%----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, foundationAx: $o).
thf(func_def_5, type, setadjoinIL: $o).
thf(func_def_6, type, setadjoinIR: $o).
thf(func_def_7, type, in__Cong: $o).
thf(func_def_8, type, upairset2E: $o).
thf(func_def_22, type, sK11: ($i > $i)).
thf(func_def_24, type, sK13: ($i > $i)).
thf(func_def_29, type, sF18: $o).
thf(func_def_30, type, sF19: $o).
thf(func_def_31, type, vNOT: ($o > $o)).
thf(f1,axiom,(
  (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : (~ ? [X1 : $i] : ((in @ X1 @ X2) & (in @ X1 @ X0)) & (in @ X2 @ X0))) = foundationAx)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx)).
thf(f2,axiom,(
  (setadjoinIL = ! [X1 : $i,X0 : $i] : (in @ X0 @ (setadjoin @ X0 @ X1)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL)).
thf(f3,axiom,(
  (setadjoinIR = ! [X2 : $i,X1 : $i,X0 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (setadjoin @ X0 @ X1))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR)).
thf(f5,axiom,(
  (! [X1 : $i,X2 : $i,X0 : $i] : ((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) => ((X2 = X0) | (X2 = X1))) = upairset2E)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E)).
thf(f6,conjecture,(
  foundationAx => (setadjoinIL => (setadjoinIR => (in__Cong => (upairset2E => ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => ~(in @ X1 @ X0))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinself2)).
thf(f7,negated_conjecture,(
  ~(foundationAx => (setadjoinIL => (setadjoinIR => (in__Cong => (upairset2E => ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => ~(in @ X1 @ X0)))))))),
  inference(negated_conjecture,[status(cth)],[f6])).
thf(f8,plain,(
  (setadjoinIR = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (setadjoin @ X2 @ X1))))),
  inference(rectify,[],[f3])).
thf(f9,plain,(
  ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ X1)) = $true) => (((in @ X0 @ (setadjoin @ X2 @ X1))) = $true)) <=> (setadjoinIR = $true)),
  inference(fool_elimination,[],[f8])).
thf(f10,plain,(
  (! [X0 : $i] : (? [X1 : $i] : (in @ X1 @ X0) => ? [X2 : $i] : (~ ? [X3 : $i] : ((in @ X3 @ X2) & (in @ X3 @ X0)) & (in @ X2 @ X0))) = foundationAx)),
  inference(rectify,[],[f1])).
thf(f11,plain,(
  ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0)) = $true) => ? [X2 : $i] : ((((in @ X2 @ X0)) = $true) & ~ ? [X3 : $i] : ((((in @ X3 @ X0)) = $true) & (((in @ X3 @ X2)) = $true)))) <=> (foundationAx = $true)),
  inference(fool_elimination,[],[f10])).
thf(f12,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => ((X1 = X2) | (X0 = X1))) = upairset2E)),
  inference(rectify,[],[f5])).
thf(f13,plain,(
  (upairset2E = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))))) => ((X0 = X1) | (X1 = X2)))),
  inference(fool_elimination,[],[f12])).
thf(f16,plain,(
  (setadjoinIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ X0)))),
  inference(rectify,[],[f2])).
thf(f17,plain,(
  (setadjoinIL = $true) <=> ! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) = $true)),
  inference(fool_elimination,[],[f16])).
thf(f18,plain,(
  ~(foundationAx => (setadjoinIL => (setadjoinIR => (in__Cong => (upairset2E => ! [X0 : $i,X1 : $i] : ((in @ X0 @ X1) => ~(in @ X1 @ X0)))))))),
  inference(rectify,[],[f7])).
thf(f19,plain,(
  ~((foundationAx = $true) => ((setadjoinIL = $true) => ((setadjoinIR = $true) => ((in__Cong = $true) => ((upairset2E = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) => ~ (((in @ X1 @ X0)) = $true)))))))),
  inference(fool_elimination,[],[f18])).
thf(f20,plain,(
  ~((foundationAx = $true) => ((setadjoinIL = $true) => ((setadjoinIR = $true) => ((in__Cong = $true) => ((upairset2E = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) => (((in @ X1 @ X0)) != $true)))))))),
  inference(flattening,[],[f19])).
thf(f21,plain,(
  ((((? [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) & (((in @ X1 @ X0)) = $true)) & (upairset2E = $true)) & (in__Cong = $true)) & (setadjoinIR = $true)) & (setadjoinIL = $true)) & (foundationAx = $true)),
  inference(ennf_transformation,[],[f20])).
thf(f22,plain,(
  (upairset2E = $true) & (foundationAx = $true) & ? [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) = $true) & (((in @ X1 @ X0)) = $true)) & (setadjoinIR = $true) & (in__Cong = $true) & (setadjoinIL = $true)),
  inference(flattening,[],[f21])).
thf(f23,plain,(
  (foundationAx = $true) <=> ! [X0 : $i] : (? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | (((in @ X3 @ X0)) != $true)) & (((in @ X2 @ X0)) = $true)) | ! [X1 : $i] : (((in @ X1 @ X0)) != $true))),
  inference(ennf_transformation,[],[f11])).
thf(f24,plain,(
  ! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X0 @ (setadjoin @ X2 @ X1))) = $true)) <=> (setadjoinIR = $true)),
  inference(ennf_transformation,[],[f9])).
thf(f26,plain,(
  (upairset2E = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((X0 = X1) | (X1 = X2)) | ($true != ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))))))),
  inference(ennf_transformation,[],[f13])).
thf(f27,plain,(
  ! [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))))) | (X1 = X2) | (X0 = X1)) <=> (upairset2E = $true)),
  inference(flattening,[],[f26])).
thf(f28,plain,(
  ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) != $true)) & (! [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) = $true) | (setadjoinIL != $true))),
  inference(nnf_transformation,[],[f17])).
thf(f29,plain,(
  ((setadjoinIL = $true) | ? [X0 : $i,X1 : $i] : (((in @ X1 @ (setadjoin @ X1 @ X0))) != $true)) & (! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X3 @ X2))) = $true) | (setadjoinIL != $true))),
  inference(rectify,[],[f28])).
thf(f30,plain,(
  ((setadjoinIL = $true) | (((in @ sK1 @ (setadjoin @ sK1 @ sK0))) != $true)) & (! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X3 @ X2))) = $true) | (setadjoinIL != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1))],[f29])).
thf(f31,plain,(
  (! [X1 : $i,X0 : $i,X2 : $i] : (($true != ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))))) | (X1 = X2) | (X0 = X1)) | (upairset2E != $true)) & ((upairset2E = $true) | ? [X1 : $i,X0 : $i,X2 : $i] : (($true = ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))))) & (X1 != X2) & (X0 != X1)))),
  inference(nnf_transformation,[],[f27])).
thf(f32,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,[],[f31])).
thf(f33,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true) | (X0 = X2) | (X0 = X1)) | (upairset2E != $true)) & ((upairset2E = $true) | ((((in @ sK2 @ (setadjoin @ sK4 @ (setadjoin @ sK3 @ emptyset)))) = $true) & (sK4 != sK2) & (sK2 != sK3)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X3,$thf(sK2)),skolemize(X4,$thf(sK3)),skolemize(X5,$thf(sK4))],[f32])).
thf(f34,plain,(
  (! [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X0 @ (setadjoin @ X2 @ X1))) = $true)) | (setadjoinIR != $true)) & ((setadjoinIR = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : ((((in @ X0 @ X1)) = $true) & (((in @ X0 @ (setadjoin @ X2 @ X1))) != $true)))),
  inference(nnf_transformation,[],[f24])).
thf(f35,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setadjoin @ X0 @ X1))) = $true)) | (setadjoinIR != $true)) & ((setadjoinIR = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : ((((in @ X5 @ X4)) = $true) & (((in @ X5 @ (setadjoin @ X3 @ X4))) != $true)))),
  inference(rectify,[],[f34])).
thf(f36,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ (setadjoin @ X0 @ X1))) = $true)) | (setadjoinIR != $true)) & ((setadjoinIR = $true) | ((((in @ sK7 @ sK6)) = $true) & (((in @ sK7 @ (setadjoin @ sK5 @ sK6))) != $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X3,$thf(sK5)),skolemize(X4,$thf(sK6)),skolemize(X5,$thf(sK7))],[f35])).
thf(f37,plain,(
  (upairset2E = $true) & (foundationAx = $true) & ((((in @ sK8 @ sK9)) = $true) & (((in @ sK9 @ sK8)) = $true)) & (setadjoinIR = $true) & (in__Cong = $true) & (setadjoinIL = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,$thf(sK8)),skolemize(X1,$thf(sK9))],[f22])).
thf(f38,plain,(
  ((foundationAx = $true) | ? [X0 : $i] : (! [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ X2)) = $true) & (((in @ X3 @ X0)) = $true)) | (((in @ X2 @ X0)) != $true)) & ? [X1 : $i] : (((in @ X1 @ X0)) = $true))) & (! [X0 : $i] : (? [X2 : $i] : (! [X3 : $i] : ((((in @ X3 @ X2)) != $true) | (((in @ X3 @ X0)) != $true)) & (((in @ X2 @ X0)) = $true)) | ! [X1 : $i] : (((in @ X1 @ X0)) != $true)) | (foundationAx != $true))),
  inference(nnf_transformation,[],[f23])).
thf(f39,plain,(
  ((foundationAx = $true) | ? [X0 : $i] : (! [X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) = $true)) | (((in @ X1 @ X0)) != $true)) & ? [X3 : $i] : (((in @ X3 @ X0)) = $true))) & (! [X4 : $i] : (? [X5 : $i] : (! [X6 : $i] : (($true != ((in @ X6 @ X5))) | ($true != ((in @ X6 @ X4)))) & (((in @ X5 @ X4)) = $true)) | ! [X7 : $i] : (((in @ X7 @ X4)) != $true)) | (foundationAx != $true))),
  inference(rectify,[],[f38])).
thf(f40,plain,(
  ((foundationAx = $true) | (! [X1 : $i] : (((((in @ (sK11 @ X1) @ X1)) = $true) & (((in @ (sK11 @ X1) @ sK10)) = $true)) | (((in @ X1 @ sK10)) != $true)) & (((in @ sK12 @ sK10)) = $true))) & (! [X4 : $i] : ((! [X6 : $i] : ((((in @ X6 @ (sK13 @ X4))) != $true) | ($true != ((in @ X6 @ X4)))) & ($true = ((in @ (sK13 @ X4) @ X4)))) | ! [X7 : $i] : (((in @ X7 @ X4)) != $true)) | (foundationAx != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK10,vAPP,sK12,vAPP]),skolemize(X0,$thf(sK10)),skolemize(X5,$thf(sK13 @ X4)),skolemize(X3,$thf(sK12)),skolemize(X5,$thf(sK13 @ X4))],[f39])).
thf(f44,plain,(
  ( ! [X2 : $i,X3 : $i] : ((setadjoinIL != $true) | (((in @ X3 @ (setadjoin @ X3 @ X2))) = $true)) )),
  inference(cnf_transformation,[],[f30])).
thf(f49,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X1) | (upairset2E != $true) | (((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true) | (X0 = X2)) )),
  inference(cnf_transformation,[],[f33])).
thf(f52,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X0 @ X1))) = $true) | (setadjoinIR != $true) | (((in @ X2 @ X1)) != $true)) )),
  inference(cnf_transformation,[],[f36])).
thf(f53,plain,(
  (setadjoinIL = $true)),
  inference(cnf_transformation,[],[f37])).
thf(f55,plain,(
  (setadjoinIR = $true)),
  inference(cnf_transformation,[],[f37])).
thf(f56,plain,(
  (((in @ sK9 @ sK8)) = $true)),
  inference(cnf_transformation,[],[f37])).
thf(f57,plain,(
  (((in @ sK8 @ sK9)) = $true)),
  inference(cnf_transformation,[],[f37])).
thf(f58,plain,(
  (foundationAx = $true)),
  inference(cnf_transformation,[],[f37])).
thf(f59,plain,(
  (upairset2E = $true)),
  inference(cnf_transformation,[],[f37])).
thf(f60,plain,(
  ( ! [X7 : $i,X4 : $i] : ((((in @ X7 @ X4)) != $true) | ($true = ((in @ (sK13 @ X4) @ X4))) | (foundationAx != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f61,plain,(
  ( ! [X6 : $i,X7 : $i,X4 : $i] : ((((in @ X6 @ (sK13 @ X4))) != $true) | (foundationAx != $true) | ($true != ((in @ X6 @ X4))) | (((in @ X7 @ X4)) != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f73,definition,(
  (sF18 = ((in @ sK8 @ sK9)))),
  introduced(definition,[new_symbols(definition,[sF18])],[function_definition])).
thf(f74,plain,(
  (((in @ sK8 @ sK9)) = sF18)),
  inference(reorient_equations,[],[f73])).
thf(f75,plain,(
  (sF18 = $true)),
  inference(definition_folding,[],[f57,f74])).
thf(f76,definition,(
  (sF19 = ((in @ sK9 @ sK8)))),
  introduced(definition,[new_symbols(definition,[sF19])],[function_definition])).
thf(f77,plain,(
  (sF19 = $true)),
  inference(definition_folding,[],[f56,f76])).
thf(f80,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (foundationAx != $true) | (((in @ X0 @ (sK13 @ X1))) != $true)) )),
  inference(condensation,[],[f61])).
thf(f82,plain,(
  (((in @ sK9 @ sK8)) = $true) | ($false = sF19)),
  inference(iff_proxy_clausification,[],[f76])).
thf(f83,plain,(
  (((in @ sK8 @ sK9)) = $true) | ($false = sF18)),
  inference(iff_proxy_clausification,[],[f74])).
thf(f91,definition,(
  spl20_2 <=> (foundationAx = $true)),
  introduced(definition,[new_symbols(definition,[spl20_2])],[avatar_definition])).
thf(f96,definition,(
  spl20_3 <=> (setadjoinIL = $true)),
  introduced(definition,[new_symbols(definition,[spl20_3])],[avatar_definition])).
thf(f127,definition,(
  spl20_10 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X1) | (X0 = X2) | (((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true))),
  introduced(definition,[new_symbols(definition,[spl20_10])],[avatar_definition])).
thf(f128,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset)))) != $true) | (X0 = X1) | (X0 = X2)) ) | ~spl20_10),
  inference(avatar_component_clause,[],[f127])).
thf(f130,definition,(
  spl20_11 <=> (upairset2E = $true)),
  introduced(definition,[new_symbols(definition,[spl20_11])],[avatar_definition])).
thf(f133,plain,(
  spl20_10 | ~spl20_11),
  inference(avatar_split_clause,[],[f49,f130,f127])).
thf(f139,definition,(
  spl20_13 <=> ! [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X0 @ (sK13 @ X1))) != $true))),
  introduced(definition,[new_symbols(definition,[spl20_13])],[avatar_definition])).
thf(f140,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ (sK13 @ X1))) != $true) | (((in @ X0 @ X1)) != $true)) ) | ~spl20_13),
  inference(avatar_component_clause,[],[f139])).
thf(f141,plain,(
  ~spl20_2 | spl20_13),
  inference(avatar_split_clause,[],[f80,f139,f91])).
thf(f143,definition,(
  spl20_14 <=> (((in @ sK9 @ sK8)) = $true)),
  introduced(definition,[new_symbols(definition,[spl20_14])],[avatar_definition])).
thf(f145,plain,(
  (((in @ sK9 @ sK8)) = $true) | ~spl20_14),
  inference(avatar_component_clause,[],[f143])).
thf(f147,definition,(
  spl20_15 <=> ($false = sF19)),
  introduced(definition,[new_symbols(definition,[spl20_15])],[avatar_definition])).
thf(f149,plain,(
  ($false = sF19) | ~spl20_15),
  inference(avatar_component_clause,[],[f147])).
thf(f150,plain,(
  spl20_14 | spl20_15),
  inference(avatar_split_clause,[],[f82,f147,f143])).
thf(f152,definition,(
  spl20_16 <=> (sF19 = $true)),
  introduced(definition,[new_symbols(definition,[spl20_16])],[avatar_definition])).
thf(f154,plain,(
  (sF19 = $true) | ~spl20_16),
  inference(avatar_component_clause,[],[f152])).
thf(f165,plain,(
  (((in @ sK8 @ sK9)) = $true) | ($false = $true)),
  inference(forward_demodulation,[],[f83,f75])).
thf(f166,plain,(
  (((in @ sK8 @ sK9)) = $true)),
  inference(trivial_inequality_removal,[],[f165])).
thf(f174,definition,(
  spl20_20 <=> ! [X4 : $i,X7 : $i] : ((((in @ X7 @ X4)) != $true) | ($true = ((in @ (sK13 @ X4) @ X4))))),
  introduced(definition,[new_symbols(definition,[spl20_20])],[avatar_definition])).
thf(f175,plain,(
  ( ! [X7 : $i,X4 : $i] : (($true = ((in @ (sK13 @ X4) @ X4))) | (((in @ X7 @ X4)) != $true)) ) | ~spl20_20),
  inference(avatar_component_clause,[],[f174])).
thf(f176,plain,(
  ~spl20_2 | spl20_20),
  inference(avatar_split_clause,[],[f60,f174,f91])).
thf(f178,definition,(
  spl20_21 <=> ! [X2 : $i,X3 : $i] : (((in @ X3 @ (setadjoin @ X3 @ X2))) = $true)),
  introduced(definition,[new_symbols(definition,[spl20_21])],[avatar_definition])).
thf(f179,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((in @ X3 @ (setadjoin @ X3 @ X2))) = $true)) ) | ~spl20_21),
  inference(avatar_component_clause,[],[f178])).
thf(f180,plain,(
  spl20_21 | ~spl20_3),
  inference(avatar_split_clause,[],[f44,f96,f178])).
thf(f181,plain,(
  spl20_11),
  inference(avatar_split_clause,[],[f59,f130])).
thf(f187,plain,(
  spl20_16),
  inference(avatar_split_clause,[],[f77,f152])).
thf(f189,definition,(
  spl20_23 <=> (setadjoinIR = $true)),
  introduced(definition,[new_symbols(definition,[spl20_23])],[avatar_definition])).
thf(f202,plain,(
  spl20_2),
  inference(avatar_split_clause,[],[f58,f91])).
thf(f208,plain,(
  spl20_3),
  inference(avatar_split_clause,[],[f53,f96])).
thf(f209,plain,(
  spl20_23),
  inference(avatar_split_clause,[],[f55,f189])).
thf(f216,definition,(
  spl20_28 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X0 @ X1))) = $true) | (((in @ X2 @ X1)) != $true))),
  introduced(definition,[new_symbols(definition,[spl20_28])],[avatar_definition])).
thf(f217,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X0 @ X1))) = $true) | (((in @ X2 @ X1)) != $true)) ) | ~spl20_28),
  inference(avatar_component_clause,[],[f216])).
thf(f218,plain,(
  ~spl20_23 | spl20_28),
  inference(avatar_split_clause,[],[f52,f216,f189])).
thf(f229,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X0) | ($true != $true) | (((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) != $true) | (((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X1)) ) | (~spl20_10 | ~spl20_20)),
  inference(superposition,[],[f128,f175])).
thf(f230,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) != $true) | (((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X0) | (((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X1)) ) | (~spl20_10 | ~spl20_20)),
  inference(trivial_inequality_removal,[],[f229])).
thf(f291,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != $true) | (((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X0) | (((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X1)) ) | (~spl20_10 | ~spl20_20 | ~spl20_21)),
  inference(superposition,[],[f230,f179])).
thf(f295,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X1) | (((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X0)) ) | (~spl20_10 | ~spl20_20 | ~spl20_21)),
  inference(trivial_inequality_removal,[],[f291])).
thf(f302,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))))) | (((sK13 @ (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) = X2) | (((in @ X1 @ X0)) != $true)) ) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21)),
  inference(superposition,[],[f140,f295])).
thf(f407,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X0) | (((in @ X0 @ X1)) != $true) | ($true != $true)) ) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21)),
  inference(superposition,[],[f302,f179])).
thf(f410,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((sK13 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = X0) | (((in @ X0 @ X1)) != $true)) ) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21)),
  inference(trivial_inequality_removal,[],[f407])).
thf(f422,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X2 @ emptyset)))) != $true) | (((in @ X1 @ X0)) != $true) | (((in @ X0 @ X2)) != $true)) ) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21)),
  inference(superposition,[],[f140,f410])).
thf(f444,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ X2)) != $true) | (((in @ X0 @ X1)) != $true) | ($true != $true) | (((in @ X0 @ (setadjoin @ X2 @ emptyset))) != $true)) ) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21 | ~spl20_28)),
  inference(superposition,[],[f422,f217])).
thf(f446,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ (setadjoin @ X2 @ emptyset))) != $true) | (((in @ X0 @ X1)) != $true) | (((in @ X1 @ X2)) != $true)) ) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21 | ~spl20_28)),
  inference(trivial_inequality_removal,[],[f444])).
thf(f450,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X1 @ X0)) != $true) | ($true != $true)) ) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21 | ~spl20_28)),
  inference(superposition,[],[f446,f179])).
thf(f453,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ X1 @ X0)) != $true) | (((in @ X0 @ X1)) != $true)) ) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21 | ~spl20_28)),
  inference(trivial_inequality_removal,[],[f450])).
thf(f460,plain,(
  (((in @ sK9 @ sK8)) != $true) | ($true != $true) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21 | ~spl20_28)),
  inference(superposition,[],[f453,f166])).
thf(f466,plain,(
  (((in @ sK9 @ sK8)) != $true) | (~spl20_10 | ~spl20_13 | ~spl20_20 | ~spl20_21 | ~spl20_28)),
  inference(trivial_inequality_removal,[],[f460])).
thf(f469,plain,(
  $false | (~spl20_10 | ~spl20_13 | ~spl20_14 | ~spl20_20 | ~spl20_21 | ~spl20_28)),
  inference(forward_subsumption_resolution,[],[f466,f145])).
thf(f470,plain,(
  ~spl20_10 | ~spl20_13 | ~spl20_14 | ~spl20_20 | ~spl20_21 | ~spl20_28),
  inference(avatar_contradiction_clause,[],[f469])).
thf(f471,plain,(
  ($false = $true) | (~spl20_15 | ~spl20_16)),
  inference(superposition,[],[f149,f154])).
thf(f475,plain,(
  $false | (~spl20_15 | ~spl20_16)),
  inference(trivial_inequality_removal,[],[f471])).
thf(f476,plain,(
  ~spl20_15 | ~spl20_16),
  inference(avatar_contradiction_clause,[],[f475])).
cnf(s5, plain, spl20_10 | ~spl20_11, inference(sat_conversion,[],[f133])).
cnf(s7, plain, ~spl20_2 | spl20_13, inference(sat_conversion,[],[f141])).
cnf(s8, plain, spl20_14 | spl20_15, inference(sat_conversion,[],[f150])).
cnf(s13, plain, ~spl20_2 | spl20_20, inference(sat_conversion,[],[f176])).
cnf(s14, plain, ~spl20_3 | spl20_21, inference(sat_conversion,[],[f180])).
cnf(s15, plain, spl20_11, inference(sat_conversion,[],[f181])).
cnf(s17, plain, spl20_16, inference(sat_conversion,[],[f187])).
cnf(s20, plain, spl20_2, inference(sat_conversion,[],[f202])).
cnf(s22, plain, spl20_3, inference(sat_conversion,[],[f208])).
cnf(s23, plain, spl20_23, inference(sat_conversion,[],[f209])).
cnf(s25, plain, ~spl20_23 | spl20_28, inference(sat_conversion,[],[f218])).
cnf(s29, plain, ~spl20_10 | ~spl20_13 | ~spl20_14 | ~spl20_20 | ~spl20_21 | ~spl20_28, inference(sat_conversion,[],[f470])).
cnf(s31, plain, ~spl20_15 | ~spl20_16, inference(sat_conversion,[],[f476])).
cnf(s32, plain, spl20_28, inference(rat,[],[s25,s23])).
cnf(s33, plain, ~spl20_15, inference(rat,[],[s31,s17])).
cnf(s34, plain, spl20_21, inference(rat,[],[s14,s22])).
cnf(s35, plain, spl20_20, inference(rat,[],[s13,s20])).
cnf(s36, plain, spl20_14, inference(rat,[],[s8,s33])).
cnf(s37, plain, spl20_13, inference(rat,[],[s7,s20])).
cnf(s38, plain, ~spl20_10, inference(rat,[],[s29,s32,s34,s35,s36,s37])).
cnf(s39, plain, $false, inference(rat,[],[s5,s15,s38])).
thf(f477,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s39])).
% SZS output end Proof for theBenchmark