# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:(?[X3]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),X3))))<=>(p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),h4s_lists_nil))))|?[X4]:?[X5]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),X2),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X4))),s(t_h4s_lists_list(X1),X5)))))))),file('i/f/list/EXISTS__LIST', ch4s_lists_EXISTSu_u_LIST)).
fof(2, axiom,p(s(t_bool,t0)),file('i/f/list/EXISTS__LIST', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/list/EXISTS__LIST', aHLu_FALSITY)).
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/list/EXISTS__LIST', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(10, axiom,![X5]:(s(t_bool,X5)=s(t_bool,t0)<=>p(s(t_bool,X5))),file('i/f/list/EXISTS__LIST', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(42, axiom,![X5]:(s(t_bool,f)=s(t_bool,X5)<=>~(p(s(t_bool,X5)))),file('i/f/list/EXISTS__LIST', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(50, axiom,(p(s(t_bool,f))<=>![X5]:p(s(t_bool,X5))),file('i/f/list/EXISTS__LIST', ah4s_bools_Fu_u_DEF)).
fof(66, axiom,![X1]:![X3]:(s(t_h4s_lists_list(X1),X3)=s(t_h4s_lists_list(X1),h4s_lists_nil)|?[X4]:?[X5]:s(t_h4s_lists_list(X1),X3)=s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(X1,t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_lists_cons),s(X1,X4))),s(t_h4s_lists_list(X1),X5)))),file('i/f/list/EXISTS__LIST', ah4s_lists_listu_u_nchotomy)).
# SZS output end CNFRefutation
