%----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 > $o)).
thf(func_def_1, type, subset: ($i > $i > $o)).
thf(func_def_2, type, subsetI1: $o).
thf(func_def_4, type, kpair: ($i > $i > $i)).
thf(func_def_5, type, cartprod: ($i > $i > $i)).
thf(func_def_6, type, breln: ($i > $i > $i > $o)).
thf(func_def_7, type, brelnall1: $o).
thf(func_def_10, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_11, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_14, type, sK0: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_15, type, sK1: (($i > $o) > $i > $i > $i > $i)).
thf(func_def_19, type, sK5: ($i > $o)).
thf(func_def_27, type, sK13: ($i > $i > $i)).
thf(func_def_28, type, vNOT: ($o > $o)).
thf(func_def_30, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(f1,axiom,(
  (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((in @ X2 @ X0) => (in @ X2 @ X1)) => (subset @ X0 @ X1)) = subsetI1)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1)).
thf(f3,axiom,(
  (! [X1 : $i,X0 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X4 : $i] : ((in @ X4 @ X2) => (X3 @ X4)))) = brelnall1)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',brelnall1)).
thf(f4,conjecture,(
  subsetI1 => (brelnall1 => ! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subbreln)).
thf(f5,negated_conjecture,(
  ~(subsetI1 => (brelnall1 => ! [X2 : $i,X0 : $i,X1 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3))))))),
  inference(negated_conjecture,[status(cth)],[f4])).
thf(f6,plain,(
  (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ X0)) => (subset @ X1 @ X0)) = subsetI1)),
  inference(rectify,[],[f1])).
thf(f7,plain,(
  (subsetI1 = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ X1)) = $true) => (((in @ X2 @ X0)) = $true)) => ($true = ((subset @ X1 @ X0))))),
  inference(fool_elimination,[],[f6])).
thf(f8,plain,(
  ~(subsetI1 => (brelnall1 => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X2 @ X0) => ! [X3 : $i] : ((breln @ X1 @ X2 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X2) => ((in @ (kpair @ X4 @ X5) @ X0) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X0 @ X3))))))),
  inference(rectify,[],[f5])).
thf(f9,plain,(
  ~((subsetI1 = $true) => ((brelnall1 = $true) => ! [X2 : $i,X0 : $i,X1 : $i] : ((((breln @ X1 @ X2 @ X0)) = $true) => ! [X3 : $i] : ((((breln @ X1 @ X2 @ X3)) = $true) => (! [X4 : $i] : (($true = ((in @ X4 @ X1))) => ! [X5 : $i] : (($true = ((in @ X5 @ X2))) => ((((in @ (kpair @ X4 @ X5) @ X0)) = $true) => (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) => ($true = ((subset @ X0 @ X3))))))))),
  inference(fool_elimination,[],[f8])).
thf(f10,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X1 @ X0 @ X2) => ! [X3 : ($i > $o)] : (! [X4 : $i] : ((in @ X4 @ X1) => ! [X5 : $i] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X2) => (X3 @ (kpair @ X4 @ X5))))) => ! [X6 : $i] : ((in @ X6 @ X2) => (X3 @ X6)))) = brelnall1)),
  inference(rectify,[],[f3])).
thf(f11,plain,(
  ! [X1 : $i,X2 : $i,X0 : $i] : (($true = ((breln @ X1 @ X0 @ X2))) => ! [X3 : ($i > $o)] : (! [X4 : $i] : (($true = ((in @ X4 @ X1))) => ! [X5 : $i] : (($true = ((in @ X5 @ X0))) => ((((in @ (kpair @ X4 @ X5) @ X2)) = $true) => (((X3 @ (kpair @ X4 @ X5))) = $true)))) => ! [X6 : $i] : (($true = ((in @ X6 @ X2))) => ($true = ((X3 @ X6)))))) <=> (brelnall1 = $true)),
  inference(fool_elimination,[],[f10])).
thf(f13,plain,(
  (subsetI1 = $true) <=> ! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true)))),
  inference(ennf_transformation,[],[f7])).
thf(f14,plain,(
  (? [X2 : $i,X0 : $i,X1 : $i] : (? [X3 : $i] : ((($true != ((subset @ X0 @ X3))) & ! [X4 : $i] : (! [X5 : $i] : (((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ (kpair @ X4 @ X5) @ X0)) != $true)) | ($true != ((in @ X5 @ X2)))) | ($true != ((in @ X4 @ X1))))) & (((breln @ X1 @ X2 @ X3)) = $true)) & (((breln @ X1 @ X2 @ X0)) = $true)) & (brelnall1 = $true)) & (subsetI1 = $true)),
  inference(ennf_transformation,[],[f9])).
thf(f15,plain,(
  (brelnall1 = $true) & ? [X2 : $i,X1 : $i,X0 : $i] : ((((breln @ X1 @ X2 @ X0)) = $true) & ? [X3 : $i] : ((((breln @ X1 @ X2 @ X3)) = $true) & ($true != ((subset @ X0 @ X3))) & ! [X4 : $i] : (($true != ((in @ X4 @ X1))) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ (kpair @ X4 @ X5) @ X0)) != $true) | ($true != ((in @ X5 @ X2))))))) & (subsetI1 = $true)),
  inference(flattening,[],[f14])).
thf(f16,plain,(
  ! [X1 : $i,X2 : $i,X0 : $i] : (! [X3 : ($i > $o)] : (! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X2)))) | ? [X4 : $i] : (? [X5 : $i] : (((((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)) & ($true = ((in @ X5 @ X0)))) & ($true = ((in @ X4 @ X1))))) | ($true != ((breln @ X1 @ X0 @ X2)))) <=> (brelnall1 = $true)),
  inference(ennf_transformation,[],[f11])).
thf(f17,plain,(
  ! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((breln @ X1 @ X0 @ X2))) | ! [X3 : ($i > $o)] : (? [X4 : $i] : (? [X5 : $i] : (($true = ((in @ X5 @ X0))) & (((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)) & ($true = ((in @ X4 @ X1)))) | ! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X2)))))) <=> (brelnall1 = $true)),
  inference(flattening,[],[f16])).
thf(f18,plain,(
  (! [X2 : $i,X1 : $i,X0 : $i] : (($true != ((breln @ X1 @ X0 @ X2))) | ! [X3 : ($i > $o)] : (? [X4 : $i] : (? [X5 : $i] : (($true = ((in @ X5 @ X0))) & (((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X2)) = $true)) & ($true = ((in @ X4 @ X1)))) | ! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X2)))))) | (brelnall1 != $true)) & ((brelnall1 = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (($true = ((breln @ X1 @ X0 @ X2))) & ? [X3 : ($i > $o)] : (! [X4 : $i] : (! [X5 : $i] : (($true != ((in @ X5 @ X0))) | (((X3 @ (kpair @ X4 @ X5))) = $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true)) | ($true != ((in @ X4 @ X1)))) & ? [X6 : $i] : (($true != ((X3 @ X6))) & ($true = ((in @ X6 @ X2)))))))),
  inference(nnf_transformation,[],[f17])).
thf(f19,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X1 @ X2 @ X0)) != $true) | ! [X3 : ($i > $o)] : (? [X4 : $i] : (? [X5 : $i] : (($true = ((in @ X5 @ X2))) & (((X3 @ (kpair @ X4 @ X5))) != $true) & (((in @ (kpair @ X4 @ X5) @ X0)) = $true)) & ($true = ((in @ X4 @ X1)))) | ! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0)))))) | (brelnall1 != $true)) & ((brelnall1 = $true) | ? [X7 : $i,X8 : $i,X9 : $i] : ((((breln @ X8 @ X9 @ X7)) = $true) & ? [X10 : ($i > $o)] : (! [X11 : $i] : (! [X12 : $i] : (($true != ((in @ X12 @ X9))) | (((X10 @ (kpair @ X11 @ X12))) = $true) | ($true != ((in @ (kpair @ X11 @ X12) @ X7)))) | (((in @ X11 @ X8)) != $true)) & ? [X13 : $i] : (($true != ((X10 @ X13))) & ($true = ((in @ X13 @ X7)))))))),
  inference(rectify,[],[f18])).
thf(f20,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((((breln @ X1 @ X2 @ X0)) != $true) | ! [X3 : ($i > $o)] : (((($true = ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2))) & (((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) & ($true = ((in @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)) @ X0)))) & (((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X1)) = $true)) | ! [X6 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0)))))) | (brelnall1 != $true)) & ((brelnall1 = $true) | (($true = ((breln @ sK3 @ sK4 @ sK2))) & (! [X11 : $i] : (! [X12 : $i] : (($true != ((in @ X12 @ sK4))) | (((sK5 @ (kpair @ X11 @ X12))) = $true) | ($true != ((in @ (kpair @ X11 @ X12) @ sK2)))) | (((in @ X11 @ sK3)) != $true)) & (($true != ((sK5 @ sK6))) & ($true = ((in @ sK6 @ sK2)))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK2,sK3,sK4,sK5,sK6]),skolemize(X5,$thf(sK1 @ X3 @ X2 @ X1 @ X0)),skolemize(X5,$thf(sK1 @ X3 @ X2 @ X1 @ X0)),skolemize(X7,$thf(sK2)),skolemize(X8,$thf(sK3)),skolemize(X9,$thf(sK4)),skolemize(X10,$thf(sK5)),skolemize(X13,$thf(sK6))],[f19])).
thf(f21,plain,(
  (brelnall1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((breln @ X1 @ X0 @ X2))) & ? [X3 : $i] : (($true = ((breln @ X1 @ X0 @ X3))) & (((subset @ X2 @ X3)) != $true) & ! [X4 : $i] : (($true != ((in @ X4 @ X1))) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X3)) = $true) | (((in @ (kpair @ X4 @ X5) @ X2)) != $true) | ($true != ((in @ X5 @ X0))))))) & (subsetI1 = $true)),
  inference(rectify,[],[f15])).
thf(f22,plain,(
  (brelnall1 = $true) & (($true = ((breln @ sK8 @ sK7 @ sK9))) & (($true = ((breln @ sK8 @ sK7 @ sK10))) & ($true != ((subset @ sK9 @ sK10))) & ! [X4 : $i] : ((((in @ X4 @ sK8)) != $true) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ sK10)) = $true) | ($true != ((in @ (kpair @ X4 @ X5) @ sK9))) | (((in @ X5 @ sK7)) != $true))))) & (subsetI1 = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10]),skolemize(X0,$thf(sK7)),skolemize(X1,$thf(sK8)),skolemize(X2,$thf(sK9)),skolemize(X3,$thf(sK10))],[f21])).
thf(f23,plain,(
  ((subsetI1 = $true) | ? [X1 : $i,X0 : $i] : (($true != ((subset @ X1 @ X0))) & ! [X2 : $i] : ((((in @ X2 @ X1)) != $true) | (((in @ X2 @ X0)) = $true)))) & (! [X1 : $i,X0 : $i] : (($true = ((subset @ X1 @ X0))) | ? [X2 : $i] : ((((in @ X2 @ X1)) = $true) & (((in @ X2 @ X0)) != $true))) | (subsetI1 != $true))),
  inference(nnf_transformation,[],[f13])).
thf(f24,plain,(
  ((subsetI1 = $true) | ? [X0 : $i,X1 : $i] : ((((subset @ X0 @ X1)) != $true) & ! [X2 : $i] : ((((in @ X2 @ X0)) != $true) | (((in @ X2 @ X1)) = $true)))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | ? [X5 : $i] : (($true = ((in @ X5 @ X3))) & ($true != ((in @ X5 @ X4))))) | (subsetI1 != $true))),
  inference(rectify,[],[f23])).
thf(f25,plain,(
  ((subsetI1 = $true) | (($true != ((subset @ sK11 @ sK12))) & ! [X2 : $i] : (($true != ((in @ X2 @ sK11))) | ($true = ((in @ X2 @ sK12)))))) & (! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | (($true = ((in @ (sK13 @ X4 @ X3) @ X3))) & ($true != ((in @ (sK13 @ X4 @ X3) @ X4))))) | (subsetI1 != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,vAPP]),skolemize(X0,$thf(sK11)),skolemize(X1,$thf(sK12)),skolemize(X5,$thf(sK1 @ X3 @ X2 @ X1 @ X0))],[f24])).
thf(f30,plain,(
  ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X1)) = $true) | ($true != ((in @ X6 @ X0))) | ($true = ((X3 @ X6))) | (brelnall1 != $true) | (((breln @ X1 @ X2 @ X0)) != $true)) )),
  inference(cnf_transformation,[],[f20])).
thf(f32,plain,(
  ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : (($true != ((in @ X6 @ X0))) | (((breln @ X1 @ X2 @ X0)) != $true) | (brelnall1 != $true) | (((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | ($true = ((X3 @ X6)))) )),
  inference(cnf_transformation,[],[f20])).
thf(f33,plain,(
  ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((brelnall1 != $true) | ($true = ((X3 @ X6))) | ($true = ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2))) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true != ((in @ X6 @ X0)))) )),
  inference(cnf_transformation,[],[f20])).
thf(f34,plain,(
  (subsetI1 = $true)),
  inference(cnf_transformation,[],[f22])).
thf(f35,plain,(
  ( ! [X4 : $i,X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ sK10)) = $true) | (((in @ X4 @ sK8)) != $true) | (((in @ X5 @ sK7)) != $true) | ($true != ((in @ (kpair @ X4 @ X5) @ sK9)))) )),
  inference(cnf_transformation,[],[f22])).
thf(f36,plain,(
  ($true != ((subset @ sK9 @ sK10)))),
  inference(cnf_transformation,[],[f22])).
thf(f38,plain,(
  ($true = ((breln @ sK8 @ sK7 @ sK9)))),
  inference(cnf_transformation,[],[f22])).
thf(f39,plain,(
  (brelnall1 = $true)),
  inference(cnf_transformation,[],[f22])).
thf(f41,plain,(
  ( ! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | (subsetI1 != $true) | ($true != ((in @ (sK13 @ X4 @ X3) @ X4)))) )),
  inference(cnf_transformation,[],[f25])).
thf(f42,plain,(
  ( ! [X3 : $i,X4 : $i] : (($true = ((subset @ X3 @ X4))) | ($true = ((in @ (sK13 @ X4 @ X3) @ X3))) | (subsetI1 != $true)) )),
  inference(cnf_transformation,[],[f25])).
thf(f47,definition,(
  spl14_1 <=> (subsetI1 = $true)),
  introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition])).
thf(f56,definition,(
  spl14_3 <=> (brelnall1 = $true)),
  introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition])).
thf(f69,definition,(
  spl14_6 <=> ! [X6 : $i,X0 : $i,X3 : ($i > $o),X2 : $i,X1 : $i] : ((((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X1)) = $true) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0))))),
  introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition])).
thf(f70,plain,(
  ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((in @ (sK0 @ X3 @ X2 @ X1 @ X0) @ X1)) = $true) | ($true != ((in @ X6 @ X0))) | ($true = ((X3 @ X6))) | (((breln @ X1 @ X2 @ X0)) != $true)) ) | ~spl14_6),
  inference(avatar_component_clause,[],[f69])).
thf(f71,plain,(
  spl14_6 | ~spl14_3),
  inference(avatar_split_clause,[],[f30,f56,f69])).
thf(f78,definition,(
  spl14_8 <=> ! [X3 : ($i > $o),X0 : $i,X6 : $i,X2 : $i,X1 : $i] : (($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0))) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true = ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2))))),
  introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition])).
thf(f79,plain,(
  ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : (($true = ((in @ (sK1 @ X3 @ X2 @ X1 @ X0) @ X2))) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true = ((X3 @ X6))) | ($true != ((in @ X6 @ X0)))) ) | ~spl14_8),
  inference(avatar_component_clause,[],[f78])).
thf(f80,plain,(
  ~spl14_3 | spl14_8),
  inference(avatar_split_clause,[],[f33,f78,f56])).
thf(f92,definition,(
  spl14_11 <=> ! [X2 : $i,X3 : ($i > $o),X0 : $i,X6 : $i,X1 : $i] : (($true != ((in @ X6 @ X0))) | ($true = ((X3 @ X6))) | (((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | (((breln @ X1 @ X2 @ X0)) != $true))),
  introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition])).
thf(f93,plain,(
  ( ! [X2 : $i,X3 : ($i > $o),X0 : $i,X1 : $i,X6 : $i] : ((((X3 @ (kpair @ (sK0 @ X3 @ X2 @ X1 @ X0) @ (sK1 @ X3 @ X2 @ X1 @ X0)))) != $true) | ($true != ((in @ X6 @ X0))) | (((breln @ X1 @ X2 @ X0)) != $true) | ($true = ((X3 @ X6)))) ) | ~spl14_11),
  inference(avatar_component_clause,[],[f92])).
thf(f94,plain,(
  spl14_11 | ~spl14_3),
  inference(avatar_split_clause,[],[f32,f56,f92])).
thf(f96,definition,(
  spl14_12 <=> ($true = ((subset @ sK9 @ sK10)))),
  introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition])).
thf(f98,plain,(
  ($true != ((subset @ sK9 @ sK10))) | spl14_12),
  inference(avatar_component_clause,[],[f96])).
thf(f99,plain,(
  ~spl14_12),
  inference(avatar_split_clause,[],[f36,f96])).
thf(f113,plain,(
  spl14_1),
  inference(avatar_split_clause,[],[f34,f47])).
thf(f115,definition,(
  spl14_16 <=> ! [X4 : $i,X3 : $i] : (($true = ((subset @ X3 @ X4))) | ($true = ((in @ (sK13 @ X4 @ X3) @ X3))))),
  introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition])).
thf(f116,plain,(
  ( ! [X3 : $i,X4 : $i] : (($true = ((in @ (sK13 @ X4 @ X3) @ X3))) | ($true = ((subset @ X3 @ X4)))) ) | ~spl14_16),
  inference(avatar_component_clause,[],[f115])).
thf(f117,plain,(
  spl14_16 | ~spl14_1),
  inference(avatar_split_clause,[],[f42,f47,f115])).
thf(f119,definition,(
  spl14_17 <=> ! [X4 : $i,X3 : $i] : (($true = ((subset @ X3 @ X4))) | ($true != ((in @ (sK13 @ X4 @ X3) @ X4))))),
  introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition])).
thf(f120,plain,(
  ( ! [X3 : $i,X4 : $i] : (($true != ((in @ (sK13 @ X4 @ X3) @ X4))) | ($true = ((subset @ X3 @ X4)))) ) | ~spl14_17),
  inference(avatar_component_clause,[],[f119])).
thf(f121,plain,(
  spl14_17 | ~spl14_1),
  inference(avatar_split_clause,[],[f41,f47,f119])).
thf(f122,plain,(
  spl14_3),
  inference(avatar_split_clause,[],[f39,f56])).
thf(f124,definition,(
  spl14_18 <=> ($true = ((breln @ sK8 @ sK7 @ sK9)))),
  introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition])).
thf(f126,plain,(
  ($true = ((breln @ sK8 @ sK7 @ sK9))) | ~spl14_18),
  inference(avatar_component_clause,[],[f124])).
thf(f127,plain,(
  spl14_18),
  inference(avatar_split_clause,[],[f38,f124])).
thf(f137,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((kpair @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3))) = X0) | ($true != ((breln @ X2 @ X1 @ X3))) | ($true != ((in @ X0 @ X3)))) ) | ~spl14_11),
  inference(leibniz_equality_elimination,[],[f93])).
thf(f162,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK1 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ sK7))) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ X1 @ X2 @ X3) @ sK8))) | (((in @ X0 @ sK9)) != $true) | ($true != ((in @ X0 @ X3))) | ($true != ((breln @ X2 @ X1 @ X3)))) ) | ~spl14_11),
  inference(superposition,[],[f35,f137])).
thf(f170,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($true != ((in @ X0 @ X2))) | ($true != $true) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true != ((in @ X3 @ X2))) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | (((in @ X0 @ sK9)) != $true) | ($true = ((in @ X0 @ sK10)))) ) | (~spl14_8 | ~spl14_11)),
  inference(superposition,[],[f162,f79])).
thf(f171,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X3 @ X2))) | ($true != ((breln @ X1 @ sK7 @ X2))) | (((in @ X0 @ sK9)) != $true) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | ($true != ((in @ X0 @ X2))) | ($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8)))) ) | (~spl14_8 | ~spl14_11)),
  inference(duplicate_literal_removal,[],[f170])).
thf(f172,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X0 @ sK10))) | ($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($true != ((in @ X0 @ X2))) | ($true != ((in @ X3 @ X2))) | ($true != ((breln @ X1 @ sK7 @ X2))) | (((in @ X0 @ sK9)) != $true) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3)))) ) | (~spl14_8 | ~spl14_11)),
  inference(trivial_inequality_removal,[],[f171])).
thf(f173,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((~ (X3 = X0))) = $true) | ($true != ((in @ X3 @ X2))) | ($true = ((in @ X0 @ sK10))) | (((in @ X0 @ sK9)) != $true) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($true != ((in @ X0 @ X2)))) ) | (~spl14_8 | ~spl14_11)),
  inference(beta-eta_normalization,[],[f172])).
thf(f174,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($false = ((X3 = X0))) | (((in @ X0 @ sK9)) != $true) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X0 @ X2))) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true != ((in @ X3 @ X2)))) ) | (~spl14_8 | ~spl14_11)),
  inference(not_proxy_clausification,[],[f173])).
thf(f175,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK0 @ (^[Y0 : $i]: (~ (Y0 = X0))) @ sK7 @ X1 @ X2) @ sK8))) | ($true != ((breln @ X1 @ sK7 @ X2))) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X0 @ X2))) | ($true != ((in @ X3 @ X2))) | (((in @ X0 @ sK9)) != $true) | (X0 != X3)) ) | (~spl14_8 | ~spl14_11)),
  inference(equality_proxy_clausification,[],[f174])).
thf(f206,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ sK9)) != $true) | (((breln @ sK8 @ sK7 @ X1)) != $true) | (((breln @ sK8 @ sK7 @ X1)) != $true) | (((in @ X2 @ X1)) != $true) | (((in @ X0 @ X1)) != $true) | ($true != ((in @ X3 @ X1))) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | ($true = ((in @ X0 @ sK10))) | ($true != $true) | (X0 != X2)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)),
  inference(superposition,[],[f175,f70])).
thf(f207,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | (((in @ X0 @ sK9)) != $true) | (((breln @ sK8 @ sK7 @ X1)) != $true) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | ($true != $true) | (X0 != X2) | (((in @ X2 @ X1)) != $true) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X3 @ X1)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)),
  inference(duplicate_literal_removal,[],[f206])).
thf(f208,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((breln @ sK8 @ sK7 @ X1)) != $true) | (((in @ X0 @ sK9)) != $true) | ($true = (((^[Y0 : $i]: (~ (Y0 = X0))) @ X3))) | ($true != ((in @ X3 @ X1))) | (((in @ X2 @ X1)) != $true) | (X0 != X2) | (((in @ X0 @ X1)) != $true) | ($true = ((in @ X0 @ sK10)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)),
  inference(trivial_inequality_removal,[],[f207])).
thf(f209,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X0 @ X1)) != $true) | ($true = ((in @ X0 @ sK10))) | (((in @ X0 @ sK9)) != $true) | (X0 != X2) | (((breln @ sK8 @ sK7 @ X1)) != $true) | (((in @ X2 @ X1)) != $true) | (((~ (X3 = X0))) = $true) | ($true != ((in @ X3 @ X1)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)),
  inference(beta-eta_normalization,[],[f208])).
thf(f210,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((X0 != X2) | ($true = ((in @ X0 @ sK10))) | ($true != ((in @ X3 @ X1))) | ($false = ((X3 = X0))) | (((in @ X2 @ X1)) != $true) | (((in @ X0 @ X1)) != $true) | (((breln @ sK8 @ sK7 @ X1)) != $true) | (((in @ X0 @ sK9)) != $true)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)),
  inference(not_proxy_clausification,[],[f209])).
thf(f211,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((breln @ sK8 @ sK7 @ X1)) != $true) | ($true != ((in @ X3 @ X1))) | (((in @ X0 @ X1)) != $true) | ($true = ((in @ X0 @ sK10))) | (((in @ X0 @ sK9)) != $true) | (((in @ X2 @ X1)) != $true) | (X0 != X3) | (X0 != X2)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11)),
  inference(equality_proxy_clausification,[],[f210])).
thf(f213,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ sK10))) | (X1 != X2) | ($true != ((in @ X1 @ sK9))) | (((in @ X0 @ sK9)) != $true) | ($true != ((in @ X1 @ sK9))) | ($true != $true) | (X0 != X1) | (((in @ X2 @ sK9)) != $true)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_18)),
  inference(superposition,[],[f211,f126])).
thf(f219,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ sK9)) != $true) | (X0 != X1) | (((in @ X0 @ sK9)) != $true) | ($true != $true) | (X1 != X2) | ($true != ((in @ X1 @ sK9))) | ($true = ((in @ X1 @ sK10)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_18)),
  inference(duplicate_literal_removal,[],[f213])).
thf(f220,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ X1 @ sK10))) | ($true != ((in @ X1 @ sK9))) | (((in @ X2 @ sK9)) != $true) | (((in @ X0 @ sK9)) != $true) | (X1 != X2) | (X0 != X1)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_18)),
  inference(trivial_inequality_removal,[],[f219])).
thf(f221,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK9))) | ($true != $true) | (((in @ X2 @ sK9)) != $true) | (((in @ (sK13 @ sK10 @ X0) @ sK9)) != $true) | (((sK13 @ sK10 @ X0)) != X2) | ($true = ((subset @ X0 @ sK10))) | (((sK13 @ sK10 @ X0)) != X1)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_17 | ~spl14_18)),
  inference(superposition,[],[f120,f220])).
thf(f222,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK13 @ sK10 @ X0) @ sK9)) != $true) | ($true = ((subset @ X0 @ sK10))) | ($true != ((in @ X1 @ sK9))) | (((sK13 @ sK10 @ X0)) != X1) | (((in @ X2 @ sK9)) != $true) | (((sK13 @ sK10 @ X0)) != X2)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_17 | ~spl14_18)),
  inference(trivial_inequality_removal,[],[f221])).
thf(f223,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK9))) | (((in @ X0 @ sK9)) != $true) | (((sK13 @ sK10 @ sK9)) != X0) | (((sK13 @ sK10 @ sK9)) != X1) | ($true = ((subset @ sK9 @ sK10))) | ($true = ((subset @ sK9 @ sK10))) | ($true != $true)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
  inference(superposition,[],[f222,f116])).
thf(f224,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ sK9 @ sK10))) | (((sK13 @ sK10 @ sK9)) != X1) | ($true != $true) | (((sK13 @ sK10 @ sK9)) != X0) | (((in @ X0 @ sK9)) != $true) | ($true != ((in @ X1 @ sK9)))) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
  inference(duplicate_literal_removal,[],[f223])).
thf(f225,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((subset @ sK9 @ sK10))) | (((sK13 @ sK10 @ sK9)) != X0) | ($true != ((in @ X1 @ sK9))) | (((in @ X0 @ sK9)) != $true) | (((sK13 @ sK10 @ sK9)) != X1)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
  inference(trivial_inequality_removal,[],[f224])).
thf(f226,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((sK13 @ sK10 @ sK9)) != X1) | (((in @ X0 @ sK9)) != $true) | ($true != ((in @ X1 @ sK9))) | (((sK13 @ sK10 @ sK9)) != X0)) ) | (~spl14_6 | ~spl14_8 | ~spl14_11 | spl14_12 | ~spl14_16 | ~spl14_17 | ~spl14_18)),
  inference(forward_subsumption_resolution,[],[f225,f98])).
thf(f228,definition,(
  spl14_19 <=> ! [X1 : $i] : ((((sK13 @ sK10 @ sK9)) != X1) | ($true != ((in @ X1 @ sK9))))),
  introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition])).
thf(f229,plain,(
  ( ! [X1 : $i] : (($true != ((in @ X1 @ sK9))) | (((sK13 @ sK10 @ sK9)) != X1)) ) | ~spl14_19),
  inference(avatar_component_clause,[],[f228])).
thf(f230,plain,(
  spl14_19 | spl14_19 | ~spl14_6 | ~spl14_8 | ~spl14_11 | spl14_12 | ~spl14_16 | ~spl14_17 | ~spl14_18),
  inference(avatar_split_clause,[],[f226,f124,f119,f115,f96,f92,f78,f69,f228,f228])).
thf(f256,plain,(
  ( ! [X0 : $i] : ((((sK13 @ X0 @ sK9)) != ((sK13 @ sK10 @ sK9))) | ($true = ((subset @ sK9 @ X0))) | ($true != $true)) ) | (~spl14_16 | ~spl14_19)),
  inference(superposition,[],[f229,f116])).
thf(f263,plain,(
  ( ! [X0 : $i] : ((((sK13 @ X0 @ sK9)) != ((sK13 @ sK10 @ sK9))) | ($true = ((subset @ sK9 @ X0)))) ) | (~spl14_16 | ~spl14_19)),
  inference(trivial_inequality_removal,[],[f256])).
thf(f264,plain,(
  ($true = ((subset @ sK9 @ sK10))) | (~spl14_16 | ~spl14_19)),
  inference(equality_resolution,[],[f263])).
thf(f265,plain,(
  $false | (spl14_12 | ~spl14_16 | ~spl14_19)),
  inference(forward_subsumption_resolution,[],[f264,f98])).
thf(f266,plain,(
  spl14_12 | ~spl14_16 | ~spl14_19),
  inference(avatar_contradiction_clause,[],[f265])).
cnf(s4, plain, ~spl14_3 | spl14_6, inference(sat_conversion,[],[f71])).
cnf(s6, plain, ~spl14_3 | spl14_8, inference(sat_conversion,[],[f80])).
cnf(s9, plain, ~spl14_3 | spl14_11, inference(sat_conversion,[],[f94])).
cnf(s10, plain, ~spl14_12, inference(sat_conversion,[],[f99])).
cnf(s14, plain, spl14_1, inference(sat_conversion,[],[f113])).
cnf(s15, plain, ~spl14_1 | spl14_16, inference(sat_conversion,[],[f117])).
cnf(s16, plain, ~spl14_1 | spl14_17, inference(sat_conversion,[],[f121])).
cnf(s17, plain, spl14_3, inference(sat_conversion,[],[f122])).
cnf(s18, plain, spl14_18, inference(sat_conversion,[],[f127])).
cnf(s19, plain, spl14_19 | ~spl14_8 | ~spl14_11 | spl14_12 | ~spl14_16 | ~spl14_17 | ~spl14_18 | ~spl14_6 | spl14_19, inference(sat_conversion,[],[f230])).
cnf(s20, plain, ~spl14_6 | ~spl14_8 | ~spl14_11 | spl14_12 | ~spl14_16 | ~spl14_17 | ~spl14_18 | spl14_19, inference(rat,[],[s19])).
cnf(s21, plain, spl14_12 | ~spl14_16 | ~spl14_19, inference(sat_conversion,[],[f266])).
cnf(s22, plain, spl14_17, inference(rat,[],[s16,s14])).
cnf(s23, plain, spl14_16, inference(rat,[],[s15,s14])).
cnf(s25, plain, ~spl14_19, inference(rat,[],[s21,s23,s10])).
cnf(s26, plain, spl14_11, inference(rat,[],[s9,s17])).
cnf(s27, plain, spl14_8, inference(rat,[],[s6,s17])).
cnf(s28, plain, ~spl14_6, inference(rat,[],[s20,s25,s18,s22,s23,s10,s26,s27])).
cnf(s29, plain, $false, inference(rat,[],[s4,s28,s17])).
thf(f267,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s29])).
% SZS output end Proof for theBenchmark