%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, a: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_3, type, diff: !>[X0: $tType, X1: $tType]:(((X0 > X1) > (X0 > X1) > X0))).
thf(func_def_4, type, sK0: (a > $o)).
thf(func_def_5, type, sK1: (a > $o)).
thf(func_def_6, type, sK2: (a > $o)).
thf(func_def_7, type, sK3: ((a > a) > a)).
thf(func_def_8, type, sK4: (a > (a > a) > a)).
thf(func_def_9, type, sK5: ((a > a) > a)).
thf(func_def_10, type, sK6: (a > a)).
thf(func_def_11, type, sK7: (a > a)).
thf(func_def_12, type, sK8: (a > a)).
thf(func_def_13, type, sK9: (a > a)).
thf(func_def_14, type, vNOT: ($o > $o)).
thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_16, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_17, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_19, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_20, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_21, type, sK11: ((a > a) > a)).
thf(func_def_22, type, sK12: ((a > a > a > a) > a)).
thf(func_def_23, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_24, type, db5: !>[X0: $tType]:(X0)).
thf(func_def_25, type, sK13: ((a > a > a > a) > a)).
thf(func_def_26, type, sK14: ((a > a > a) > a)).
thf(func_def_27, type, sK15: ((a > a > a > a) > a)).
thf(func_def_28, type, sK16: ((a > a > a > a) > a)).
thf(func_def_29, type, sK17: ((a > a) > (a > a > a) > a)).
thf(func_def_30, type, sK18: ((a > a > a) > a)).
thf(func_def_31, type, sK19: ((a > a > a) > a)).
thf(func_def_32, type, sK20: ((a > a > a) > a)).
thf(func_def_33, type, sK21: ((a > a > a) > a)).
thf(func_def_34, type, sK22: ((a > a > a) > a)).
thf(func_def_35, type, sK23: ((a > a > a) > a)).
thf(func_def_36, type, sK24: ((a > a > a) > a)).
thf(func_def_37, type, sK25: ((a > a > a) > a)).
thf(func_def_38, type, sK26: ((a > a > a) > a)).
thf(func_def_39, type, sK27: ((a > a > a > a) > a)).
thf(func_def_40, type, sK28: ((a > a > a) > a)).
thf(func_def_41, type, sK29: a).
thf(func_def_42, type, sK30: a).
thf(func_def_43, type, sK31: a).
thf(func_def_44, type, sK32: a).
thf(func_def_45, type, sK33: ((a > a > a) > a)).
thf(func_def_46, type, sK34: ((a > a > a) > a)).
thf(func_def_47, type, sK35: ((a > a > a) > a)).
thf(func_def_48, type, sK36: ((a > a > a) > a)).
thf(func_def_49, type, sK37: ((a > a > a) > a)).
thf(func_def_50, type, sK38: ((a > a > a) > a)).
thf(func_def_51, type, sK39: ((a > a > a) > a)).
thf(func_def_52, type, sK40: ((a > a > a) > a)).
thf(func_def_53, type, sK41: ((a > a > a) > a)).
thf(func_def_54, type, sK42: ((a > a > a) > a)).
thf(func_def_55, type, sK43: ((a > a > a) > a)).
thf(func_def_56, type, sK44: ((a > a > a) > a)).
thf(func_def_57, type, sK45: ((a > a > a) > a)).
thf(func_def_58, type, sK46: ((a > a > a) > a)).
thf(func_def_59, type, sK47: ((a > a > a) > a)).
thf(func_def_60, type, sK48: ((a > a > a) > a)).
thf(func_def_61, type, sK49: ((a > a > a) > a)).
thf(func_def_62, type, sK50: a).
thf(func_def_63, type, sK51: a).
thf(func_def_64, type, sK52: a).
thf(func_def_65, type, sK53: a).
thf(func_def_66, type, sK54: a).
thf(func_def_67, type, sK55: a).
thf(func_def_68, type, sK56: a).
thf(func_def_69, type, sK57: a).
thf(func_def_70, type, sK58: a).
thf(func_def_71, type, sK59: a).
thf(func_def_72, type, sK60: a).
thf(func_def_73, type, sK61: a).
thf(func_def_74, type, sK62: ((a > a > a) > a)).
thf(func_def_75, type, sK63: ((a > a > a) > a)).
thf(func_def_76, type, sK64: ((a > a > a) > a)).
thf(func_def_77, type, sK65: ((a > a > a) > a)).
thf(func_def_78, type, sK66: ((a > a > a) > a)).
thf(func_def_79, type, sK67: ((a > a > a) > a)).
thf(func_def_80, type, sK68: ((a > a > a) > a)).
thf(func_def_81, type, sK69: ((a > a > a > a) > a)).
thf(f1,conjecture,(
  ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((? [X3 : (a > a)] : (! [X5 : a] : ((X0 @ X5) => (X1 @ (X3 @ X5))) & ! [X4 : a] : ((X1 @ X4) => ? [X5 : a] : (! [X6 : a] : (((X4 = ((X3 @ X6))) & (X0 @ X6)) => (X6 = X5)) & (X0 @ X5) & (X4 = ((X3 @ X5)))))) & ? [X3 : (a > a)] : (! [X5 : a] : ((X1 @ X5) => (X2 @ (X3 @ X5))) & ! [X4 : a] : ((X2 @ X4) => ? [X5 : a] : ((X1 @ X5) & ! [X6 : a] : (((X4 = ((X3 @ X6))) & (X1 @ X6)) => (X6 = X5)) & (X4 = ((X3 @ X5))))))) => ? [X3 : (a > a)] : (! [X5 : a] : ((X0 @ X5) => (X2 @ (X3 @ X5))) & ! [X4 : a] : ((X2 @ X4) => ? [X5 : a] : (! [X6 : a] : (((X4 = ((X3 @ X6))) & (X0 @ X6)) => (X6 = X5)) & (X4 = ((X3 @ X5))) & (X0 @ X5)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEQP1_1C_pme)).
thf(f2,negated_conjecture,(
  ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((? [X3 : (a > a)] : (! [X5 : a] : ((X0 @ X5) => (X1 @ (X3 @ X5))) & ! [X4 : a] : ((X1 @ X4) => ? [X5 : a] : (! [X6 : a] : (((X4 = ((X3 @ X6))) & (X0 @ X6)) => (X6 = X5)) & (X0 @ X5) & (X4 = ((X3 @ X5)))))) & ? [X3 : (a > a)] : (! [X5 : a] : ((X1 @ X5) => (X2 @ (X3 @ X5))) & ! [X4 : a] : ((X2 @ X4) => ? [X5 : a] : ((X1 @ X5) & ! [X6 : a] : (((X4 = ((X3 @ X6))) & (X1 @ X6)) => (X6 = X5)) & (X4 = ((X3 @ X5))))))) => ? [X3 : (a > a)] : (! [X5 : a] : ((X0 @ X5) => (X2 @ (X3 @ X5))) & ! [X4 : a] : ((X2 @ X4) => ? [X5 : a] : (! [X6 : a] : (((X4 = ((X3 @ X6))) & (X0 @ X6)) => (X6 = X5)) & (X4 = ((X3 @ X5))) & (X0 @ X5)))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,plain,(
  ~ ! [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : ((? [X3 : (a > a)] : (! [X4 : a] : ((X0 @ X4) => (X1 @ (X3 @ X4))) & ! [X5 : a] : ((X1 @ X5) => ? [X6 : a] : (! [X7 : a] : (((((X3 @ X7)) = X5) & (X0 @ X7)) => (X6 = X7)) & (X0 @ X6) & (((X3 @ X6)) = X5)))) & ? [X8 : (a > a)] : (! [X9 : a] : ((X1 @ X9) => (X2 @ (X8 @ X9))) & ! [X10 : a] : ((X2 @ X10) => ? [X11 : a] : ((X1 @ X11) & ! [X12 : a] : (((((X8 @ X12)) = X10) & (X1 @ X12)) => (X11 = X12)) & (((X8 @ X11)) = X10))))) => ? [X13 : (a > a)] : (! [X14 : a] : ((X0 @ X14) => (X2 @ (X13 @ X14))) & ! [X15 : a] : ((X2 @ X15) => ? [X16 : a] : (! [X17 : a] : (((((X13 @ X17)) = X15) & (X0 @ X17)) => (X16 = X17)) & (((X13 @ X16)) = X15) & (X0 @ X16)))))),
  inference(rectify,[],[f2])).
thf(f4,plain,(
  ~ ! [X2 : (a > $o),X1 : (a > $o),X0 : (a > $o)] : ((? [X8 : (a > a)] : (! [X9 : a] : ((((X1 @ X9)) = $true) => (((X2 @ (X8 @ X9))) = $true)) & ! [X10 : a] : ((((X2 @ X10)) = $true) => ? [X11 : a] : ((((X8 @ X11)) = X10) & (((X1 @ X11)) = $true) & ! [X12 : a] : ((($true = ((X1 @ X12))) & (((X8 @ X12)) = X10)) => (X11 = X12))))) & ? [X3 : (a > a)] : (! [X4 : a] : ((((X0 @ X4)) = $true) => (((X1 @ (X3 @ X4))) = $true)) & ! [X5 : a] : ((((X1 @ X5)) = $true) => ? [X6 : a] : (! [X7 : a] : (((((X3 @ X7)) = X5) & (((X0 @ X7)) = $true)) => (X6 = X7)) & (((X0 @ X6)) = $true) & (((X3 @ X6)) = X5))))) => ? [X13 : (a > a)] : (! [X14 : a] : ((((X0 @ X14)) = $true) => ($true = ((X2 @ (X13 @ X14))))) & ! [X15 : a] : (($true = ((X2 @ X15))) => ? [X16 : a] : ((((X13 @ X16)) = X15) & ! [X17 : a] : (((((X13 @ X17)) = X15) & (((X0 @ X17)) = $true)) => (X16 = X17)) & (((X0 @ X16)) = $true)))))),
  inference(fool_elimination,[],[f3])).
thf(f6,plain,(
  ? [X2 : (a > $o),X1 : (a > $o),X0 : (a > $o)] : (! [X13 : (a > a)] : (? [X14 : a] : ((((X0 @ X14)) = $true) & ($true != ((X2 @ (X13 @ X14))))) | ? [X15 : a] : (! [X16 : a] : ((((X13 @ X16)) != X15) | ? [X17 : a] : ((X16 != X17) & ((((X13 @ X17)) = X15) & (((X0 @ X17)) = $true))) | (((X0 @ X16)) != $true)) & ($true = ((X2 @ X15))))) & (? [X8 : (a > a)] : (! [X9 : a] : ((((X1 @ X9)) != $true) | (((X2 @ (X8 @ X9))) = $true)) & ! [X10 : a] : (? [X11 : a] : ((((X8 @ X11)) = X10) & (((X1 @ X11)) = $true) & ! [X12 : a] : ((X11 = X12) | (($true != ((X1 @ X12))) | (((X8 @ X12)) != X10)))) | (((X2 @ X10)) != $true))) & ? [X3 : (a > a)] : (! [X4 : a] : ((((X0 @ X4)) != $true) | (((X1 @ (X3 @ X4))) = $true)) & ! [X5 : a] : (? [X6 : a] : (! [X7 : a] : ((X6 = X7) | ((((X3 @ X7)) != X5) | (((X0 @ X7)) != $true))) & (((X0 @ X6)) = $true) & (((X3 @ X6)) = X5)) | (((X1 @ X5)) != $true)))))),
  inference(ennf_transformation,[],[f4])).
thf(f7,plain,(
  ? [X1 : (a > $o),X0 : (a > $o),X2 : (a > $o)] : (! [X13 : (a > a)] : (? [X15 : a] : (! [X16 : a] : ((((X0 @ X16)) != $true) | ? [X17 : a] : ((X16 != X17) & (((X13 @ X17)) = X15) & (((X0 @ X17)) = $true)) | (((X13 @ X16)) != X15)) & ($true = ((X2 @ X15)))) | ? [X14 : a] : ((((X0 @ X14)) = $true) & ($true != ((X2 @ (X13 @ X14)))))) & ? [X3 : (a > a)] : (! [X5 : a] : ((((X1 @ X5)) != $true) | ? [X6 : a] : (! [X7 : a] : ((((X3 @ X7)) != X5) | (((X0 @ X7)) != $true) | (X6 = X7)) & (((X3 @ X6)) = X5) & (((X0 @ X6)) = $true))) & ! [X4 : a] : ((((X0 @ X4)) != $true) | (((X1 @ (X3 @ X4))) = $true))) & ? [X8 : (a > a)] : (! [X9 : a] : ((((X1 @ X9)) != $true) | (((X2 @ (X8 @ X9))) = $true)) & ! [X10 : a] : (? [X11 : a] : ((((X8 @ X11)) = X10) & (((X1 @ X11)) = $true) & ! [X12 : a] : ((X11 = X12) | ($true != ((X1 @ X12))) | (((X8 @ X12)) != X10))) | (((X2 @ X10)) != $true))))),
  inference(flattening,[],[f6])).
thf(f8,plain,(
  ? [X0 : (a > $o),X1 : (a > $o),X2 : (a > $o)] : (! [X3 : (a > a)] : (? [X4 : a] : (! [X5 : a] : ((((X1 @ X5)) != $true) | ? [X6 : a] : ((X5 != X6) & (((X3 @ X6)) = X4) & (((X1 @ X6)) = $true)) | (((X3 @ X5)) != X4)) & (((X2 @ X4)) = $true)) | ? [X7 : a] : ((((X1 @ X7)) = $true) & (((X2 @ (X3 @ X7))) != $true))) & ? [X8 : (a > a)] : (! [X9 : a] : ((((X0 @ X9)) != $true) | ? [X10 : a] : (! [X11 : a] : ((((X8 @ X11)) != X9) | (((X1 @ X11)) != $true) | (X10 = X11)) & (((X8 @ X10)) = X9) & (((X1 @ X10)) = $true))) & ! [X12 : a] : (($true != ((X1 @ X12))) | (((X0 @ (X8 @ X12))) = $true))) & ? [X13 : (a > a)] : (! [X14 : a] : ((((X0 @ X14)) != $true) | ($true = ((X2 @ (X13 @ X14))))) & ! [X15 : a] : (? [X16 : a] : ((((X13 @ X16)) = X15) & (((X0 @ X16)) = $true) & ! [X17 : a] : ((X16 = X17) | (((X0 @ X17)) != $true) | (((X13 @ X17)) != X15))) | ($true != ((X2 @ X15))))))),
  inference(rectify,[],[f7])).
thf(f9,plain,(
  ! [X3 : (a > a)] : ((! [X5 : a] : (($true != ((sK1 @ X5))) | ((((sK4 @ X5 @ X3)) != X5) & (((sK3 @ X3)) = ((X3 @ (sK4 @ X5 @ X3)))) & ($true = ((sK1 @ (sK4 @ X5 @ X3))))) | (((X3 @ X5)) != ((sK3 @ X3)))) & (((sK2 @ (sK3 @ X3))) = $true)) | ((((sK1 @ (sK5 @ X3))) = $true) & ($true != ((sK2 @ (X3 @ (sK5 @ X3))))))) & (! [X9 : a] : ((((sK0 @ X9)) != $true) | (! [X11 : a] : ((((sK6 @ X11)) != X9) | ($true != ((sK1 @ X11))) | (((sK7 @ X9)) = X11)) & (((sK6 @ (sK7 @ X9))) = X9) & (((sK1 @ (sK7 @ X9))) = $true))) & ! [X12 : a] : ((((sK1 @ X12)) != $true) | ($true = ((sK0 @ (sK6 @ X12)))))) & (! [X14 : a] : ((((sK0 @ X14)) != $true) | (((sK2 @ (sK8 @ X14))) = $true)) & ! [X15 : a] : (((((sK8 @ (sK9 @ X15))) = X15) & (((sK0 @ (sK9 @ X15))) = $true) & ! [X17 : a] : ((((sK9 @ X15)) = X17) | (((sK0 @ X17)) != $true) | (((sK8 @ X17)) != X15))) | (((sK2 @ X15)) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,vAPP,sK6,vAPP,sK8,vAPP]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X2,$thf(sK2)),skolemize(X16,$thf(sK9 @ X15)),skolemize(X16,$thf(sK9 @ X15)),skolemize(X16,$thf(sK9 @ X15)),skolemize(X8,$thf(sK6)),skolemize(X16,$thf(sK9 @ X15)),skolemize(X13,$thf(sK8)),skolemize(X16,$thf(sK9 @ X15))],[f8])).
thf(f10,plain,(
  ( ! [X17 : a,X15 : a] : ((((sK9 @ X15)) = X17) | (((sK0 @ X17)) != $true) | (((sK8 @ X17)) != X15) | (((sK2 @ X15)) != $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f11,plain,(
  ( ! [X15 : a] : ((((sK0 @ (sK9 @ X15))) = $true) | (((sK2 @ X15)) != $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f12,plain,(
  ( ! [X15 : a] : ((((sK8 @ (sK9 @ X15))) = X15) | (((sK2 @ X15)) != $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f13,plain,(
  ( ! [X14 : a] : ((((sK2 @ (sK8 @ X14))) = $true) | (((sK0 @ X14)) != $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f14,plain,(
  ( ! [X12 : a] : (($true = ((sK0 @ (sK6 @ X12)))) | (((sK1 @ X12)) != $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f15,plain,(
  ( ! [X9 : a] : ((((sK1 @ (sK7 @ X9))) = $true) | (((sK0 @ X9)) != $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f16,plain,(
  ( ! [X9 : a] : ((((sK6 @ (sK7 @ X9))) = X9) | (((sK0 @ X9)) != $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f17,plain,(
  ( ! [X11 : a,X9 : a] : ((((sK0 @ X9)) != $true) | (((sK6 @ X11)) != X9) | ($true != ((sK1 @ X11))) | (((sK7 @ X9)) = X11)) )),
  inference(cnf_transformation,[],[f9])).
thf(f18,plain,(
  ( ! [X3 : (a > a)] : (($true != ((sK2 @ (X3 @ (sK5 @ X3))))) | (((sK2 @ (sK3 @ X3))) = $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f19,plain,(
  ( ! [X3 : (a > a)] : ((((sK2 @ (sK3 @ X3))) = $true) | (((sK1 @ (sK5 @ X3))) = $true)) )),
  inference(cnf_transformation,[],[f9])).
thf(f20,plain,(
  ( ! [X3 : (a > a),X5 : a] : (($true = ((sK1 @ (sK4 @ X5 @ X3)))) | ($true != ((sK2 @ (X3 @ (sK5 @ X3))))) | ($true != ((sK1 @ X5))) | (((X3 @ X5)) != ((sK3 @ X3)))) )),
  inference(cnf_transformation,[],[f9])).
thf(f21,plain,(
  ( ! [X3 : (a > a),X5 : a] : (($true = ((sK1 @ (sK4 @ X5 @ X3)))) | (((sK1 @ (sK5 @ X3))) = $true) | ($true != ((sK1 @ X5))) | (((X3 @ X5)) != ((sK3 @ X3)))) )),
  inference(cnf_transformation,[],[f9])).
thf(f22,plain,(
  ( ! [X3 : (a > a),X5 : a] : ((((sK3 @ X3)) = ((X3 @ (sK4 @ X5 @ X3)))) | ($true != ((sK2 @ (X3 @ (sK5 @ X3))))) | (((X3 @ X5)) != ((sK3 @ X3))) | ($true != ((sK1 @ X5)))) )),
  inference(cnf_transformation,[],[f9])).
thf(f23,plain,(
  ( ! [X3 : (a > a),X5 : a] : ((((sK3 @ X3)) = ((X3 @ (sK4 @ X5 @ X3)))) | (((sK1 @ (sK5 @ X3))) = $true) | ($true != ((sK1 @ X5))) | (((X3 @ X5)) != ((sK3 @ X3)))) )),
  inference(cnf_transformation,[],[f9])).
thf(f24,plain,(
  ( ! [X3 : (a > a),X5 : a] : (($true != ((sK2 @ (X3 @ (sK5 @ X3))))) | (((X3 @ X5)) != ((sK3 @ X3))) | (((sK4 @ X5 @ X3)) != X5) | ($true != ((sK1 @ X5)))) )),
  inference(cnf_transformation,[],[f9])).
thf(f25,plain,(
  ( ! [X3 : (a > a),X5 : a] : ((((sK4 @ X5 @ X3)) != X5) | (((X3 @ X5)) != ((sK3 @ X3))) | (((sK1 @ (sK5 @ X3))) = $true) | ($true != ((sK1 @ X5)))) )),
  inference(cnf_transformation,[],[f9])).
thf(f28,plain,(
  ( ! [X11 : a] : ((((sK7 @ (sK6 @ X11))) = X11) | ($true != ((sK1 @ X11))) | (((sK0 @ (sK6 @ X11))) != $true)) )),
  inference(equality_resolution,[],[f17])).
thf(f29,plain,(
  ( ! [X17 : a] : ((((sK9 @ (sK8 @ X17))) = X17) | (((sK0 @ X17)) != $true) | (((sK2 @ (sK8 @ X17))) != $true)) )),
  inference(equality_resolution,[],[f10])).
thf(f32,plain,(
  ( ! [X11 : a] : ((((sK7 @ (sK6 @ X11))) = X11) | ($true != ((sK1 @ X11)))) )),
  inference(forward_subsumption_resolution,[],[f28,f14])).
thf(f34,plain,(
  ( ! [X17 : a] : ((((sK9 @ (sK8 @ X17))) = X17) | (((sK0 @ X17)) != $true)) )),
  inference(forward_subsumption_resolution,[],[f29,f13])).
thf(f40,plain,(
  ( ! [X0 : (a > a),X1 : a] : ((((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = $true) | ($true != ((sK0 @ X1))) | ($true != $true) | (((X0 @ (sK5 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) != X1)) )),
  inference(constrained_superposition,[],[f18,f13])).
thf(f44,plain,(
  ( ! [X0 : (a > a),X1 : a] : ((((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = $true) | ($true != ((sK0 @ X1))) | (((X0 @ (sK5 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) != X1)) )),
  inference(trivial_inequality_removal,[],[f40])).
thf(f86,plain,(
  ( ! [X2 : a,X0 : (a > a),X1 : a] : ((((X0 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) != X1) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = X1) | ((((^[Y0 : a]: (sK8 @ (X0 @ Y0))) @ X2)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = $true) | ($true != ((sK0 @ X1))) | (((sK1 @ X2)) != $true)) )),
  inference(constrained_superposition,[],[f34,f23])).
thf(f115,plain,(
  ( ! [X2 : a,X0 : (a > a),X1 : a] : ((((sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0))))) != ((sK8 @ (X0 @ X2)))) | (((sK1 @ X2)) != $true) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = X1) | ($true != ((sK0 @ X1))) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = $true) | (((X0 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) != X1)) )),
  inference(beta-eta_normalization,[],[f86])).
thf(f179,plain,(
  ( ! [X2 : a,X0 : (a > a),X1 : a] : ((((sK1 @ X2)) != $true) | ($true != ((sK0 @ X1))) | (((X0 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) != X1) | (((sK2 @ ((^[Y0 : a]: (sK8 @ (X0 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0))))))) != $true) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = X1) | ((((^[Y0 : a]: (sK8 @ (X0 @ Y0))) @ X2)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0))))))) )),
  inference(constrained_superposition,[],[f34,f22])).
thf(f227,plain,(
  ( ! [X2 : a,X0 : (a > a),X1 : a] : ((((sK2 @ (sK8 @ (X0 @ (sK5 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))))) != $true) | ($true != ((sK0 @ X1))) | (((sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0))))) != ((sK8 @ (X0 @ X2)))) | (((sK1 @ X2)) != $true) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = X1) | (((X0 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) != X1)) )),
  inference(beta-eta_normalization,[],[f179])).
thf(f396,definition,(
  spl10_12 <=> ! [X2 : a] : ((((sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X2) | (((sK0 @ X2)) != $true))),
  introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition])).
thf(f397,plain,(
  ( ! [X2 : a] : ((((sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X2) | (((sK0 @ X2)) != $true)) ) | ~spl10_12),
  inference(avatar_component_clause,[],[f396])).
thf(f2251,definition,(
  spl10_189 <=> (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl10_189])],[avatar_definition])).
thf(f2252,plain,(
  (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | spl10_189),
  inference(avatar_component_clause,[],[f2251])).
thf(f2255,definition,(
  spl10_190 <=> ! [X2 : a,X0 : a,X3 : a] : ((((sK0 @ X2)) != $true) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X2) | ($true != ((sK0 @ X0))) | (((sK7 @ X0)) != X3) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X3)) != $true) | (((sK6 @ (sK4 @ X3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X2))),
  introduced(definition,[new_symbols(definition,[spl10_190])],[avatar_definition])).
thf(f2256,plain,(
  ( ! [X2 : a,X3 : a,X0 : a] : ((((sK6 @ (sK4 @ X3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X2) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ X0)) != X3) | (((sK1 @ X3)) != $true) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X2) | ($true != ((sK0 @ X0))) | (((sK0 @ X2)) != $true)) ) | ~spl10_190),
  inference(avatar_component_clause,[],[f2255])).
thf(f2803,definition,(
  spl10_203 <=> (((sK0 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl10_203])],[avatar_definition])).
thf(f2804,plain,(
  (((sK0 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) = $true) | ~spl10_203),
  inference(avatar_component_clause,[],[f2803])).
thf(f2805,plain,(
  (((sK0 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | spl10_203),
  inference(avatar_component_clause,[],[f2803])).
thf(f2807,definition,(
  spl10_204 <=> (((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl10_204])],[avatar_definition])).
thf(f2808,plain,(
  (((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | spl10_204),
  inference(avatar_component_clause,[],[f2807])).
thf(f2809,plain,(
  (((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | ~spl10_204),
  inference(avatar_component_clause,[],[f2807])).
thf(f2811,plain,(
  (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | ($true != $true) | spl10_203),
  inference(constrained_superposition,[],[f2805,f14])).
thf(f2812,plain,(
  (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | spl10_203),
  inference(trivial_inequality_removal,[],[f2811])).
thf(f3007,plain,(
  ( ! [X2 : a,X0 : (a > a),X1 : a] : ((((sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0))))) != ((sK8 @ (X0 @ X2)))) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = X1) | ($true != ((sK0 @ X1))) | (((sK0 @ (X0 @ (sK5 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0))))))) != $true) | ($true != $true) | (((sK1 @ X2)) != $true) | (((X0 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) != X1)) )),
  inference(constrained_superposition,[],[f227,f13])).
thf(f3016,plain,(
  ( ! [X2 : a,X0 : (a > a),X1 : a] : ((((sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0))))) != ((sK8 @ (X0 @ X2)))) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) = X1) | ($true != ((sK0 @ X1))) | (((sK1 @ X2)) != $true) | (((sK0 @ (X0 @ (sK5 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0))))))) != $true) | (((X0 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (X0 @ Y0)))))) != X1)) )),
  inference(trivial_inequality_removal,[],[f3007])).
thf(f3032,plain,(
  ( ! [X2 : a,X3 : a,X0 : a] : ((((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) = X2) | ($true != ((sK0 @ X0))) | (((sK7 @ X0)) != X3) | (((sK1 @ X3)) != $true) | ((((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK4 @ X3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) != X2) | (((sK0 @ ((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))) != $true) | (((sK0 @ X2)) != $true)) )),
  inference(constrained_superposition,[],[f3016,f16])).
thf(f3058,plain,(
  ( ! [X2 : a,X3 : a,X0 : a] : ((((sK7 @ X0)) != X3) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK0 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X2) | ($true != ((sK0 @ X0))) | (((sK6 @ (sK4 @ X3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X2) | (((sK0 @ X2)) != $true) | (((sK1 @ X3)) != $true)) )),
  inference(beta-eta_normalization,[],[f3032])).
thf(f3074,plain,(
  ( ! [X2 : a,X3 : a,X0 : a] : ((((sK6 @ (sK4 @ X3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X2) | (((sK1 @ X3)) != $true) | (((sK7 @ X0)) != X3) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X0))) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X2) | (((sK0 @ X2)) != $true)) ) | ~spl10_203),
  inference(forward_subsumption_resolution,[],[f3058,f2804])).
thf(f3075,plain,(
  spl10_190 | ~spl10_203),
  inference(avatar_split_clause,[],[f3074,f2803,f2255])).
thf(f3080,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = ((sK6 @ (sK4 @ X1 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) | ($true != ((sK0 @ X0))) | (((sK1 @ X1)) != $true) | (((sK7 @ X0)) != X1) | (((sK0 @ (sK6 @ (sK4 @ X1 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_190),
  inference(equality_resolution,[],[f2256])).
thf(f4344,definition,(
  spl10_324 <=> (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) = ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))),
  introduced(definition,[new_symbols(definition,[spl10_324])],[avatar_definition])).
thf(f4345,plain,(
  (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) = ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ~spl10_324),
  inference(avatar_component_clause,[],[f4344])).
thf(f4346,plain,(
  (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | spl10_324),
  inference(avatar_component_clause,[],[f4344])).
thf(f4466,definition,(
  spl10_354 <=> (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl10_354])],[avatar_definition])).
thf(f4467,plain,(
  (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | spl10_354),
  inference(avatar_component_clause,[],[f4466])).
thf(f4468,plain,(
  (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) = $true) | ~spl10_354),
  inference(avatar_component_clause,[],[f4466])).
thf(f4470,definition,(
  spl10_355 <=> ! [X0 : a,X1 : a] : ((((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK1 @ X0)) != $true) | ($true != ((sK0 @ X1))) | (((sK7 @ X1)) != X0) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))),
  introduced(definition,[new_symbols(definition,[spl10_355])],[avatar_definition])).
thf(f4471,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK1 @ X0)) != $true) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X1))) | (((sK7 @ X1)) != X0)) ) | ~spl10_355),
  inference(avatar_component_clause,[],[f4470])).
thf(f4512,plain,(
  ($true != $true) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | spl10_204),
  inference(constrained_superposition,[],[f2808,f19])).
thf(f4513,plain,(
  ( ! [X0 : a] : (((((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) != X0) | ($true != ((sK0 @ X0))) | ($true != $true)) ) | spl10_204),
  inference(constrained_superposition,[],[f2808,f44])).
thf(f4517,plain,(
  (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | spl10_204),
  inference(trivial_inequality_removal,[],[f4512])).
thf(f4521,plain,(
  ( ! [X0 : a] : (((((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) != X0) | ($true != ((sK0 @ X0)))) ) | spl10_204),
  inference(trivial_inequality_removal,[],[f4513])).
thf(f4522,plain,(
  ( ! [X0 : a] : ((((sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X0) | ($true != ((sK0 @ X0)))) ) | spl10_204),
  inference(beta-eta_normalization,[],[f4521])).
thf(f4525,plain,(
  spl10_12 | spl10_204),
  inference(avatar_split_clause,[],[f4522,f2807,f396])).
thf(f4528,plain,(
  ($true != $true) | (((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | spl10_354),
  inference(constrained_superposition,[],[f4467,f11])).
thf(f4531,plain,(
  (((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | spl10_354),
  inference(trivial_inequality_removal,[],[f4528])).
thf(f4532,plain,(
  (((sK0 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | ~spl10_12),
  inference(equality_resolution,[],[f397])).
thf(f4533,plain,(
  $false | (~spl10_12 | ~spl10_203)),
  inference(forward_subsumption_resolution,[],[f4532,f2804])).
thf(f4534,plain,(
  ~spl10_12 | ~spl10_203),
  inference(avatar_contradiction_clause,[],[f4533])).
thf(f4535,plain,(
  ~spl10_204 | spl10_354),
  inference(avatar_split_clause,[],[f4531,f4466,f2807])).
thf(f4603,plain,(
  (((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | spl10_324),
  inference(constrained_superposition,[],[f4346,f12])).
thf(f4604,plain,(
  (((sK2 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | spl10_324),
  inference(trivial_inequality_removal,[],[f4603])).
thf(f4607,plain,(
  $false | (~spl10_204 | spl10_324)),
  inference(forward_subsumption_resolution,[],[f4604,f2809])).
thf(f4608,plain,(
  ~spl10_204 | spl10_324),
  inference(avatar_contradiction_clause,[],[f4607])).
thf(f5100,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | ((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | (((sK1 @ X0)) != $true) | ($true != $true) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ X1)) != X0) | ($true != ((sK0 @ X1)))) ) | ~spl10_355),
  inference(constrained_superposition,[],[f4471,f20])).
thf(f5107,plain,(
  ( ! [X0 : a,X1 : a] : (((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | (((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK7 @ X1)) != X0) | ($true != ((sK0 @ X1))) | ($true != $true)) ) | ~spl10_355),
  inference(duplicate_literal_removal,[],[f5100])).
thf(f5108,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK1 @ X0)) != $true) | ($true != ((sK0 @ X1))) | (((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK7 @ X1)) != X0) | ((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_355),
  inference(trivial_inequality_removal,[],[f5107])).
thf(f5109,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | (((sK7 @ X1)) != X0) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X1))) | ($true != ((sK2 @ (sK8 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))))) ) | ~spl10_355),
  inference(beta-eta_normalization,[],[f5108])).
thf(f5111,definition,(
  spl10_396 <=> ($true = ((sK2 @ (sK8 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))))),
  introduced(definition,[new_symbols(definition,[spl10_396])],[avatar_definition])).
thf(f5112,plain,(
  ($true = ((sK2 @ (sK8 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) | ~spl10_396),
  inference(avatar_component_clause,[],[f5111])).
thf(f5113,plain,(
  ($true != ((sK2 @ (sK8 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) | spl10_396),
  inference(avatar_component_clause,[],[f5111])).
thf(f5115,definition,(
  spl10_397 <=> ! [X0 : a,X1 : a] : ((((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X1))) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ X1)) != X0) | (((sK1 @ X0)) != $true))),
  introduced(definition,[new_symbols(definition,[spl10_397])],[avatar_definition])).
thf(f5116,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ X1)) != X0) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | ($true != ((sK0 @ X1)))) ) | ~spl10_397),
  inference(avatar_component_clause,[],[f5115])).
thf(f5117,plain,(
  ~spl10_396 | spl10_397 | ~spl10_355),
  inference(avatar_split_clause,[],[f5109,f4470,f5115,f5111])).
thf(f5118,plain,(
  (((sK0 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | ($true != $true) | spl10_396),
  inference(constrained_superposition,[],[f5113,f13])).
thf(f5119,plain,(
  (((sK0 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | spl10_396),
  inference(trivial_inequality_removal,[],[f5118])).
thf(f5123,plain,(
  ( ! [X0 : (a > a),X1 : a] : ((((sK4 @ X1 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ (X0 @ Y1))) @ Y0))))) != X1) | ($true != $true) | (((X0 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ (X0 @ Y0))))))) != ((sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ (X0 @ Y1))) @ Y0))))) != (((^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ (X0 @ Y1))) @ Y0))) @ X1))) | (((sK1 @ X1)) != $true)) ) | ~spl10_396),
  inference(constrained_superposition,[],[f24,f5112])).
thf(f5129,plain,(
  ( ! [X0 : a,X1 : a] : (($true != $true) | ((((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK4 @ X1 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) != X0) | (((sK8 @ ((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X1))) != ((sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) | (((sK1 @ X1)) != $true) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) = X0) | ($true != ((sK0 @ X0)))) ) | ~spl10_396),
  inference(constrained_superposition,[],[f227,f5112])).
thf(f5133,plain,(
  ( ! [X0 : a,X1 : a] : (((((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK4 @ X1 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) != X0) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) = X0) | ($true != ((sK0 @ X0))) | (((sK8 @ ((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ X1))) != ((sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) | (((sK1 @ X1)) != $true)) ) | ~spl10_396),
  inference(trivial_inequality_removal,[],[f5129])).
thf(f5134,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK6 @ (sK4 @ X1 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X0) | (((sK8 @ (sK6 @ X1))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X0) | (((sK1 @ X1)) != $true) | ($true != ((sK0 @ X0)))) ) | ~spl10_396),
  inference(beta-eta_normalization,[],[f5133])).
thf(f5149,plain,(
  ( ! [X0 : (a > a),X1 : a] : ((((X0 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ (X0 @ Y0))))))) != ((sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ (X0 @ Y1))) @ Y0))))) != (((^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ (X0 @ Y1))) @ Y0))) @ X1))) | (((sK1 @ X1)) != $true) | (((sK4 @ X1 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ (X0 @ Y1))) @ Y0))))) != X1)) ) | ~spl10_396),
  inference(trivial_inequality_removal,[],[f5123])).
thf(f5150,plain,(
  ( ! [X0 : (a > a),X1 : a] : ((((X0 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ (X0 @ Y0))))))) != ((sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X1)) != $true) | (((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ (X0 @ Y0)))))) != ((sK8 @ (sK6 @ (X0 @ X1))))) | (((sK4 @ X1 @ (^[Y0 : a]: (sK8 @ (sK6 @ (X0 @ Y0)))))) != X1)) ) | ~spl10_396),
  inference(beta-eta_normalization,[],[f5149])).
thf(f5155,plain,(
  ( ! [X0 : a,X1 : a] : (($true != ((sK0 @ X1))) | (((sK7 @ X0)) != ((sK7 @ X1))) | ($true != ((sK1 @ (sK7 @ X0)))) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X0)))) ) | ~spl10_397),
  inference(constrained_superposition,[],[f5116,f16])).
thf(f5169,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X1))) | (((sK7 @ X0)) != ((sK7 @ X1))) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X0)))) ) | ~spl10_397),
  inference(forward_subsumption_resolution,[],[f5155,f15])).
thf(f5173,plain,(
  ( ! [X0 : a] : ((((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X0))) | (((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK7 @ X0))) | (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true)) ) | (~spl10_324 | ~spl10_397)),
  inference(constrained_superposition,[],[f5169,f4345])).
thf(f5178,plain,(
  ( ! [X0 : a] : ((((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X0))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK7 @ X0)))) ) | (~spl10_324 | ~spl10_397)),
  inference(trivial_inequality_removal,[],[f5173])).
thf(f5182,plain,(
  ( ! [X0 : a] : ((((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK7 @ X0))) | ($true != ((sK0 @ X0))) | (((sK8 @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | (~spl10_324 | ~spl10_354 | ~spl10_397)),
  inference(forward_subsumption_resolution,[],[f5178,f4468])).
thf(f5188,plain,(
  (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (~spl10_324 | ~spl10_354 | ~spl10_397)),
  inference(equality_resolution,[],[f5182])).
thf(f5193,plain,(
  (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (~spl10_324 | ~spl10_354 | ~spl10_397)),
  inference(forward_subsumption_resolution,[],[f5188,f4468])).
thf(f5195,plain,(
  $false | (~spl10_324 | ~spl10_354 | ~spl10_397)),
  inference(forward_subsumption_resolution,[],[f5193,f4345])).
thf(f5196,plain,(
  ~spl10_324 | ~spl10_354 | ~spl10_397),
  inference(avatar_contradiction_clause,[],[f5195])).
thf(f5762,plain,(
  ( ! [X0 : a] : ((((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = ((sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ X0)) != $true)) ) | ~spl10_396),
  inference(equality_resolution,[],[f5134])).
thf(f6681,plain,(
  ( ! [X0 : a] : ((((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) != ((sK8 @ (sK6 @ ((^[Y0 : a]: (Y0)) @ X0))))) | (((sK1 @ X0)) != $true) | (((sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0)))))) != X0)) ) | ~spl10_396),
  inference(equality_resolution,[],[f5150])).
thf(f6692,plain,(
  ( ! [X0 : a] : ((((sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))) != X0) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true)) ) | ~spl10_396),
  inference(beta-eta_normalization,[],[f6681])).
thf(f6887,plain,(
  ( ! [X0 : a] : ((((sK1 @ X0)) != $true) | (((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))) = ((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) ) | ~spl10_396),
  inference(constrained_superposition,[],[f32,f5762])).
thf(f7027,plain,(
  ( ! [X0 : a] : ((((sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))) = ((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) | (((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true)) ) | ~spl10_396),
  inference(forward_subsumption_resolution,[],[f6887,f14])).
thf(f7135,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK1 @ X0)) != $true) | (((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_396),
  inference(constrained_superposition,[],[f6692,f7027])).
thf(f7156,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true)) ) | ~spl10_396),
  inference(duplicate_literal_removal,[],[f7135])).
thf(f7263,definition,(
  spl10_430 <=> ! [X1 : a] : ((((sK1 @ X1)) != $true) | (((sK1 @ (sK4 @ X1 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK8 @ (sK6 @ X1))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))),
  introduced(definition,[new_symbols(definition,[spl10_430])],[avatar_definition])).
thf(f7264,plain,(
  ( ! [X1 : a] : ((((sK1 @ (sK4 @ X1 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK8 @ (sK6 @ X1))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X1)) != $true)) ) | ~spl10_430),
  inference(avatar_component_clause,[],[f7263])).
thf(f7277,definition,(
  spl10_434 <=> (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = ((sK6 @ (sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))))),
  introduced(definition,[new_symbols(definition,[spl10_434])],[avatar_definition])).
thf(f7278,plain,(
  (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != ((sK6 @ (sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) | spl10_434),
  inference(avatar_component_clause,[],[f7277])).
thf(f7279,plain,(
  (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = ((sK6 @ (sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) | ~spl10_434),
  inference(avatar_component_clause,[],[f7277])).
thf(f7416,definition,(
  spl10_468 <=> ! [X0 : a] : ((((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true))),
  introduced(definition,[new_symbols(definition,[spl10_468])],[avatar_definition])).
thf(f7417,plain,(
  ( ! [X0 : a] : ((((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_468),
  inference(avatar_component_clause,[],[f7416])).
thf(f7433,definition,(
  spl10_472 <=> (((sK1 @ (sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) = $true)),
  introduced(definition,[new_symbols(definition,[spl10_472])],[avatar_definition])).
thf(f7434,plain,(
  (((sK1 @ (sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) != $true) | spl10_472),
  inference(avatar_component_clause,[],[f7433])).
thf(f7529,plain,(
  ( ! [X0 : a] : (((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ X0)) != $true) | (((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != $true)) ) | ~spl10_430),
  inference(constrained_superposition,[],[f7264,f20])).
thf(f7536,plain,(
  ( ! [X0 : a] : (((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != $true) | (((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true)) ) | ~spl10_430),
  inference(duplicate_literal_removal,[],[f7529])).
thf(f7537,plain,(
  ( ! [X0 : a] : (((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | (((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_430),
  inference(trivial_inequality_removal,[],[f7536])).
thf(f7538,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | ($true != ((sK2 @ (sK8 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_430),
  inference(beta-eta_normalization,[],[f7537])).
thf(f7539,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK2 @ (sK8 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) | (((sK1 @ X0)) != $true)) ) | ~spl10_430),
  inference(duplicate_literal_removal,[],[f7538])).
thf(f7542,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true)) ) | (~spl10_396 | ~spl10_430)),
  inference(forward_subsumption_resolution,[],[f7539,f5112])).
thf(f7547,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK7 @ X1)) != X0) | ($true != ((sK0 @ X1))) | (((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true)) ) | (~spl10_190 | ~spl10_396 | ~spl10_430)),
  inference(constrained_superposition,[],[f7542,f3080])).
thf(f7558,plain,(
  ( ! [X0 : a,X1 : a] : ((((sK1 @ X0)) != $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK7 @ X1)) != X0) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | ($true != ((sK0 @ X1)))) ) | (~spl10_190 | ~spl10_324 | ~spl10_396 | ~spl10_430)),
  inference(forward_subsumption_resolution,[],[f7547,f4345])).
thf(f7560,plain,(
  ( ! [X0 : a,X1 : a] : (($true != ((sK0 @ X1))) | (((sK7 @ X1)) != X0) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK8 @ X1)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true)) ) | (~spl10_190 | ~spl10_324 | ~spl10_396 | ~spl10_430)),
  inference(forward_subsumption_resolution,[],[f7558,f14])).
thf(f7561,plain,(
  spl10_355 | ~spl10_190 | ~spl10_324 | ~spl10_396 | ~spl10_430),
  inference(avatar_split_clause,[],[f7560,f7263,f5111,f4344,f2255,f4470])).
thf(f8474,plain,(
  spl10_468 | ~spl10_396),
  inference(avatar_split_clause,[],[f7156,f5111,f7416])).
thf(f8478,plain,(
  ( ! [X0 : a] : ((((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ X0)) != $true) | ($true != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | ((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true)) ) | ~spl10_468),
  inference(constrained_superposition,[],[f7417,f20])).
thf(f8479,plain,(
  ( ! [X0 : a] : ((((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK1 @ X0)) != $true) | ($true != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | ((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_468),
  inference(constrained_superposition,[],[f7417,f21])).
thf(f8480,plain,(
  ( ! [X0 : a] : ((((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != $true) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK1 @ X0)) != $true)) ) | ~spl10_468),
  inference(duplicate_literal_removal,[],[f8479])).
thf(f8481,plain,(
  ( ! [X0 : a] : ((((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ X0)) != $true) | ((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_468),
  inference(trivial_inequality_removal,[],[f8480])).
thf(f8482,plain,(
  ( ! [X0 : a] : ((((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_468),
  inference(beta-eta_normalization,[],[f8481])).
thf(f8483,plain,(
  ( ! [X0 : a] : ((((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_468),
  inference(duplicate_literal_removal,[],[f8482])).
thf(f8484,plain,(
  ( ! [X0 : a] : ((((sK1 @ X0)) != $true) | ($true != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_468),
  inference(duplicate_literal_removal,[],[f8478])).
thf(f8485,plain,(
  ( ! [X0 : a] : (((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK2 @ ((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_468),
  inference(trivial_inequality_removal,[],[f8484])).
thf(f8486,plain,(
  ( ! [X0 : a] : (($true != ((sK2 @ (sK8 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0)) ) | ~spl10_468),
  inference(beta-eta_normalization,[],[f8485])).
thf(f8487,plain,(
  ( ! [X0 : a] : ((((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK2 @ (sK8 @ (sK6 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0)) ) | ~spl10_468),
  inference(duplicate_literal_removal,[],[f8486])).
thf(f8491,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ X0)) != $true)) ) | (~spl10_396 | ~spl10_468)),
  inference(forward_subsumption_resolution,[],[f8487,f5112])).
thf(f8496,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))) != ((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) | (((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ X0)) != $true) | (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | (~spl10_396 | ~spl10_468)),
  inference(constrained_superposition,[],[f8491,f5762])).
thf(f8512,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | (~spl10_396 | ~spl10_468)),
  inference(forward_subsumption_resolution,[],[f8496,f7027])).
thf(f8516,plain,(
  ( ! [X0 : a] : ((((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true)) ) | (~spl10_324 | ~spl10_396 | ~spl10_468)),
  inference(forward_subsumption_resolution,[],[f8512,f4345])).
thf(f8517,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK1 @ X0)) != $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true)) ) | (~spl10_324 | ~spl10_396 | ~spl10_468)),
  inference(forward_subsumption_resolution,[],[f8516,f14])).
thf(f8518,plain,(
  spl10_430 | ~spl10_324 | ~spl10_396 | ~spl10_468),
  inference(avatar_split_clause,[],[f8517,f7416,f5111,f4344,f7263])).
thf(f8616,plain,(
  ~spl10_189 | spl10_203),
  inference(avatar_split_clause,[],[f2812,f2803,f2251])).
thf(f8618,definition,(
  spl10_562 <=> ! [X0 : a] : ((((sK1 @ X0)) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0))),
  introduced(definition,[new_symbols(definition,[spl10_562])],[avatar_definition])).
thf(f8619,plain,(
  ( ! [X0 : a] : ((((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ X0)) != $true)) ) | ~spl10_562),
  inference(avatar_component_clause,[],[f8618])).
thf(f8620,plain,(
  spl10_189 | spl10_562 | ~spl10_468),
  inference(avatar_split_clause,[],[f8483,f7416,f8618,f2251])).
thf(f8621,plain,(
  ~spl10_203 | spl10_396),
  inference(avatar_split_clause,[],[f5119,f5111,f2803])).
thf(f8681,definition,(
  spl10_575 <=> ! [X2 : a,X1 : a] : ((((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X1) | ($true != ((sK0 @ X1))) | (((sK1 @ X2)) != $true) | (((sK6 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X1) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X2))),
  introduced(definition,[new_symbols(definition,[spl10_575])],[avatar_definition])).
thf(f8682,plain,(
  ( ! [X2 : a,X1 : a] : ((((sK6 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X1) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X2) | ($true != ((sK0 @ X1))) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X1) | (((sK1 @ X2)) != $true)) ) | ~spl10_575),
  inference(avatar_component_clause,[],[f8681])).
thf(f12194,plain,(
  (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != ((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) | (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | spl10_434),
  inference(constrained_superposition,[],[f7278,f16])).
thf(f12197,plain,(
  (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | spl10_434),
  inference(trivial_inequality_removal,[],[f12194])).
thf(f12273,plain,(
  ( ! [X2 : a,X1 : a] : ((((sK1 @ X2)) != $true) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) = X1) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X2) | ($true = ((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))) | (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) | ((((^[Y0 : a]: (sK6 @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ ((^[Y1 : a]: (sK6 @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) != X1) | ($true != ((sK0 @ X1)))) ) | ~spl10_434),
  inference(constrained_superposition,[],[f115,f7279])).
thf(f12390,plain,(
  ( ! [X2 : a,X1 : a] : ((((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | ($true != ((sK0 @ X1))) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X1) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X2) | (((sK1 @ X2)) != $true) | (((sK6 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X1) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true)) ) | ~spl10_434),
  inference(beta-eta_normalization,[],[f12273])).
thf(f12450,plain,(
  ( ! [X2 : a,X1 : a] : ((((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X1) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X2) | (((sK6 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X1) | ($true != ((sK0 @ X1))) | (((sK1 @ X2)) != $true)) ) | (~spl10_324 | ~spl10_434)),
  inference(forward_subsumption_resolution,[],[f12390,f4345])).
thf(f12475,plain,(
  ( ! [X2 : a,X1 : a] : ((((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X2) | (((sK1 @ X2)) != $true) | ($true != ((sK0 @ X1))) | (((sK6 @ (sK4 @ X2 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != X1) | (((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = X1)) ) | (spl10_189 | ~spl10_324 | ~spl10_434)),
  inference(forward_subsumption_resolution,[],[f12450,f2252])).
thf(f12481,plain,(
  spl10_575 | spl10_189 | ~spl10_324 | ~spl10_434),
  inference(avatar_split_clause,[],[f12475,f7277,f4344,f2251,f8681])).
thf(f13467,plain,(
  (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) | (((sK1 @ (sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) != $true) | (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (~spl10_434 | ~spl10_562)),
  inference(constrained_superposition,[],[f8619,f7279])).
thf(f13476,plain,(
  (((sK1 @ (sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) != $true) | (((sK8 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (~spl10_434 | ~spl10_562)),
  inference(trivial_inequality_removal,[],[f13467])).
thf(f13482,plain,(
  (((sK1 @ (sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) != $true) | (~spl10_324 | ~spl10_434 | ~spl10_562)),
  inference(forward_subsumption_resolution,[],[f13476,f4345])).
thf(f13485,plain,(
  ~spl10_472 | ~spl10_324 | ~spl10_434 | ~spl10_562),
  inference(avatar_split_clause,[],[f13482,f8618,f7277,f4344,f7433])).
thf(f13489,plain,(
  ($true != $true) | (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | spl10_472),
  inference(constrained_superposition,[],[f7434,f15])).
thf(f13492,plain,(
  (((sK0 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | spl10_472),
  inference(trivial_inequality_removal,[],[f13489])).
thf(f13495,plain,(
  $false | (~spl10_354 | spl10_472)),
  inference(forward_subsumption_resolution,[],[f13492,f4468])).
thf(f13496,plain,(
  ~spl10_354 | spl10_472),
  inference(avatar_contradiction_clause,[],[f13495])).
thf(f13928,plain,(
  ( ! [X0 : a] : ((((sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = ((sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) | (((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0)) ) | ~spl10_575),
  inference(equality_resolution,[],[f8682])).
thf(f16323,plain,(
  ( ! [X0 : a] : ((((sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))) = ((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK0 @ (sK6 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != $true) | (((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0)) ) | ~spl10_575),
  inference(constrained_superposition,[],[f32,f13928])).
thf(f16486,plain,(
  ( ! [X0 : a] : ((((sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))) = ((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))))) | (((sK1 @ X0)) != $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0)) ) | ~spl10_575),
  inference(forward_subsumption_resolution,[],[f16323,f14])).
thf(f16621,plain,(
  ( ! [X0 : a] : (((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK1 @ X0)) != $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0)) ) | ~spl10_575),
  inference(constrained_superposition,[],[f25,f16486])).
thf(f16648,plain,(
  ( ! [X0 : a] : ((((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | ((((^[Y0 : a]: (sK8 @ (sK6 @ Y0))) @ X0)) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ X0)) != $true)) ) | ~spl10_575),
  inference(duplicate_literal_removal,[],[f16621])).
thf(f16649,plain,(
  ( ! [X0 : a] : ((((sK1 @ (sK5 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) = $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ X0)) != $true) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | ~spl10_575),
  inference(beta-eta_normalization,[],[f16648])).
thf(f16772,plain,(
  ( ! [X0 : a] : ((((sK1 @ X0)) != $true) | (((sK7 @ (sK9 @ (sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) != X0) | (((sK1 @ (sK4 @ X0 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0)))))) != $true) | (((sK8 @ (sK6 @ X0))) != ((sK3 @ (^[Y0 : a]: (sK8 @ (sK6 @ Y0))))))) ) | (spl10_189 | ~spl10_575)),
  inference(forward_subsumption_resolution,[],[f16649,f2252])).
thf(f16794,plain,(
  spl10_468 | spl10_189 | ~spl10_575),
  inference(avatar_split_clause,[],[f16772,f8681,f2251,f7416])).
thf(f16809,plain,(
  $false | (spl10_189 | spl10_204)),
  inference(forward_subsumption_resolution,[],[f4517,f2252])).
thf(f16810,plain,(
  spl10_189 | spl10_204),
  inference(avatar_contradiction_clause,[],[f16809])).
thf(f16812,plain,(
  ~spl10_354 | spl10_434),
  inference(avatar_split_clause,[],[f12197,f7277,f4466])).
cnf(s142, plain, spl10_190 | ~spl10_203, inference(sat_conversion,[],[f3075])).
cnf(s255, plain, spl10_12 | spl10_204, inference(sat_conversion,[],[f4525])).
cnf(s256, plain, ~spl10_12 | ~spl10_203, inference(sat_conversion,[],[f4534])).
cnf(s257, plain, ~spl10_204 | spl10_354, inference(sat_conversion,[],[f4535])).
cnf(s258, plain, ~spl10_204 | spl10_324, inference(sat_conversion,[],[f4608])).
cnf(s288, plain, ~spl10_355 | ~spl10_396 | spl10_397, inference(sat_conversion,[],[f5117])).
cnf(s290, plain, ~spl10_324 | ~spl10_354 | ~spl10_397, inference(sat_conversion,[],[f5196])).
cnf(s348, plain, ~spl10_190 | ~spl10_324 | spl10_355 | ~spl10_396 | ~spl10_430, inference(sat_conversion,[],[f7561])).
cnf(s396, plain, ~spl10_396 | spl10_468, inference(sat_conversion,[],[f8474])).
cnf(s398, plain, ~spl10_324 | ~spl10_396 | spl10_430 | ~spl10_468, inference(sat_conversion,[],[f8518])).
cnf(s427, plain, ~spl10_189 | spl10_203, inference(sat_conversion,[],[f8616])).
cnf(s428, plain, spl10_189 | ~spl10_468 | spl10_562, inference(sat_conversion,[],[f8620])).
cnf(s429, plain, ~spl10_203 | spl10_396, inference(sat_conversion,[],[f8621])).
cnf(s822, plain, spl10_189 | ~spl10_324 | ~spl10_434 | spl10_575, inference(sat_conversion,[],[f12481])).
cnf(s895, plain, ~spl10_324 | ~spl10_434 | ~spl10_472 | ~spl10_562, inference(sat_conversion,[],[f13485])).
cnf(s896, plain, ~spl10_354 | spl10_472, inference(sat_conversion,[],[f13496])).
cnf(s969, plain, spl10_189 | spl10_468 | ~spl10_575, inference(sat_conversion,[],[f16794])).
cnf(s975, plain, spl10_189 | spl10_204, inference(sat_conversion,[],[f16810])).
cnf(s977, plain, ~spl10_354 | spl10_434, inference(sat_conversion,[],[f16812])).
cnf(s983, plain, spl10_189, inference(rat,[],[s428,s969,s895,s822,s896,s977,s257,s258,s975])).
cnf(s984, plain, spl10_203, inference(rat,[],[s427,s983])).
cnf(s985, plain, spl10_396, inference(rat,[],[s429,s984])).
cnf(s986, plain, ~spl10_12, inference(rat,[],[s256,s984])).
cnf(s987, plain, spl10_190, inference(rat,[],[s142,s984])).
cnf(s988, plain, spl10_468, inference(rat,[],[s396,s985])).
cnf(s989, plain, spl10_204, inference(rat,[],[s255,s986])).
cnf(s992, plain, spl10_324, inference(rat,[],[s258,s989])).
cnf(s993, plain, spl10_354, inference(rat,[],[s257,s989])).
cnf(s1005, plain, spl10_430, inference(rat,[],[s398,s988,s985,s992])).
cnf(s1006, plain, spl10_355, inference(rat,[],[s348,s1005,s985,s987,s992])).
cnf(s1011, plain, ~spl10_397, inference(rat,[],[s290,s992,s993])).
cnf(s1018, plain, $false, inference(rat,[],[s288,s985,s1011,s1006])).
thf(f16826,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s1018])).
% SZS output end Proof for theBenchmark