%---------------- iProver v3.0 (CASC-27) ----------------%


------  iProver source info 

git: date: 2019-08-21 14:25:56 +0100
git: sha1: aef4729e525848973f587b098cdb2be67e368c05
git: non_committed_changes: true
git: last_make_outside_of_git: false


------ Parsing...
------ Clausification by vclausify_rel  & Parsing by iProver...



------ Preprocessing... sf_s  rm: 1 0s  sf_e 

------ Preprocessing... gs_s  sp: 4 0s  gs_e  snvd_s sp: 0 0s snvd_e 

------ Preprocessing... sf_s  rm: 3 0s  sf_e  sf_s  rm: 0 0s  sf_e 
------ Proving...
------ Problem Properties 


clauses                                 35
conjectures                             5
EPR                                     9
Horn                                    30
unary                                   6
binary                                  12
lits                                    100
lits eq                                 10

------ Input Options Time Limit: Unbounded


------ Current options:





------ Proving...


% SZS status Theorem for HL405138+2.p

% SZS output start CNFRefutation for HL405138+2.p

fof(f21,axiom,(
  ! [X8] : (ne(X8) => ! [X10] : (ne(X10) => ! [X11] : (mem(X11,X10) => ! [X12] : (mem(X12,ty_2Elist_2Elist(X10)) => (ap(ap(c_2Epred__set_2EINSERT(X10),X11),ap(c_2Elist_2ELIST__TO__SET(X10),X12)) = ap(c_2Elist_2ELIST__TO__SET(X10),ap(ap(c_2Elist_2ECONS(X10),X11),X12)) & ap(c_2Elist_2ELIST__TO__SET(X8),c_2Elist_2ENIL(X8)) = c_2Epred__set_2EEMPTY(X8))))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL405138+2.p',unknown)).

fof(f24,plain,(
  ! [X0] : (ne(X0) => ! [X1] : (ne(X1) => ! [X2] : (mem(X2,X1) => ! [X3] : (mem(X3,ty_2Elist_2Elist(X1)) => (ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) = ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) & ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) = c_2Epred__set_2EEMPTY(X0))))))),
  inference(rectify,[],[f21])).

fof(f39,plain,(
  ! [X0] : (! [X1] : (! [X2] : (! [X3] : ((ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) = ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) & ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) = c_2Epred__set_2EEMPTY(X0)) | ~mem(X3,ty_2Elist_2Elist(X1))) | ~mem(X2,X1)) | ~ne(X1)) | ~ne(X0))),
  inference(ennf_transformation,[],[f24])).

fof(f73,plain,(
  ( ! [X2,X0,X3,X1] : (ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) = c_2Epred__set_2EEMPTY(X0) | ~mem(X3,ty_2Elist_2Elist(X1)) | ~mem(X2,X1) | ~ne(X1) | ~ne(X0)) )),
  inference(cnf_transformation,[],[f39])).

fof(f22,conjecture,(
  ! [X8] : (ne(X8) => ! [X10] : (ne(X10) => ! [X11] : (mem(X11,X10) => ! [X12] : (mem(X12,ty_2Elist_2Elist(X10)) => (ap(ap(c_2Epred__set_2EINSERT(X10),X11),ap(c_2Elist_2ELIST__TO__SET(X10),X12)) = ap(c_2Elist_2ELIST__TO__SET(X10),ap(ap(c_2Elist_2ECONS(X10),X11),X12)) & ap(c_2Elist_2ELIST__TO__SET(X8),c_2Elist_2ENIL(X8)) = c_2Epred__set_2EEMPTY(X8))))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL405138+2.p',unknown)).

fof(f23,negated_conjecture,(
  ~! [X8] : (ne(X8) => ! [X10] : (ne(X10) => ! [X11] : (mem(X11,X10) => ! [X12] : (mem(X12,ty_2Elist_2Elist(X10)) => (ap(ap(c_2Epred__set_2EINSERT(X10),X11),ap(c_2Elist_2ELIST__TO__SET(X10),X12)) = ap(c_2Elist_2ELIST__TO__SET(X10),ap(ap(c_2Elist_2ECONS(X10),X11),X12)) & ap(c_2Elist_2ELIST__TO__SET(X8),c_2Elist_2ENIL(X8)) = c_2Epred__set_2EEMPTY(X8))))))),
  inference(negated_conjecture,[],[f22])).

fof(f25,plain,(
  ~! [X0] : (ne(X0) => ! [X1] : (ne(X1) => ! [X2] : (mem(X2,X1) => ! [X3] : (mem(X3,ty_2Elist_2Elist(X1)) => (ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) = ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) & ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) = c_2Epred__set_2EEMPTY(X0))))))),
  inference(rectify,[],[f23])).

fof(f40,plain,(
  ? [X0] : (? [X1] : (? [X2] : (? [X3] : ((ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) != ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) != c_2Epred__set_2EEMPTY(X0)) & mem(X3,ty_2Elist_2Elist(X1))) & mem(X2,X1)) & ne(X1)) & ne(X0))),
  inference(ennf_transformation,[],[f25])).

fof(f61,plain,(
  ( ! [X2,X0,X1] : (? [X3] : ((ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) != ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) != c_2Epred__set_2EEMPTY(X0)) & mem(X3,ty_2Elist_2Elist(X1))) => ((ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),sK3)) != ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),sK3)) | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) != c_2Epred__set_2EEMPTY(X0)) & mem(sK3,ty_2Elist_2Elist(X1)))) )),
  introduced(choice_axiom,[])).

fof(f60,plain,(
  ( ! [X0,X1] : (? [X2] : (? [X3] : ((ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) != ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) != c_2Epred__set_2EEMPTY(X0)) & mem(X3,ty_2Elist_2Elist(X1))) & mem(X2,X1)) => (? [X3] : ((ap(ap(c_2Epred__set_2EINSERT(X1),sK2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) != ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),sK2),X3)) | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) != c_2Epred__set_2EEMPTY(X0)) & mem(X3,ty_2Elist_2Elist(X1))) & mem(sK2,X1))) )),
  introduced(choice_axiom,[])).

fof(f59,plain,(
  ( ! [X0] : (? [X1] : (? [X2] : (? [X3] : ((ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) != ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) != c_2Epred__set_2EEMPTY(X0)) & mem(X3,ty_2Elist_2Elist(X1))) & mem(X2,X1)) & ne(X1)) => (? [X2] : (? [X3] : ((ap(ap(c_2Epred__set_2EINSERT(sK1),X2),ap(c_2Elist_2ELIST__TO__SET(sK1),X3)) != ap(c_2Elist_2ELIST__TO__SET(sK1),ap(ap(c_2Elist_2ECONS(sK1),X2),X3)) | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) != c_2Epred__set_2EEMPTY(X0)) & mem(X3,ty_2Elist_2Elist(sK1))) & mem(X2,sK1)) & ne(sK1))) )),
  introduced(choice_axiom,[])).

fof(f58,plain,(
  ? [X0] : (? [X1] : (? [X2] : (? [X3] : ((ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) != ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) != c_2Epred__set_2EEMPTY(X0)) & mem(X3,ty_2Elist_2Elist(X1))) & mem(X2,X1)) & ne(X1)) & ne(X0)) => (? [X1] : (? [X2] : (? [X3] : ((ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) != ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) | ap(c_2Elist_2ELIST__TO__SET(sK0),c_2Elist_2ENIL(sK0)) != c_2Epred__set_2EEMPTY(sK0)) & mem(X3,ty_2Elist_2Elist(X1))) & mem(X2,X1)) & ne(X1)) & ne(sK0))),
  introduced(choice_axiom,[])).

fof(f62,plain,(
  ((((ap(ap(c_2Epred__set_2EINSERT(sK1),sK2),ap(c_2Elist_2ELIST__TO__SET(sK1),sK3)) != ap(c_2Elist_2ELIST__TO__SET(sK1),ap(ap(c_2Elist_2ECONS(sK1),sK2),sK3)) | ap(c_2Elist_2ELIST__TO__SET(sK0),c_2Elist_2ENIL(sK0)) != c_2Epred__set_2EEMPTY(sK0)) & mem(sK3,ty_2Elist_2Elist(sK1))) & mem(sK2,sK1)) & ne(sK1)) & ne(sK0)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f40,f61,f60,f59,f58])).

fof(f79,plain,(
  ap(ap(c_2Epred__set_2EINSERT(sK1),sK2),ap(c_2Elist_2ELIST__TO__SET(sK1),sK3)) != ap(c_2Elist_2ELIST__TO__SET(sK1),ap(ap(c_2Elist_2ECONS(sK1),sK2),sK3)) | ap(c_2Elist_2ELIST__TO__SET(sK0),c_2Elist_2ENIL(sK0)) != c_2Epred__set_2EEMPTY(sK0)),
  inference(cnf_transformation,[],[f62])).

fof(f76,plain,(
  ne(sK1)),
  inference(cnf_transformation,[],[f62])).

fof(f77,plain,(
  mem(sK2,sK1)),
  inference(cnf_transformation,[],[f62])).

fof(f78,plain,(
  mem(sK3,ty_2Elist_2Elist(sK1))),
  inference(cnf_transformation,[],[f62])).

fof(f74,plain,(
  ( ! [X2,X0,X3,X1] : (ap(ap(c_2Epred__set_2EINSERT(X1),X2),ap(c_2Elist_2ELIST__TO__SET(X1),X3)) = ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X2),X3)) | ~mem(X3,ty_2Elist_2Elist(X1)) | ~mem(X2,X1) | ~ne(X1) | ~ne(X0)) )),
  inference(cnf_transformation,[],[f39])).

fof(f1,axiom,(
  ne(bool)),
  file('/export/starexec/sandbox/benchmark/Problems/HL405138+2.p',unknown)).

fof(f92,plain,(
  ne(bool)),
  inference(cnf_transformation,[],[f1])).

fof(f75,plain,(
  ne(sK0)),
  inference(cnf_transformation,[],[f62])).

cnf(c_1,plain,
    ( ~ mem(X0,X1)
    | ~ mem(X2,ty_2Elist_2Elist(X1))
    | ~ ne(X1)
    | ~ ne(X3)
    | ap(c_2Elist_2ELIST__TO__SET(X3),c_2Elist_2ENIL(X3)) = c_2Epred__set_2EEMPTY(X3) ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_300,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,ty_2Elist_2Elist(X0))
    | ~ ne(X0)
    | ~ ne(X1)
    | ap(c_2Elist_2ELIST__TO__SET(X1),c_2Elist_2ENIL(X1)) = c_2Epred__set_2EEMPTY(X1) ),
    inference(subtyping,[status(esa)],[c_1]) ).

cnf(c_306,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,ty_2Elist_2Elist(X0))
    | ~ ne(X0)
    | ~ sP3_iProver_split ),
    inference(splitting,
              [splitting(split),new_symbols(definition,[sP3_iProver_split])],
              [c_300]) ).

cnf(c_1307,plain,
    ( ~ mem(X0,sK1)
    | ~ mem(sK3,ty_2Elist_2Elist(sK1))
    | ~ ne(sK1)
    | ~ sP3_iProver_split ),
    inference(instantiation,[status(thm)],[c_306]) ).

cnf(c_2169,plain,
    ( ~ mem(sK3,ty_2Elist_2Elist(sK1))
    | ~ mem(sK2,sK1)
    | ~ ne(sK1)
    | ~ sP3_iProver_split ),
    inference(instantiation,[status(thm)],[c_1307]) ).

cnf(c_305,plain,
    ( ~ ne(X0)
    | ap(c_2Elist_2ELIST__TO__SET(X0),c_2Elist_2ENIL(X0)) = c_2Epred__set_2EEMPTY(X0)
    | ~ sP2_iProver_split ),
    inference(splitting,
              [splitting(split),new_symbols(definition,[sP2_iProver_split])],
              [c_300]) ).

cnf(c_311,plain,
    ( X0 != X1 | X2 != X3 | ap(X0,X2) = ap(X1,X3) ),
    theory(equality) ).

cnf(c_2,negated_conjecture,
    ( ap(ap(c_2Epred__set_2EINSERT(sK1),sK2),ap(c_2Elist_2ELIST__TO__SET(sK1),sK3)) != ap(c_2Elist_2ELIST__TO__SET(sK1),ap(ap(c_2Elist_2ECONS(sK1),sK2),sK3))
    | ap(c_2Elist_2ELIST__TO__SET(sK0),c_2Elist_2ENIL(sK0)) != c_2Epred__set_2EEMPTY(sK0) ),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_299,negated_conjecture,
    ( ap(ap(c_2Epred__set_2EINSERT(sK1),sK2),ap(c_2Elist_2ELIST__TO__SET(sK1),sK3)) != ap(c_2Elist_2ELIST__TO__SET(sK1),ap(ap(c_2Elist_2ECONS(sK1),sK2),sK3))
    | ap(c_2Elist_2ELIST__TO__SET(sK0),c_2Elist_2ENIL(sK0)) != c_2Epred__set_2EEMPTY(sK0) ),
    inference(subtyping,[status(esa)],[c_2]) ).

cnf(c_1488,plain,
    ( ap(c_2Elist_2ELIST__TO__SET(sK0),c_2Elist_2ENIL(sK0)) != c_2Epred__set_2EEMPTY(sK0)
    | ap(c_2Elist_2ELIST__TO__SET(sK1),sK3) != ap(ap(c_2Elist_2ECONS(sK1),sK2),sK3)
    | ap(c_2Epred__set_2EINSERT(sK1),sK2) != c_2Elist_2ELIST__TO__SET(sK1) ),
    inference(resolution,[status(thm)],[c_311,c_299]) ).

cnf(c_5,negated_conjecture,
    ( ne(sK1) ),
    inference(cnf_transformation,[],[f76]) ).

cnf(c_4,negated_conjecture,
    ( mem(sK2,sK1) ),
    inference(cnf_transformation,[],[f77]) ).

cnf(c_3,negated_conjecture,
    ( mem(sK3,ty_2Elist_2Elist(sK1)) ),
    inference(cnf_transformation,[],[f78]) ).

cnf(c_0,plain,
    ( ~ mem(X0,X1)
    | ~ mem(X2,ty_2Elist_2Elist(X1))
    | ~ ne(X1)
    | ~ ne(X3)
    | ap(ap(c_2Epred__set_2EINSERT(X1),X0),ap(c_2Elist_2ELIST__TO__SET(X1),X2)) = ap(c_2Elist_2ELIST__TO__SET(X1),ap(ap(c_2Elist_2ECONS(X1),X0),X2)) ),
    inference(cnf_transformation,[],[f74]) ).

cnf(c_301,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,ty_2Elist_2Elist(X0))
    | ~ ne(X0)
    | ~ ne(X1)
    | ap(ap(c_2Epred__set_2EINSERT(X0),X0),ap(c_2Elist_2ELIST__TO__SET(X0),X1)) = ap(c_2Elist_2ELIST__TO__SET(X0),ap(ap(c_2Elist_2ECONS(X0),X0),X1)) ),
    inference(subtyping,[status(esa)],[c_0]) ).

cnf(c_303,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,ty_2Elist_2Elist(X0))
    | ~ ne(X0)
    | ap(ap(c_2Epred__set_2EINSERT(X0),X0),ap(c_2Elist_2ELIST__TO__SET(X0),X1)) = ap(c_2Elist_2ELIST__TO__SET(X0),ap(ap(c_2Elist_2ECONS(X0),X0),X1))
    | ~ sP1_iProver_split ),
    inference(splitting,
              [splitting(split),new_symbols(definition,[sP1_iProver_split])],
              [c_301]) ).

cnf(c_19,plain,( ne(bool) ),inference(cnf_transformation,[],[f92]) ).

cnf(c_304,plain,
    ( sP1_iProver_split | sP0_iProver_split ),
    inference(splitting,
              [splitting(split),new_symbols(definition,[])],
              [c_301]) ).

cnf(c_302,plain,
    ( ~ ne(X0) | ~ sP0_iProver_split ),
    inference(splitting,
              [splitting(split),new_symbols(definition,[sP0_iProver_split])],
              [c_301]) ).

cnf(c_324,plain,
    ( ~ ne(bool) | ~ sP0_iProver_split ),
    inference(instantiation,[status(thm)],[c_302]) ).

cnf(c_511,plain,
    ( ap(ap(c_2Epred__set_2EINSERT(X0),X0),ap(c_2Elist_2ELIST__TO__SET(X0),X1)) = ap(c_2Elist_2ELIST__TO__SET(X0),ap(ap(c_2Elist_2ECONS(X0),X0),X1))
    | ~ ne(X0)
    | ~ mem(X1,ty_2Elist_2Elist(X0))
    | ~ mem(X0,X0) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_303,c_19,c_304,c_324]) ).

cnf(c_512,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,ty_2Elist_2Elist(X0))
    | ~ ne(X0)
    | ap(ap(c_2Epred__set_2EINSERT(X0),X0),ap(c_2Elist_2ELIST__TO__SET(X0),X1)) = ap(c_2Elist_2ELIST__TO__SET(X0),ap(ap(c_2Elist_2ECONS(X0),X0),X1)) ),
    inference(renaming,[status(thm)],[c_511]) ).

cnf(c_1317,plain,
    ( ~ mem(X0,sK1)
    | ~ mem(sK3,ty_2Elist_2Elist(sK1))
    | ~ ne(sK1)
    | ap(ap(c_2Epred__set_2EINSERT(sK1),X0),ap(c_2Elist_2ELIST__TO__SET(sK1),sK3)) = ap(c_2Elist_2ELIST__TO__SET(sK1),ap(ap(c_2Elist_2ECONS(sK1),X0),sK3)) ),
    inference(instantiation,[status(thm)],[c_512]) ).

cnf(c_1538,plain,
    ( ~ mem(sK3,ty_2Elist_2Elist(sK1))
    | ~ mem(sK2,sK1)
    | ~ ne(sK1)
    | ap(ap(c_2Epred__set_2EINSERT(sK1),sK2),ap(c_2Elist_2ELIST__TO__SET(sK1),sK3)) = ap(c_2Elist_2ELIST__TO__SET(sK1),ap(ap(c_2Elist_2ECONS(sK1),sK2),sK3)) ),
    inference(instantiation,[status(thm)],[c_1317]) ).

cnf(c_1652,plain,
    ( ap(c_2Elist_2ELIST__TO__SET(sK0),c_2Elist_2ENIL(sK0)) != c_2Epred__set_2EEMPTY(sK0) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_1488,c_5,c_4,c_3,c_299,c_1538]) ).

cnf(c_2151,plain,
    ( ~ ne(sK0) | ~ sP2_iProver_split ),
    inference(resolution,[status(thm)],[c_305,c_1652]) ).

cnf(c_307,plain,
    ( sP3_iProver_split | sP2_iProver_split ),
    inference(splitting,
              [splitting(split),new_symbols(definition,[])],
              [c_300]) ).

cnf(c_6,negated_conjecture,
    ( ne(sK0) ),
    inference(cnf_transformation,[],[f75]) ).

cnf(contradiction,plain,
    ( $false ),
    inference(minisat,
              [status(thm)],
              [c_2169,c_2151,c_307,c_3,c_4,c_5,c_6]) ).


% SZS output end CNFRefutation for HL405138+2.p

USED TIME: 0.10 CPU 0.12 WC

3.46000000002095/0.680000000007567	EOF