# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:((p(s(t_bool,h4s_relations_total(s(t_fun(X1,t_fun(X1,t_bool)),X2))))&(p(s(t_bool,h4s_relations_transitive(s(t_fun(X1,t_fun(X1,t_bool)),X2))))&p(s(t_bool,h4s_relations_antisymmetric(s(t_fun(X1,t_fun(X1,t_bool)),X2))))))=>![X3]:![X4]:(s(t_h4s_lists_list(X1),h4s_sortings_qsort(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(t_h4s_lists_list(X1),X3)))=s(t_h4s_lists_list(X1),h4s_sortings_qsort(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(t_h4s_lists_list(X1),X4)))<=>p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X3),s(t_h4s_lists_list(X1),X4)))))),file('i/f/sorting/QSORT__eq__if__PERM', ch4s_sortings_QSORTu_u_equ_u_ifu_u_PERM)).
fof(2, axiom,![X5]:![X6]:((p(s(t_bool,X6))=>p(s(t_bool,X5)))=>((p(s(t_bool,X5))=>p(s(t_bool,X6)))=>s(t_bool,X6)=s(t_bool,X5))),file('i/f/sorting/QSORT__eq__if__PERM', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(20, axiom,![X1]:![X16]:![X14]:![X15]:((p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X15),s(t_h4s_lists_list(X1),X14))))&p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X14),s(t_h4s_lists_list(X1),X16)))))=>p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X15),s(t_h4s_lists_list(X1),X16))))),file('i/f/sorting/QSORT__eq__if__PERM', ah4s_sortings_PERMu_u_TRANS)).
fof(21, axiom,![X1]:![X4]:![X3]:s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X3),s(t_h4s_lists_list(X1),X4)))=s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X4),s(t_h4s_lists_list(X1),X3))),file('i/f/sorting/QSORT__eq__if__PERM', ah4s_sortings_PERMu_u_SYM)).
fof(22, axiom,![X1]:![X2]:![X17]:p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X17),s(t_h4s_lists_list(X1),h4s_sortings_qsort(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(t_h4s_lists_list(X1),X17)))))),file('i/f/sorting/QSORT__eq__if__PERM', ah4s_sortings_QSORTu_u_PERM)).
fof(23, 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_antisymmetric(s(t_fun(X1,t_fun(X1,t_bool)),X2)))))=>![X3]:![X4]:((p(s(t_bool,h4s_sortings_sorted(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(t_h4s_lists_list(X1),X3))))&(p(s(t_bool,h4s_sortings_sorted(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(t_h4s_lists_list(X1),X4))))&p(s(t_bool,h4s_sortings_perm(s(t_h4s_lists_list(X1),X3),s(t_h4s_lists_list(X1),X4))))))=>s(t_h4s_lists_list(X1),X3)=s(t_h4s_lists_list(X1),X4))),file('i/f/sorting/QSORT__eq__if__PERM', ah4s_sortings_SORTEDu_u_PERMu_u_EQ)).
fof(24, axiom,![X1]:![X2]:![X17]:((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),h4s_sortings_qsort(s(t_fun(X1,t_fun(X1,t_bool)),X2),s(t_h4s_lists_list(X1),X17))))))),file('i/f/sorting/QSORT__eq__if__PERM', ah4s_sortings_QSORTu_u_SORTED)).
# SZS output end CNFRefutation
