# 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(X1,t_fun(X1,t_bool)),X5),s(t_fun(X1,X2),X4),s(t_fun(X2,X1),X3))))=>![X6]:s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X2),X6)))=s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_map(s(t_fun(X2,X1),X3),s(t_h4s_lists_list(X2),X6)))))),file('i/f/quotient_list/NULL__PRS', ch4s_quotientu_u_lists_NULLu_u_PRS)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/quotient_list/NULL__PRS', aHLu_TRUTH)).
fof(4, axiom,![X7]:(s(t_bool,X7)=s(t_bool,t)|s(t_bool,X7)=s(t_bool,f)),file('i/f/quotient_list/NULL__PRS', aHLu_BOOLu_CASES)).
fof(9, axiom,![X7]:(s(t_bool,t)=s(t_bool,X7)<=>p(s(t_bool,X7))),file('i/f/quotient_list/NULL__PRS', ah4s_bools_EQu_u_CLAUSESu_c0)).
fof(11, axiom,![X7]:(s(t_bool,f)=s(t_bool,X7)<=>~(p(s(t_bool,X7)))),file('i/f/quotient_list/NULL__PRS', ah4s_bools_EQu_u_CLAUSESu_c2)).
fof(12, axiom,![X1]:p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_nil)))),file('i/f/quotient_list/NULL__PRS', ah4s_lists_NULL0u_c0)).
fof(13, axiom,![X1]:![X7]:![X10]:~(p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X10),s(t_h4s_lists_list(X1),X7))))))),file('i/f/quotient_list/NULL__PRS', ah4s_lists_NULL0u_c1)).
fof(14, axiom,![X1]:![X2]:![X11]:s(t_h4s_lists_list(X2),h4s_lists_map(s(t_fun(X1,X2),X11),s(t_h4s_lists_list(X1),h4s_lists_nil)))=s(t_h4s_lists_list(X2),h4s_lists_nil),file('i/f/quotient_list/NULL__PRS', ah4s_lists_MAP0u_c0)).
fof(15, axiom,![X2]:![X1]:![X7]:![X10]:![X11]:s(t_h4s_lists_list(X2),h4s_lists_map(s(t_fun(X1,X2),X11),s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X10),s(t_h4s_lists_list(X1),X7)))))=s(t_h4s_lists_list(X2),h4s_lists_cons(s(X2,happ(s(t_fun(X1,X2),X11),s(X1,X10))),s(t_h4s_lists_list(X2),h4s_lists_map(s(t_fun(X1,X2),X11),s(t_h4s_lists_list(X1),X7))))),file('i/f/quotient_list/NULL__PRS', ah4s_lists_MAP0u_c1)).
fof(16, axiom,![X1]:![X6]:(s(t_h4s_lists_list(X1),X6)=s(t_h4s_lists_list(X1),h4s_lists_nil)|?[X10]:?[X7]:s(t_h4s_lists_list(X1),X6)=s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X10),s(t_h4s_lists_list(X1),X7)))),file('i/f/quotient_list/NULL__PRS', ah4s_lists_listu_u_nchotomy)).
# SZS output end CNFRefutation
