# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:s(t_h4s_integers_int,h4s_omegas_sumc(s(t_h4s_lists_list(t_h4s_integers_int),h4s_lists_map(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),X1),s(t_h4s_lists_list(t_h4s_integers_int),h4s_lists_cons(s(t_h4s_integers_int,X2),s(t_h4s_lists_list(t_h4s_integers_int),h4s_lists_nil))))),s(t_h4s_lists_list(t_h4s_integers_int),h4s_lists_cons(s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_lists_list(t_h4s_integers_int),h4s_lists_nil)))))=s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),X1),s(t_h4s_integers_int,X2))),file('i/f/Omega/sumc__singleton', ch4s_Omegas_sumcu_u_singleton)).
fof(6, axiom,![X13]:![X14]:![X15]:![X2]:s(t_h4s_integers_int,h4s_omegas_sumc(s(t_h4s_lists_list(t_h4s_integers_int),h4s_lists_cons(s(t_h4s_integers_int,X2),s(t_h4s_lists_list(t_h4s_integers_int),X15))),s(t_h4s_lists_list(t_h4s_integers_int),h4s_lists_cons(s(t_h4s_integers_int,X14),s(t_h4s_lists_list(t_h4s_integers_int),X13)))))=s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X2),s(t_h4s_integers_int,X14))))),s(t_h4s_integers_int,h4s_omegas_sumc(s(t_h4s_lists_list(t_h4s_integers_int),X15),s(t_h4s_lists_list(t_h4s_integers_int),X13))))),file('i/f/Omega/sumc__singleton', ah4s_Omegas_sumcu_u_thmu_c2)).
fof(7, axiom,![X13]:s(t_h4s_integers_int,h4s_omegas_sumc(s(t_h4s_lists_list(t_h4s_integers_int),h4s_lists_nil),s(t_h4s_lists_list(t_h4s_integers_int),X13)))=s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))),file('i/f/Omega/sumc__singleton', ah4s_Omegas_sumcu_u_thmu_c0)).
fof(19, axiom,![X5]:s(t_h4s_integers_int,h4s_integers_intu_u_mul(s(t_h4s_integers_int,X5),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))=s(t_h4s_integers_int,X5),file('i/f/Omega/sumc__singleton', ah4s_integers_INTu_u_MULu_u_RID)).
fof(21, axiom,![X9]:![X3]:![X10]:![X20]:![X1]:s(t_h4s_lists_list(X9),h4s_lists_map(s(t_fun(X3,X9),X1),s(t_h4s_lists_list(X3),h4s_lists_cons(s(X3,X20),s(t_h4s_lists_list(X3),X10)))))=s(t_h4s_lists_list(X9),h4s_lists_cons(s(X9,happ(s(t_fun(X3,X9),X1),s(X3,X20))),s(t_h4s_lists_list(X9),h4s_lists_map(s(t_fun(X3,X9),X1),s(t_h4s_lists_list(X3),X10))))),file('i/f/Omega/sumc__singleton', ah4s_lists_MAP0u_c1)).
fof(22, axiom,![X3]:![X9]:![X1]:s(t_h4s_lists_list(X9),h4s_lists_map(s(t_fun(X3,X9),X1),s(t_h4s_lists_list(X3),h4s_lists_nil)))=s(t_h4s_lists_list(X9),h4s_lists_nil),file('i/f/Omega/sumc__singleton', ah4s_lists_MAP0u_c0)).
fof(42, axiom,![X5]:s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,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,X5)))=s(t_h4s_integers_int,X5),file('i/f/Omega/sumc__singleton', ah4s_integers_INTu_u_ADDu_u_LID)).
fof(44, axiom,![X4]:![X5]:s(t_h4s_integers_int,happ(s(t_fun(t_h4s_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,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_integers_int,t_h4s_integers_int),happ(s(t_fun(t_h4s_integers_int,t_fun(t_h4s_integers_int,t_h4s_integers_int)),h4s_integers_intu_u_add),s(t_h4s_integers_int,X4))),s(t_h4s_integers_int,X5))),file('i/f/Omega/sumc__singleton', ah4s_integers_INTu_u_ADDu_u_COMM)).
# SZS output end CNFRefutation
