# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, axiom,p(s(t_bool,t)),file('i/f/list/EXISTS__CONG', aHLu_TRUTH)).
fof(2, axiom,~(p(s(t_bool,f))),file('i/f/list/EXISTS__CONG', aHLu_FALSITY)).
fof(3, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)|s(t_bool,X1)=s(t_bool,f)),file('i/f/list/EXISTS__CONG', aHLu_BOOLu_CASES)).
fof(5, axiom,![X7]:![X8]:((p(s(t_bool,X8))=>p(s(t_bool,X7)))=>((p(s(t_bool,X7))=>p(s(t_bool,X8)))=>s(t_bool,X8)=s(t_bool,X7))),file('i/f/list/EXISTS__CONG', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X9]:![X12]:![X13]:(p(s(t_bool,h4s_lists_exists(s(t_fun(X9,t_bool),X13),s(t_h4s_lists_list(X9),X12))))<=>?[X14]:(p(s(t_bool,h4s_bools_in(s(X9,X14),s(t_fun(X9,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X9),X12))))))&p(s(t_bool,happ(s(t_fun(X9,t_bool),X13),s(X9,X14)))))),file('i/f/list/EXISTS__CONG', ah4s_lists_EXISTSu_u_MEM)).
fof(24, axiom,![X1]:(s(t_bool,X1)=s(t_bool,t)<=>p(s(t_bool,X1))),file('i/f/list/EXISTS__CONG', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(37, axiom,![X9]:![X13]:s(t_bool,h4s_lists_exists(s(t_fun(X9,t_bool),X13),s(t_h4s_lists_list(X9),h4s_lists_nil)))=s(t_bool,f),file('i/f/list/EXISTS__CONG', ah4s_lists_EXISTSu_u_DEFu_c0)).
fof(53, axiom,![X9]:s(t_h4s_lists_list(X9),h4s_lists_nil)=s(t_h4s_lists_list(X9),h4s_lists_u_20u_40indu_u_typelist0),file('i/f/list/EXISTS__CONG', ah4s_lists_NIL0)).
fof(60, axiom,![X1]:(s(t_bool,f)=s(t_bool,X1)<=>~(p(s(t_bool,X1)))),file('i/f/list/EXISTS__CONG', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(133, conjecture,![X9]:![X19]:![X20]:![X51]:![X13]:((s(t_h4s_lists_list(X9),X20)=s(t_h4s_lists_list(X9),X19)&![X6]:(p(s(t_bool,h4s_bools_in(s(X9,X6),s(t_fun(X9,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(X9),X19))))))=>s(t_bool,happ(s(t_fun(X9,t_bool),X13),s(X9,X6)))=s(t_bool,happ(s(t_fun(X9,t_bool),X51),s(X9,X6)))))=>s(t_bool,h4s_lists_exists(s(t_fun(X9,t_bool),X13),s(t_h4s_lists_list(X9),X20)))=s(t_bool,h4s_lists_exists(s(t_fun(X9,t_bool),X51),s(t_h4s_lists_list(X9),X19)))),file('i/f/list/EXISTS__CONG', ch4s_lists_EXISTSu_u_CONG)).
# SZS output end CNFRefutation
