%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, del: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, bool: del).
thf(func_def_1, type, ind: del).
thf(func_def_2, type, arr: (del > del > del)).
thf(func_def_3, type, mem: ($i > del > $o)).
thf(func_def_4, type, ap: ($i > $i > $i)).
thf(func_def_5, type, lam: (del > ($i > $i) > $i)).
thf(func_def_6, type, p: ($i > $o)).
thf(func_def_7, type, inj__o: ($o > $i)).
thf(func_def_10, type, c_2Epred__set_2ESUBSET: (del > $i)).
thf(func_def_13, type, c_2Ebool_2EIN: (del > $i)).
thf(func_def_14, type, c_2Epred__set_2ECHOICE: (del > $i)).
thf(func_def_15, type, c_2Epred__set_2EDELETE: (del > $i)).
thf(func_def_16, type, c_2Epred__set_2EREST: (del > $i)).
thf(func_def_17, type, c_2Emin_2E_3D: (del > $i)).
thf(func_def_18, type, c_2Ebool_2E_21: (del > $i)).
thf(func_def_22, type, sK1: del).
thf(func_def_23, type, sK2: ($i > del > $i > $i)).
thf(func_def_24, type, sK3: ($i > $i > del > $i)).
thf(func_def_25, type, vNOT: ($o > $o)).
thf(f5,axiom,(
  ! [X2 : $i,X0 : del,X1 : del] : ((mem @ X2 @ (arr @ X0 @ X1)) => ! [X3 : $i] : ((mem @ X3 @ X0) => (mem @ (ap @ X2 @ X3) @ X1)))),
  file('/export/starexec/sandbox2/benchmark/Axioms/ITP001/ITP001^2.ax',ap_tp)).
thf(f12,axiom,(
  ! [X0 : del] : (mem @ (c_2Epred__set_2EDELETE @ X0) @ (arr @ (arr @ X0 @ bool) @ (arr @ X0 @ (arr @ X0 @ bool))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2EDELETE)).
thf(f13,conjecture,(
  ! [X1 : $i,X0 : del] : ((mem @ X1 @ (arr @ X0 @ bool)) => (p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1)) @ X1)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EREST__SUBSET)).
thf(f14,negated_conjecture,(
  ~ ! [X1 : $i,X0 : del] : ((mem @ X1 @ (arr @ X0 @ bool)) => (p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1)) @ X1)))),
  inference(negated_conjecture,[status(cth)],[f13])).
thf(f16,axiom,(
  ! [X0 : del] : (mem @ (c_2Epred__set_2ECHOICE @ X0) @ (arr @ (arr @ X0 @ bool) @ X0))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mem_c_2Epred__set_2ECHOICE)).
thf(f18,axiom,(
  ! [X1 : $i,X0 : del] : ((mem @ X1 @ (arr @ X0 @ bool)) => (((ap @ (c_2Epred__set_2EREST @ X0) @ X1)) = ((ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2EREST__DEF)).
thf(f25,axiom,(
  ! [X1 : $i,X0 : del] : ((mem @ X1 @ (arr @ X0 @ bool)) => ! [X2 : $i] : ((mem @ X2 @ (arr @ X0 @ bool)) => ((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ X1) @ X2)) <=> ! [X3 : $i] : ((mem @ X3 @ X0) => ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X3) @ X1)) => (p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X3) @ X2)))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_thm_2Epred__set_2ESUBSET__DEF)).
thf(f26,axiom,(
  ! [X0 : del,X1 : $i] : ((mem @ X1 @ (arr @ X0 @ bool)) => ! [X2 : $i] : ((mem @ X2 @ X0) => ! [X3 : $i] : ((mem @ X3 @ X0) => ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3))) <=> ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1)) & (X2 != X3))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_thm_2Epred__set_2EIN__DELETE)).
thf(f30,plain,(
  ! [X0 : $i,X1 : del] : ((mem @ X0 @ (arr @ X1 @ bool)) => (((ap @ (c_2Epred__set_2EREST @ X1) @ X0)) = ((ap @ (ap @ (c_2Epred__set_2EDELETE @ X1) @ X0) @ (ap @ (c_2Epred__set_2ECHOICE @ X1) @ X0)))))),
  inference(rectify,[],[f18])).
thf(f31,plain,(
  ! [X0 : $i,X1 : del] : (($true = ((mem @ X0 @ (arr @ X1 @ bool)))) => (((ap @ (c_2Epred__set_2EREST @ X1) @ X0)) = ((ap @ (ap @ (c_2Epred__set_2EDELETE @ X1) @ X0) @ (ap @ (c_2Epred__set_2ECHOICE @ X1) @ X0)))))),
  inference(fool_elimination,[],[f30])).
thf(f36,plain,(
  ! [X0 : del] : (mem @ (c_2Epred__set_2EDELETE @ X0) @ (arr @ (arr @ X0 @ bool) @ (arr @ X0 @ (arr @ X0 @ bool))))),
  inference(rectify,[],[f12])).
thf(f37,plain,(
  ! [X0 : del] : (((mem @ (c_2Epred__set_2EDELETE @ X0) @ (arr @ (arr @ X0 @ bool) @ (arr @ X0 @ (arr @ X0 @ bool))))) = $true)),
  inference(fool_elimination,[],[f36])).
thf(f42,plain,(
  ! [X0 : del] : (mem @ (c_2Epred__set_2ECHOICE @ X0) @ (arr @ (arr @ X0 @ bool) @ X0))),
  inference(rectify,[],[f16])).
thf(f43,plain,(
  ! [X0 : del] : (((mem @ (c_2Epred__set_2ECHOICE @ X0) @ (arr @ (arr @ X0 @ bool) @ X0))) = $true)),
  inference(fool_elimination,[],[f42])).
thf(f48,plain,(
  ! [X0 : $i,X1 : del,X2 : del] : ((mem @ X0 @ (arr @ X1 @ X2)) => ! [X3 : $i] : ((mem @ X3 @ X1) => (mem @ (ap @ X0 @ X3) @ X2)))),
  inference(rectify,[],[f5])).
thf(f49,plain,(
  ! [X1 : del,X0 : $i,X2 : del] : ((((mem @ X0 @ (arr @ X1 @ X2))) = $true) => ! [X3 : $i] : (($true = ((mem @ X3 @ X1))) => ($true = ((mem @ (ap @ X0 @ X3) @ X2)))))),
  inference(fool_elimination,[],[f48])).
thf(f50,plain,(
  ! [X0 : del,X1 : $i] : ((mem @ X1 @ (arr @ X0 @ bool)) => ! [X2 : $i] : ((mem @ X2 @ X0) => ! [X3 : $i] : ((mem @ X3 @ X0) => ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3))) <=> ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1)) & (X2 != X3))))))),
  inference(rectify,[],[f26])).
thf(f51,plain,(
  ! [X1 : $i,X0 : del] : ((((mem @ X1 @ (arr @ X0 @ bool))) = $true) => ! [X2 : $i] : ((((mem @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((mem @ X3 @ X0)) = $true) => (((X2 != X3) & (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1))) = $true)) <=> (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3)))) = $true)))))),
  inference(fool_elimination,[],[f50])).
thf(f58,plain,(
  ! [X0 : $i,X1 : del] : ((mem @ X0 @ (arr @ X1 @ bool)) => ! [X2 : $i] : ((mem @ X2 @ (arr @ X1 @ bool)) => ((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2)) <=> ! [X3 : $i] : ((mem @ X3 @ X1) => ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X0)) => (p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X2)))))))),
  inference(rectify,[],[f25])).
thf(f59,plain,(
  ! [X0 : $i,X1 : del] : (($true = ((mem @ X0 @ (arr @ X1 @ bool)))) => ! [X2 : $i] : ((((mem @ X2 @ (arr @ X1 @ bool))) = $true) => ((((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true) <=> ! [X3 : $i] : (($true = ((mem @ X3 @ X1))) => ((((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X0))) = $true) => ($true = ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X2)))))))))),
  inference(fool_elimination,[],[f58])).
thf(f60,plain,(
  ~ ! [X0 : $i,X1 : del] : ((mem @ X0 @ (arr @ X1 @ bool)) => (p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ (ap @ (c_2Epred__set_2EREST @ X1) @ X0)) @ X0)))),
  inference(rectify,[],[f14])).
thf(f61,plain,(
  ~ ! [X1 : del,X0 : $i] : (($true = ((mem @ X0 @ (arr @ X1 @ bool)))) => ($true = ((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ (ap @ (c_2Epred__set_2EREST @ X1) @ X0)) @ X0)))))),
  inference(fool_elimination,[],[f60])).
thf(f78,plain,(
  ? [X0 : $i,X1 : del] : (($true = ((mem @ X0 @ (arr @ X1 @ bool)))) & ($true != ((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ (ap @ (c_2Epred__set_2EREST @ X1) @ X0)) @ X0)))))),
  inference(ennf_transformation,[],[f61])).
thf(f81,plain,(
  ! [X1 : del,X0 : $i] : (($true != ((mem @ X0 @ (arr @ X1 @ bool)))) | (((ap @ (c_2Epred__set_2EREST @ X1) @ X0)) = ((ap @ (ap @ (c_2Epred__set_2EDELETE @ X1) @ X0) @ (ap @ (c_2Epred__set_2ECHOICE @ X1) @ X0)))))),
  inference(ennf_transformation,[],[f31])).
thf(f82,plain,(
  ! [X0 : $i,X1 : del,X2 : del] : (! [X3 : $i] : (($true != ((mem @ X3 @ X1))) | ($true = ((mem @ (ap @ X0 @ X3) @ X2)))) | (((mem @ X0 @ (arr @ X1 @ X2))) != $true))),
  inference(ennf_transformation,[],[f49])).
thf(f83,plain,(
  ! [X0 : $i,X1 : del] : (! [X2 : $i] : (((((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true) <=> ! [X3 : $i] : ((($true = ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X2)))) | (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X0))) != $true)) | ($true != ((mem @ X3 @ X1))))) | (((mem @ X2 @ (arr @ X1 @ bool))) != $true)) | ($true != ((mem @ X0 @ (arr @ X1 @ bool)))))),
  inference(ennf_transformation,[],[f59])).
thf(f84,plain,(
  ! [X0 : $i,X1 : del] : (($true != ((mem @ X0 @ (arr @ X1 @ bool)))) | ! [X2 : $i] : (((((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true) <=> ! [X3 : $i] : (($true = ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X2)))) | (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X0))) != $true) | ($true != ((mem @ X3 @ X1))))) | (((mem @ X2 @ (arr @ X1 @ bool))) != $true)))),
  inference(flattening,[],[f83])).
thf(f85,plain,(
  ! [X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X0 @ bool))) != $true) | ! [X2 : $i] : (! [X3 : $i] : ((((mem @ X3 @ X0)) != $true) | (((X2 != X3) & (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1))) = $true)) <=> (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3)))) = $true))) | (((mem @ X2 @ X0)) != $true)))),
  inference(ennf_transformation,[],[f51])).
thf(f86,plain,(
  ($true = ((mem @ sK0 @ (arr @ sK1 @ bool)))) & (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ sK1) @ (ap @ (c_2Epred__set_2EREST @ sK1) @ sK0)) @ sK0))) != $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1))],[f78])).
thf(f87,plain,(
  ! [X0 : $i,X1 : del] : (($true != ((mem @ X0 @ (arr @ X1 @ bool)))) | ! [X2 : $i] : ((((((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true) | ? [X3 : $i] : (($true != ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X2)))) & (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X0))) = $true) & ($true = ((mem @ X3 @ X1))))) & (! [X3 : $i] : (($true = ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X2)))) | (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X0))) != $true) | ($true != ((mem @ X3 @ X1)))) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) != $true))) | (((mem @ X2 @ (arr @ X1 @ bool))) != $true)))),
  inference(nnf_transformation,[],[f84])).
thf(f88,plain,(
  ! [X0 : $i,X1 : del] : (($true != ((mem @ X0 @ (arr @ X1 @ bool)))) | ! [X2 : $i] : ((((((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true) | ? [X3 : $i] : (($true != ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X2)))) & (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X3) @ X0))) = $true) & ($true = ((mem @ X3 @ X1))))) & (! [X4 : $i] : ((((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X4) @ X2))) = $true) | ($true != ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X4) @ X0)))) | (((mem @ X4 @ X1)) != $true)) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) != $true))) | (((mem @ X2 @ (arr @ X1 @ bool))) != $true)))),
  inference(rectify,[],[f87])).
thf(f89,plain,(
  ! [X0 : $i,X1 : del] : (($true != ((mem @ X0 @ (arr @ X1 @ bool)))) | ! [X2 : $i] : ((((((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true) | (($true != ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ (sK2 @ X2 @ X1 @ X0)) @ X2)))) & (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ (sK2 @ X2 @ X1 @ X0)) @ X0))) = $true) & ($true = ((mem @ (sK2 @ X2 @ X1 @ X0) @ X1))))) & (! [X4 : $i] : ((((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X4) @ X2))) = $true) | ($true != ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ X4) @ X0)))) | (((mem @ X4 @ X1)) != $true)) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) != $true))) | (((mem @ X2 @ (arr @ X1 @ bool))) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,$thf(sK2 @ X2 @ X1 @ X0))],[f88])).
thf(f92,plain,(
  ! [X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X0 @ bool))) != $true) | ! [X2 : $i] : (! [X3 : $i] : ((((mem @ X3 @ X0)) != $true) | ((((X2 != X3) & (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1))) = $true)) | (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3)))) != $true)) & ((((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3)))) = $true) | ((X2 = X3) | (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1))) != $true))))) | (((mem @ X2 @ X0)) != $true)))),
  inference(nnf_transformation,[],[f85])).
thf(f93,plain,(
  ! [X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X0 @ bool))) != $true) | ! [X2 : $i] : (! [X3 : $i] : ((((mem @ X3 @ X0)) != $true) | ((((X2 != X3) & (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1))) = $true)) | (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3)))) != $true)) & ((((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3)))) = $true) | (X2 = X3) | (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1))) != $true)))) | (((mem @ X2 @ X0)) != $true)))),
  inference(flattening,[],[f92])).
thf(f94,plain,(
  ! [X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((ap @ (c_2Epred__set_2EREST @ X0) @ X1)) = ((ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1)))))),
  inference(rectify,[],[f81])).
thf(f95,plain,(
  (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ sK1) @ (ap @ (c_2Epred__set_2EREST @ sK1) @ sK0)) @ sK0))) != $true)),
  inference(cnf_transformation,[],[f86])).
thf(f96,plain,(
  ($true = ((mem @ sK0 @ (arr @ sK1 @ bool))))),
  inference(cnf_transformation,[],[f86])).
thf(f98,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : del] : (($true = ((mem @ (sK2 @ X2 @ X1 @ X0) @ X1))) | (((mem @ X2 @ (arr @ X1 @ bool))) != $true) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true) | ($true != ((mem @ X0 @ (arr @ X1 @ bool))))) )),
  inference(cnf_transformation,[],[f89])).
thf(f99,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : del] : ((((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ (sK2 @ X2 @ X1 @ X0)) @ X0))) = $true) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true) | (((mem @ X2 @ (arr @ X1 @ bool))) != $true) | ($true != ((mem @ X0 @ (arr @ X1 @ bool))))) )),
  inference(cnf_transformation,[],[f89])).
thf(f100,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : del] : (($true != ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X1) @ (sK2 @ X2 @ X1 @ X0)) @ X2)))) | ($true != ((mem @ X0 @ (arr @ X1 @ bool)))) | (((mem @ X2 @ (arr @ X1 @ bool))) != $true) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X1) @ X0) @ X2))) = $true)) )),
  inference(cnf_transformation,[],[f89])).
thf(f101,plain,(
  ( ! [X0 : del] : ((((mem @ (c_2Epred__set_2ECHOICE @ X0) @ (arr @ (arr @ X0 @ bool) @ X0))) = $true)) )),
  inference(cnf_transformation,[],[f43])).
thf(f102,plain,(
  ( ! [X2 : del,X3 : $i,X0 : $i,X1 : del] : (($true = ((mem @ (ap @ X0 @ X3) @ X2))) | ($true != ((mem @ X3 @ X1))) | (((mem @ X0 @ (arr @ X1 @ X2))) != $true)) )),
  inference(cnf_transformation,[],[f82])).
thf(f106,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : $i] : ((((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X3)))) != $true) | (((mem @ X2 @ X0)) != $true) | (((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ X2) @ X1))) = $true) | (((mem @ X3 @ X0)) != $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true)) )),
  inference(cnf_transformation,[],[f93])).
thf(f108,plain,(
  ( ! [X0 : del,X1 : $i] : ((((ap @ (c_2Epred__set_2EREST @ X0) @ X1)) = ((ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1)))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true)) )),
  inference(cnf_transformation,[],[f94])).
thf(f112,plain,(
  ( ! [X0 : del] : ((((mem @ (c_2Epred__set_2EDELETE @ X0) @ (arr @ (arr @ X0 @ bool) @ (arr @ X0 @ (arr @ X0 @ bool))))) = $true)) )),
  inference(cnf_transformation,[],[f37])).
thf(f114,definition,(
  ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
  introduced(theory,[fool_exhaustiveness_axiom])).
thf(f119,plain,(
  (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ sK1) @ (ap @ (c_2Epred__set_2EREST @ sK1) @ sK0)) @ sK0))) = $false) | ($true != $true)),
  inference(superposition,[],[f95,f114])).
thf(f125,plain,(
  (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ sK1) @ (ap @ (c_2Epred__set_2EREST @ sK1) @ sK0)) @ sK0))) = $false)),
  inference(trivial_inequality_removal,[],[f119])).
thf(f129,plain,(
  ( ! [X2 : del,X3 : del,X0 : del,X1 : $i] : (($true != ((mem @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ (arr @ X3 @ X2)))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1) @ X2)) = $true) | (((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X3)) != $true)) )),
  inference(superposition,[],[f102,f108])).
thf(f151,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : $i] : ((((mem @ X3 @ X0)) != $true) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3)) @ X1))) = $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | ($true = ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ (sK2 @ X1 @ X0 @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3))) @ X2)))) | ($true != $true) | (((mem @ X2 @ (arr @ X0 @ bool))) != $true) | ($true != ((mem @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3) @ (arr @ X0 @ bool)))) | ($true != ((mem @ (sK2 @ X1 @ X0 @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3)) @ X0)))) )),
  inference(superposition,[],[f106,f99])).
thf(f156,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : $i] : ((((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3)) @ X1))) = $true) | ($true != ((mem @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3) @ (arr @ X0 @ bool)))) | (((mem @ X2 @ (arr @ X0 @ bool))) != $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | ($true = ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ (sK2 @ X1 @ X0 @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3))) @ X2)))) | ($true != ((mem @ (sK2 @ X1 @ X0 @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3)) @ X0))) | (((mem @ X3 @ X0)) != $true)) )),
  inference(trivial_inequality_removal,[],[f151])).
thf(f157,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : del,X1 : $i] : (($true = ((p @ (ap @ (ap @ (c_2Ebool_2EIN @ X0) @ (sK2 @ X1 @ X0 @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3))) @ X2)))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ X2 @ (arr @ X0 @ bool))) != $true) | (((mem @ X3 @ X0)) != $true) | ($true != ((mem @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3) @ (arr @ X0 @ bool)))) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X2) @ X3)) @ X1))) = $true)) )),
  inference(forward_subsumption_resolution,[],[f156,f98])).
thf(f169,plain,(
  ( ! [X2 : del,X3 : del,X0 : del,X1 : $i,X4 : del] : ((((mem @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1) @ X3)) = $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ (c_2Epred__set_2EDELETE @ X0) @ (arr @ X4 @ (arr @ X2 @ X3)))) != $true) | ($true != $true) | ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X2))) | (((mem @ X1 @ X4)) != $true)) )),
  inference(superposition,[],[f129,f102])).
thf(f172,plain,(
  ( ! [X2 : del,X3 : del,X0 : del,X1 : $i,X4 : del] : ((((mem @ (c_2Epred__set_2EDELETE @ X0) @ (arr @ X4 @ (arr @ X2 @ X3)))) != $true) | (((mem @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1) @ X3)) = $true) | ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X2))) | (((mem @ X1 @ X4)) != $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true)) )),
  inference(trivial_inequality_removal,[],[f169])).
thf(f229,plain,(
  ( ! [X0 : del,X1 : $i] : (($true != $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1) @ (arr @ X0 @ bool))) = $true) | ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X0))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true)) )),
  inference(superposition,[],[f172,f112])).
thf(f231,plain,(
  ( ! [X0 : del,X1 : $i] : (($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X0))) | ($true != $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1) @ (arr @ X0 @ bool))) = $true)) )),
  inference(duplicate_literal_removal,[],[f229])).
thf(f232,plain,(
  ( ! [X0 : del,X1 : $i] : ((((mem @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1) @ (arr @ X0 @ bool))) = $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X0)))) )),
  inference(trivial_inequality_removal,[],[f231])).
thf(f403,plain,(
  ( ! [X2 : $i,X0 : del,X1 : $i] : (($true = ((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X2)) @ X1)))) | ($true != ((mem @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X2) @ (arr @ X0 @ bool)))) | ($true = ((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X2)) @ X1)))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ X2 @ X0)) != $true) | ($true != $true) | ($true != ((mem @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X2) @ (arr @ X0 @ bool)))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true)) )),
  inference(superposition,[],[f100,f157])).
thf(f410,plain,(
  ( ! [X2 : $i,X0 : del,X1 : $i] : ((((mem @ X2 @ X0)) != $true) | ($true = ((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X2)) @ X1)))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | ($true != $true) | ($true != ((mem @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X2) @ (arr @ X0 @ bool))))) )),
  inference(duplicate_literal_removal,[],[f403])).
thf(f411,plain,(
  ( ! [X2 : $i,X0 : del,X1 : $i] : (($true = ((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X2)) @ X1)))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | ($true != ((mem @ (ap @ (ap @ (c_2Epred__set_2EDELETE @ X0) @ X1) @ X2) @ (arr @ X0 @ bool)))) | (((mem @ X2 @ X0)) != $true)) )),
  inference(trivial_inequality_removal,[],[f410])).
thf(f439,plain,(
  ( ! [X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1) @ (arr @ X0 @ bool))) != $true) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1)) @ X1))) = $true) | ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X0)))) )),
  inference(superposition,[],[f411,f108])).
thf(f441,plain,(
  ( ! [X0 : del,X1 : $i] : ((((mem @ X1 @ (arr @ X0 @ bool))) != $true) | (((mem @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1) @ (arr @ X0 @ bool))) != $true) | ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X0))) | (((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1)) @ X1))) = $true)) )),
  inference(duplicate_literal_removal,[],[f439])).
thf(f444,plain,(
  ( ! [X0 : del,X1 : $i] : ((((p @ (ap @ (ap @ (c_2Epred__set_2ESUBSET @ X0) @ (ap @ (c_2Epred__set_2EREST @ X0) @ X1)) @ X1))) = $true) | ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ X0) @ X1) @ X0))) | (((mem @ X1 @ (arr @ X0 @ bool))) != $true)) )),
  inference(forward_subsumption_resolution,[],[f441,f232])).
thf(f456,plain,(
  ($true != ((mem @ sK0 @ (arr @ sK1 @ bool)))) | ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ sK1) @ sK0) @ sK1))) | ($true = $false)),
  inference(superposition,[],[f444,f125])).
thf(f461,plain,(
  ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ sK1) @ sK0) @ sK1))) | ($true != ((mem @ sK0 @ (arr @ sK1 @ bool))))),
  inference(trivial_inequality_removal,[],[f456])).
thf(f468,plain,(
  ($true != ((mem @ (ap @ (c_2Epred__set_2ECHOICE @ sK1) @ sK0) @ sK1)))),
  inference(forward_subsumption_resolution,[],[f461,f96])).
thf(f498,plain,(
  ( ! [X0 : del] : ((((mem @ (c_2Epred__set_2ECHOICE @ sK1) @ (arr @ X0 @ sK1))) != $true) | ($true != ((mem @ sK0 @ X0))) | ($true != $true)) )),
  inference(superposition,[],[f468,f102])).
thf(f500,plain,(
  ( ! [X0 : del] : ((((mem @ (c_2Epred__set_2ECHOICE @ sK1) @ (arr @ X0 @ sK1))) != $true) | ($true != ((mem @ sK0 @ X0)))) )),
  inference(trivial_inequality_removal,[],[f498])).
thf(f550,plain,(
  ($true != $true) | ($true != ((mem @ sK0 @ (arr @ sK1 @ bool))))),
  inference(superposition,[],[f500,f101])).
thf(f553,plain,(
  ($true != ((mem @ sK0 @ (arr @ sK1 @ bool))))),
  inference(trivial_inequality_removal,[],[f550])).
thf(f554,plain,(
  $false),
  inference(forward_subsumption_resolution,[],[f553,f96])).
% SZS output end Proof for theBenchmark