%---------------- 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: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 

------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
------ Proving...
------ Problem Properties 


clauses                                 41
conjectures                             4
EPR                                     7
Horn                                    40
unary                                   17
binary                                  15
lits                                    81
lits eq                                 13

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


------ Current options:





------ Proving...


% SZS status Theorem for HL406570+2.p

% SZS output start CNFRefutation for HL406570+2.p

fof(f44,conjecture,(
  ! [X8] : (ne(X8) => ! [X21] : (mem(X21,ty_2Enum_2Enum) => ! [X22] : (mem(X22,X8) => ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X21),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) = ap(c_2Esptree_2Edomain(X8),ap(ap(ap(c_2Esptree_2Einsert(X8),X21),X22),c_2Esptree_2ELN(X8))))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406570+2.p',unknown)).

fof(f45,negated_conjecture,(
  ~! [X8] : (ne(X8) => ! [X21] : (mem(X21,ty_2Enum_2Enum) => ! [X22] : (mem(X22,X8) => ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X21),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) = ap(c_2Esptree_2Edomain(X8),ap(ap(ap(c_2Esptree_2Einsert(X8),X21),X22),c_2Esptree_2ELN(X8))))))),
  inference(negated_conjecture,[],[f44])).

fof(f47,plain,(
  ~! [X0] : (ne(X0) => ! [X1] : (mem(X1,ty_2Enum_2Enum) => ! [X2] : (mem(X2,X0) => ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) = ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),X2),c_2Esptree_2ELN(X0))))))),
  inference(rectify,[],[f45])).

fof(f66,plain,(
  ? [X0] : (? [X1] : (? [X2] : (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),X2),c_2Esptree_2ELN(X0))) & mem(X2,X0)) & mem(X1,ty_2Enum_2Enum)) & ne(X0))),
  inference(ennf_transformation,[],[f47])).

fof(f89,plain,(
  ( ! [X0,X1] : (? [X2] : (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),X2),c_2Esptree_2ELN(X0))) & mem(X2,X0)) => (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),sK2),c_2Esptree_2ELN(X0))) & mem(sK2,X0))) )),
  introduced(choice_axiom,[])).

fof(f88,plain,(
  ( ! [X0] : (? [X1] : (? [X2] : (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),X2),c_2Esptree_2ELN(X0))) & mem(X2,X0)) & mem(X1,ty_2Enum_2Enum)) => (? [X2] : (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),sK1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),sK1),X2),c_2Esptree_2ELN(X0))) & mem(X2,X0)) & mem(sK1,ty_2Enum_2Enum))) )),
  introduced(choice_axiom,[])).

fof(f87,plain,(
  ? [X0] : (? [X1] : (? [X2] : (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),X2),c_2Esptree_2ELN(X0))) & mem(X2,X0)) & mem(X1,ty_2Enum_2Enum)) & ne(X0)) => (? [X1] : (? [X2] : (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),X1),X2),c_2Esptree_2ELN(sK0))) & mem(X2,sK0)) & mem(X1,ty_2Enum_2Enum)) & ne(sK0))),
  introduced(choice_axiom,[])).

fof(f90,plain,(
  ((ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),sK1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),sK1),sK2),c_2Esptree_2ELN(sK0))) & mem(sK2,sK0)) & mem(sK1,ty_2Enum_2Enum)) & ne(sK0)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f66,f89,f88,f87])).

fof(f95,plain,(
  mem(sK1,ty_2Enum_2Enum)),
  inference(cnf_transformation,[],[f90])).

fof(f96,plain,(
  mem(sK2,sK0)),
  inference(cnf_transformation,[],[f90])).

fof(f30,axiom,(
  ! [X8] : (ne(X8) => mem(c_2Esptree_2ELN(X8),ty_2Esptree_2Espt(X8)))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406570+2.p',unknown)).

fof(f54,plain,(
  ! [X0] : (ne(X0) => mem(c_2Esptree_2ELN(X0),ty_2Esptree_2Espt(X0)))),
  inference(rectify,[],[f30])).

fof(f76,plain,(
  ! [X0] : (mem(c_2Esptree_2ELN(X0),ty_2Esptree_2Espt(X0)) | ~ne(X0))),
  inference(ennf_transformation,[],[f54])).

fof(f112,plain,(
  ( ! [X0] : (mem(c_2Esptree_2ELN(X0),ty_2Esptree_2Espt(X0)) | ~ne(X0)) )),
  inference(cnf_transformation,[],[f76])).

fof(f43,axiom,(
  ! [X8] : (ne(X8) => ! [X21] : (mem(X21,ty_2Enum_2Enum) => ! [X22] : (mem(X22,X8) => ! [X23] : (mem(X23,ty_2Esptree_2Espt(X8)) => ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X21),ap(c_2Esptree_2Edomain(X8),X23)) = ap(c_2Esptree_2Edomain(X8),ap(ap(ap(c_2Esptree_2Einsert(X8),X21),X22),X23))))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406570+2.p',unknown)).

fof(f46,plain,(
  ! [X0] : (ne(X0) => ! [X1] : (mem(X1,ty_2Enum_2Enum) => ! [X2] : (mem(X2,X0) => ! [X3] : (mem(X3,ty_2Esptree_2Espt(X0)) => ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),ap(c_2Esptree_2Edomain(X0),X3)) = ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),X2),X3))))))),
  inference(rectify,[],[f43])).

fof(f65,plain,(
  ! [X0] : (! [X1] : (! [X2] : (! [X3] : (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),ap(c_2Esptree_2Edomain(X0),X3)) = ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),X2),X3)) | ~mem(X3,ty_2Esptree_2Espt(X0))) | ~mem(X2,X0)) | ~mem(X1,ty_2Enum_2Enum)) | ~ne(X0))),
  inference(ennf_transformation,[],[f46])).

fof(f93,plain,(
  ( ! [X2,X0,X3,X1] : (ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X1),ap(c_2Esptree_2Edomain(X0),X3)) = ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X1),X2),X3)) | ~mem(X3,ty_2Esptree_2Espt(X0)) | ~mem(X2,X0) | ~mem(X1,ty_2Enum_2Enum) | ~ne(X0)) )),
  inference(cnf_transformation,[],[f65])).

fof(f94,plain,(
  ne(sK0)),
  inference(cnf_transformation,[],[f90])).

fof(f97,plain,(
  ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),sK1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),sK1),sK2),c_2Esptree_2ELN(sK0)))),
  inference(cnf_transformation,[],[f90])).

cnf(c_3,negated_conjecture,
    ( mem(sK1,ty_2Enum_2Enum) ),
    inference(cnf_transformation,[],[f95]) ).

cnf(c_380,negated_conjecture,
    ( mem(sK1,ty_2Enum_2Enum) ),
    inference(subtyping,[status(esa)],[c_3]) ).

cnf(c_947,plain,
    ( mem(sK1,ty_2Enum_2Enum) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_380]) ).

cnf(c_2,negated_conjecture,
    ( mem(sK2,sK0) ),
    inference(cnf_transformation,[],[f96]) ).

cnf(c_381,negated_conjecture,
    ( mem(sK2,sK0) ),
    inference(subtyping,[status(esa)],[c_2]) ).

cnf(c_946,plain,
    ( mem(sK2,sK0) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_381]) ).

cnf(c_19,plain,
    ( mem(c_2Esptree_2ELN(X0),ty_2Esptree_2Espt(X0)) | ~ ne(X0) ),
    inference(cnf_transformation,[],[f112]) ).

cnf(c_364,plain,
    ( mem(c_2Esptree_2ELN(X0),ty_2Esptree_2Espt(X0)) | ~ ne(X0) ),
    inference(subtyping,[status(esa)],[c_19]) ).

cnf(c_963,plain,
    ( mem(c_2Esptree_2ELN(X0),ty_2Esptree_2Espt(X0)) = iProver_top
    | ne(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_364]) ).

cnf(c_0,plain,
    ( ~ mem(X0,X1)
    | ~ mem(X2,ty_2Esptree_2Espt(X1))
    | ~ mem(X3,ty_2Enum_2Enum)
    | ~ ne(X1)
    | ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X3),ap(c_2Esptree_2Edomain(X1),X2)) = ap(c_2Esptree_2Edomain(X1),ap(ap(ap(c_2Esptree_2Einsert(X1),X3),X0),X2)) ),
    inference(cnf_transformation,[],[f93]) ).

cnf(c_383,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,ty_2Esptree_2Espt(X0))
    | ~ mem(X2,ty_2Enum_2Enum)
    | ~ ne(X0)
    | ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X2),ap(c_2Esptree_2Edomain(X0),X1)) = ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X2),X0),X1)) ),
    inference(subtyping,[status(esa)],[c_0]) ).

cnf(c_945,plain,
    ( ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X0),ap(c_2Esptree_2Edomain(X0),X1)) = ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X0),X2),X1))
    | mem(X2,X0) != iProver_top
    | mem(X1,ty_2Esptree_2Espt(X0)) != iProver_top
    | mem(X0,ty_2Enum_2Enum) != iProver_top
    | ne(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_383]) ).

cnf(c_2532,plain,
    ( ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X0),ap(c_2Esptree_2Edomain(X0),c_2Esptree_2ELN(X0))) = ap(c_2Esptree_2Edomain(X0),ap(ap(ap(c_2Esptree_2Einsert(X0),X0),X1),c_2Esptree_2ELN(X0)))
    | mem(X1,X0) != iProver_top
    | mem(X0,ty_2Enum_2Enum) != iProver_top
    | ne(X0) != iProver_top ),
    inference(superposition,[status(thm)],[c_963,c_945]) ).

cnf(c_8272,plain,
    ( ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X0),ap(c_2Esptree_2Edomain(sK0),c_2Esptree_2ELN(sK0))) = ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),X0),sK2),c_2Esptree_2ELN(sK0)))
    | mem(X0,ty_2Enum_2Enum) != iProver_top
    | ne(sK0) != iProver_top ),
    inference(superposition,[status(thm)],[c_946,c_2532]) ).

cnf(c_8276,plain,
    ( ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),X0),sK2),c_2Esptree_2ELN(sK0))) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X0),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum))
    | mem(X0,ty_2Enum_2Enum) != iProver_top
    | ne(sK0) != iProver_top ),
    inference(light_normalisation,[status(thm)],[c_8272]) ).

cnf(c_4,negated_conjecture,
    ( ne(sK0) ),
    inference(cnf_transformation,[],[f94]) ).

cnf(c_41,plain,
    ( ne(sK0) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_4]) ).

cnf(c_9102,plain,
    ( mem(X0,ty_2Enum_2Enum) != iProver_top
    | ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),X0),sK2),c_2Esptree_2ELN(sK0))) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X0),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_8276,c_41]) ).

cnf(c_9103,plain,
    ( ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),X0),sK2),c_2Esptree_2ELN(sK0))) = ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),X0),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum))
    | mem(X0,ty_2Enum_2Enum) != iProver_top ),
    inference(renaming,[status(thm)],[c_9102]) ).

cnf(c_9110,plain,
    ( ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),sK1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) = ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),sK1),sK2),c_2Esptree_2ELN(sK0))) ),
    inference(superposition,[status(thm)],[c_947,c_9103]) ).

cnf(c_1,negated_conjecture,
    ( ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),sK1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),sK1),sK2),c_2Esptree_2ELN(sK0))) ),
    inference(cnf_transformation,[],[f97]) ).

cnf(c_382,negated_conjecture,
    ( ap(ap(c_2Epred__set_2EINSERT(ty_2Enum_2Enum),sK1),c_2Epred__set_2EEMPTY(ty_2Enum_2Enum)) != ap(c_2Esptree_2Edomain(sK0),ap(ap(ap(c_2Esptree_2Einsert(sK0),sK1),sK2),c_2Esptree_2ELN(sK0))) ),
    inference(subtyping,[status(esa)],[c_1]) ).

cnf(contradiction,plain,
    ( $false ),
    inference(minisat,[status(thm)],[c_9110,c_382]) ).


% SZS output end CNFRefutation for HL406570+2.p

USED TIME: 0.25 CPU 0.28 WC

0.199999999953434/0.679999999993015	EOF