# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X3))),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,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X4),s(t_h4s_integers_int,X2))),s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X1))))),file('i/f/integer/INT__ADD2__SUB2', ch4s_integers_INTu_u_ADD2u_u_SUB2)).
fof(4, axiom,![X11]:![X12]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X12),s(t_h4s_integers_int,X11)))=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,X12))),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,X11))))))),file('i/f/integer/INT__ADD2__SUB2', ah4s_integers_intu_u_add0)).
fof(5, axiom,![X6]:![X7]:s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X6)))=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X6))))),file('i/f/integer/INT__ADD2__SUB2', ah4s_integers_intu_u_sub0)).
fof(6, axiom,![X6]:![X7]:s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X7),s(t_h4s_integers_int,X6)))))=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X7))),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X6))))),file('i/f/integer/INT__ADD2__SUB2', ah4s_integers_INTu_u_NEGu_u_ADD)).
fof(8, axiom,![X5]:![X17]:![X18]:![X19]:![X20]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X5,t_fun(X5,t_bool)),X20),s(t_fun(X5,X17),X19),s(t_fun(X17,X5),X18))))=>![X7]:![X6]:(s(X17,X7)=s(X17,X6)<=>p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X20),s(X5,happ(s(t_fun(X17,X5),X18),s(X17,X7))))),s(X5,happ(s(t_fun(X17,X5),X18),s(X17,X6)))))))),file('i/f/integer/INT__ADD2__SUB2', ah4s_quotients_EQUALSu_u_PRS)).
fof(10, axiom,![X17]:![X5]:![X18]:![X19]:![X25]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X5,t_fun(X5,t_bool)),X25),s(t_fun(X5,X17),X19),s(t_fun(X17,X5),X18))))=>![X21]:![X22]:(p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X25),s(X5,X21))),s(X5,X22))))=>p(s(t_bool,happ(s(t_fun(X5,t_bool),happ(s(t_fun(X5,t_fun(X5,t_bool)),X25),s(X5,X21))),s(X5,happ(s(t_fun(X17,X5),X18),s(X17,happ(s(t_fun(X5,X17),X19),s(X5,X22)))))))))),file('i/f/integer/INT__ADD2__SUB2', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(11, axiom,![X6]:![X7]: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),X7),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X6)))=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),X6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X7))),file('i/f/integer/INT__ADD2__SUB2', ah4s_integers_TINTu_u_ADDu_u_SYM)).
fof(12, axiom,![X26]:![X6]:![X7]: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),X7),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),X6),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X26)))))=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),h4s_integers_tintu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X7),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X6))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X26))),file('i/f/integer/INT__ADD2__SUB2', ah4s_integers_TINTu_u_ADDu_u_ASSOC)).
fof(13, axiom,![X24]:![X23]:![X22]:![X21]:((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),X21))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X22))))&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),X23))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X24)))))=>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),h4s_integers_tintu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X21),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X23))))),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),X22),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X24))))))),file('i/f/integer/INT__ADD2__SUB2', ah4s_integers_TINTu_u_ADDu_u_WELLDEF)).
fof(14, 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__ADD2__SUB2', ah4s_integers_intu_u_QUOTIENT)).
fof(15, axiom,![X27]:![X28]:(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),X28))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X27))))<=>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),X28)))=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),X27)))),file('i/f/integer/INT__ADD2__SUB2', ah4s_integers_TINTu_u_EQu_u_EQUIV)).
fof(16, axiom,![X27]:![X28]:(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X28)=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X27)=>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),X28))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X27))))),file('i/f/integer/INT__ADD2__SUB2', ah4s_integers_TINTu_u_EQu_u_AP)).
# SZS output end CNFRefutation
