# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:(p(s(t_bool,h4s_paths_mem(s(X2,X4),s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3))))))<=>s(X2,X4)=s(X2,X3)),file('i/f/path/mem__thm_c0', ch4s_paths_memu_u_thmu_c0)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/path/mem__thm_c0', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/path/mem__thm_c0', aHLu_FALSITY)).
fof(4, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t)|s(t_bool,X5)=s(t_bool,f)),file('i/f/path/mem__thm_c0', aHLu_BOOLu_CASES)).
fof(6, axiom,![X6]:![X7]:((p(s(t_bool,X7))=>p(s(t_bool,X6)))=>((p(s(t_bool,X6))=>p(s(t_bool,X7)))=>s(t_bool,X7)=s(t_bool,X6))),file('i/f/path/mem__thm_c0', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X2]:![X1]:![X4]:![X8]:(p(s(t_bool,h4s_paths_mem(s(X2,X4),s(t_h4s_paths_path(X2,X1),X8))))<=>?[X9]:(p(s(t_bool,h4s_bools_in(s(t_h4s_nums_num,X9),s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(X2,X1),X8))))))&s(X2,X4)=s(X2,h4s_paths_el(s(t_h4s_nums_num,X9),s(t_h4s_paths_path(X2,X1),X8))))),file('i/f/path/mem__thm_c0', ah4s_paths_memu_u_def)).
fof(11, axiom,![X1]:![X2]:![X3]:s(X2,h4s_paths_first(s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))))=s(X2,X3),file('i/f/path/mem__thm_c0', ah4s_paths_firstu_u_thmu_c0)).
fof(12, axiom,![X1]:![X2]:![X3]:s(t_fun(t_h4s_nums_num,t_bool),h4s_paths_pl(s(t_h4s_paths_path(X2,X1),h4s_paths_stoppedu_u_at(s(X2,X3)))))=s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_insert(s(t_h4s_nums_num,h4s_nums_0),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_empty))),file('i/f/path/mem__thm_c0', ah4s_paths_PLu_u_thmu_c0)).
fof(13, axiom,![X2]:![X1]:![X8]:s(X2,h4s_paths_el(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_paths_path(X2,X1),X8)))=s(X2,h4s_paths_first(s(t_h4s_paths_path(X2,X1),X8))),file('i/f/path/mem__thm_c0', ah4s_paths_elu_u_defu_c0)).
fof(14, axiom,![X2]:![X3]:~(p(s(t_bool,h4s_bools_in(s(X2,X3),s(t_fun(X2,t_bool),h4s_predu_u_sets_empty))))),file('i/f/path/mem__thm_c0', ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY)).
fof(15, axiom,![X2]:![X10]:![X3]:![X4]:(p(s(t_bool,h4s_bools_in(s(X2,X3),s(t_fun(X2,t_bool),h4s_predu_u_sets_insert(s(X2,X10),s(t_fun(X2,t_bool),X4))))))<=>(s(X2,X3)=s(X2,X10)|p(s(t_bool,h4s_bools_in(s(X2,X3),s(t_fun(X2,t_bool),X4)))))),file('i/f/path/mem__thm_c0', ah4s_predu_u_sets_INu_u_INSERT)).
# SZS output end CNFRefutation
