# 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),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X1),X3))),s(t_h4s_lists_list(X1),X2))))<=>s(t_fun(t_h4s_lists_list(X1),t_bool),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X1),X3)))=s(t_fun(t_h4s_lists_list(X1),t_bool),happ(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_bool)),h4s_sortings_perm),s(t_h4s_lists_list(X1),X2)))),file('i/f/sorting/PERM__EQUIVALENCE__ALT__DEF', ch4s_sortings_PERMu_u_EQUIVALENCEu_u_ALTu_u_DEF)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/sorting/PERM__EQUIVALENCE__ALT__DEF', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/sorting/PERM__EQUIVALENCE__ALT__DEF', aHLu_FALSITY)).
fof(4, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/sorting/PERM__EQUIVALENCE__ALT__DEF', aHLu_BOOLu_CASES)).
fof(8, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/sorting/PERM__EQUIVALENCE__ALT__DEF', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(9, axiom,![X1]:![X9]:(p(s(t_bool,h4s_relations_equivalence(s(t_fun(X1,t_fun(X1,t_bool)),X9))))<=>![X3]:![X2]:(p(s(t_bool,happ(s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X9),s(X1,X3))),s(X1,X2))))<=>s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X9),s(X1,X3)))=s(t_fun(X1,t_bool),happ(s(t_fun(X1,t_fun(X1,t_bool)),X9),s(X1,X2))))),file('i/f/sorting/PERM__EQUIVALENCE__ALT__DEF', ah4s_relations_ALTu_u_equivalence)).
fof(10, axiom,![X1]:p(s(t_bool,h4s_relations_equivalence(s(t_fun(t_h4s_lists_list(X1),t_fun(t_h4s_lists_list(X1),t_bool)),h4s_sortings_perm)))),file('i/f/sorting/PERM__EQUIVALENCE__ALT__DEF', ah4s_sortings_PERMu_u_EQUIVALENCE)).
# SZS output end CNFRefutation
