%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, in: ($i > $i > $o)).
thf(func_def_2, type, setadjoin: ($i > $i > $i)).
thf(func_def_3, type, setext: $o).
thf(func_def_5, type, setadjoinIL: $o).
thf(func_def_6, type, uniqinunit: $o).
thf(func_def_7, type, eqinunit: $o).
thf(func_def_8, type, upairset2E: $o).
thf(func_def_13, type, sK2: ($i > $i > $i)).
thf(func_def_14, type, sK3: ($i > $i > $i)).
thf(func_def_26, type, vNOT: ($o > $o)).
thf(f1,axiom,(
  (setext = ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (X0 = X1))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext)).
thf(f2,axiom,(
  (! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)) = setadjoinIL)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL)).
thf(f3,axiom,(
  (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit)).
thf(f4,axiom,(
  (eqinunit = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit)).
thf(f5,axiom,(
  (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X2 = X1) | (X2 = X0))) = upairset2E)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E)).
thf(f6,conjecture,(
  setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X1 : $i,X0 : $i] : ((X0 = X1) => (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11)).
thf(f7,negated_conjecture,(
  ~(setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X1 : $i,X0 : $i] : ((X0 = X1) => (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset)))))))))),
  inference(negated_conjecture,[status(cth)],[f6])).
thf(f8,plain,(
  ~(setext => (setadjoinIL => (uniqinunit => (eqinunit => (upairset2E => ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((setadjoin @ X1 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))))))))),
  inference(rectify,[],[f7])).
thf(f9,plain,(
  ~((setext = $true) => ((setadjoinIL = $true) => ((uniqinunit = $true) => ((eqinunit = $true) => ((upairset2E = $true) => ! [X1 : $i,X0 : $i] : ((X0 = X1) => (((setadjoin @ X1 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))))))))),
  inference(fool_elimination,[],[f8])).
thf(f10,plain,(
  (eqinunit = ! [X0 : $i,X1 : $i] : ((X0 = X1) => (in @ X0 @ (setadjoin @ X1 @ emptyset))))),
  inference(rectify,[],[f4])).
thf(f11,plain,(
  ! [X0 : $i,X1 : $i] : ((X0 = X1) => (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true)) <=> (eqinunit = $true)),
  inference(fool_elimination,[],[f10])).
thf(f12,plain,(
  (setext = ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => (in @ X3 @ X1)) => (X0 = X1))))),
  inference(rectify,[],[f1])).
thf(f13,plain,(
  (setext = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => (! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X1)) = $true)) => (X0 = X1)))),
  inference(fool_elimination,[],[f12])).
thf(f14,plain,(
  (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
  inference(rectify,[],[f3])).
thf(f15,plain,(
  ! [X1 : $i,X0 : $i] : ((((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true) => (X0 = X1)) <=> (uniqinunit = $true)),
  inference(fool_elimination,[],[f14])).
thf(f16,plain,(
  (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)) = setadjoinIL)),
  inference(rectify,[],[f2])).
thf(f17,plain,(
  ! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) = $true) <=> (setadjoinIL = $true)),
  inference(fool_elimination,[],[f16])).
thf(f18,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => ((X0 = X1) | (X1 = X2))) = upairset2E)),
  inference(rectify,[],[f5])).
thf(f19,plain,(
  (upairset2E = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) = $true) => ((X0 = X1) | (X1 = X2)))),
  inference(fool_elimination,[],[f18])).
thf(f20,plain,(
  (setext = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) != $true))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)))),
  inference(ennf_transformation,[],[f13])).
thf(f21,plain,(
  (setext = $true) <=> ! [X0 : $i,X1 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) != $true)) | (X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)))),
  inference(flattening,[],[f20])).
thf(f22,plain,(
  ! [X1 : $i,X0 : $i] : ((X0 = X1) | (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) <=> (uniqinunit = $true)),
  inference(ennf_transformation,[],[f15])).
thf(f23,plain,(
  ((((? [X0 : $i,X1 : $i] : ((((setadjoin @ X1 @ emptyset)) != ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) & (X0 = X1)) & (upairset2E = $true)) & (eqinunit = $true)) & (uniqinunit = $true)) & (setadjoinIL = $true)) & (setext = $true)),
  inference(ennf_transformation,[],[f9])).
thf(f24,plain,(
  (eqinunit = $true) & (upairset2E = $true) & (uniqinunit = $true) & (setext = $true) & ? [X0 : $i,X1 : $i] : ((((setadjoin @ X1 @ emptyset)) != ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) & (X0 = X1)) & (setadjoinIL = $true)),
  inference(flattening,[],[f23])).
thf(f25,plain,(
  (upairset2E = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : (((X0 = X1) | (X1 = X2)) | (((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) != $true))),
  inference(ennf_transformation,[],[f19])).
thf(f26,plain,(
  ! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) != $true) | (X1 = X2) | (X0 = X1)) <=> (upairset2E = $true)),
  inference(flattening,[],[f25])).
thf(f27,plain,(
  ! [X1 : $i,X0 : $i] : ((X0 != X1) | (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true)) <=> (eqinunit = $true)),
  inference(ennf_transformation,[],[f11])).
thf(f28,plain,(
  ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X3 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ X1)) = $true)) & (X0 != X1) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))) & (! [X0 : $i,X1 : $i] : (? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X1)) != $true)) | (X0 = X1) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (setext != $true))),
  inference(nnf_transformation,[],[f21])).
thf(f29,plain,(
  ((setext = $true) | ? [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)) & (X0 != X1) & ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X3 @ X0)) = $true)))) & (! [X4 : $i,X5 : $i] : (? [X6 : $i] : ((((in @ X6 @ X4)) = $true) & (((in @ X6 @ X5)) != $true)) | (X4 = X5) | ? [X7 : $i] : ((((in @ X7 @ X5)) = $true) & ($true != ((in @ X7 @ X4))))) | (setext != $true))),
  inference(rectify,[],[f28])).
thf(f30,plain,(
  ((setext = $true) | (! [X2 : $i] : ((((in @ X2 @ sK0)) != $true) | (((in @ X2 @ sK1)) = $true)) & (sK1 != sK0) & ! [X3 : $i] : ((((in @ X3 @ sK1)) != $true) | (((in @ X3 @ sK0)) = $true)))) & (! [X4 : $i,X5 : $i] : (((((in @ (sK2 @ X5 @ X4) @ X4)) = $true) & (((in @ (sK2 @ X5 @ X4) @ X5)) != $true)) | (X4 = X5) | ((((in @ (sK3 @ X5 @ X4) @ X5)) = $true) & (((in @ (sK3 @ X5 @ X4) @ X4)) != $true))) | (setext != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,vAPP]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X7,$thf(sK3 @ X5 @ X4)),skolemize(X7,$thf(sK3 @ X5 @ X4))],[f29])).
thf(f31,plain,(
  (eqinunit = $true) & (upairset2E = $true) & (uniqinunit = $true) & (setext = $true) & ((((setadjoin @ sK5 @ emptyset)) != ((setadjoin @ sK5 @ (setadjoin @ sK4 @ emptyset)))) & (sK4 = sK5)) & (setadjoinIL = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,$thf(sK4)),skolemize(X1,$thf(sK5))],[f24])).
thf(f32,plain,(
  (! [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X1 : $i,X0 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) != $true))),
  inference(nnf_transformation,[],[f17])).
thf(f33,plain,(
  (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1))) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ? [X2 : $i,X3 : $i] : ($true != ((in @ X2 @ (setadjoin @ X2 @ X3)))))),
  inference(rectify,[],[f32])).
thf(f34,plain,(
  (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X0 @ X1))) = $true) | (setadjoinIL != $true)) & ((setadjoinIL = $true) | ($true != ((in @ sK6 @ (setadjoin @ sK6 @ sK7)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X2,$thf(sK6)),skolemize(X3,$thf(sK7))],[f33])).
thf(f35,plain,(
  (! [X1 : $i,X0 : $i] : ((X0 = X1) | (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X1 : $i,X0 : $i] : ((X0 != X1) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true)))),
  inference(nnf_transformation,[],[f22])).
thf(f36,plain,(
  (! [X0 : $i,X1 : $i] : ((X0 = X1) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ? [X2 : $i,X3 : $i] : ((X2 != X3) & ($true = ((in @ X3 @ (setadjoin @ X2 @ emptyset))))))),
  inference(rectify,[],[f35])).
thf(f37,plain,(
  (! [X0 : $i,X1 : $i] : ((X0 = X1) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true)) | (uniqinunit != $true)) & ((uniqinunit = $true) | ((sK9 != sK8) & (((in @ sK9 @ (setadjoin @ sK8 @ emptyset))) = $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X2,$thf(sK8)),skolemize(X3,$thf(sK9))],[f36])).
thf(f38,plain,(
  (! [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) != $true) | (X1 = X2) | (X0 = X1)) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) = $true) & (X1 != X2) & (X0 != X1)))),
  inference(nnf_transformation,[],[f26])).
thf(f39,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true) | (X0 = X2) | (X0 = X1)) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X3 @ (setadjoin @ X5 @ (setadjoin @ X4 @ emptyset)))) = $true) & (X3 != X5) & (X3 != X4)))),
  inference(rectify,[],[f38])).
thf(f40,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true) | (X0 = X2) | (X0 = X1)) | (upairset2E != $true)) & ((upairset2E = $true) | ((((in @ sK10 @ (setadjoin @ sK12 @ (setadjoin @ sK11 @ emptyset)))) = $true) & (sK12 != sK10) & (sK11 != sK10)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X3,$thf(sK10)),skolemize(X4,$thf(sK11)),skolemize(X5,$thf(sK12))],[f39])).
thf(f41,plain,(
  (! [X1 : $i,X0 : $i] : ((X0 != X1) | (((in @ X0 @ (setadjoin @ X1 @ emptyset))) = $true)) | (eqinunit != $true)) & ((eqinunit = $true) | ? [X1 : $i,X0 : $i] : ((X0 = X1) & (((in @ X0 @ (setadjoin @ X1 @ emptyset))) != $true)))),
  inference(nnf_transformation,[],[f27])).
thf(f42,plain,(
  (! [X0 : $i,X1 : $i] : ((X0 != X1) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true)) | (eqinunit != $true)) & ((eqinunit = $true) | ? [X2 : $i,X3 : $i] : ((X2 = X3) & ($true != ((in @ X3 @ (setadjoin @ X2 @ emptyset))))))),
  inference(rectify,[],[f41])).
thf(f43,plain,(
  (! [X0 : $i,X1 : $i] : ((X0 != X1) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true)) | (eqinunit != $true)) & ((eqinunit = $true) | ((sK14 = sK13) & (((in @ sK14 @ (setadjoin @ sK13 @ emptyset))) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK13,sK14]),skolemize(X2,$thf(sK13)),skolemize(X3,$thf(sK14))],[f42])).
thf(f44,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X5)) != $true) | (X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X4)) != $true) | (setext != $true)) )),
  inference(cnf_transformation,[],[f30])).
thf(f45,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X5)) != $true) | (X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X5)) = $true) | (setext != $true)) )),
  inference(cnf_transformation,[],[f30])).
thf(f46,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X4)) = $true) | (X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X4)) != $true) | (setext != $true)) )),
  inference(cnf_transformation,[],[f30])).
thf(f47,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X4)) = $true) | (X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X5)) = $true) | (setext != $true)) )),
  inference(cnf_transformation,[],[f30])).
thf(f51,plain,(
  (setadjoinIL = $true)),
  inference(cnf_transformation,[],[f31])).
thf(f52,plain,(
  (sK4 = sK5)),
  inference(cnf_transformation,[],[f31])).
thf(f53,plain,(
  (((setadjoin @ sK5 @ emptyset)) != ((setadjoin @ sK5 @ (setadjoin @ sK4 @ emptyset))))),
  inference(cnf_transformation,[],[f31])).
thf(f54,plain,(
  (setext = $true)),
  inference(cnf_transformation,[],[f31])).
thf(f55,plain,(
  (uniqinunit = $true)),
  inference(cnf_transformation,[],[f31])).
thf(f56,plain,(
  (upairset2E = $true)),
  inference(cnf_transformation,[],[f31])).
thf(f57,plain,(
  (eqinunit = $true)),
  inference(cnf_transformation,[],[f31])).
thf(f59,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X0 @ X1))) = $true) | (setadjoinIL != $true)) )),
  inference(cnf_transformation,[],[f34])).
thf(f62,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 = X1) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) | (uniqinunit != $true)) )),
  inference(cnf_transformation,[],[f37])).
thf(f66,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true) | (X0 = X2) | (X0 = X1) | (upairset2E != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f69,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 != X1) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (eqinunit != $true)) )),
  inference(cnf_transformation,[],[f43])).
thf(f75,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X5)) = $true) | (((in @ (sK2 @ X5 @ X4) @ X4)) = $true) | (X4 = X5) | ($true != $true)) )),
  inference(definition_unfolding,[],[f47,f54])).
thf(f76,plain,(
  ( ! [X4 : $i,X5 : $i] : (($true != $true) | (X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X4)) != $true) | (((in @ (sK2 @ X5 @ X4) @ X4)) = $true)) )),
  inference(definition_unfolding,[],[f46,f54])).
thf(f77,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X5)) != $true) | ($true != $true) | (X4 = X5) | (((in @ (sK3 @ X5 @ X4) @ X5)) = $true)) )),
  inference(definition_unfolding,[],[f45,f54])).
thf(f78,plain,(
  ( ! [X4 : $i,X5 : $i] : ((X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X5)) != $true) | ($true != $true) | (((in @ (sK3 @ X5 @ X4) @ X4)) != $true)) )),
  inference(definition_unfolding,[],[f44,f54])).
thf(f79,plain,(
  (((setadjoin @ sK5 @ emptyset)) != ((setadjoin @ sK5 @ (setadjoin @ sK5 @ emptyset))))),
  inference(definition_unfolding,[],[f53,f52])).
thf(f80,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X0 @ X1))) = $true) | ($true != $true)) )),
  inference(definition_unfolding,[],[f59,f51])).
thf(f82,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) | (X0 = X1)) )),
  inference(definition_unfolding,[],[f62,f55])).
thf(f85,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X1) | (X0 = X2) | (((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true) | ($true != $true)) )),
  inference(definition_unfolding,[],[f66,f56])).
thf(f89,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 != X1) | (((in @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | ($true != $true)) )),
  inference(definition_unfolding,[],[f69,f57])).
thf(f92,plain,(
  ( ! [X1 : $i] : (($true = ((in @ X1 @ (setadjoin @ X1 @ emptyset)))) | ($true != $true)) )),
  inference(equality_resolution,[],[f89])).
thf(f93,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X4)) != $true) | (X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X5)) != $true)) )),
  inference(trivial_inequality_removal,[],[f78])).
thf(f94,plain,(
  ( ! [X1 : $i] : (($true = ((in @ X1 @ (setadjoin @ X1 @ emptyset))))) )),
  inference(trivial_inequality_removal,[],[f92])).
thf(f95,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true) | (X0 = X1) | (X0 = X2)) )),
  inference(trivial_inequality_removal,[],[f85])).
thf(f96,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK2 @ X5 @ X4) @ X5)) != $true) | (((in @ (sK3 @ X5 @ X4) @ X5)) = $true) | (X4 = X5)) )),
  inference(trivial_inequality_removal,[],[f77])).
thf(f97,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X4)) != $true) | (X4 = X5) | (((in @ (sK2 @ X5 @ X4) @ X4)) = $true)) )),
  inference(trivial_inequality_removal,[],[f76])).
thf(f98,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (sK3 @ X5 @ X4) @ X5)) = $true) | (((in @ (sK2 @ X5 @ X4) @ X4)) = $true) | (X4 = X5)) )),
  inference(trivial_inequality_removal,[],[f75])).
thf(f99,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ emptyset))) != $true) | (X0 = X1)) )),
  inference(trivial_inequality_removal,[],[f82])).
thf(f100,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X0 @ X1))) = $true)) )),
  inference(trivial_inequality_removal,[],[f80])).
thf(f103,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK3 @ X0 @ (setadjoin @ X1 @ emptyset)) @ X0)) = $true) | (((setadjoin @ X1 @ emptyset)) = X0) | (((sK2 @ X0 @ (setadjoin @ X1 @ emptyset))) = X1) | ($true != $true)) )),
  inference(constrained_superposition,[],[f99,f98])).
thf(f105,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK3 @ X0 @ (setadjoin @ X1 @ emptyset)) @ X0)) = $true) | (((sK2 @ X0 @ (setadjoin @ X1 @ emptyset))) = X1) | (((setadjoin @ X1 @ emptyset)) = X0)) )),
  inference(trivial_inequality_removal,[],[f103])).
thf(f110,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X1) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) | ($true != $true) | (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X0)) )),
  inference(constrained_superposition,[],[f95,f105])).
thf(f112,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X1) | (((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X0) | (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset)))) )),
  inference(trivial_inequality_removal,[],[f110])).
thf(f179,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X0) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) | (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (X0 != X1)) )),
  inference(equality_factoring,[],[f112])).
thf(f180,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X1) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) | (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (X0 != X1)) )),
  inference(equality_factoring,[],[f112])).
thf(f197,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) | (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (((in @ (sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = $true) | (((in @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (X0 != X1)) )),
  inference(constrained_superposition,[],[f97,f179])).
thf(f202,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) | (((in @ (sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = $true) | (X0 != X1) | (((in @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2)) )),
  inference(duplicate_literal_removal,[],[f197])).
thf(f207,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X2 @ emptyset))) | (X0 != X1)) )),
  inference(forward_subsumption_resolution,[],[f202,f99])).
thf(f217,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (X0 != X1) | (((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X0) | ($true != $true)) )),
  inference(constrained_superposition,[],[f207,f100])).
thf(f219,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X0) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (X0 != X1)) )),
  inference(trivial_inequality_removal,[],[f217])).
thf(f228,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) != $true) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | ($true = ((in @ (sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (X0 != X1)) )),
  inference(constrained_superposition,[],[f96,f219])).
thf(f231,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) != $true) | (X0 != X1) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | ($true = ((in @ (sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))) )),
  inference(duplicate_literal_removal,[],[f228])).
thf(f232,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))))) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (X0 != X1)) )),
  inference(forward_subsumption_resolution,[],[f231,f100])).
thf(f236,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 != X1) | (((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X0) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | ($true != $true) | (((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X1)) )),
  inference(constrained_superposition,[],[f95,f232])).
thf(f237,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X1) | (((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X0) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (X0 != X1)) )),
  inference(trivial_inequality_removal,[],[f236])).
thf(f244,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK2 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X2 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = $true) | (((sK2 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (X0 != X1) | (((setadjoin @ X2 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) | (((in @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (((setadjoin @ X2 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))) )),
  inference(constrained_superposition,[],[f97,f180])).
thf(f251,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK2 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X2 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = $true) | (((setadjoin @ X2 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) | (((sK2 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (((in @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (X0 != X1)) )),
  inference(duplicate_literal_removal,[],[f244])).
thf(f259,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (((sK2 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X2 @ emptyset))) = X2) | (((setadjoin @ X2 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) | (X0 != X1)) )),
  inference(forward_subsumption_resolution,[],[f251,f99])).
thf(f269,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((sK2 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X0) | (((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) | (X0 != X1)) )),
  inference(constrained_superposition,[],[f259,f94])).
thf(f272,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((sK2 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X0) | (((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) | (X0 != X1)) )),
  inference(trivial_inequality_removal,[],[f269])).
thf(f305,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X0) | (X0 != X1) | (X0 != X1)) )),
  inference(equality_factoring,[],[f237])).
thf(f319,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((sK3 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset))) = X0) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (X0 != X1)) )),
  inference(duplicate_literal_removal,[],[f305])).
thf(f354,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) != $true) | (((in @ X0 @ (setadjoin @ X0 @ emptyset))) != $true) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (X0 != X1) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset)))) )),
  inference(constrained_superposition,[],[f93,f319])).
thf(f369,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) != $true) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (((in @ X0 @ (setadjoin @ X0 @ emptyset))) != $true) | (X0 != X1)) )),
  inference(duplicate_literal_removal,[],[f354])).
thf(f373,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X0 @ emptyset)) @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) != $true) | (((setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = ((setadjoin @ X0 @ emptyset))) | (X0 != X1)) )),
  inference(forward_subsumption_resolution,[],[f369,f100])).
thf(f390,plain,(
  ( ! [X0 : $i] : ((((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X0 @ (setadjoin @ X0 @ emptyset)))) | (X0 != X0) | ($true != ((in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X0 @ emptyset))))) | (((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X0 @ (setadjoin @ X0 @ emptyset)))) | (X0 != X0)) )),
  inference(constrained_superposition,[],[f373,f272])).
thf(f392,plain,(
  ( ! [X0 : $i] : ((X0 != X0) | (((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X0 @ (setadjoin @ X0 @ emptyset)))) | ($true != ((in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X0 @ emptyset)))))) )),
  inference(duplicate_literal_removal,[],[f390])).
thf(f393,plain,(
  ( ! [X0 : $i] : (($true != ((in @ X0 @ (setadjoin @ X0 @ (setadjoin @ X0 @ emptyset))))) | (((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X0 @ (setadjoin @ X0 @ emptyset))))) )),
  inference(trivial_inequality_removal,[],[f392])).
thf(f396,plain,(
  ( ! [X0 : $i] : ((((setadjoin @ X0 @ emptyset)) = ((setadjoin @ X0 @ (setadjoin @ X0 @ emptyset))))) )),
  inference(forward_subsumption_resolution,[],[f393,f100])).
thf(f408,plain,(
  (((setadjoin @ sK5 @ emptyset)) != ((setadjoin @ sK5 @ emptyset)))),
  inference(constrained_superposition,[],[f79,f396])).
thf(f418,plain,(
  $false),
  inference(trivial_inequality_removal,[],[f408])).
% SZS output end Proof for theBenchmark