# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,h4s_integers_intu_u_sub(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X1))),s(t_h4s_integers_int,X2)))=s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1))),file('i/f/integer/INT__SUB__SUB', ch4s_integers_INTu_u_SUBu_u_SUB)).
fof(4, axiom,![X1]:![X2]:s(t_h4s_integers_int,h4s_integers_intu_u_sub(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,X2),s(t_h4s_integers_int,h4s_integers_intu_u_neg(s(t_h4s_integers_int,X1))))),file('i/f/integer/INT__SUB__SUB', ah4s_integers_intu_u_sub0)).
fof(5, axiom,![X2]: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,X2))),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/integer/INT__SUB__SUB', ah4s_integers_INTu_u_ADDu_u_LINV)).
fof(6, axiom,![X7]:![X8]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X8),s(t_h4s_integers_int,X7)))=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,X8))),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,X7))))))),file('i/f/integer/INT__SUB__SUB', ah4s_integers_intu_u_add0)).
fof(7, 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/integer/INT__SUB__SUB', ah4s_integers_INTu_u_ADDu_u_LID)).
fof(9, axiom,![X3]:![X13]:![X14]:![X15]:![X16]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X16),s(t_fun(X3,X13),X15),s(t_fun(X13,X3),X14))))=>![X2]:![X1]:(s(X13,X2)=s(X13,X1)<=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X16),s(X3,happ(s(t_fun(X13,X3),X14),s(X13,X2))))),s(X3,happ(s(t_fun(X13,X3),X14),s(X13,X1)))))))),file('i/f/integer/INT__SUB__SUB', ah4s_quotients_EQUALSu_u_PRS)).
fof(11, axiom,![X13]:![X3]:![X14]:![X15]:![X21]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X3,t_fun(X3,t_bool)),X21),s(t_fun(X3,X13),X15),s(t_fun(X13,X3),X14))))=>![X17]:![X18]:(p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X21),s(X3,X17))),s(X3,X18))))=>p(s(t_bool,happ(s(t_fun(X3,t_bool),happ(s(t_fun(X3,t_fun(X3,t_bool)),X21),s(X3,X17))),s(X3,happ(s(t_fun(X13,X3),X14),s(X13,happ(s(t_fun(X3,X13),X15),s(X3,X18)))))))))),file('i/f/integer/INT__SUB__SUB', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(12, axiom,![X1]:![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),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1)))=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),X1),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X2))),file('i/f/integer/INT__SUB__SUB', ah4s_integers_TINTu_u_ADDu_u_SYM)).
fof(13, axiom,![X22]:![X1]:![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),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),X1),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),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),X2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X1))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X22))),file('i/f/integer/INT__SUB__SUB', ah4s_integers_TINTu_u_ADDu_u_ASSOC)).
fof(14, axiom,![X20]:![X19]:![X18]:![X17]:((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),X17))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X18))))&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),X19))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X20)))))=>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),X17),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X19))))),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),X18),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X20))))))),file('i/f/integer/INT__SUB__SUB', ah4s_integers_TINTu_u_ADDu_u_WELLDEF)).
fof(15, 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__SUB__SUB', ah4s_integers_intu_u_QUOTIENT)).
fof(16, axiom,![X23]:![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),X24))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X23))))<=>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),X24)))=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)))),file('i/f/integer/INT__SUB__SUB', ah4s_integers_TINTu_u_EQu_u_EQUIV)).
fof(17, axiom,![X23]:![X24]:(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X24)=s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X23)=>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),X24))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X23))))),file('i/f/integer/INT__SUB__SUB', ah4s_integers_TINTu_u_EQu_u_AP)).
# SZS output end CNFRefutation
