# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:((p(s(t_bool,h4s_relations_transitive(s(t_fun(X1,t_fun(X1,t_bool)),X2))))&p(s(t_bool,h4s_relations_total(s(t_fun(X1,t_fun(X1,t_bool)),X2)))))=>p(s(t_bool,h4s_sortings_sorted(s(t_fun(X1,t_fun(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(t_fun(X1,t_fun(X1,t_bool)),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_sortings_qsort3),s(t_fun(X1,t_fun(X1,t_bool)),X2))),s(t_h4s_lists_list(X1),X3))))))),file('i/f/sorting/QSORT3__SORTED', ch4s_sortings_QSORT3u_u_SORTED)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/sorting/QSORT3__SORTED', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/sorting/QSORT3__SORTED', aHLu_FALSITY)).
fof(5, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)<=>p(s(t_bool,X4))),file('i/f/sorting/QSORT3__SORTED', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(6, axiom,![X1]:![X2]:((p(s(t_bool,h4s_relations_transitive(s(t_fun(X1,t_fun(X1,t_bool)),X2))))&p(s(t_bool,h4s_relations_total(s(t_fun(X1,t_fun(X1,t_bool)),X2)))))=>p(s(t_bool,h4s_sortings_sorts(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),h4s_sortings_qsort3),s(t_fun(X1,t_fun(X1,t_bool)),X2))))),file('i/f/sorting/QSORT3__SORTED', ah4s_sortings_QSORT3u_u_SORTS)).
fof(7, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/sorting/QSORT3__SORTED', aHLu_BOOLu_CASES)).
fof(9, axiom,![X1]:![X7]:![X2]:(p(s(t_bool,h4s_sortings_sorts(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),X7),s(t_fun(X1,t_fun(X1,t_bool)),X2))))<=>![X10]:(p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X10),s(t_h4s_lists_list(X1),happ(s(t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1)),happ(s(t_fun(t_fun(X1,t_fun(X1,t_bool)),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),X7),s(t_fun(X1,t_fun(X1,t_bool)),X2))),s(t_h4s_lists_list(X1),X10))))))&p(s(t_bool,h4s_sortings_sorted(s(t_fun(X1,t_fun(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(t_fun(X1,t_fun(X1,t_bool)),t_fun(t_h4s_lists_list(X1),t_h4s_lists_list(X1))),X7),s(t_fun(X1,t_fun(X1,t_bool)),X2))),s(t_h4s_lists_list(X1),X10)))))))),file('i/f/sorting/QSORT3__SORTED', ah4s_sortings_SORTSu_u_DEF)).
# SZS output end CNFRefutation
