%---------------- 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                                 32
conjectures                             6
EPR                                     11
Horn                                    25
unary                                   6
binary                                  12
lits                                    83
lits eq                                 15

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


------ Current options:





------ Proving...


% SZS status Theorem for HL406320+2.p

% SZS output start CNFRefutation for HL406320+2.p

fof(f27,conjecture,(
  ! [X8] : (ne(X8) => (! [X16] : (mem(X16,ty_2Etoto_2Etoto(X8)) => ! [X17] : (mem(X17,X8) => ! [X18] : (mem(X18,X8) => (ap(ap(ap(c_2Etoto_2Eapto(X8),X16),X17),X18) = c_2EternaryComparisons_2EGREATER => X17 != X18)))) & ! [X13] : (mem(X13,ty_2Etoto_2Etoto(X8)) => ! [X14] : (mem(X14,X8) => ! [X15] : (mem(X15,X8) => (ap(ap(ap(c_2Etoto_2Eapto(X8),X13),X14),X15) = c_2EternaryComparisons_2ELESS => X14 != X15)))) & ! [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_2EEQUAL => X11 = X12))))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406320+2.p',unknown)).

fof(f28,negated_conjecture,(
  ~! [X8] : (ne(X8) => (! [X16] : (mem(X16,ty_2Etoto_2Etoto(X8)) => ! [X17] : (mem(X17,X8) => ! [X18] : (mem(X18,X8) => (ap(ap(ap(c_2Etoto_2Eapto(X8),X16),X17),X18) = c_2EternaryComparisons_2EGREATER => X17 != X18)))) & ! [X13] : (mem(X13,ty_2Etoto_2Etoto(X8)) => ! [X14] : (mem(X14,X8) => ! [X15] : (mem(X15,X8) => (ap(ap(ap(c_2Etoto_2Eapto(X8),X13),X14),X15) = c_2EternaryComparisons_2ELESS => X14 != X15)))) & ! [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_2EEQUAL => X11 = X12))))))),
  inference(negated_conjecture,[],[f27])).

fof(f31,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 => X2 != X3)))) & ! [X4] : (mem(X4,ty_2Etoto_2Etoto(X0)) => ! [X5] : (mem(X5,X0) => ! [X6] : (mem(X6,X0) => (ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) = c_2EternaryComparisons_2ELESS => X5 != X6)))) & ! [X7] : (mem(X7,ty_2Etoto_2Etoto(X0)) => ! [X8] : (mem(X8,X0) => ! [X9] : (mem(X9,X0) => (ap(ap(ap(c_2Etoto_2Eapto(X0),X7),X8),X9) = c_2EternaryComparisons_2EEQUAL => X8 = X9))))))),
  inference(rectify,[],[f28])).

fof(f40,plain,(
  ? [X0] : ((? [X1] : (? [X2] : (? [X3] : ((X2 = X3 & 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))) | ? [X4] : (? [X5] : (? [X6] : ((X5 = X6 & ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) = c_2EternaryComparisons_2ELESS) & mem(X6,X0)) & mem(X5,X0)) & mem(X4,ty_2Etoto_2Etoto(X0))) | ? [X7] : (? [X8] : (? [X9] : ((X8 != X9 & ap(ap(ap(c_2Etoto_2Eapto(X0),X7),X8),X9) = c_2EternaryComparisons_2EEQUAL) & mem(X9,X0)) & mem(X8,X0)) & mem(X7,ty_2Etoto_2Etoto(X0)))) & ne(X0))),
  inference(ennf_transformation,[],[f31])).

fof(f41,plain,(
  ? [X0] : ((? [X1] : (? [X2] : (? [X3] : (X2 = X3 & 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))) | ? [X4] : (? [X5] : (? [X6] : (X5 = X6 & ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) = c_2EternaryComparisons_2ELESS & mem(X6,X0)) & mem(X5,X0)) & mem(X4,ty_2Etoto_2Etoto(X0))) | ? [X7] : (? [X8] : (? [X9] : (X8 != X9 & ap(ap(ap(c_2Etoto_2Eapto(X0),X7),X8),X9) = c_2EternaryComparisons_2EEQUAL & mem(X9,X0)) & mem(X8,X0)) & mem(X7,ty_2Etoto_2Etoto(X0)))) & ne(X0))),
  inference(flattening,[],[f40])).

fof(f51,plain,(
  ! [X0] : (? [X4] : (? [X5] : (? [X6] : (X5 = X6 & ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) = c_2EternaryComparisons_2ELESS & mem(X6,X0)) & mem(X5,X0)) & mem(X4,ty_2Etoto_2Etoto(X0))) | ~sP1(X0))),
  introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])])).

fof(f50,plain,(
  ! [X0] : (? [X7] : (? [X8] : (? [X9] : (X8 != X9 & ap(ap(ap(c_2Etoto_2Eapto(X0),X7),X8),X9) = c_2EternaryComparisons_2EEQUAL & mem(X9,X0)) & mem(X8,X0)) & mem(X7,ty_2Etoto_2Etoto(X0))) | ~sP0(X0))),
  introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])])).

fof(f52,plain,(
  ? [X0] : ((? [X1] : (? [X2] : (? [X3] : (X2 = X3 & 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))) | sP1(X0) | sP0(X0)) & ne(X0))),
  inference(definition_folding,[],[f41,f51,f50])).

fof(f68,plain,(
  ( ! [X2,X0,X1] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EGREATER & mem(X3,X0)) => (sK11 = X2 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),sK11) = c_2EternaryComparisons_2EGREATER & mem(sK11,X0))) )),
  introduced(choice_axiom,[])).

fof(f67,plain,(
  ( ! [X0,X1] : (? [X2] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EGREATER & mem(X3,X0)) & mem(X2,X0)) => (? [X3] : (sK10 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),sK10),X3) = c_2EternaryComparisons_2EGREATER & mem(X3,X0)) & mem(sK10,X0))) )),
  introduced(choice_axiom,[])).

fof(f66,plain,(
  ( ! [X0] : (? [X1] : (? [X2] : (? [X3] : (X2 = X3 & 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))) => (? [X2] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),sK9),X2),X3) = c_2EternaryComparisons_2EGREATER & mem(X3,X0)) & mem(X2,X0)) & mem(sK9,ty_2Etoto_2Etoto(X0)))) )),
  introduced(choice_axiom,[])).

fof(f65,plain,(
  ? [X0] : ((? [X1] : (? [X2] : (? [X3] : (X2 = X3 & 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))) | sP1(X0) | sP0(X0)) & ne(X0)) => ((? [X1] : (? [X2] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(sK8),X1),X2),X3) = c_2EternaryComparisons_2EGREATER & mem(X3,sK8)) & mem(X2,sK8)) & mem(X1,ty_2Etoto_2Etoto(sK8))) | sP1(sK8) | sP0(sK8)) & ne(sK8))),
  introduced(choice_axiom,[])).

fof(f69,plain,(
  ((((sK10 = sK11 & ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) = c_2EternaryComparisons_2EGREATER & mem(sK11,sK8)) & mem(sK10,sK8)) & mem(sK9,ty_2Etoto_2Etoto(sK8))) | sP1(sK8) | sP0(sK8)) & ne(sK8)),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f52,f68,f67,f66,f65])).

fof(f91,plain,(
  sK10 = sK11 | sP1(sK8) | sP0(sK8)),
  inference(cnf_transformation,[],[f69])).

fof(f59,plain,(
  ! [X0] : (? [X7] : (? [X8] : (? [X9] : (X8 != X9 & ap(ap(ap(c_2Etoto_2Eapto(X0),X7),X8),X9) = c_2EternaryComparisons_2EEQUAL & mem(X9,X0)) & mem(X8,X0)) & mem(X7,ty_2Etoto_2Etoto(X0))) | ~sP0(X0))),
  inference(nnf_transformation,[],[f50])).

fof(f60,plain,(
  ! [X0] : (? [X1] : (? [X2] : (? [X3] : (X2 != X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EEQUAL & mem(X3,X0)) & mem(X2,X0)) & mem(X1,ty_2Etoto_2Etoto(X0))) | ~sP0(X0))),
  inference(rectify,[],[f59])).

fof(f63,plain,(
  ( ! [X2,X1] : (! [X0] : (? [X3] : (X2 != X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EEQUAL & mem(X3,X0)) => (sK7(X0) != X2 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),sK7(X0)) = c_2EternaryComparisons_2EEQUAL & mem(sK7(X0),X0)))) )),
  introduced(choice_axiom,[])).

fof(f62,plain,(
  ( ! [X1] : (! [X0] : (? [X2] : (? [X3] : (X2 != X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EEQUAL & mem(X3,X0)) & mem(X2,X0)) => (? [X3] : (sK6(X0) != X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),sK6(X0)),X3) = c_2EternaryComparisons_2EEQUAL & mem(X3,X0)) & mem(sK6(X0),X0)))) )),
  introduced(choice_axiom,[])).

fof(f61,plain,(
  ! [X0] : (? [X1] : (? [X2] : (? [X3] : (X2 != X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2EEQUAL & mem(X3,X0)) & mem(X2,X0)) & mem(X1,ty_2Etoto_2Etoto(X0))) => (? [X2] : (? [X3] : (X2 != X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),sK5(X0)),X2),X3) = c_2EternaryComparisons_2EEQUAL & mem(X3,X0)) & mem(X2,X0)) & mem(sK5(X0),ty_2Etoto_2Etoto(X0))))),
  introduced(choice_axiom,[])).

fof(f64,plain,(
  ! [X0] : ((((sK6(X0) != sK7(X0) & ap(ap(ap(c_2Etoto_2Eapto(X0),sK5(X0)),sK6(X0)),sK7(X0)) = c_2EternaryComparisons_2EEQUAL & mem(sK7(X0),X0)) & mem(sK6(X0),X0)) & mem(sK5(X0),ty_2Etoto_2Etoto(X0))) | ~sP0(X0))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f60,f63,f62,f61])).

fof(f84,plain,(
  ( ! [X0] : (ap(ap(ap(c_2Etoto_2Eapto(X0),sK5(X0)),sK6(X0)),sK7(X0)) = c_2EternaryComparisons_2EEQUAL | ~sP0(X0)) )),
  inference(cnf_transformation,[],[f64])).

fof(f53,plain,(
  ! [X0] : (? [X4] : (? [X5] : (? [X6] : (X5 = X6 & ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) = c_2EternaryComparisons_2ELESS & mem(X6,X0)) & mem(X5,X0)) & mem(X4,ty_2Etoto_2Etoto(X0))) | ~sP1(X0))),
  inference(nnf_transformation,[],[f51])).

fof(f54,plain,(
  ! [X0] : (? [X1] : (? [X2] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2ELESS & mem(X3,X0)) & mem(X2,X0)) & mem(X1,ty_2Etoto_2Etoto(X0))) | ~sP1(X0))),
  inference(rectify,[],[f53])).

fof(f57,plain,(
  ( ! [X2,X1] : (! [X0] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2ELESS & mem(X3,X0)) => (sK4(X0) = X2 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),sK4(X0)) = c_2EternaryComparisons_2ELESS & mem(sK4(X0),X0)))) )),
  introduced(choice_axiom,[])).

fof(f56,plain,(
  ( ! [X1] : (! [X0] : (? [X2] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2ELESS & mem(X3,X0)) & mem(X2,X0)) => (? [X3] : (sK3(X0) = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),sK3(X0)),X3) = c_2EternaryComparisons_2ELESS & mem(X3,X0)) & mem(sK3(X0),X0)))) )),
  introduced(choice_axiom,[])).

fof(f55,plain,(
  ! [X0] : (? [X1] : (? [X2] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) = c_2EternaryComparisons_2ELESS & mem(X3,X0)) & mem(X2,X0)) & mem(X1,ty_2Etoto_2Etoto(X0))) => (? [X2] : (? [X3] : (X2 = X3 & ap(ap(ap(c_2Etoto_2Eapto(X0),sK2(X0)),X2),X3) = c_2EternaryComparisons_2ELESS & mem(X3,X0)) & mem(X2,X0)) & mem(sK2(X0),ty_2Etoto_2Etoto(X0))))),
  introduced(choice_axiom,[])).

fof(f58,plain,(
  ! [X0] : ((((sK3(X0) = sK4(X0) & ap(ap(ap(c_2Etoto_2Eapto(X0),sK2(X0)),sK3(X0)),sK4(X0)) = c_2EternaryComparisons_2ELESS & mem(sK4(X0),X0)) & mem(sK3(X0),X0)) & mem(sK2(X0),ty_2Etoto_2Etoto(X0))) | ~sP1(X0))),
  inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f54,f57,f56,f55])).

fof(f76,plain,(
  ( ! [X0] : (mem(sK2(X0),ty_2Etoto_2Etoto(X0)) | ~sP1(X0)) )),
  inference(cnf_transformation,[],[f58])).

fof(f80,plain,(
  ( ! [X0] : (sK3(X0) = sK4(X0) | ~sP1(X0)) )),
  inference(cnf_transformation,[],[f58])).

fof(f25,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_2EEQUAL => X11 = X12)))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406320+2.p',unknown)).

fof(f29,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_2EEQUAL => X2 = X3)))))),
  inference(rectify,[],[f25])).

fof(f36,plain,(
  ! [X0] : (! [X1] : (! [X2] : (! [X3] : ((X2 = X3 | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) != c_2EternaryComparisons_2EEQUAL) | ~mem(X3,X0)) | ~mem(X2,X0)) | ~mem(X1,ty_2Etoto_2Etoto(X0))) | ~ne(X0))),
  inference(ennf_transformation,[],[f29])).

fof(f37,plain,(
  ! [X0] : (! [X1] : (! [X2] : (! [X3] : (X2 = X3 | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) != c_2EternaryComparisons_2EEQUAL | ~mem(X3,X0)) | ~mem(X2,X0)) | ~mem(X1,ty_2Etoto_2Etoto(X0))) | ~ne(X0))),
  inference(flattening,[],[f36])).

fof(f73,plain,(
  ( ! [X2,X0,X3,X1] : (X2 = X3 | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X2),X3) != c_2EternaryComparisons_2EEQUAL | ~mem(X3,X0) | ~mem(X2,X0) | ~mem(X1,ty_2Etoto_2Etoto(X0)) | ~ne(X0)) )),
  inference(cnf_transformation,[],[f37])).

fof(f86,plain,(
  ne(sK8)),
  inference(cnf_transformation,[],[f69])).

fof(f81,plain,(
  ( ! [X0] : (mem(sK5(X0),ty_2Etoto_2Etoto(X0)) | ~sP0(X0)) )),
  inference(cnf_transformation,[],[f64])).

fof(f82,plain,(
  ( ! [X0] : (mem(sK6(X0),X0) | ~sP0(X0)) )),
  inference(cnf_transformation,[],[f64])).

fof(f83,plain,(
  ( ! [X0] : (mem(sK7(X0),X0) | ~sP0(X0)) )),
  inference(cnf_transformation,[],[f64])).

fof(f85,plain,(
  ( ! [X0] : (sK6(X0) != sK7(X0) | ~sP0(X0)) )),
  inference(cnf_transformation,[],[f64])).

fof(f79,plain,(
  ( ! [X0] : (ap(ap(ap(c_2Etoto_2Eapto(X0),sK2(X0)),sK3(X0)),sK4(X0)) = c_2EternaryComparisons_2ELESS | ~sP1(X0)) )),
  inference(cnf_transformation,[],[f58])).

fof(f26,axiom,(
  ! [X8] : (ne(X8) => (! [X13] : (mem(X13,ty_2Etoto_2Etoto(X8)) => ! [X14] : (mem(X14,X8) => ! [X15] : (mem(X15,X8) => (ap(ap(ap(c_2Etoto_2Eapto(X8),X13),X14),X15) = c_2EternaryComparisons_2EGREATER => X14 != X15)))) & ! [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_2ELESS => X11 != X12))))))),
  file('/export/starexec/sandbox/benchmark/Problems/HL406320+2.p',unknown)).

fof(f30,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 => X2 != X3)))) & ! [X4] : (mem(X4,ty_2Etoto_2Etoto(X0)) => ! [X5] : (mem(X5,X0) => ! [X6] : (mem(X6,X0) => (ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) = c_2EternaryComparisons_2ELESS => X5 != X6))))))),
  inference(rectify,[],[f26])).

fof(f38,plain,(
  ! [X0] : ((! [X1] : (! [X2] : (! [X3] : ((X2 != X3 | 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))) & ! [X4] : (! [X5] : (! [X6] : ((X5 != X6 | ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) != c_2EternaryComparisons_2ELESS) | ~mem(X6,X0)) | ~mem(X5,X0)) | ~mem(X4,ty_2Etoto_2Etoto(X0)))) | ~ne(X0))),
  inference(ennf_transformation,[],[f30])).

fof(f39,plain,(
  ! [X0] : ((! [X1] : (! [X2] : (! [X3] : (X2 != X3 | 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))) & ! [X4] : (! [X5] : (! [X6] : (X5 != X6 | ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) != c_2EternaryComparisons_2ELESS | ~mem(X6,X0)) | ~mem(X5,X0)) | ~mem(X4,ty_2Etoto_2Etoto(X0)))) | ~ne(X0))),
  inference(flattening,[],[f38])).

fof(f74,plain,(
  ( ! [X6,X4,X0,X5] : (X5 != X6 | ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X5),X6) != c_2EternaryComparisons_2ELESS | ~mem(X6,X0) | ~mem(X5,X0) | ~mem(X4,ty_2Etoto_2Etoto(X0)) | ~ne(X0)) )),
  inference(cnf_transformation,[],[f39])).

fof(f106,plain,(
  ( ! [X6,X4,X0] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X4),X6),X6) != c_2EternaryComparisons_2ELESS | ~mem(X6,X0) | ~mem(X6,X0) | ~mem(X4,ty_2Etoto_2Etoto(X0)) | ~ne(X0)) )),
  inference(equality_resolution,[],[f74])).

fof(f77,plain,(
  ( ! [X0] : (mem(sK3(X0),X0) | ~sP1(X0)) )),
  inference(cnf_transformation,[],[f58])).

fof(f90,plain,(
  ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) = c_2EternaryComparisons_2EGREATER | sP1(sK8) | sP0(sK8)),
  inference(cnf_transformation,[],[f69])).

fof(f87,plain,(
  mem(sK9,ty_2Etoto_2Etoto(sK8)) | sP1(sK8) | sP0(sK8)),
  inference(cnf_transformation,[],[f69])).

fof(f88,plain,(
  mem(sK10,sK8) | sP1(sK8) | sP0(sK8)),
  inference(cnf_transformation,[],[f69])).

fof(f75,plain,(
  ( ! [X2,X0,X3,X1] : (X2 != X3 | 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,[],[f39])).

fof(f105,plain,(
  ( ! [X0,X3,X1] : (ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X3),X3) != c_2EternaryComparisons_2EGREATER | ~mem(X3,X0) | ~mem(X3,X0) | ~mem(X1,ty_2Etoto_2Etoto(X0)) | ~ne(X0)) )),
  inference(equality_resolution,[],[f75])).

cnf(c_13,negated_conjecture,
    ( sP0(sK8) | sP1(sK8) | sK10 = sK11 ),
    inference(cnf_transformation,[],[f91]) ).

cnf(c_295,negated_conjecture,
    ( sP0(sK8) | sP1(sK8) | sK10 = sK11 ),
    inference(subtyping,[status(esa)],[c_13]) ).

cnf(c_773,plain,
    ( sK10 = sK11 | sP0(sK8) = iProver_top | sP1(sK8) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_295]) ).

cnf(c_9,plain,
    ( ~ sP0(X0)
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(X0),sK5(X0)),sK6(X0)),sK7(X0)) ),
    inference(cnf_transformation,[],[f84]) ).

cnf(c_299,plain,
    ( ~ sP0(X0)
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(X0),sK5(X0)),sK6(X0)),sK7(X0)) ),
    inference(subtyping,[status(esa)],[c_9]) ).

cnf(c_769,plain,
    ( c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(X0),sK5(X0)),sK6(X0)),sK7(X0))
    | sP0(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_299]) ).

cnf(c_3702,plain,
    ( sK10 = sK11
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8))
    | sP1(sK8) = iProver_top ),
    inference(superposition,[status(thm)],[c_773,c_769]) ).

cnf(c_7,plain,
    ( mem(sK2(X0),ty_2Etoto_2Etoto(X0)) | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f76]) ).

cnf(c_301,plain,
    ( mem(sK2(X0),ty_2Etoto_2Etoto(X0)) | ~ sP1(X0) ),
    inference(subtyping,[status(esa)],[c_7]) ).

cnf(c_767,plain,
    ( mem(sK2(X0),ty_2Etoto_2Etoto(X0)) = iProver_top
    | sP1(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_301]) ).

cnf(c_3,plain,
    ( ~ sP1(X0) | sK3(X0) = sK4(X0) ),
    inference(cnf_transformation,[],[f80]) ).

cnf(c_305,plain,
    ( ~ sP1(X0) | sK3(X0) = sK4(X0) ),
    inference(subtyping,[status(esa)],[c_3]) ).

cnf(c_763,plain,
    ( sK3(X0) = sK4(X0) | sP1(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_305]) ).

cnf(c_4090,plain,
    ( sK3(sK8) = sK4(sK8)
    | sK10 = sK11
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8)) ),
    inference(superposition,[status(thm)],[c_3702,c_763]) ).

cnf(c_0,plain,
    ( ~ mem(X0,X1)
    | ~ mem(X2,X1)
    | ~ mem(X3,ty_2Etoto_2Etoto(X1))
    | ~ ne(X1)
    | X2 = X0
    | ap(ap(ap(c_2Etoto_2Eapto(X1),X3),X2),X0) != c_2EternaryComparisons_2EEQUAL ),
    inference(cnf_transformation,[],[f73]) ).

cnf(c_308,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,X0)
    | ~ mem(X2,ty_2Etoto_2Etoto(X0))
    | ~ ne(X0)
    | X1 = X0
    | ap(ap(ap(c_2Etoto_2Eapto(X0),X2),X1),X0) != c_2EternaryComparisons_2EEQUAL ),
    inference(subtyping,[status(esa)],[c_0]) ).

cnf(c_760,plain,
    ( X0 = X1
    | ap(ap(ap(c_2Etoto_2Eapto(X0),X2),X0),X1) != c_2EternaryComparisons_2EEQUAL
    | mem(X1,X0) != iProver_top
    | mem(X0,X0) != iProver_top
    | mem(X2,ty_2Etoto_2Etoto(X0)) != iProver_top
    | ne(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_308]) ).

cnf(c_4245,plain,
    ( sK6(sK8) = sK7(sK8)
    | sK3(sK8) = sK4(sK8)
    | sK10 = sK11
    | mem(sK5(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK7(sK8),sK8) != iProver_top
    | mem(sK6(sK8),sK8) != iProver_top
    | ne(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_4090,c_760]) ).

cnf(c_18,negated_conjecture,
    ( ne(sK8) ),
    inference(cnf_transformation,[],[f86]) ).

cnf(c_12,plain,
    ( mem(sK5(X0),ty_2Etoto_2Etoto(X0)) | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f81]) ).

cnf(c_68,plain,
    ( mem(sK5(sK8),ty_2Etoto_2Etoto(sK8)) | ~ sP0(sK8) ),
    inference(instantiation,[status(thm)],[c_12]) ).

cnf(c_11,plain,
    ( mem(sK6(X0),X0) | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f82]) ).

cnf(c_71,plain,
    ( mem(sK6(sK8),sK8) | ~ sP0(sK8) ),
    inference(instantiation,[status(thm)],[c_11]) ).

cnf(c_10,plain,
    ( mem(sK7(X0),X0) | ~ sP0(X0) ),
    inference(cnf_transformation,[],[f83]) ).

cnf(c_74,plain,
    ( mem(sK7(sK8),sK8) | ~ sP0(sK8) ),
    inference(instantiation,[status(thm)],[c_10]) ).

cnf(c_326,plain,
    ( ~ sP1(sK8) | sK3(sK8) = sK4(sK8) ),
    inference(instantiation,[status(thm)],[c_305]) ).

cnf(c_8,plain,
    ( ~ sP0(X0) | sK6(X0) != sK7(X0) ),
    inference(cnf_transformation,[],[f85]) ).

cnf(c_300,plain,
    ( ~ sP0(X0) | sK6(X0) != sK7(X0) ),
    inference(subtyping,[status(esa)],[c_8]) ).

cnf(c_335,plain,
    ( ~ sP0(sK8) | sK6(sK8) != sK7(sK8) ),
    inference(instantiation,[status(thm)],[c_300]) ).

cnf(c_4260,plain,
    ( ~ mem(sK5(sK8),ty_2Etoto_2Etoto(sK8))
    | ~ mem(sK7(sK8),sK8)
    | ~ mem(sK6(sK8),sK8)
    | ~ ne(sK8)
    | sK6(sK8) = sK7(sK8)
    | sK3(sK8) = sK4(sK8)
    | sK10 = sK11 ),
    inference(predicate_to_equality_rev,[status(thm)],[c_4245]) ).

cnf(c_4779,plain,
    ( sK3(sK8) = sK4(sK8) | sK10 = sK11 ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_4245,c_18,c_68,c_71,c_74,c_326,c_335,c_295,c_4260]) ).

cnf(c_4,plain,
    ( ~ sP1(X0)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(X0),sK2(X0)),sK3(X0)),sK4(X0)) ),
    inference(cnf_transformation,[],[f79]) ).

cnf(c_304,plain,
    ( ~ sP1(X0)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(X0),sK2(X0)),sK3(X0)),sK4(X0)) ),
    inference(subtyping,[status(esa)],[c_4]) ).

cnf(c_764,plain,
    ( c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(X0),sK2(X0)),sK3(X0)),sK4(X0))
    | sP1(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_304]) ).

cnf(c_4083,plain,
    ( sK10 = sK11
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8)) ),
    inference(superposition,[status(thm)],[c_3702,c_764]) ).

cnf(c_4662,plain,
    ( sK6(sK8) = sK7(sK8)
    | sK10 = sK11
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | mem(sK5(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK7(sK8),sK8) != iProver_top
    | mem(sK6(sK8),sK8) != iProver_top
    | ne(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_4083,c_760]) ).

cnf(c_329,plain,
    ( ~ sP1(sK8)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8)) ),
    inference(instantiation,[status(thm)],[c_304]) ).

cnf(c_4677,plain,
    ( ~ mem(sK5(sK8),ty_2Etoto_2Etoto(sK8))
    | ~ mem(sK7(sK8),sK8)
    | ~ mem(sK6(sK8),sK8)
    | ~ ne(sK8)
    | sK6(sK8) = sK7(sK8)
    | sK10 = sK11
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8)) ),
    inference(predicate_to_equality_rev,[status(thm)],[c_4662]) ).

cnf(c_5155,plain,
    ( sK10 = sK11
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8)) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_4662,c_18,c_68,c_71,c_74,c_329,c_335,c_295,c_4677]) ).

cnf(c_5159,plain,
    ( sK10 = sK11
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK3(sK8)) ),
    inference(superposition,[status(thm)],[c_4779,c_5155]) ).

cnf(c_2,plain,
    ( ~ mem(X0,X1)
    | ~ mem(X2,ty_2Etoto_2Etoto(X1))
    | ~ ne(X1)
    | ap(ap(ap(c_2Etoto_2Eapto(X1),X2),X0),X0) != c_2EternaryComparisons_2ELESS ),
    inference(cnf_transformation,[],[f106]) ).

cnf(c_306,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,ty_2Etoto_2Etoto(X0))
    | ~ ne(X0)
    | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X0),X0) != c_2EternaryComparisons_2ELESS ),
    inference(subtyping,[status(esa)],[c_2]) ).

cnf(c_762,plain,
    ( ap(ap(ap(c_2Etoto_2Eapto(X0),X0),X1),X1) != c_2EternaryComparisons_2ELESS
    | mem(X1,X0) != iProver_top
    | mem(X0,ty_2Etoto_2Etoto(X0)) != iProver_top
    | ne(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_306]) ).

cnf(c_5232,plain,
    ( sK10 = sK11
    | mem(sK2(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK3(sK8),sK8) != iProver_top
    | ne(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_5159,c_762]) ).

cnf(c_32,plain,
    ( ne(sK8) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_18]) ).

cnf(c_5276,plain,
    ( mem(sK3(sK8),sK8) != iProver_top
    | mem(sK2(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | sK10 = sK11 ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_5232,c_32]) ).

cnf(c_5277,plain,
    ( sK10 = sK11
    | mem(sK2(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK3(sK8),sK8) != iProver_top ),
    inference(renaming,[status(thm)],[c_5276]) ).

cnf(c_5283,plain,
    ( sK10 = sK11
    | mem(sK3(sK8),sK8) != iProver_top
    | sP1(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_767,c_5277]) ).

cnf(c_6,plain,
    ( mem(sK3(X0),X0) | ~ sP1(X0) ),
    inference(cnf_transformation,[],[f77]) ).

cnf(c_85,plain,
    ( mem(sK3(X0),X0) = iProver_top | sP1(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_6]) ).

cnf(c_87,plain,
    ( mem(sK3(sK8),sK8) = iProver_top | sP1(sK8) != iProver_top ),
    inference(instantiation,[status(thm)],[c_85]) ).

cnf(c_5292,plain,
    ( sK10 = sK11 | sP1(sK8) != iProver_top ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_5283,c_87]) ).

cnf(c_5305,plain,
    ( sK10 = sK11
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8)) ),
    inference(superposition,[status(thm)],[c_3702,c_5292]) ).

cnf(c_5320,plain,
    ( sK6(sK8) = sK7(sK8)
    | sK10 = sK11
    | mem(sK5(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK7(sK8),sK8) != iProver_top
    | mem(sK6(sK8),sK8) != iProver_top
    | ne(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_5305,c_760]) ).

cnf(c_67,plain,
    ( mem(sK5(X0),ty_2Etoto_2Etoto(X0)) = iProver_top
    | sP0(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_12]) ).

cnf(c_69,plain,
    ( mem(sK5(sK8),ty_2Etoto_2Etoto(sK8)) = iProver_top
    | sP0(sK8) != iProver_top ),
    inference(instantiation,[status(thm)],[c_67]) ).

cnf(c_70,plain,
    ( mem(sK6(X0),X0) = iProver_top | sP0(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_11]) ).

cnf(c_72,plain,
    ( mem(sK6(sK8),sK8) = iProver_top | sP0(sK8) != iProver_top ),
    inference(instantiation,[status(thm)],[c_70]) ).

cnf(c_73,plain,
    ( mem(sK7(X0),X0) = iProver_top | sP0(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_10]) ).

cnf(c_75,plain,
    ( mem(sK7(sK8),sK8) = iProver_top | sP0(sK8) != iProver_top ),
    inference(instantiation,[status(thm)],[c_73]) ).

cnf(c_334,plain,
    ( sK6(X0) != sK7(X0) | sP0(X0) != iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_300]) ).

cnf(c_336,plain,
    ( sK6(sK8) != sK7(sK8) | sP0(sK8) != iProver_top ),
    inference(instantiation,[status(thm)],[c_334]) ).

cnf(c_343,plain,
    ( sK10 = sK11 | sP0(sK8) = iProver_top | sP1(sK8) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_295]) ).

cnf(c_5335,plain,
    ( sK10 = sK11 ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_5320,c_32,c_69,c_72,c_75,c_336,c_343,c_5292]) ).

cnf(c_14,negated_conjecture,
    ( sP0(sK8)
    | sP1(sK8)
    | ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) = c_2EternaryComparisons_2EGREATER ),
    inference(cnf_transformation,[],[f90]) ).

cnf(c_294,negated_conjecture,
    ( sP0(sK8)
    | sP1(sK8)
    | ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) = c_2EternaryComparisons_2EGREATER ),
    inference(subtyping,[status(esa)],[c_14]) ).

cnf(c_774,plain,
    ( ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) = c_2EternaryComparisons_2EGREATER
    | sP0(sK8) = iProver_top
    | sP1(sK8) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_294]) ).

cnf(c_5342,plain,
    ( c_2EternaryComparisons_2EGREATER = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK10)
    | sP0(sK8) = iProver_top
    | sP1(sK8) = iProver_top ),
    inference(demodulation,[status(thm)],[c_5335,c_774]) ).

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

cnf(c_1404,plain,
    ( sP0(sK8)
    | sP1(sK8)
    | X0 != c_2EternaryComparisons_2EGREATER
    | ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) = X0 ),
    inference(resolution,[status(thm)],[c_311,c_294]) ).

cnf(c_5137,plain,
    ( ~ mem(sK9,ty_2Etoto_2Etoto(sK8))
    | ~ mem(sK11,sK8)
    | ~ mem(sK10,sK8)
    | sP0(sK8)
    | sP1(sK8)
    | ~ ne(sK8)
    | sK10 = sK11
    | c_2EternaryComparisons_2EEQUAL != c_2EternaryComparisons_2EGREATER ),
    inference(resolution,[status(thm)],[c_308,c_1404]) ).

cnf(c_17,negated_conjecture,
    ( mem(sK9,ty_2Etoto_2Etoto(sK8)) | sP0(sK8) | sP1(sK8) ),
    inference(cnf_transformation,[],[f87]) ).

cnf(c_16,negated_conjecture,
    ( mem(sK10,sK8) | sP0(sK8) | sP1(sK8) ),
    inference(cnf_transformation,[],[f88]) ).

cnf(c_1,plain,
    ( ~ mem(X0,X1)
    | ~ mem(X2,ty_2Etoto_2Etoto(X1))
    | ~ ne(X1)
    | ap(ap(ap(c_2Etoto_2Eapto(X1),X2),X0),X0) != c_2EternaryComparisons_2EGREATER ),
    inference(cnf_transformation,[],[f105]) ).

cnf(c_307,plain,
    ( ~ mem(X0,X0)
    | ~ mem(X1,ty_2Etoto_2Etoto(X0))
    | ~ ne(X0)
    | ap(ap(ap(c_2Etoto_2Eapto(X0),X1),X0),X0) != c_2EternaryComparisons_2EGREATER ),
    inference(subtyping,[status(esa)],[c_1]) ).

cnf(c_312,plain,
    ( X0 != X1 | X2 != X3 | ap(X0,X2) = ap(X1,X3) ),
    theory(equality) ).

cnf(c_1419,plain,
    ( X0 != X1 | X2 != X3 | X4 != ap(X1,X3) | ap(X0,X2) = X4 ),
    inference(resolution,[status(thm)],[c_312,c_311]) ).

cnf(c_310,plain,( X0 = X0 ),theory(equality) ).

cnf(c_1412,plain,
    ( X0 != X1 | X1 = X0 ),
    inference(resolution,[status(thm)],[c_311,c_310]) ).

cnf(c_2143,plain,
    ( sP0(sK8)
    | sP1(sK8)
    | c_2EternaryComparisons_2EGREATER = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) ),
    inference(resolution,[status(thm)],[c_1412,c_294]) ).

cnf(c_3927,plain,
    ( sP0(sK8)
    | sP1(sK8)
    | X0 != ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10)
    | X1 != sK11
    | ap(X0,X1) = c_2EternaryComparisons_2EGREATER ),
    inference(resolution,[status(thm)],[c_1419,c_2143]) ).

cnf(c_3971,plain,
    ( sP0(sK8)
    | sP1(sK8)
    | X0 != sK11
    | ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),X0) = c_2EternaryComparisons_2EGREATER ),
    inference(resolution,[status(thm)],[c_3927,c_310]) ).

cnf(c_5105,plain,
    ( ~ mem(sK9,ty_2Etoto_2Etoto(sK8))
    | ~ mem(sK10,sK8)
    | sP0(sK8)
    | sP1(sK8)
    | ~ ne(sK8)
    | sK10 != sK11 ),
    inference(resolution,[status(thm)],[c_307,c_3971]) ).

cnf(c_5167,plain,
    ( sP1(sK8) | sP0(sK8) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_5137,c_18,c_17,c_16,c_295,c_5105]) ).

cnf(c_5168,plain,
    ( sP0(sK8) | sP1(sK8) ),
    inference(renaming,[status(thm)],[c_5167]) ).

cnf(c_5169,plain,
    ( sP0(sK8) = iProver_top | sP1(sK8) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_5168]) ).

cnf(c_5440,plain,
    ( sP0(sK8) = iProver_top | sP1(sK8) = iProver_top ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_5342,c_5169]) ).

cnf(c_5446,plain,
    ( c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8))
    | sP1(sK8) = iProver_top ),
    inference(superposition,[status(thm)],[c_5440,c_769]) ).

cnf(c_3695,plain,
    ( c_2EternaryComparisons_2EGREATER = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11)
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8))
    | sP1(sK8) = iProver_top ),
    inference(superposition,[status(thm)],[c_774,c_769]) ).

cnf(c_4101,plain,
    ( c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | c_2EternaryComparisons_2EGREATER = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11)
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8)) ),
    inference(superposition,[status(thm)],[c_3695,c_764]) ).

cnf(c_4681,plain,
    ( sK6(sK8) = sK7(sK8)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | c_2EternaryComparisons_2EGREATER = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11)
    | mem(sK5(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK7(sK8),sK8) != iProver_top
    | mem(sK6(sK8),sK8) != iProver_top
    | ne(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_4101,c_760]) ).

cnf(c_4696,plain,
    ( ~ mem(sK5(sK8),ty_2Etoto_2Etoto(sK8))
    | ~ mem(sK7(sK8),sK8)
    | ~ mem(sK6(sK8),sK8)
    | ~ ne(sK8)
    | sK6(sK8) = sK7(sK8)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | c_2EternaryComparisons_2EGREATER = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) ),
    inference(predicate_to_equality_rev,[status(thm)],[c_4681]) ).

cnf(c_5223,plain,
    ( c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | c_2EternaryComparisons_2EGREATER = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_4681,c_18,c_17,c_16,c_68,c_71,c_74,c_329,c_335,c_295,
               c_4696,c_5105]) ).

cnf(c_5338,plain,
    ( c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | c_2EternaryComparisons_2EGREATER = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK10) ),
    inference(demodulation,[status(thm)],[c_5335,c_5223]) ).

cnf(c_5854,plain,
    ( c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8)) ),
    inference(superposition,[status(thm)],[c_5446,c_764]) ).

cnf(c_6003,plain,
    ( sK6(sK8) = sK7(sK8)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8))
    | mem(sK5(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK7(sK8),sK8) != iProver_top
    | mem(sK6(sK8),sK8) != iProver_top
    | ne(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_5854,c_760]) ).

cnf(c_6016,plain,
    ( ~ mem(sK5(sK8),ty_2Etoto_2Etoto(sK8))
    | ~ mem(sK7(sK8),sK8)
    | ~ mem(sK6(sK8),sK8)
    | ~ ne(sK8)
    | sK6(sK8) = sK7(sK8)
    | c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8)) ),
    inference(predicate_to_equality_rev,[status(thm)],[c_6003]) ).

cnf(c_6069,plain,
    ( c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK4(sK8)) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_5338,c_18,c_17,c_16,c_68,c_71,c_74,c_329,c_335,c_295,
               c_5105,c_6016]) ).

cnf(c_6071,plain,
    ( c_2EternaryComparisons_2ELESS = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK2(sK8)),sK3(sK8)),sK3(sK8)) ),
    inference(light_normalisation,[status(thm)],[c_6069]) ).

cnf(c_6074,plain,
    ( mem(sK2(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK3(sK8),sK8) != iProver_top
    | ne(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_6071,c_762]) ).

cnf(c_6667,plain,
    ( mem(sK3(sK8),sK8) != iProver_top
    | mem(sK2(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_6074,c_32]) ).

cnf(c_6668,plain,
    ( mem(sK2(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK3(sK8),sK8) != iProver_top ),
    inference(renaming,[status(thm)],[c_6667]) ).

cnf(c_6673,plain,
    ( mem(sK3(sK8),sK8) != iProver_top | sP1(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_767,c_6668]) ).

cnf(c_6680,plain,
    ( sP1(sK8) != iProver_top ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_6673,c_87]) ).

cnf(c_6685,plain,
    ( c_2EternaryComparisons_2EEQUAL = ap(ap(ap(c_2Etoto_2Eapto(sK8),sK5(sK8)),sK6(sK8)),sK7(sK8)) ),
    inference(superposition,[status(thm)],[c_5446,c_6680]) ).

cnf(c_6788,plain,
    ( sK6(sK8) = sK7(sK8)
    | mem(sK5(sK8),ty_2Etoto_2Etoto(sK8)) != iProver_top
    | mem(sK7(sK8),sK8) != iProver_top
    | mem(sK6(sK8),sK8) != iProver_top
    | ne(sK8) != iProver_top ),
    inference(superposition,[status(thm)],[c_6685,c_760]) ).

cnf(c_313,plain,
    ( ~ mem(X0,X0) | mem(X1,X0) | X1 != X0 ),
    theory(equality) ).

cnf(c_1421,plain,
    ( ~ mem(ap(X0,X1),X0) | mem(ap(X2,X3),X0) | X2 != X0 | X3 != X1 ),
    inference(resolution,[status(thm)],[c_312,c_313]) ).

cnf(c_1390,plain,
    ( mem(ap(ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10),sK11),X0)
    | ~ mem(c_2EternaryComparisons_2EGREATER,X0)
    | sP0(sK8)
    | sP1(sK8) ),
    inference(resolution,[status(thm)],[c_313,c_294]) ).

cnf(c_3742,plain,
    ( mem(ap(X0,X1),X0)
    | ~ mem(c_2EternaryComparisons_2EGREATER,X0)
    | sP0(sK8)
    | sP1(sK8)
    | X0 != ap(ap(c_2Etoto_2Eapto(sK8),sK9),sK10)
    | X1 != sK11 ),
    inference(resolution,[status(thm)],[c_1421,c_1390]) ).

cnf(c_4137,plain,
    ( mem(ap(ap(X0,X1),X2),X0)
    | ~ mem(c_2EternaryComparisons_2EGREATER,X0)
    | sP0(sK8)
    | sP1(sK8)
    | X0 != ap(c_2Etoto_2Eapto(sK8),sK9)
    | X2 != sK11
    | X1 != sK10 ),
    inference(resolution,[status(thm)],[c_3742,c_312]) ).

cnf(c_83,plain,
    ( mem(sK2(sK8),ty_2Etoto_2Etoto(sK8)) | ~ sP1(sK8) ),
    inference(instantiation,[status(thm)],[c_7]) ).

cnf(c_86,plain,
    ( mem(sK3(sK8),sK8) | ~ sP1(sK8) ),
    inference(instantiation,[status(thm)],[c_6]) ).

cnf(c_6082,plain,
    ( ~ mem(sK2(sK8),ty_2Etoto_2Etoto(sK8))
    | ~ mem(sK3(sK8),sK8)
    | ~ ne(sK8) ),
    inference(predicate_to_equality_rev,[status(thm)],[c_6074]) ).

cnf(c_6113,plain,
    ( sP0(sK8) ),
    inference(global_propositional_subsumption,
              [status(thm)],
              [c_4137,c_18,c_17,c_16,c_83,c_86,c_295,c_5105,c_6082]) ).

cnf(c_6115,plain,
    ( sP0(sK8) = iProver_top ),
    inference(predicate_to_equality,[status(thm)],[c_6113]) ).

cnf(contradiction,plain,
    ( $false ),
    inference(minisat,
              [status(thm)],
              [c_6788,c_6115,c_6113,c_335,c_75,c_72,c_69,c_32]) ).


% SZS output end CNFRefutation for HL406320+2.p

USED TIME: 0.18 CPU 0.24 WC

4.73999999999069/0.679999999993015	EOF