# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(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,X1)))=s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X1))),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__RDISTRIB', ch4s_integers_INTu_u_RDISTRIB)).
fof(6, axiom,![X13]:![X14]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X14),s(t_h4s_integers_int,X13)))=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,X14))),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,X13))))))),file('i/f/integer/INT__RDISTRIB', ah4s_integers_intu_u_add0)).
fof(7, axiom,![X13]:![X14]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X14),s(t_h4s_integers_int,X13)))=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,X14))),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,X13))))))),file('i/f/integer/INT__RDISTRIB', ah4s_integers_intu_u_mul0)).
fof(8, axiom,![X2]:![X3]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X3),s(t_h4s_integers_int,X2)))=s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X3))),file('i/f/integer/INT__RDISTRIB', ah4s_integers_INTu_u_MULu_u_COMM)).
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__RDISTRIB', ah4s_integers_intu_u_QUOTIENT)).
fof(10, axiom,![X8]:![X15]:![X16]:![X17]:![X18]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X8,t_fun(X8,t_bool)),X18),s(t_fun(X8,X15),X17),s(t_fun(X15,X8),X16))))=>![X3]:![X2]:(s(X15,X3)=s(X15,X2)<=>p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X18),s(X8,happ(s(t_fun(X15,X8),X16),s(X15,X3))))),s(X8,happ(s(t_fun(X15,X8),X16),s(X15,X2)))))))),file('i/f/integer/INT__RDISTRIB', ah4s_quotients_EQUALSu_u_PRS)).
fof(12, axiom,![X15]:![X8]:![X16]:![X17]:![X23]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X8,t_fun(X8,t_bool)),X23),s(t_fun(X8,X15),X17),s(t_fun(X15,X8),X16))))=>![X19]:![X20]:(p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X23),s(X8,X19))),s(X8,X20))))=>p(s(t_bool,happ(s(t_fun(X8,t_bool),happ(s(t_fun(X8,t_fun(X8,t_bool)),X23),s(X8,X19))),s(X8,happ(s(t_fun(X15,X8),X16),s(X15,happ(s(t_fun(X8,X15),X17),s(X8,X20)))))))))),file('i/f/integer/INT__RDISTRIB', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(13, axiom,![X1]:![X2]:![X3]: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),X3),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),h4s_integers_tintu_u_mul(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_mul(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__RDISTRIB', ah4s_integers_TINTu_u_LDISTRIB)).
fof(14, axiom,![X22]:![X21]:![X20]:![X19]:((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),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),h4s_integers_tintu_u_add(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),X21))))),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),X20),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X22))))))),file('i/f/integer/INT__RDISTRIB', ah4s_integers_TINTu_u_ADDu_u_WELLDEF)).
fof(15, axiom,![X24]:![X25]:(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),X25))),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),X25)))=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)))),file('i/f/integer/INT__RDISTRIB', ah4s_integers_TINTu_u_EQu_u_EQUIV)).
fof(16, axiom,![X24]:![X25]:(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X25)=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),X25))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X24))))),file('i/f/integer/INT__RDISTRIB', ah4s_integers_TINTu_u_EQu_u_AP)).
fof(17, axiom,![X22]:![X21]:![X20]:![X19]:((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),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),h4s_integers_tintu_u_mul(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),X21))))),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),X20),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X22))))))),file('i/f/integer/INT__RDISTRIB', ah4s_integers_TINTu_u_MULu_u_WELLDEF)).
# SZS output end CNFRefutation
