# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:![X5]:(p(s(t_bool,h4s_quotients_quotient(s(t_fun(X2,t_fun(X2,t_bool)),X5),s(t_fun(X2,X1),X4),s(t_fun(X1,X2),X3))))=>![X6]:![X7]:(p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X2),t_bool),happ(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X2),t_bool)),h4s_lists_listu_u_rel(s(t_fun(X2,t_fun(X2,t_bool)),X5))),s(t_h4s_lists_list(X2),X6))),s(t_h4s_lists_list(X2),X7))))=>s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X2),X6)))=s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X2),X7))))),file('i/f/quotient_list/NULL__RSP', ch4s_quotientu_u_lists_NULLu_u_RSP)).
fof(3, axiom,![X2]:![X9]:![X10]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X2),happ(s(t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X2)),happ(s(t_fun(X2,t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X2))),h4s_lists_cons),s(X2,X10))),s(t_h4s_lists_list(X2),X9)))))=s(t_bool,f),file('i/f/quotient_list/NULL__RSP', ah4s_lists_NULLu_u_DEFu_c1)).
fof(4, axiom,![X2]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X2),h4s_lists_nil)))=s(t_bool,t),file('i/f/quotient_list/NULL__RSP', ah4s_lists_NULLu_u_DEFu_c0)).
fof(7, axiom,![X11]:![X12]:((p(s(t_bool,X12))=>p(s(t_bool,X11)))=>((p(s(t_bool,X11))=>p(s(t_bool,X12)))=>s(t_bool,X12)=s(t_bool,X11))),file('i/f/quotient_list/NULL__RSP', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(28, axiom,![X2]:![X1]:![X29]:![X30]:![X5]:s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),happ(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X1),t_bool)),h4s_lists_listu_u_rel(s(t_fun(X2,t_fun(X1,t_bool)),X5))),s(t_h4s_lists_list(X2),happ(s(t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X2)),happ(s(t_fun(X2,t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X2))),h4s_lists_cons),s(X2,X30))),s(t_h4s_lists_list(X2),X29))))),s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_bool,f),file('i/f/quotient_list/NULL__RSP', ah4s_lists_LISTu_u_RELu_u_defu_c1)).
fof(29, axiom,![X2]:![X1]:![X31]:![X32]:![X5]:s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),happ(s(t_fun(t_h4s_lists_list(X2),t_fun(t_h4s_lists_list(X1),t_bool)),h4s_lists_listu_u_rel(s(t_fun(X2,t_fun(X1,t_bool)),X5))),s(t_h4s_lists_list(X2),h4s_lists_nil))),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,X32))),s(t_h4s_lists_list(X1),X31)))))=s(t_bool,f),file('i/f/quotient_list/NULL__RSP', ah4s_lists_LISTu_u_RELu_u_defu_c2)).
fof(44, axiom,~(p(s(t_bool,f))),file('i/f/quotient_list/NULL__RSP', aHLu_FALSITY)).
fof(47, axiom,![X9]:(s(t_bool,f)=s(t_bool,X9)<=>~(p(s(t_bool,X9)))),file('i/f/quotient_list/NULL__RSP', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(59, axiom,![X2]:![X41]:(s(t_h4s_lists_list(X2),X41)=s(t_h4s_lists_list(X2),h4s_lists_nil)|?[X10]:?[X9]:s(t_h4s_lists_list(X2),X41)=s(t_h4s_lists_list(X2),happ(s(t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X2)),happ(s(t_fun(X2,t_fun(t_h4s_lists_list(X2),t_h4s_lists_list(X2))),h4s_lists_cons),s(X2,X10))),s(t_h4s_lists_list(X2),X9)))),file('i/f/quotient_list/NULL__RSP', ah4s_lists_listu_u_nchotomy)).
fof(64, axiom,p(s(t_bool,t)),file('i/f/quotient_list/NULL__RSP', aHLu_TRUTH)).
fof(65, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/quotient_list/NULL__RSP', aHLu_BOOLu_CASES)).
fof(67, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/quotient_list/NULL__RSP', ah4s_bools_EQu_u_CLAUSESu_c1)).
# SZS output end CNFRefutation
