%---------------- 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                                 23
conjectures                             8
EPR                                     10
Horn                                    21
unary                                   12
binary                                  2
lits                                    60
lits eq                                 15

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


------ Current options:





------ Proving...


% SZS status Theorem for HL406326+2.p

% SZS output start CNFRefutation for HL406326+2.p

fof(f23,axiom,(
  ! [X8] : (ne(X8) => ! [X10] : (mem(X10,ty_2Etoto_2Etoto(X8)) => ! [X11] : (mem(X11,X8) => ! [X12] : (mem(X12,X8) => ! [X13] : (mem(X13,X8) => ((ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X12),X13) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X11),X12) = c_2EternaryComparisons_2ELESS) => ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X11),X13) = c_2EternaryComparisons_2ELESS))))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406326+2.p',unknown)).

fof(f27,plain,(
  ! [X0] : (ne(X0) => ! [X1] : (mem(X1,ty_2Etoto_2Etoto(X0)) => ! [X2] : (mem(X2,X0) => ! [X3] : (mem(X3,X0) => ! [X4] : (mem(X4,X0) => ((ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2ELESS) => ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) = c_2EternaryComparisons_2ELESS))))))),
  inference(rectify,[],[f23])).

fof(f34,plain,(
  ! [X0] : (! [X1] : (! [X2] : (! [X3] : (! [X4] : ((ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) = c_2EternaryComparisons_2ELESS | (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) != c_2EternaryComparisons_2ELESS | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) != c_2EternaryComparisons_2ELESS)) | ~mem(X4,X0)) | ~mem(X3,X0)) | ~mem(X2,X0)) | ~mem(X1,ty_2Etoto_2Etoto(X0))) | ~ne(X0))),
  inference(ennf_transformation,[],[f27])).

fof(f35,plain,(
  ! [X0] : (! [X1] : (! [X2] : (! [X3] : (! [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) = c_2EternaryComparisons_2ELESS | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) != c_2EternaryComparisons_2ELESS | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) != c_2EternaryComparisons_2ELESS | ~mem(X4,X0)) | ~mem(X3,X0)) | ~mem(X2,X0)) | ~mem(X1,ty_2Etoto_2Etoto(X0))) | ~ne(X0))),
  inference(flattening,[],[f34])).

fof(f58,plain,(
  ( ! [X4,X2,X0,X3,X1] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) = c_2EternaryComparisons_2ELESS | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) != c_2EternaryComparisons_2ELESS | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) != c_2EternaryComparisons_2ELESS | ~mem(X4,X0) | ~mem(X3,X0) | ~mem(X2,X0) | ~mem(X1,ty_2Etoto_2Etoto(X0)) | ~ne(X0)) )),
  inference(cnf_transformation,[],[f35])).

fof(f22,axiom,(
  ! [X8] : (ne(X8) => ! [X10] : (mem(X10,ty_2Etoto_2Etoto(X8)) => ! [X11] : (mem(X11,X8) => ! [X12] : (mem(X12,X8) => (ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X11),X12) = c_2EternaryComparisons_2EGREATER <=> ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X12),X11) = c_2EternaryComparisons_2ELESS)))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406326+2.p',unknown)).

fof(f26,plain,(
  ! [X0] : (ne(X0) => ! [X1] : (mem(X1,ty_2Etoto_2Etoto(X0)) => ! [X2] : (mem(X2,X0) => ! [X3] : (mem(X3,X0) => (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EGREATER <=> ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2ELESS)))))),
  inference(rectify,[],[f22])).

fof(f33,plain,(
  ! [X0] : (! [X1] : (! [X2] : (! [X3] : ((ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EGREATER <=> ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2ELESS) | ~mem(X3,X0)) | ~mem(X2,X0)) | ~mem(X1,ty_2Etoto_2Etoto(X0))) | ~ne(X0))),
  inference(ennf_transformation,[],[f26])).

fof(f46,plain,(
  ! [X0] : (! [X1] : (! [X2] : (! [X3] : (((ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EGREATER | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) != c_2EternaryComparisons_2ELESS) & (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2ELESS | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) != c_2EternaryComparisons_2EGREATER)) | ~mem(X3,X0)) | ~mem(X2,X0)) | ~mem(X1,ty_2Etoto_2Etoto(X0))) | ~ne(X0))),
  inference(nnf_transformation,[],[f33])).

fof(f56,plain,(
  ( ! [X2,X0,X3,X1] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2ELESS | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) != c_2EternaryComparisons_2EGREATER | ~mem(X3,X0) | ~mem(X2,X0) | ~mem(X1,ty_2Etoto_2Etoto(X0)) | ~ne(X0)) )),
  inference(cnf_transformation,[],[f46])).

fof(f24,conjecture,(
  ! [X8] : (ne(X8) => ! [X10] : (mem(X10,ty_2Etoto_2Etoto(X8)) => ! [X11] : (mem(X11,X8) => ! [X12] : (mem(X12,X8) => ! [X13] : (mem(X13,X8) => ((ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X12),X13) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X12),X11) = c_2EternaryComparisons_2EGREATER) => ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X11),X13) = c_2EternaryComparisons_2ELESS))))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406326+2.p',unknown)).

fof(f25,negated_conjecture,(
  ~! [X8] : (ne(X8) => ! [X10] : (mem(X10,ty_2Etoto_2Etoto(X8)) => ! [X11] : (mem(X11,X8) => ! [X12] : (mem(X12,X8) => ! [X13] : (mem(X13,X8) => ((ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X12),X13) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X12),X11) = c_2EternaryComparisons_2EGREATER) => ap(ap(ap(c_2Etoto_2Eapto(X8),X10),X11),X13) = c_2EternaryComparisons_2ELESS))))))),
  inference(negated_conjecture,[],[f24])).

fof(f28,plain,(
  ~! [X0] : (ne(X0) => ! [X1] : (mem(X1,ty_2Etoto_2Etoto(X0)) => ! [X2] : (mem(X2,X0) => ! [X3] : (mem(X3,X0) => ! [X4] : (mem(X4,X0) => ((ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER) => ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) = c_2EternaryComparisons_2ELESS))))))),
  inference(rectify,[],[f25])).

fof(f36,plain,(
  ? [X0] : (? [X1] : (? [X2] : (? [X3] : (? [X4] : ((ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER)) & mem(X4,X0)) & mem(X3,X0)) & mem(X2,X0)) & mem(X1,ty_2Etoto_2Etoto(X0))) & ne(X0))),
  inference(ennf_transformation,[],[f28])).

fof(f37,plain,(
  ? [X0] : (? [X1] : (? [X2] : (? [X3] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) & mem(X3,X0)) & mem(X2,X0)) & mem(X1,ty_2Etoto_2Etoto(X0))) & ne(X0))),
  inference(flattening,[],[f36])).

fof(f51,plain,(
  ( ! [X2,X0,X3,X1] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) => (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),sK4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),sK4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(sK4,X0))) )),
  introduced(choice_axiom,[])).

fof(f50,plain,(
  ( ! [X2,X0,X1] : (? [X3] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) & mem(X3,X0)) => (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),sK3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),sK3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) & mem(sK3,X0))) )),
  introduced(choice_axiom,[])).

fof(f49,plain,(
  ( ! [X0,X1] : (? [X2] : (? [X3] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) & mem(X3,X0)) & mem(X2,X0)) => (? [X3] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),sK2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),sK2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) & mem(X3,X0)) & mem(sK2,X0))) )),
  introduced(choice_axiom,[])).

fof(f48,plain,(
  ( ! [X0] : (? [X1] : (? [X2] : (? [X3] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) & mem(X3,X0)) & mem(X2,X0)) & mem(X1,ty_2Etoto_2Etoto(X0))) => (? [X2] : (? [X3] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),sK1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),sK1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),sK1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) & mem(X3,X0)) & mem(X2,X0)) & mem(sK1,ty_2Etoto_2Etoto(X0)))) )),
  introduced(choice_axiom,[])).

fof(f47,plain,(
  ? [X0] : (? [X1] : (? [X2] : (? [X3] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,X0)) & mem(X3,X0)) & mem(X2,X0)) & mem(X1,ty_2Etoto_2Etoto(X0))) & ne(X0)) => (? [X1] : (? [X2] : (? [X3] : (? [X4] : (ap(ap(ap(c_2Etoto_2Eapto(sK0),X1),X2),X4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(sK0),X1),X3),X4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(sK0),X1),X3),X2) = c_2EternaryComparisons_2EGREATER & mem(X4,sK0)) & mem(X3,sK0)) & mem(X2,sK0)) & mem(X1,ty_2Etoto_2Etoto(sK0))) & ne(sK0))),
  introduced(choice_axiom,[])).

fof(f52,plain,(
  ((((ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) != c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK4) = c_2EternaryComparisons_2ELESS & ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK2) = c_2EternaryComparisons_2EGREATER & mem(sK4,sK0)) & mem(sK3,sK0)) & mem(sK2,sK0)) & mem(sK1,ty_2Etoto_2Etoto(sK0))) & ne(sK0)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f37,f51,f50,f49,f48,f47])).

fof(f65,plain,(
  ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK4) = c_2EternaryComparisons_2ELESS),
  inference(cnf_transformation,[],[f52])).

fof(f64,plain,(
  ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK2) = c_2EternaryComparisons_2EGREATER),
  inference(cnf_transformation,[],[f52])).

fof(f66,plain,(
  ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) != c_2EternaryComparisons_2ELESS),
  inference(cnf_transformation,[],[f52])).

fof(f63,plain,(
  mem(sK4,sK0)),
  inference(cnf_transformation,[],[f52])).

fof(f62,plain,(
  mem(sK3,sK0)),
  inference(cnf_transformation,[],[f52])).

fof(f61,plain,(
  mem(sK2,sK0)),
  inference(cnf_transformation,[],[f52])).

fof(f60,plain,(
  mem(sK1,ty_2Etoto_2Etoto(sK0))),
  inference(cnf_transformation,[],[f52])).

fof(f59,plain,(
  ne(sK0)),
  inference(cnf_transformation,[],[f52])).

cnf(c_2,plain,
    ( ~ mem(X0,X1)
    | ~ mem(X2,X1)
    | ~ mem(X3,X1)
    | ~ mem(X4,ty_2Etoto_2Etoto(X1))
    | ~ ne(X1)
    | ap(ap(ap(c_2Etoto_2Eapto(X1),X4),X2),X0) != c_2EternaryComparisons_2ELESS
    | c_2EternaryComparisons_2ELESS != ap(ap(ap(c_2Etoto_2Eapto(X1),X4),X0),X3)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(X1),X4),X2),X3) ),
    inference(cnf_transformation,[],[f58]) ).

cnf(c_192,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,X0)
    | ~ mem(X2,X0)
    | ~ mem(X3,ty_2Etoto_2Etoto(X0))
    | ~ ne(X0)
    | ap(ap(ap(c_2Etoto_2Eapto(X0),X3),X1),X0) != c_2EternaryComparisons_2ELESS
    | c_2EternaryComparisons_2ELESS != ap(ap(ap(c_2Etoto_2Eapto(X0),X3),X0),X2)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(X0),X3),X1),X2) ),
    inference(subtyping,[status(esa)],[c_2]) ).

cnf(c_714,plain,
    ( ~ mem(X0,sK0)
    | ~ mem(X1,sK0)
    | ~ mem(X2,sK0)
    | ~ mem(sK1,ty_2Etoto_2Etoto(sK0))
    | ~ ne(sK0)
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X1),X0) != c_2EternaryComparisons_2ELESS
    | c_2EternaryComparisons_2ELESS != ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X0),X2)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X1),X2) ),
    inference(instantiation,[status(thm)],[c_192]) ).

cnf(c_799,plain,
    ( ~ mem(X0,sK0)
    | ~ mem(X1,sK0)
    | ~ mem(sK4,sK0)
    | ~ mem(sK1,ty_2Etoto_2Etoto(sK0))
    | ~ ne(sK0)
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X1),X0) != c_2EternaryComparisons_2ELESS
    | c_2EternaryComparisons_2ELESS != ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X0),sK4)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X1),sK4) ),
    inference(instantiation,[status(thm)],[c_714]) ).

cnf(c_1048,plain,
    ( ~ mem(X0,sK0)
    | ~ mem(sK4,sK0)
    | ~ mem(sK2,sK0)
    | ~ mem(sK1,ty_2Etoto_2Etoto(sK0))
    | ~ ne(sK0)
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),X0) != c_2EternaryComparisons_2ELESS
    | c_2EternaryComparisons_2ELESS != ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X0),sK4)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) ),
    inference(instantiation,[status(thm)],[c_799]) ).

cnf(c_1356,plain,
    ( ~ mem(sK3,sK0)
    | ~ mem(sK4,sK0)
    | ~ mem(sK2,sK0)
    | ~ mem(sK1,ty_2Etoto_2Etoto(sK0))
    | ~ ne(sK0)
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK3) != c_2EternaryComparisons_2ELESS
    | c_2EternaryComparisons_2ELESS != ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK4)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) ),
    inference(instantiation,[status(thm)],[c_1048]) ).

cnf(c_196,plain,( X0 = X0 ),theory(equality) ).

cnf(c_1331,plain,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) = ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) ),
    inference(instantiation,[status(thm)],[c_196]) ).

cnf(c_1,plain,
    ( ~ mem(X0,X1)
    | ~ mem(X2,X1)
    | ~ mem(X3,ty_2Etoto_2Etoto(X1))
    | ~ ne(X1)
    | ap(ap(ap(c_2Etoto_2Eapto(X1),X3),X0),X2) = c_2EternaryComparisons_2ELESS
    | ap(ap(ap(c_2Etoto_2Eapto(X1),X3),X2),X0) != c_2EternaryComparisons_2EGREATER ),
    inference(cnf_transformation,[],[f56]) ).

cnf(c_193,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,X0)
    | ~ mem(X2,ty_2Etoto_2Etoto(X0))
    | ~ ne(X0)
    | ap(ap(ap(c_2Etoto_2Eapto(X0),X2),X0),X1) = c_2EternaryComparisons_2ELESS
    | ap(ap(ap(c_2Etoto_2Eapto(X0),X2),X1),X0) != c_2EternaryComparisons_2EGREATER ),
    inference(subtyping,[status(esa)],[c_1]) ).

cnf(c_718,plain,
    ( ~ mem(X0,sK0)
    | ~ mem(X1,sK0)
    | ~ mem(sK1,ty_2Etoto_2Etoto(sK0))
    | ~ ne(sK0)
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X0),X1) = c_2EternaryComparisons_2ELESS
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X1),X0) != c_2EternaryComparisons_2EGREATER ),
    inference(instantiation,[status(thm)],[c_193]) ).

cnf(c_828,plain,
    ( ~ mem(X0,sK0)
    | ~ mem(sK3,sK0)
    | ~ mem(sK1,ty_2Etoto_2Etoto(sK0))
    | ~ ne(sK0)
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),X0),sK3) = c_2EternaryComparisons_2ELESS
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),X0) != c_2EternaryComparisons_2EGREATER ),
    inference(instantiation,[status(thm)],[c_718]) ).

cnf(c_1160,plain,
    ( ~ mem(sK3,sK0)
    | ~ mem(sK2,sK0)
    | ~ mem(sK1,ty_2Etoto_2Etoto(sK0))
    | ~ ne(sK0)
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK2) != c_2EternaryComparisons_2EGREATER
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK3) = c_2EternaryComparisons_2ELESS ),
    inference(instantiation,[status(thm)],[c_828]) ).

cnf(c_197,plain,( X0 != X1 | X2 != X1 | X2 = X0 ),theory(equality) ).

cnf(c_989,plain,
    ( X0 != X1 | X1 = X0 ),
    inference(resolution,[status(thm)],[c_197,c_196]) ).

cnf(c_4,negated_conjecture,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK4) = c_2EternaryComparisons_2ELESS ),
    inference(cnf_transformation,[],[f65]) ).

cnf(c_190,negated_conjecture,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK4) = c_2EternaryComparisons_2ELESS ),
    inference(subtyping,[status(esa)],[c_4]) ).

cnf(c_1092,plain,
    ( c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK4) ),
    inference(resolution,[status(thm)],[c_989,c_190]) ).

cnf(c_660,plain,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) != X0
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) = c_2EternaryComparisons_2ELESS
    | c_2EternaryComparisons_2ELESS != X0 ),
    inference(instantiation,[status(thm)],[c_197]) ).

cnf(c_795,plain,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) != ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4)
    | ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) = c_2EternaryComparisons_2ELESS
    | c_2EternaryComparisons_2ELESS != ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) ),
    inference(instantiation,[status(thm)],[c_660]) ).

cnf(c_5,negated_conjecture,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK2) = c_2EternaryComparisons_2EGREATER ),
    inference(cnf_transformation,[],[f64]) ).

cnf(c_189,negated_conjecture,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK3),sK2) = c_2EternaryComparisons_2EGREATER ),
    inference(subtyping,[status(esa)],[c_5]) ).

cnf(c_3,negated_conjecture,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) != c_2EternaryComparisons_2ELESS ),
    inference(cnf_transformation,[],[f66]) ).

cnf(c_191,negated_conjecture,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK0),sK1),sK2),sK4) != c_2EternaryComparisons_2ELESS ),
    inference(subtyping,[status(esa)],[c_3]) ).

cnf(c_6,negated_conjecture,
    ( mem(sK4,sK0) ),
    inference(cnf_transformation,[],[f63]) ).

cnf(c_7,negated_conjecture,
    ( mem(sK3,sK0) ),
    inference(cnf_transformation,[],[f62]) ).

cnf(c_8,negated_conjecture,
    ( mem(sK2,sK0) ),
    inference(cnf_transformation,[],[f61]) ).

cnf(c_9,negated_conjecture,
    ( mem(sK1,ty_2Etoto_2Etoto(sK0)) ),
    inference(cnf_transformation,[],[f60]) ).

cnf(c_10,negated_conjecture,
    ( ne(sK0) ),
    inference(cnf_transformation,[],[f59]) ).

cnf(contradiction,plain,
    ( $false ),
    inference(minisat,
              [status(thm)],
              [c_1356,c_1331,c_1160,c_1092,c_795,c_189,c_191,c_6,c_7,
               c_8,c_9,c_10]) ).


% SZS output end CNFRefutation for HL406326+2.p

USED TIME: 0.04 CPU 0.08 WC

1.88000000000466/0.660000000003492	EOF