# 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_lt(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X3),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/integer/INT__LT__LADD__IMP', ch4s_integers_INTu_u_LTu_u_LADDu_u_IMP)).
fof(3, axiom,![X7]:![X8]:![X9]:![X10]:![X11]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X8,t_fun(X8,t_bool)),X11),s(t_fun(X8,X7),X10),s(t_fun(X7,X8),X9))))=>![X12]:![X13]:(p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X11),s(X8,X12))),s(X8,X13))))=>p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X11),s(X8,X12))),s(X8,happ(s(t_fun(X7,X8),X9),s(X7,happ(s(t_fun(X8,X7),X10),s(X8,X13)))))))))),file('i/f/integer/INT__LT__LADD__IMP', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(6, axiom,![X18]:![X19]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X19),s(t_h4s_integers_int,X18)))=s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_integers_intu_u_rep),s(t_h4s_integers_int,X19))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_integers_intu_u_rep),s(t_h4s_integers_int,X18))))),file('i/f/integer/INT__LT__LADD__IMP', ah4s_integers_intu_u_lt0)).
fof(7, axiom,![X18]:![X19]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X19),s(t_h4s_integers_int,X18)))=s(t_h4s_integers_int,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_integers_int),h4s_integers_intu_u_abs),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_integers_tintu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_integers_intu_u_rep),s(t_h4s_integers_int,X19))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_integers_intu_u_rep),s(t_h4s_integers_int,X18))))))),file('i/f/integer/INT__LT__LADD__IMP', ah4s_integers_intu_u_add0)).
fof(8, axiom,p(s(t_bool,h4s_quotients_quotient(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_integers_tintu_u_eq),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_integers_int),h4s_integers_intu_u_abs),s(t_fun(t_h4s_integers_int,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_integers_intu_u_rep)))),file('i/f/integer/INT__LT__LADD__IMP', ah4s_integers_intu_u_QUOTIENT)).
fof(13, axiom,![X29]:![X30]:(p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_integers_tintu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X30))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X29))))<=>s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_integers_tintu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X30)))=s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_integers_tintu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X29)))),file('i/f/integer/INT__LT__LADD__IMP', ah4s_integers_TINTu_u_EQu_u_EQUIV)).
fof(15, axiom,![X31]:![X32]:![X13]:![X12]:((p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_integers_tintu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X12))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X13))))&p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_integers_tintu_u_eq),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X32))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X31)))))=>s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X12),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X32)))=s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X13),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X31)))),file('i/f/integer/INT__LT__LADD__IMP', ah4s_integers_TINTu_u_LTu_u_WELLDEF)).
fof(20, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1))))=>p(s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_integers_tintu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_integers_tintu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X3),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1))))))),file('i/f/integer/INT__LT__LADD__IMP', ah4s_integers_TINTu_u_LTu_u_ADD)).
# SZS output end CNFRefutation
