X1)=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X2),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,X4))))&p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X3))))))),file('i/f/int_arith/in__additive__range', ch4s_intu_u_ariths_inu_u_additiveu_u_range)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/int_arith/in__additive__range', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/int_arith/in__additive__range', aHLu_FALSITY)).
fof(8, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)<=>p(s(t_bool,X7))),file('i/f/int_arith/in__additive__range', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X9]:![X1]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X9)))=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X9),s(t_h4s_integers_int,X1))),file('i/f/int_arith/in__additive__range', ah4s_integers_INTu_u_ADDu_u_COMM)).
fof(10, axiom,![X10]:![X9]:![X1]:s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X9))),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X10)))))=s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X9),s(t_h4s_integers_int,X10))),file('i/f/int_arith/in__additive__range', ah4s_integers_INTu_u_LEu_u_LADD)).
fof(11, axiom,![X10]:![X9]:![X1]:s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X9))),s(t_h4s_integers_int,X10)))=s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X10),s(t_h4s_integers_int,X9))))),file('i/f/int_arith/in__additive__range', ah4s_integers_INTu_u_LEu_u_SUBu_u_RADD)).
fof(12, axiom,![X1]: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,X1)))=s(t_h4s_integers_int,X1),file('i/f/int_arith/in__additive__range', ah4s_integers_INTu_u_ADDu_u_LID)).
fof(13, axiom,![X9]:![X1]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X9),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X1),s(t_h4s_integers_int,X9)))))=s(t_h4s_integers_int,X1),file('i/f/int_arith/in__additive__range', ah4s_integers_INTu_u_SUBu_u_ADD2)).
fof(14, axiom,![X9]:![X1]: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,X1),s(t_h4s_integers_int,X9)))))=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,X9))),file('i/f/int_arith/in__additive__range', ah4s_integers_INTu_u_LTu_u_ADDR)).
fof(16, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/int_arith/in__additive__range', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
