# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,X2))))&p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,X1)))))=>p(s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integers_intu_u_0),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))))))),file('i/f/integer/INT__LT__MUL', ch4s_integers_INTu_u_LTu_u_MUL)).
fof(4, axiom,![X9]:![X6]:![X10]:![X11]:![X12]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X6,t_fun(X6,t_bool)),X12),s(t_fun(X6,X9),X11),s(t_fun(X9,X6),X10))))=>![X13]:![X14]:(p(s(t_bool,happ(s(t_fun(X6,t_bool),happ(s(t_fun(X6,t_fun(X6,t_bool)),X12),s(X6,X13))),s(X6,X14))))=>p(s(t_bool,happ(s(t_fun(X6,t_bool),happ(s(t_fun(X6,t_fun(X6,t_bool)),X12),s(X6,X13))),s(X6,happ(s(t_fun(X9,X6),X10),s(X9,happ(s(t_fun(X6,X9),X11),s(X6,X14)))))))))),file('i/f/integer/INT__LT__MUL', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(7, axiom,![X19]:![X20]:s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19)))=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,X20))),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))))),file('i/f/integer/INT__LT__MUL', ah4s_integers_intu_u_lt0)).
fof(8, axiom,![X19]:![X20]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X20),s(t_h4s_integers_int,X19)))=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_mul(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,X20))),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))))))),file('i/f/integer/INT__LT__MUL', ah4s_integers_intu_u_mul0)).
fof(9, 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__MUL', ah4s_integers_intu_u_QUOTIENT)).
fof(10, axiom,s(t_h4s_integers_int,h4s_integers_intu_u_0)=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_0))),file('i/f/integer/INT__LT__MUL', ah4s_integers_intu_u_00)).
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__MUL', ah4s_integers_TINTu_u_EQu_u_EQUIV)).
fof(19, axiom,![X1]:![X2]:((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_0),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2))))&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_0),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_0),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_integers_tintu_u_mul(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))))))),file('i/f/integer/INT__LT__MUL', ah4s_integers_TINTu_u_LTu_u_MUL)).
fof(20, axiom,![X32]:![X33]:![X14]:![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),X13))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X14))))&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),X33))),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),X33)))=s(t_bool,h4s_integers_tintu_u_lt(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X14),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X32)))),file('i/f/integer/INT__LT__MUL', ah4s_integers_TINTu_u_LTu_u_WELLDEF)).
# SZS output end CNFRefutation
