# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]: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,X1)))=s(t_h4s_integers_int,X1),file('i/f/integer/INT__ADD__LID', ch4s_integers_INTu_u_ADDu_u_LID)).
fof(3, axiom,![X4]:![X5]:s(t_h4s_integers_int,h4s_integers_intu_u_add(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,X4)))=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,X5))),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,X4))))))),file('i/f/integer/INT__ADD__LID', ah4s_integers_intu_u_add0)).
fof(4, axiom,s(t_h4s_integers_int,h4s_integers_intu_u_0)=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__ADD__LID', ah4s_integers_INTu_u_0)).
fof(6, axiom,![X2]:![X10]:(![X1]:![X3]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X1))),s(X2,X3))))<=>s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X1)))=s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X3))))<=>(![X1]:p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X1))),s(X2,X1))))&(![X1]:![X3]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X1))),s(X2,X3))))=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X3))),s(X2,X1)))))&![X1]:![X3]:![X11]:((p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X1))),s(X2,X3))))&p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X3))),s(X2,X11)))))=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,X1))),s(X2,X11)))))))),file('i/f/integer/INT__ADD__LID', ah4s_quotients_EQUIVu_u_REFLu_u_SYMu_u_TRANS)).
fof(7, axiom,![X12]:![X13]:![X14]:![X15]:((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),X15))),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),X13))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),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),h4s_integers_tintu_u_add(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),X15),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),h4s_integers_tintu_u_add(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),X12))))))),file('i/f/integer/INT__ADD__LID', ah4s_integers_TINTu_u_ADDu_u_WELLDEF)).
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__ADD__LID', ah4s_integers_intu_u_QUOTIENT)).
fof(9, 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__ADD__LID', ah4s_integers_intu_u_00)).
fof(12, axiom,![X20]:![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),X20))))<=>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_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),X20)))),file('i/f/integer/INT__ADD__LID', ah4s_integers_TINTu_u_EQu_u_EQUIV)).
fof(13, axiom,![X2]:![X22]:![X23]:![X24]:![X10]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(t_fun(X2,X22),X24),s(t_fun(X22,X2),X23))))=>![X1]:![X3]:(s(X22,X1)=s(X22,X3)<=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X10),s(X2,happ(s(t_fun(X22,X2),X23),s(X22,X1))))),s(X2,happ(s(t_fun(X22,X2),X23),s(X22,X3)))))))),file('i/f/integer/INT__ADD__LID', ah4s_quotients_EQUALSu_u_PRS)).
fof(15, axiom,![X22]:![X2]:![X23]:![X24]:![X25]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X25),s(t_fun(X2,X22),X24),s(t_fun(X22,X2),X23))))=>![X15]:![X14]:(p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X25),s(X2,X15))),s(X2,X14))))=>p(s(t_bool,happ(s(t_fun(X2,t_bool),happ(s(t_fun(X2,t_fun(X2,t_bool)),X25),s(X2,X15))),s(X2,happ(s(t_fun(X22,X2),X23),s(X22,happ(s(t_fun(X2,X22),X24),s(X2,X14)))))))))),file('i/f/integer/INT__ADD__LID', ah4s_quotients_REPu_u_ABSu_u_RSP)).
fof(16, axiom,![X1]: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),h4s_integers_tintu_u_0),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),X1)))),file('i/f/integer/INT__ADD__LID', ah4s_integers_TINTu_u_ADDu_u_LID)).
# SZS output end CNFRefutation
