# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:![X2]:![X3]:![X4]:s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X3),s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X2),s(t_h4s_lists_list(X1),X4)))))))=s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X2),s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X3),s(t_h4s_lists_list(X1),X4))))))),file('i/f/sorting/PERM__FUN__SWAP__AT__FRONT', ch4s_sortings_PERMu_u_FUNu_u_SWAPu_u_ATu_u_FRONT)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/sorting/PERM__FUN__SWAP__AT__FRONT', aHLu_TRUTH)).
fof(7, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)<=>p(s(t_bool,X9))),file('i/f/sorting/PERM__FUN__SWAP__AT__FRONT', ah4s_bools_EQu_u_CLAUSESu_c1)).
fof(8, axiom,![X1]:![X10]:p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(X1),X10))),s(t_h4s_lists_list(X1),X10)))),file('i/f/sorting/PERM__FUN__SWAP__AT__FRONT', ah4s_sortings_PERMu_u_REFL)).
fof(9, axiom,![X1]:![X2]:![X3]:(p(s(t_bool,happ(s(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),h4s_sortings_perm(s(t_h4s_lists_list(X1),X3)))=s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(X1),X2)))),file('i/f/sorting/PERM__FUN__SWAP__AT__FRONT', ah4s_sortings_PERMu_u_EQUIVALENCEu_u_ALTu_u_DEF)).
fof(10, axiom,![X1]:![X2]:![X3]:![X11]:![X12]:s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X3),s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X2),s(t_h4s_lists_list(X1),X12))))))),s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X2),s(t_h4s_lists_list(X1),h4s_lists_cons(s(X1,X3),s(t_h4s_lists_list(X1),X11)))))))=s(t_bool,happ(s(t_fun(t_h4s_lists_list(X1),t_bool),h4s_sortings_perm(s(t_h4s_lists_list(X1),X12))),s(t_h4s_lists_list(X1),X11))),file('i/f/sorting/PERM__FUN__SWAP__AT__FRONT', ah4s_sortings_PERMu_u_SWAPu_u_ATu_u_FRONT)).
fof(11, axiom,~(p(s(t_bool,f))),file('i/f/sorting/PERM__FUN__SWAP__AT__FRONT', aHLu_FALSITY)).
fof(12, axiom,![X9]:(s(t_bool,X9)=s(t_bool,t)|s(t_bool,X9)=s(t_bool,f)),file('i/f/sorting/PERM__FUN__SWAP__AT__FRONT', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
