# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:(s(t_h4s_pairs_prod(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),h4s_pairs_u_2c(s(t_h4s_lists_list(X1),X3),s(t_h4s_lists_list(X1),X2)))=s(t_h4s_pairs_prod(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),h4s_sortings_part(s(t_fun(X1,t_bool),X6),s(t_h4s_lists_list(X1),X7),s(t_h4s_lists_list(X1),X5),s(t_h4s_lists_list(X1),X4)))=>(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X3))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X7))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X5))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X4))))))))&p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X2))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X7))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X5))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X4)))))))))),file('i/f/sorting/PART__LENGTH__LEM', ch4s_sortings_PARTu_u_LENGTHu_u_LEM)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/sorting/PART__LENGTH__LEM', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/sorting/PART__LENGTH__LEM', aHLu_FALSITY)).
fof(10, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)<=>p(s(t_bool,X8))),file('i/f/sorting/PART__LENGTH__LEM', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(27, axiom,![X20]:![X21]:p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X20)))))),file('i/f/sorting/PART__LENGTH__LEM', ah4s_arithmetics_LESSu_u_EQu_u_ADD)).
fof(30, axiom,![X20]:![X21]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X20)))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X21))),file('i/f/sorting/PART__LENGTH__LEM', ah4s_arithmetics_ADDu_u_SYM)).
fof(31, axiom,![X3]:![X20]:![X21]:s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X3)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,X3))),file('i/f/sorting/PART__LENGTH__LEM', ah4s_arithmetics_ADDu_u_ASSOC)).
fof(33, axiom,![X3]:![X20]:![X21]:s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X3)))))=s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X20),s(t_h4s_nums_num,X3))),file('i/f/sorting/PART__LENGTH__LEM', ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ)).
fof(34, axiom,![X20]:![X21]:(~(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X21),s(t_h4s_nums_num,X20)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X20))),s(t_h4s_nums_num,X21))))),file('i/f/sorting/PART__LENGTH__LEM', ah4s_arithmetics_NOTu_u_LEQ)).
fof(40, axiom,![X1]:![X2]:![X3]:![X4]:![X5]:![X6]:![X7]:(s(t_h4s_pairs_prod(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),h4s_pairs_u_2c(s(t_h4s_lists_list(X1),X3),s(t_h4s_lists_list(X1),X2)))=s(t_h4s_pairs_prod(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),h4s_sortings_part(s(t_fun(X1,t_bool),X6),s(t_h4s_lists_list(X1),X7),s(t_h4s_lists_list(X1),X5),s(t_h4s_lists_list(X1),X4)))=>s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X7))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X5))))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X4)))))=s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X3))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(X1),X2)))))),file('i/f/sorting/PART__LENGTH__LEM', ah4s_sortings_PARTu_u_LENGTH)).
fof(42, axiom,![X8]:(s(t_bool,X8)=s(t_bool,t)|s(t_bool,X8)=s(t_bool,f)),file('i/f/sorting/PART__LENGTH__LEM', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
