%----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 > $i)).
thf(func_def_3, type, dsetconstr: ($i > ($i > $o) > $i)).
thf(func_def_4, type, subset: ($i > $i > $o)).
thf(func_def_5, type, kpair: ($i > $i > $i)).
thf(func_def_6, type, cartprod: ($i > $i > $i)).
thf(func_def_7, type, singleton: ($i > $o)).
thf(func_def_9, type, ex1: ($i > ($i > $o) > $o)).
thf(func_def_10, type, breln: ($i > $i > $i > $o)).
thf(func_def_11, type, func: ($i > $i > $i > $o)).
thf(func_def_12, type, ap: ($i > $i > $i > $i > $i)).
thf(func_def_13, type, funcGraphProp1: $o).
thf(func_def_14, type, funcGraphProp2: $o).
thf(func_def_15, type, eqbreln: $o).
thf(func_def_18, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_19, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_20, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_21, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_22, type, vAND: ($o > $o > $o)).
thf(func_def_23, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_24, type, vIMP: ($o > $o > $o)).
thf(func_def_25, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_26, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_27, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_28, type, sP0: $o).
thf(func_def_42, type, sK14: ($i > $i > $i > $i > $i)).
thf(func_def_43, type, sK15: ($i > $i > $i > $i > $i)).
thf(func_def_44, type, sK16: ($i > $i > $i > $i > $i)).
thf(func_def_45, type, sK17: ($i > $i > $i > $i > $i)).
thf(func_def_51, type, sK23: ($i > $i)).
thf(func_def_52, type, sK24: ($i > $i > $i > $i)).
thf(f4,axiom,(
  (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) & (breln @ X0 @ X1 @ X2))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',func)).
thf(f5,axiom,(
  (! [X2 : $i,X1 : $i,X0 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => (in @ (kpair @ X3 @ (ap @ X0 @ X1 @ X2 @ X3)) @ X2))) = funcGraphProp1)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp1)).
thf(f6,axiom,(
  (! [X1 : $i,X0 : $i,X2 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ X2) => (((ap @ X0 @ X1 @ X2 @ X3)) = X4))))) = funcGraphProp2)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcGraphProp2)).
thf(f7,axiom,(
  (! [X2 : $i,X1 : $i,X0 : $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)))) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X3) => (in @ (kpair @ X4 @ X5) @ X2)))) => (X2 = X3))))) = eqbreln)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqbreln)).
thf(f8,conjecture,(
  funcGraphProp1 => (funcGraphProp2 => (eqbreln => ! [X0 : $i,X2 : $i,X1 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((func @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) => (X2 = X3))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',funcext)).
thf(f9,negated_conjecture,(
  ~(funcGraphProp1 => (funcGraphProp2 => (eqbreln => ! [X0 : $i,X2 : $i,X1 : $i] : ((func @ X0 @ X1 @ X2) => ! [X3 : $i] : ((func @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X1 @ X2 @ X4)) = ((ap @ X0 @ X1 @ X3 @ X4)))) => (X2 = X3)))))))),
  inference(negated_conjecture,[status(cth)],[f8])).
thf(f10,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X2) => (((ap @ X1 @ X0 @ X2 @ X3)) = X4))))) = funcGraphProp2)),
  inference(rectify,[],[f6])).
thf(f11,plain,(
  ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((func @ X1 @ X0 @ X2))) => ! [X3 : $i] : (($true = ((in @ X3 @ X1))) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((in @ (kpair @ X3 @ X4) @ X2)) = $true) => (((ap @ X1 @ X0 @ X2 @ X3)) = X4))))) <=> (funcGraphProp2 = $true)),
  inference(fool_elimination,[],[f10])).
thf(f13,plain,(
  (func = (^[X0 : $i, X1 : $i, X2 : $i] : (! [X3 : $i] : ((in @ X3 @ X0) => (ex1 @ X1 @ (^[X4 : $i] : ((in @ (kpair @ X3 @ X4) @ X2))))) & (breln @ X0 @ X1 @ X2))))),
  inference(rectify,[],[f4])).
thf(f14,plain,(
  (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
  inference(fool_elimination,[],[f13])).
thf(f15,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X2 @ X1 @ X0) => ! [X3 : $i] : ((in @ X3 @ X2) => (in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0))) = funcGraphProp1)),
  inference(rectify,[],[f5])).
thf(f16,plain,(
  ! [X2 : $i,X1 : $i,X0 : $i] : ((((func @ X2 @ X1 @ X0)) = $true) => ! [X3 : $i] : (($true = ((in @ X3 @ X2))) => ($true = ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0))))) <=> (funcGraphProp1 = $true)),
  inference(fool_elimination,[],[f15])).
thf(f17,plain,(
  ~(funcGraphProp1 => (funcGraphProp2 => (eqbreln => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X0 @ X2 @ X1) => ! [X3 : $i] : ((func @ X0 @ X2 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => (((ap @ X0 @ X2 @ X3 @ X4)) = ((ap @ X0 @ X2 @ X1 @ X4)))) => (X1 = X3)))))))),
  inference(rectify,[],[f9])).
thf(f18,plain,(
  ~((funcGraphProp1 = $true) => ((funcGraphProp2 = $true) => ((eqbreln = $true) => ! [X2 : $i,X1 : $i,X0 : $i] : ((((func @ X0 @ X2 @ X1)) = $true) => ! [X3 : $i] : ((((func @ X0 @ X2 @ X3)) = $true) => (! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => (((ap @ X0 @ X2 @ X3 @ X4)) = ((ap @ X0 @ X2 @ X1 @ X4)))) => (X1 = X3)))))))),
  inference(fool_elimination,[],[f17])).
thf(f19,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i] : ((breln @ X2 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X6 : $i] : ((in @ X6 @ X2) => ! [X7 : $i] : ((in @ X7 @ X1) => ((in @ (kpair @ X6 @ X7) @ X3) => (in @ (kpair @ X6 @ X7) @ X0)))) => (X0 = X3))))) = eqbreln)),
  inference(rectify,[],[f7])).
thf(f20,plain,(
  ! [X0 : $i,X2 : $i,X1 : $i] : (($true = ((breln @ X2 @ X1 @ X0))) => ! [X3 : $i] : ((((breln @ X2 @ X1 @ X3)) = $true) => (! [X4 : $i] : (($true = ((in @ X4 @ X2))) => ! [X5 : $i] : ((((in @ X5 @ X1)) = $true) => (($true = ((in @ (kpair @ X4 @ X5) @ X0))) => (((in @ (kpair @ X4 @ X5) @ X3)) = $true)))) => (! [X6 : $i] : (($true = ((in @ X6 @ X2))) => ! [X7 : $i] : (($true = ((in @ X7 @ X1))) => (($true = ((in @ (kpair @ X6 @ X7) @ X3))) => ($true = ((in @ (kpair @ X6 @ X7) @ X0)))))) => (X0 = X3))))) <=> (eqbreln = $true)),
  inference(fool_elimination,[],[f19])).
thf(f25,plain,(
  ((? [X2 : $i,X1 : $i,X0 : $i] : (? [X3 : $i] : (((X1 != X3) & ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | (((ap @ X0 @ X2 @ X3 @ X4)) = ((ap @ X0 @ X2 @ X1 @ X4))))) & (((func @ X0 @ X2 @ X3)) = $true)) & (((func @ X0 @ X2 @ X1)) = $true)) & (eqbreln = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp1 = $true)),
  inference(ennf_transformation,[],[f18])).
thf(f26,plain,(
  (funcGraphProp1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((X1 != X3) & ! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | (((ap @ X0 @ X2 @ X3 @ X4)) = ((ap @ X0 @ X2 @ X1 @ X4)))) & (((func @ X0 @ X2 @ X3)) = $true)) & (((func @ X0 @ X2 @ X1)) = $true)) & (funcGraphProp2 = $true) & (eqbreln = $true)),
  inference(flattening,[],[f25])).
thf(f27,plain,(
  ! [X0 : $i,X2 : $i,X1 : $i] : (! [X3 : $i] : ((((X0 = X3) | ? [X6 : $i] : (? [X7 : $i] : ((($true != ((in @ (kpair @ X6 @ X7) @ X0))) & ($true = ((in @ (kpair @ X6 @ X7) @ X3)))) & ($true = ((in @ X7 @ X1)))) & ($true = ((in @ X6 @ X2))))) | ? [X4 : $i] : (? [X5 : $i] : (((((in @ (kpair @ X4 @ X5) @ X3)) != $true) & ($true = ((in @ (kpair @ X4 @ X5) @ X0)))) & (((in @ X5 @ X1)) = $true)) & ($true = ((in @ X4 @ X2))))) | (((breln @ X2 @ X1 @ X3)) != $true)) | ($true != ((breln @ X2 @ X1 @ X0)))) <=> (eqbreln = $true)),
  inference(ennf_transformation,[],[f20])).
thf(f28,plain,(
  (eqbreln = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (! [X3 : $i] : (? [X4 : $i] : (($true = ((in @ X4 @ X2))) & ? [X5 : $i] : (($true = ((in @ (kpair @ X4 @ X5) @ X0))) & (((in @ X5 @ X1)) = $true) & (((in @ (kpair @ X4 @ X5) @ X3)) != $true))) | (X0 = X3) | ? [X6 : $i] : (($true = ((in @ X6 @ X2))) & ? [X7 : $i] : (($true = ((in @ X7 @ X1))) & ($true != ((in @ (kpair @ X6 @ X7) @ X0))) & ($true = ((in @ (kpair @ X6 @ X7) @ X3))))) | (((breln @ X2 @ X1 @ X3)) != $true)) | ($true != ((breln @ X2 @ X1 @ X0))))),
  inference(flattening,[],[f27])).
thf(f29,plain,(
  ! [X2 : $i,X0 : $i,X1 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((((ap @ X1 @ X0 @ X2 @ X3)) = X4) | (((in @ (kpair @ X3 @ X4) @ X2)) != $true)) | (((in @ X4 @ X0)) != $true)) | ($true != ((in @ X3 @ X1)))) | ($true != ((func @ X1 @ X0 @ X2)))) <=> (funcGraphProp2 = $true)),
  inference(ennf_transformation,[],[f11])).
thf(f30,plain,(
  ! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((func @ X1 @ X0 @ X2))) | ! [X3 : $i] : (($true != ((in @ X3 @ X1))) | ! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) != $true) | (((ap @ X1 @ X0 @ X2 @ X3)) = X4) | (((in @ X4 @ X0)) != $true)))) <=> (funcGraphProp2 = $true)),
  inference(flattening,[],[f29])).
thf(f31,plain,(
  (funcGraphProp1 = $true) <=> ! [X0 : $i,X2 : $i,X1 : $i] : ((((func @ X2 @ X1 @ X0)) != $true) | ! [X3 : $i] : (($true != ((in @ X3 @ X2))) | ($true = ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0)))))),
  inference(ennf_transformation,[],[f16])).
thf(f32,definition,(
  (sP0 = $true) <=> ! [X2 : $i,X1 : $i,X0 : $i] : (! [X3 : $i] : (? [X4 : $i] : (($true = ((in @ X4 @ X2))) & ? [X5 : $i] : (($true = ((in @ (kpair @ X4 @ X5) @ X0))) & (((in @ X5 @ X1)) = $true) & (((in @ (kpair @ X4 @ X5) @ X3)) != $true))) | (X0 = X3) | ? [X6 : $i] : (($true = ((in @ X6 @ X2))) & ? [X7 : $i] : (($true = ((in @ X7 @ X1))) & ($true != ((in @ (kpair @ X6 @ X7) @ X0))) & ($true = ((in @ (kpair @ X6 @ X7) @ X3))))) | (((breln @ X2 @ X1 @ X3)) != $true)) | ($true != ((breln @ X2 @ X1 @ X0))))),
  introduced(definition,[new_symbols(definition,[=])],[predicate_definition_introduction])).
thf(f33,plain,(
  (eqbreln = $true) <=> (sP0 = $true)),
  inference(definition_folding,[],[f28,f32])).
thf(f34,plain,(
  (funcGraphProp1 = $true) & (((sK2 != sK4) & ! [X4 : $i] : (($true != ((in @ X4 @ sK1))) | (((ap @ sK1 @ sK3 @ sK2 @ X4)) = ((ap @ sK1 @ sK3 @ sK4 @ X4)))) & (((func @ sK1 @ sK3 @ sK4)) = $true)) & ($true = ((func @ sK1 @ sK3 @ sK2)))) & (funcGraphProp2 = $true) & (eqbreln = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,$thf(sK1)),skolemize(X1,$thf(sK2)),skolemize(X2,$thf(sK3)),skolemize(X3,$thf(sK4))],[f26])).
thf(f35,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((func @ X1 @ X0 @ X2))) | ! [X3 : $i] : (($true != ((in @ X3 @ X1))) | ! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) != $true) | (((ap @ X1 @ X0 @ X2 @ X3)) = X4) | (((in @ X4 @ X0)) != $true)))) | (funcGraphProp2 != $true)) & ((funcGraphProp2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((func @ X1 @ X0 @ X2))) & ? [X3 : $i] : (($true = ((in @ X3 @ X1))) & ? [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) = $true) & (((ap @ X1 @ X0 @ X2 @ X3)) != X4) & (((in @ X4 @ X0)) = $true)))))),
  inference(nnf_transformation,[],[f30])).
thf(f36,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((func @ X1 @ X0 @ X2))) | ! [X3 : $i] : (($true != ((in @ X3 @ X1))) | ! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) != $true) | (((ap @ X1 @ X0 @ X2 @ X3)) = X4) | (((in @ X4 @ X0)) != $true)))) | (funcGraphProp2 != $true)) & ((funcGraphProp2 = $true) | ? [X5 : $i,X6 : $i,X7 : $i] : ((((func @ X6 @ X5 @ X7)) = $true) & ? [X8 : $i] : (($true = ((in @ X8 @ X6))) & ? [X9 : $i] : ((((in @ (kpair @ X8 @ X9) @ X7)) = $true) & (((ap @ X6 @ X5 @ X7 @ X8)) != X9) & ($true = ((in @ X9 @ X5)))))))),
  inference(rectify,[],[f35])).
thf(f37,plain,(
  (! [X0 : $i,X1 : $i,X2 : $i] : (($true != ((func @ X1 @ X0 @ X2))) | ! [X3 : $i] : (($true != ((in @ X3 @ X1))) | ! [X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) != $true) | (((ap @ X1 @ X0 @ X2 @ X3)) = X4) | (((in @ X4 @ X0)) != $true)))) | (funcGraphProp2 != $true)) & ((funcGraphProp2 = $true) | ((((func @ sK6 @ sK5 @ sK7)) = $true) & ((((in @ sK8 @ sK6)) = $true) & (($true = ((in @ (kpair @ sK8 @ sK9) @ sK7))) & (sK9 != ((ap @ sK6 @ sK5 @ sK7 @ sK8))) & (((in @ sK9 @ sK5)) = $true)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9]),skolemize(X5,$thf(sK5)),skolemize(X6,$thf(sK6)),skolemize(X7,$thf(sK7)),skolemize(X8,$thf(sK8)),skolemize(X9,$thf(sK9))],[f36])).
thf(f38,plain,(
  ((sP0 = $true) | ? [X2 : $i,X1 : $i,X0 : $i] : (? [X3 : $i] : (! [X4 : $i] : (($true != ((in @ X4 @ X2))) | ! [X5 : $i] : (($true != ((in @ (kpair @ X4 @ X5) @ X0))) | (((in @ X5 @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true))) & (X0 != X3) & ! [X6 : $i] : (($true != ((in @ X6 @ X2))) | ! [X7 : $i] : (($true != ((in @ X7 @ X1))) | ($true = ((in @ (kpair @ X6 @ X7) @ X0))) | ($true != ((in @ (kpair @ X6 @ X7) @ X3))))) & (((breln @ X2 @ X1 @ X3)) = $true)) & ($true = ((breln @ X2 @ X1 @ X0))))) & (! [X2 : $i,X1 : $i,X0 : $i] : (! [X3 : $i] : (? [X4 : $i] : (($true = ((in @ X4 @ X2))) & ? [X5 : $i] : (($true = ((in @ (kpair @ X4 @ X5) @ X0))) & (((in @ X5 @ X1)) = $true) & (((in @ (kpair @ X4 @ X5) @ X3)) != $true))) | (X0 = X3) | ? [X6 : $i] : (($true = ((in @ X6 @ X2))) & ? [X7 : $i] : (($true = ((in @ X7 @ X1))) & ($true != ((in @ (kpair @ X6 @ X7) @ X0))) & ($true = ((in @ (kpair @ X6 @ X7) @ X3))))) | (((breln @ X2 @ X1 @ X3)) != $true)) | ($true != ((breln @ X2 @ X1 @ X0)))) | (sP0 != $true))),
  inference(nnf_transformation,[],[f32])).
thf(f39,plain,(
  ((sP0 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (! [X4 : $i] : ((((in @ X4 @ X0)) != $true) | ! [X5 : $i] : ((((in @ (kpair @ X4 @ X5) @ X2)) != $true) | (((in @ X5 @ X1)) != $true) | (((in @ (kpair @ X4 @ X5) @ X3)) = $true))) & (X2 != X3) & ! [X6 : $i] : ((((in @ X6 @ X0)) != $true) | ! [X7 : $i] : (($true != ((in @ X7 @ X1))) | ($true = ((in @ (kpair @ X6 @ X7) @ X2))) | ($true != ((in @ (kpair @ X6 @ X7) @ X3))))) & (((breln @ X0 @ X1 @ X3)) = $true)) & (((breln @ X0 @ X1 @ X2)) = $true))) & (! [X8 : $i,X9 : $i,X10 : $i] : (! [X11 : $i] : (? [X12 : $i] : (($true = ((in @ X12 @ X8))) & ? [X13 : $i] : (($true = ((in @ (kpair @ X12 @ X13) @ X10))) & ($true = ((in @ X13 @ X9))) & ($true != ((in @ (kpair @ X12 @ X13) @ X11))))) | (X10 = X11) | ? [X14 : $i] : ((((in @ X14 @ X8)) = $true) & ? [X15 : $i] : ((((in @ X15 @ X9)) = $true) & (((in @ (kpair @ X14 @ X15) @ X10)) != $true) & ($true = ((in @ (kpair @ X14 @ X15) @ X11))))) | ($true != ((breln @ X8 @ X9 @ X11)))) | ($true != ((breln @ X8 @ X9 @ X10)))) | (sP0 != $true))),
  inference(rectify,[],[f38])).
thf(f40,plain,(
  ((sP0 = $true) | ((! [X4 : $i] : (($true != ((in @ X4 @ sK10))) | ! [X5 : $i] : (($true != ((in @ (kpair @ X4 @ X5) @ sK12))) | ($true != ((in @ X5 @ sK11))) | ($true = ((in @ (kpair @ X4 @ X5) @ sK13))))) & (sK12 != sK13) & ! [X6 : $i] : (($true != ((in @ X6 @ sK10))) | ! [X7 : $i] : (($true != ((in @ X7 @ sK11))) | (((in @ (kpair @ X6 @ X7) @ sK12)) = $true) | ($true != ((in @ (kpair @ X6 @ X7) @ sK13))))) & ($true = ((breln @ sK10 @ sK11 @ sK13)))) & (((breln @ sK10 @ sK11 @ sK12)) = $true))) & (! [X8 : $i,X9 : $i,X10 : $i] : (! [X11 : $i] : ((($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) & (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) & (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) & ($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))))) | (X10 = X11) | ((((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) & (($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) & (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) & ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))))) | ($true != ((breln @ X8 @ X9 @ X11)))) | ($true != ((breln @ X8 @ X9 @ X10)))) | (sP0 != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13,vAPP]),skolemize(X0,$thf(sK10)),skolemize(X1,$thf(sK11)),skolemize(X2,$thf(sK12)),skolemize(X3,$thf(sK13)),skolemize(X15,$thf(sK17 @ X11 @ X10 @ X9 @ X8)),skolemize(X15,$thf(sK17 @ X11 @ X10 @ X9 @ X8)),skolemize(X15,$thf(sK17 @ X11 @ X10 @ X9 @ X8)),skolemize(X15,$thf(sK17 @ X11 @ X10 @ X9 @ X8))],[f39])).
thf(f41,plain,(
  ((eqbreln = $true) | (sP0 != $true)) & ((sP0 = $true) | (eqbreln != $true))),
  inference(nnf_transformation,[],[f33])).
thf(f42,plain,(
  ((funcGraphProp1 = $true) | ? [X0 : $i,X2 : $i,X1 : $i] : ((((func @ X2 @ X1 @ X0)) = $true) & ? [X3 : $i] : (($true = ((in @ X3 @ X2))) & ($true != ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0)))))) & (! [X0 : $i,X2 : $i,X1 : $i] : ((((func @ X2 @ X1 @ X0)) != $true) | ! [X3 : $i] : (($true != ((in @ X3 @ X2))) | ($true = ((in @ (kpair @ X3 @ (ap @ X2 @ X1 @ X0 @ X3)) @ X0))))) | (funcGraphProp1 != $true))),
  inference(nnf_transformation,[],[f31])).
thf(f43,plain,(
  ((funcGraphProp1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = ((func @ X1 @ X2 @ X0))) & ? [X3 : $i] : (($true = ((in @ X3 @ X1))) & (((in @ (kpair @ X3 @ (ap @ X1 @ X2 @ X0 @ X3)) @ X0)) != $true)))) & (! [X4 : $i,X5 : $i,X6 : $i] : ((((func @ X5 @ X6 @ X4)) != $true) | ! [X7 : $i] : ((((in @ X7 @ X5)) != $true) | (((in @ (kpair @ X7 @ (ap @ X5 @ X6 @ X4 @ X7)) @ X4)) = $true))) | (funcGraphProp1 != $true))),
  inference(rectify,[],[f42])).
thf(f44,plain,(
  ((funcGraphProp1 = $true) | ((((func @ sK19 @ sK20 @ sK18)) = $true) & ((((in @ sK21 @ sK19)) = $true) & (((in @ (kpair @ sK21 @ (ap @ sK19 @ sK20 @ sK18 @ sK21)) @ sK18)) != $true)))) & (! [X4 : $i,X5 : $i,X6 : $i] : ((((func @ X5 @ X6 @ X4)) != $true) | ! [X7 : $i] : ((((in @ X7 @ X5)) != $true) | (((in @ (kpair @ X7 @ (ap @ X5 @ X6 @ X4 @ X7)) @ X4)) = $true))) | (funcGraphProp1 != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK18,sK19,sK20,sK21]),skolemize(X0,$thf(sK18)),skolemize(X1,$thf(sK19)),skolemize(X2,$thf(sK20)),skolemize(X3,$thf(sK21))],[f43])).
thf(f45,plain,(
  (eqbreln = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f46,plain,(
  (funcGraphProp2 = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f47,plain,(
  ($true = ((func @ sK1 @ sK3 @ sK2)))),
  inference(cnf_transformation,[],[f34])).
thf(f48,plain,(
  (((func @ sK1 @ sK3 @ sK4)) = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f49,plain,(
  ( ! [X4 : $i] : ((((ap @ sK1 @ sK3 @ sK2 @ X4)) = ((ap @ sK1 @ sK3 @ sK4 @ X4))) | ($true != ((in @ X4 @ sK1)))) )),
  inference(cnf_transformation,[],[f34])).
thf(f50,plain,(
  (sK2 != sK4)),
  inference(cnf_transformation,[],[f34])).
thf(f51,plain,(
  (funcGraphProp1 = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f58,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) != $true) | ($true != ((func @ X1 @ X0 @ X2))) | ($true != ((in @ X3 @ X1))) | (((in @ X4 @ X0)) != $true) | (((ap @ X1 @ X0 @ X2 @ X3)) = X4) | (funcGraphProp2 != $true)) )),
  inference(cnf_transformation,[],[f37])).
thf(f59,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | (X10 = X11) | (sP0 != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f60,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : ((X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | (sP0 != $true) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11)))) )),
  inference(cnf_transformation,[],[f40])).
thf(f61,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | ($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (sP0 != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f62,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : ((((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | ($true != ((breln @ X8 @ X9 @ X10))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | (sP0 != $true) | ($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11)))) )),
  inference(cnf_transformation,[],[f40])).
thf(f63,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | (sP0 != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f64,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : ((sP0 != $true) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f65,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : ((((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) | ($true != ((breln @ X8 @ X9 @ X10))) | (sP0 != $true) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11)))) )),
  inference(cnf_transformation,[],[f40])).
thf(f66,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : ((X10 = X11) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | (sP0 != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f67,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | (X10 = X11) | (sP0 != $true) | ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11)))) )),
  inference(cnf_transformation,[],[f40])).
thf(f68,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | (X10 = X11) | (sP0 != $true) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f69,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | ($true != ((breln @ X8 @ X9 @ X10))) | (sP0 != $true) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9)))) )),
  inference(cnf_transformation,[],[f40])).
thf(f70,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | (sP0 != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f71,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (sP0 != $true)) )),
  inference(cnf_transformation,[],[f40])).
thf(f72,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((breln @ X8 @ X9 @ X10))) | (sP0 != $true) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8)))) )),
  inference(cnf_transformation,[],[f40])).
thf(f73,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | (sP0 != $true) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) | (X10 = X11)) )),
  inference(cnf_transformation,[],[f40])).
thf(f74,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11))) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | (sP0 != $true) | (X10 = X11) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8)))) )),
  inference(cnf_transformation,[],[f40])).
thf(f80,plain,(
  (eqbreln != $true) | (sP0 = $true)),
  inference(cnf_transformation,[],[f41])).
thf(f82,plain,(
  (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
  inference(cnf_transformation,[],[f14])).
thf(f84,plain,(
  ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((func @ X5 @ X6 @ X4)) != $true) | (funcGraphProp1 != $true) | (((in @ (kpair @ X7 @ (ap @ X5 @ X6 @ X4 @ X7)) @ X4)) = $true) | (((in @ X7 @ X5)) != $true)) )),
  inference(cnf_transformation,[],[f44])).
thf(f92,definition,(
  spl22_1 <=> (funcGraphProp2 = $true)),
  introduced(definition,[new_symbols(definition,[spl22_1])],[avatar_definition])).
thf(f101,definition,(
  spl22_3 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))))),
  introduced(definition,[new_symbols(definition,[spl22_3])],[avatar_definition])).
thf(f102,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9)))) ) | ~spl22_3),
  inference(avatar_component_clause,[],[f101])).
thf(f104,definition,(
  spl22_4 <=> (sP0 = $true)),
  introduced(definition,[new_symbols(definition,[spl22_4])],[avatar_definition])).
thf(f107,plain,(
  spl22_3 | ~spl22_4),
  inference(avatar_split_clause,[],[f61,f104,f101])).
thf(f114,definition,(
  spl22_6 <=> (eqbreln = $true)),
  introduced(definition,[new_symbols(definition,[spl22_6])],[avatar_definition])).
thf(f117,plain,(
  spl22_4 | ~spl22_6),
  inference(avatar_split_clause,[],[f80,f114,f104])).
thf(f119,definition,(
  spl22_7 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : ((X10 = X11) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true != ((breln @ X8 @ X9 @ X11))))),
  introduced(definition,[new_symbols(definition,[spl22_7])],[avatar_definition])).
thf(f120,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : ((((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | (X10 = X11)) ) | ~spl22_7),
  inference(avatar_component_clause,[],[f119])).
thf(f121,plain,(
  ~spl22_4 | spl22_7),
  inference(avatar_split_clause,[],[f64,f119,f104])).
thf(f128,definition,(
  spl22_9 <=> (sK2 = sK4)),
  introduced(definition,[new_symbols(definition,[spl22_9])],[avatar_definition])).
thf(f130,plain,(
  (sK2 != sK4) | spl22_9),
  inference(avatar_component_clause,[],[f128])).
thf(f131,plain,(
  ~spl22_9),
  inference(avatar_split_clause,[],[f50,f128])).
thf(f142,definition,(
  spl22_12 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11))),
  introduced(definition,[new_symbols(definition,[spl22_12])],[avatar_definition])).
thf(f143,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11)) ) | ~spl22_12),
  inference(avatar_component_clause,[],[f142])).
thf(f144,plain,(
  spl22_12 | ~spl22_4),
  inference(avatar_split_clause,[],[f68,f104,f142])).
thf(f146,definition,(
  spl22_13 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))))),
  introduced(definition,[new_symbols(definition,[spl22_13])],[avatar_definition])).
thf(f147,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) | (X10 = X11)) ) | ~spl22_13),
  inference(avatar_component_clause,[],[f146])).
thf(f148,plain,(
  ~spl22_4 | spl22_13),
  inference(avatar_split_clause,[],[f69,f146,f104])).
thf(f150,definition,(
  spl22_14 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))))),
  introduced(definition,[new_symbols(definition,[spl22_14])],[avatar_definition])).
thf(f151,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true)) ) | ~spl22_14),
  inference(avatar_component_clause,[],[f150])).
thf(f152,plain,(
  ~spl22_4 | spl22_14),
  inference(avatar_split_clause,[],[f70,f150,f104])).
thf(f155,definition,(
  spl22_15 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10))) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (X10 = X11))),
  introduced(definition,[new_symbols(definition,[spl22_15])],[avatar_definition])).
thf(f156,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | (X10 = X11) | ($true = ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X10)))) ) | ~spl22_15),
  inference(avatar_component_clause,[],[f155])).
thf(f157,plain,(
  spl22_15 | ~spl22_4),
  inference(avatar_split_clause,[],[f67,f104,f155])).
thf(f164,definition,(
  spl22_17 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11))),
  introduced(definition,[new_symbols(definition,[spl22_17])],[avatar_definition])).
thf(f165,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : ((((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | (X10 = X11) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11)))) ) | ~spl22_17),
  inference(avatar_component_clause,[],[f164])).
thf(f166,plain,(
  spl22_17 | ~spl22_4),
  inference(avatar_split_clause,[],[f72,f104,f164])).
thf(f168,definition,(
  spl22_18 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : ((((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | ($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))))),
  introduced(definition,[new_symbols(definition,[spl22_18])],[avatar_definition])).
thf(f169,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | ($true != ((breln @ X8 @ X9 @ X11)))) ) | ~spl22_18),
  inference(avatar_component_clause,[],[f168])).
thf(f170,plain,(
  spl22_18 | ~spl22_4),
  inference(avatar_split_clause,[],[f62,f104,f168])).
thf(f172,definition,(
  spl22_19 <=> (funcGraphProp1 = $true)),
  introduced(definition,[new_symbols(definition,[spl22_19])],[avatar_definition])).
thf(f195,plain,(
  spl22_1),
  inference(avatar_split_clause,[],[f46,f92])).
thf(f197,definition,(
  spl22_24 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | (X10 = X11) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))))),
  introduced(definition,[new_symbols(definition,[spl22_24])],[avatar_definition])).
thf(f198,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11)))) ) | ~spl22_24),
  inference(avatar_component_clause,[],[f197])).
thf(f199,plain,(
  spl22_24 | ~spl22_4),
  inference(avatar_split_clause,[],[f73,f104,f197])).
thf(f200,plain,(
  spl22_6),
  inference(avatar_split_clause,[],[f45,f114])).
thf(f207,definition,(
  spl22_26 <=> ! [X5 : $i,X4 : $i,X7 : $i,X6 : $i] : ((((func @ X5 @ X6 @ X4)) != $true) | (((in @ X7 @ X5)) != $true) | (((in @ (kpair @ X7 @ (ap @ X5 @ X6 @ X4 @ X7)) @ X4)) = $true))),
  introduced(definition,[new_symbols(definition,[spl22_26])],[avatar_definition])).
thf(f208,plain,(
  ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((in @ (kpair @ X7 @ (ap @ X5 @ X6 @ X4 @ X7)) @ X4)) = $true) | (((in @ X7 @ X5)) != $true) | (((func @ X5 @ X6 @ X4)) != $true)) ) | ~spl22_26),
  inference(avatar_component_clause,[],[f207])).
thf(f209,plain,(
  ~spl22_19 | spl22_26),
  inference(avatar_split_clause,[],[f84,f207,f172])).
thf(f211,definition,(
  spl22_27 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | (X10 = X11) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | ($true != ((breln @ X8 @ X9 @ X11))))),
  introduced(definition,[new_symbols(definition,[spl22_27])],[avatar_definition])).
thf(f212,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10)))) ) | ~spl22_27),
  inference(avatar_component_clause,[],[f211])).
thf(f213,plain,(
  ~spl22_4 | spl22_27),
  inference(avatar_split_clause,[],[f74,f211,f104])).
thf(f215,definition,(
  spl22_28 <=> ! [X4 : $i,X0 : $i,X3 : $i,X2 : $i,X1 : $i] : ((((in @ (kpair @ X3 @ X4) @ X2)) != $true) | (((ap @ X1 @ X0 @ X2 @ X3)) = X4) | (((in @ X4 @ X0)) != $true) | ($true != ((in @ X3 @ X1))) | ($true != ((func @ X1 @ X0 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl22_28])],[avatar_definition])).
thf(f216,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((ap @ X1 @ X0 @ X2 @ X3)) = X4) | ($true != ((func @ X1 @ X0 @ X2))) | ($true != ((in @ X3 @ X1))) | (((in @ X4 @ X0)) != $true) | (((in @ (kpair @ X3 @ X4) @ X2)) != $true)) ) | ~spl22_28),
  inference(avatar_component_clause,[],[f215])).
thf(f217,plain,(
  ~spl22_1 | spl22_28),
  inference(avatar_split_clause,[],[f58,f215,f92])).
thf(f233,definition,(
  spl22_32 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : ((X10 = X11) | ($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true != ((breln @ X8 @ X9 @ X11))))),
  introduced(definition,[new_symbols(definition,[spl22_32])],[avatar_definition])).
thf(f234,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X10)) != $true) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11)) ) | ~spl22_32),
  inference(avatar_component_clause,[],[f233])).
thf(f235,plain,(
  spl22_32 | ~spl22_4),
  inference(avatar_split_clause,[],[f60,f104,f233])).
thf(f237,definition,(
  spl22_33 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : ((X10 = X11) | (((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11))) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true))),
  introduced(definition,[new_symbols(definition,[spl22_33])],[avatar_definition])).
thf(f238,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : ((((in @ (sK16 @ X11 @ X10 @ X9 @ X8) @ X8)) = $true) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10)))) ) | ~spl22_33),
  inference(avatar_component_clause,[],[f237])).
thf(f239,plain,(
  spl22_33 | ~spl22_4),
  inference(avatar_split_clause,[],[f66,f104,f237])).
thf(f240,plain,(
  spl22_19),
  inference(avatar_split_clause,[],[f51,f172])).
thf(f242,definition,(
  spl22_34 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X11))))),
  introduced(definition,[new_symbols(definition,[spl22_34])],[avatar_definition])).
thf(f243,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((in @ (kpair @ (sK14 @ X11 @ X10 @ X9 @ X8) @ (sK15 @ X11 @ X10 @ X9 @ X8)) @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true != ((breln @ X8 @ X9 @ X11)))) ) | ~spl22_34),
  inference(avatar_component_clause,[],[f242])).
thf(f244,plain,(
  spl22_34 | ~spl22_4),
  inference(avatar_split_clause,[],[f59,f104,f242])).
thf(f251,definition,(
  spl22_36 <=> ($true = ((func @ sK1 @ sK3 @ sK2)))),
  introduced(definition,[new_symbols(definition,[spl22_36])],[avatar_definition])).
thf(f253,plain,(
  ($true = ((func @ sK1 @ sK3 @ sK2))) | ~spl22_36),
  inference(avatar_component_clause,[],[f251])).
thf(f254,plain,(
  spl22_36),
  inference(avatar_split_clause,[],[f47,f251])).
thf(f256,definition,(
  spl22_37 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true != ((breln @ X8 @ X9 @ X10))) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))))),
  introduced(definition,[new_symbols(definition,[spl22_37])],[avatar_definition])).
thf(f257,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X11))) | ($true != ((breln @ X8 @ X9 @ X10))) | (X10 = X11) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true)) ) | ~spl22_37),
  inference(avatar_component_clause,[],[f256])).
thf(f258,plain,(
  spl22_37 | ~spl22_4),
  inference(avatar_split_clause,[],[f63,f104,f256])).
thf(f265,definition,(
  spl22_39 <=> (((func @ sK1 @ sK3 @ sK4)) = $true)),
  introduced(definition,[new_symbols(definition,[spl22_39])],[avatar_definition])).
thf(f267,plain,(
  (((func @ sK1 @ sK3 @ sK4)) = $true) | ~spl22_39),
  inference(avatar_component_clause,[],[f265])).
thf(f268,plain,(
  spl22_39),
  inference(avatar_split_clause,[],[f48,f265])).
thf(f270,definition,(
  spl22_40 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : ((((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | ($true != ((breln @ X8 @ X9 @ X10))) | ($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))))),
  introduced(definition,[new_symbols(definition,[spl22_40])],[avatar_definition])).
thf(f271,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (sK17 @ X11 @ X10 @ X9 @ X8) @ X9))) | ($true != ((breln @ X8 @ X9 @ X11))) | (((in @ (sK15 @ X11 @ X10 @ X9 @ X8) @ X9)) = $true) | ($true != ((breln @ X8 @ X9 @ X10))) | (X10 = X11)) ) | ~spl22_40),
  inference(avatar_component_clause,[],[f270])).
thf(f272,plain,(
  ~spl22_4 | spl22_40),
  inference(avatar_split_clause,[],[f65,f270,f104])).
thf(f274,definition,(
  spl22_41 <=> (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))))),
  introduced(definition,[new_symbols(definition,[spl22_41])],[avatar_definition])).
thf(f276,plain,(
  (func = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))) | ~spl22_41),
  inference(avatar_component_clause,[],[f274])).
thf(f277,plain,(
  spl22_41),
  inference(avatar_split_clause,[],[f82,f274])).
thf(f279,definition,(
  spl22_42 <=> ! [X10 : $i,X11 : $i,X9 : $i,X8 : $i] : (($true != ((breln @ X8 @ X9 @ X11))) | ($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | ($true != ((breln @ X8 @ X9 @ X10))) | (X10 = X11))),
  introduced(definition,[new_symbols(definition,[spl22_42])],[avatar_definition])).
thf(f280,plain,(
  ( ! [X10 : $i,X11 : $i,X8 : $i,X9 : $i] : (($true = ((in @ (kpair @ (sK16 @ X11 @ X10 @ X9 @ X8) @ (sK17 @ X11 @ X10 @ X9 @ X8)) @ X11))) | ($true != ((breln @ X8 @ X9 @ X11))) | (X10 = X11) | ($true = ((in @ (sK14 @ X11 @ X10 @ X9 @ X8) @ X8))) | ($true != ((breln @ X8 @ X9 @ X10)))) ) | ~spl22_42),
  inference(avatar_component_clause,[],[f279])).
thf(f281,plain,(
  spl22_42 | ~spl22_4),
  inference(avatar_split_clause,[],[f71,f104,f279])).
thf(f285,plain,(
  ( ! [X0 : $i] : (($true != ((func @ sK1 @ sK3 @ sK2))) | (((in @ (kpair @ X0 @ (ap @ sK1 @ sK3 @ sK4 @ X0)) @ sK2)) = $true) | ($true != ((in @ X0 @ sK1))) | ($true != ((in @ X0 @ sK1)))) ) | ~spl22_26),
  inference(superposition,[],[f208,f49])).
thf(f286,plain,(
  ( ! [X0 : $i] : (($true != ((in @ X0 @ sK1))) | ($true != ((func @ sK1 @ sK3 @ sK2))) | (((in @ (kpair @ X0 @ (ap @ sK1 @ sK3 @ sK4 @ X0)) @ sK2)) = $true)) ) | ~spl22_26),
  inference(duplicate_literal_removal,[],[f285])).
thf(f287,plain,(
  ( ! [X0 : $i] : ((((in @ (kpair @ X0 @ (ap @ sK1 @ sK3 @ sK4 @ X0)) @ sK2)) = $true) | ($true != ((in @ X0 @ sK1)))) ) | (~spl22_26 | ~spl22_36)),
  inference(forward_subsumption_resolution,[],[f286,f253])).
thf(f290,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (kpair @ X1 @ X0) @ sK2))) | ($true != ((in @ X0 @ sK3))) | ($true != ((in @ X1 @ sK1))) | (((ap @ sK1 @ sK3 @ sK4 @ X1)) = X0) | ($true != ((in @ X1 @ sK1))) | ($true != ((func @ sK1 @ sK3 @ sK2)))) ) | ~spl22_28),
  inference(superposition,[],[f49,f216])).
thf(f292,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((func @ sK1 @ sK3 @ sK2))) | ($true != ((in @ X1 @ sK1))) | ($true != ((in @ (kpair @ X1 @ X0) @ sK2))) | ($true != ((in @ X0 @ sK3))) | (((ap @ sK1 @ sK3 @ sK4 @ X1)) = X0)) ) | ~spl22_28),
  inference(duplicate_literal_removal,[],[f290])).
thf(f296,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((ap @ sK1 @ sK3 @ sK4 @ X1)) = X0) | ($true != ((in @ X0 @ sK3))) | ($true != ((in @ (kpair @ X1 @ X0) @ sK2))) | ($true != ((in @ X1 @ sK1)))) ) | (~spl22_28 | ~spl22_36)),
  inference(forward_subsumption_resolution,[],[f292,f253])).
thf(f300,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK1))) | (((in @ (kpair @ X1 @ X0) @ sK4)) != $true) | ($true != ((in @ X0 @ sK3))) | (((func @ sK1 @ sK3 @ sK4)) != $true) | ($true != ((in @ X1 @ sK1))) | ($true = ((in @ (kpair @ X1 @ X0) @ sK2)))) ) | (~spl22_26 | ~spl22_28 | ~spl22_36)),
  inference(superposition,[],[f287,f216])).
thf(f301,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK1))) | ($true = ((in @ (kpair @ X1 @ X0) @ sK2))) | (((in @ (kpair @ X1 @ X0) @ sK4)) != $true) | (((func @ sK1 @ sK3 @ sK4)) != $true) | ($true != ((in @ X0 @ sK3)))) ) | (~spl22_26 | ~spl22_28 | ~spl22_36)),
  inference(duplicate_literal_removal,[],[f300])).
thf(f302,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (kpair @ X1 @ X0) @ sK2))) | (((in @ (kpair @ X1 @ X0) @ sK4)) != $true) | ($true != ((in @ X1 @ sK1))) | ($true != ((in @ X0 @ sK3)))) ) | (~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f301,f267])).
thf(f307,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ sK3))) | (((func @ sK1 @ sK3 @ sK4)) != $true) | ($true != ((in @ X1 @ sK1))) | ($true != ((in @ (kpair @ X1 @ X0) @ sK2))) | ($true != ((in @ X1 @ sK1))) | (((in @ (kpair @ X1 @ X0) @ sK4)) = $true)) ) | (~spl22_26 | ~spl22_28 | ~spl22_36)),
  inference(superposition,[],[f208,f296])).
thf(f308,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ X1 @ sK1))) | ($true != ((in @ X0 @ sK3))) | (((func @ sK1 @ sK3 @ sK4)) != $true) | ($true != ((in @ (kpair @ X1 @ X0) @ sK2))) | (((in @ (kpair @ X1 @ X0) @ sK4)) = $true)) ) | (~spl22_26 | ~spl22_28 | ~spl22_36)),
  inference(duplicate_literal_removal,[],[f307])).
thf(f313,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (kpair @ X1 @ X0) @ sK4)) = $true) | ($true != ((in @ X0 @ sK3))) | ($true != ((in @ X1 @ sK1))) | ($true != ((in @ (kpair @ X1 @ X0) @ sK2)))) ) | (~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f308,f267])).
thf(f473,plain,(
  ( ! [X1 : $i] : ((((func @ X1)) = (((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((breln @ Y0 @ Y1 @ Y2) & (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => (ex1 @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2)))))))))))) @ X1)))) ) | ~spl22_41),
  inference(argument_congruence,[],[f276])).
thf(f474,plain,(
  ( ! [X1 : $i] : (((^[Y0 : $i]: ((^[Y1 : $i]: ((breln @ X1 @ Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (ex1 @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y2 @ Y3) @ Y1)))))))))) = ((func @ X1)))) ) | ~spl22_41),
  inference(beta-eta_normalization,[],[f473])).
thf(f516,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK15 @ sK2 @ X0 @ X1 @ X2) @ sK3)) != $true) | ($true != ((breln @ X2 @ X1 @ sK2))) | ($true != ((breln @ X2 @ X1 @ X0))) | (((in @ (kpair @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ (sK15 @ sK2 @ X0 @ X1 @ X2)) @ sK4)) != $true) | ($true != $true) | ($true = ((in @ (sK17 @ sK2 @ X0 @ X1 @ X2) @ X1))) | (sK2 = X0) | ($true != ((in @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ sK1)))) ) | (~spl22_3 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f102,f302])).
thf(f519,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (kpair @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ (sK15 @ sK2 @ X0 @ X1 @ X2)) @ sK4)) != $true) | ($true != ((breln @ X2 @ X1 @ X0))) | (sK2 = X0) | ($true != ((in @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ sK1))) | ($true = ((in @ (sK17 @ sK2 @ X0 @ X1 @ X2) @ X1))) | (((in @ (sK15 @ sK2 @ X0 @ X1 @ X2) @ sK3)) != $true) | ($true != ((breln @ X2 @ X1 @ sK2)))) ) | (~spl22_3 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f516])).
thf(f526,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ X0 @ sK4 @ X1 @ X2) @ sK3)) != $true) | ($true != $true) | ($true = ((in @ (sK15 @ X0 @ sK4 @ X1 @ X2) @ X1))) | ($true != ((breln @ X2 @ X1 @ sK4))) | (sK4 = X0) | (((in @ (kpair @ (sK16 @ X0 @ sK4 @ X1 @ X2) @ (sK17 @ X0 @ sK4 @ X1 @ X2)) @ sK2)) != $true) | ($true != ((breln @ X2 @ X1 @ X0))) | (((in @ (sK16 @ X0 @ sK4 @ X1 @ X2) @ sK1)) != $true)) ) | (~spl22_7 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f120,f313])).
thf(f528,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (kpair @ (sK16 @ X0 @ sK4 @ X1 @ X2) @ (sK17 @ X0 @ sK4 @ X1 @ X2)) @ sK2)) != $true) | (((in @ (sK16 @ X0 @ sK4 @ X1 @ X2) @ sK1)) != $true) | ($true != ((breln @ X2 @ X1 @ sK4))) | (sK4 = X0) | ($true != ((breln @ X2 @ X1 @ X0))) | (((in @ (sK17 @ X0 @ sK4 @ X1 @ X2) @ sK3)) != $true) | ($true = ((in @ (sK15 @ X0 @ sK4 @ X1 @ X2) @ X1)))) ) | (~spl22_7 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f526])).
thf(f531,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ X0)) = $true) | (sK2 = sK4) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (sK2 = sK4) | (((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ X0)) = $true) | ($true != $true)) ) | (~spl22_3 | ~spl22_13 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f519,f147])).
thf(f546,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | (sK2 = sK4) | ($true != $true) | (((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ X0)) = $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1)))) ) | (~spl22_3 | ~spl22_13 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f531])).
thf(f547,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ X0)) = $true) | (sK2 = sK4) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((breln @ X1 @ X0 @ sK2)))) ) | (~spl22_3 | ~spl22_13 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f546])).
thf(f551,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ X0)) = $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((breln @ X1 @ X0 @ sK2)))) ) | (~spl22_3 | spl22_9 | ~spl22_13 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f547,f130])).
thf(f610,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | ($true != ((breln @ X2 @ X1 @ sK4))) | (((in @ (sK14 @ X0 @ sK4 @ X1 @ X2) @ X2)) = $true) | ($true != ((breln @ X2 @ X1 @ X0))) | (((in @ (sK16 @ X0 @ sK4 @ X1 @ X2) @ sK1)) != $true) | (((in @ (kpair @ (sK16 @ X0 @ sK4 @ X1 @ X2) @ (sK17 @ X0 @ sK4 @ X1 @ X2)) @ sK2)) != $true) | (((in @ (sK17 @ X0 @ sK4 @ X1 @ X2) @ sK3)) != $true) | (sK4 = X0)) ) | (~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f165,f313])).
thf(f613,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (kpair @ (sK16 @ X0 @ sK4 @ X1 @ X2) @ (sK17 @ X0 @ sK4 @ X1 @ X2)) @ sK2)) != $true) | (sK4 = X0) | (((in @ (sK14 @ X0 @ sK4 @ X1 @ X2) @ X2)) = $true) | ($true != ((breln @ X2 @ X1 @ sK4))) | ($true != ((breln @ X2 @ X1 @ X0))) | (((in @ (sK17 @ X0 @ sK4 @ X1 @ X2) @ sK3)) != $true) | (((in @ (sK16 @ X0 @ sK4 @ X1 @ X2) @ sK1)) != $true)) ) | (~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f610])).
thf(f615,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK16 @ sK2 @ X0 @ X1 @ X2) @ X2)) = $true) | (((in @ (kpair @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ (sK15 @ sK2 @ X0 @ X1 @ X2)) @ sK4)) != $true) | ($true != ((in @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ sK1))) | ($true != ((breln @ X2 @ X1 @ X0))) | (((in @ (sK15 @ sK2 @ X0 @ X1 @ X2) @ sK3)) != $true) | ($true != ((breln @ X2 @ X1 @ sK2))) | ($true != $true) | (sK2 = X0)) ) | (~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f169,f302])).
thf(f619,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (kpair @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ (sK15 @ sK2 @ X0 @ X1 @ X2)) @ sK4)) != $true) | (((in @ (sK15 @ sK2 @ X0 @ X1 @ X2) @ sK3)) != $true) | ($true != ((in @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ sK1))) | ($true != ((breln @ X2 @ X1 @ sK2))) | ($true != ((breln @ X2 @ X1 @ X0))) | (sK2 = X0) | (((in @ (sK16 @ sK2 @ X0 @ X1 @ X2) @ X2)) = $true)) ) | (~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f615])).
thf(f641,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (sK2 = sK4) | ($true != $true) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | (sK2 = sK4) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true = ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ X0))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true = ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ X0)))) ) | (~spl22_7 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39)),
  inference(superposition,[],[f528,f257])).
thf(f667,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK2))) | ($true = ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ X0))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | (sK2 = sK4)) ) | (~spl22_7 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f641])).
thf(f668,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK2))) | ($true = ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ X0))) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (sK2 = sK4)) ) | (~spl22_7 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f667])).
thf(f672,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ X0))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2)))) ) | (~spl22_7 | spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f668,f130])).
thf(f674,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | (sK2 = sK4) | (sK2 = sK4) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true = ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ X1))) | ($true = ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ X1)))) ) | (~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42)),
  inference(superposition,[],[f613,f280])).
thf(f698,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | (sK2 = sK4) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true = ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ X1))) | ($true != ((breln @ X1 @ X0 @ sK2)))) ) | (~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42)),
  inference(duplicate_literal_removal,[],[f674])).
thf(f699,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ X1))) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (sK2 = sK4) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true)) ) | (~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42)),
  inference(trivial_inequality_removal,[],[f698])).
thf(f705,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ X1))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((breln @ X1 @ X0 @ sK2))) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true)) ) | (spl22_9 | ~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42)),
  inference(forward_subsumption_resolution,[],[f699,f130])).
thf(f711,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK2))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (sK2 = sK4) | ($true != $true) | ($true = ((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ X1))) | (sK2 = sK4) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true = ((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ X1)))) ) | (~spl22_14 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f619,f151])).
thf(f719,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true = ((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ X1))) | ($true != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((breln @ X1 @ X0 @ sK2))) | (sK2 = sK4)) ) | (~spl22_14 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f711])).
thf(f720,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((breln @ X1 @ X0 @ sK2))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true = ((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ X1))) | (sK2 = sK4)) ) | (~spl22_14 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f719])).
thf(f721,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ X1))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3)))) ) | (spl22_9 | ~spl22_14 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f720,f130])).
thf(f826,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((sK2 = X0) | (((in @ (sK15 @ sK2 @ X0 @ X1 @ X2) @ sK3)) != $true) | (((in @ (kpair @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ (sK15 @ sK2 @ X0 @ X1 @ X2)) @ sK4)) != $true) | ($true != $true) | ($true != ((breln @ X2 @ X1 @ X0))) | ($true != ((in @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ sK1))) | ($true != ((breln @ X2 @ X1 @ sK2))) | ($true != ((in @ (kpair @ (sK16 @ sK2 @ X0 @ X1 @ X2) @ (sK17 @ sK2 @ X0 @ X1 @ X2)) @ X0)))) ) | (~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f234,f302])).
thf(f829,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (kpair @ (sK16 @ sK2 @ X0 @ X1 @ X2) @ (sK17 @ sK2 @ X0 @ X1 @ X2)) @ X0))) | (sK2 = X0) | (((in @ (sK15 @ sK2 @ X0 @ X1 @ X2) @ sK3)) != $true) | ($true != ((breln @ X2 @ X1 @ sK2))) | (((in @ (kpair @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ (sK15 @ sK2 @ X0 @ X1 @ X2)) @ sK4)) != $true) | ($true != ((breln @ X2 @ X1 @ X0))) | ($true != ((in @ (sK14 @ sK2 @ X0 @ X1 @ X2) @ sK1)))) ) | (~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f826])).
thf(f898,definition,(
  spl22_50 <=> ($true = ((breln @ sK1 @ sK3 @ sK2)))),
  introduced(definition,[new_symbols(definition,[spl22_50])],[avatar_definition])).
thf(f899,plain,(
  ($true = ((breln @ sK1 @ sK3 @ sK2))) | ~spl22_50),
  inference(avatar_component_clause,[],[f898])).
thf(f902,definition,(
  spl22_51 <=> ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3)))),
  introduced(definition,[new_symbols(definition,[spl22_51])],[avatar_definition])).
thf(f904,plain,(
  ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | spl22_51),
  inference(avatar_component_clause,[],[f902])).
thf(f914,definition,(
  spl22_54 <=> ($true = ((breln @ sK1 @ sK3 @ sK4)))),
  introduced(definition,[new_symbols(definition,[spl22_54])],[avatar_definition])).
thf(f915,plain,(
  ($true = ((breln @ sK1 @ sK3 @ sK4))) | ~spl22_54),
  inference(avatar_component_clause,[],[f914])).
thf(f922,definition,(
  spl22_56 <=> (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) = $true)),
  introduced(definition,[new_symbols(definition,[spl22_56])],[avatar_definition])).
thf(f924,plain,(
  (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) != $true) | spl22_56),
  inference(avatar_component_clause,[],[f922])).
thf(f981,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (sK2 = sK4) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != $true) | ($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK2))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) != $true)) ) | (~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f829,f313])).
thf(f983,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (((breln @ X1 @ X0 @ sK4)) != $true) | (sK2 = sK4) | ($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK2))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) != $true) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2)))) ) | (~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f981])).
thf(f984,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK2))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((breln @ X1 @ X0 @ sK2))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3)))) ) | (spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f983,f130])).
thf(f989,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK2))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (sK2 = sK4) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK2)) != $true) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != $true)) ) | (spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f984,f243])).
thf(f997,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK2)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != $true) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) != $true) | (sK2 = sK4) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3)))) ) | (spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f989])).
thf(f998,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK2)) != $true) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (sK2 = sK4)) ) | (spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f997])).
thf(f1004,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK2)) != $true) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3)))) ) | (spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f998,f130])).
thf(f1005,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | (((breln @ X1 @ X0 @ sK4)) != $true)) ) | (spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f1004,f302])).
thf(f1081,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK4))) | ($true != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | (sK2 = sK4) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2)))) ) | (spl22_9 | ~spl22_12 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f1005,f143])).
thf(f1092,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (sK2 = sK4) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK4))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true)) ) | (spl22_9 | ~spl22_12 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f1081])).
thf(f1093,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (sK2 = sK4) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK4))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true)) ) | (spl22_9 | ~spl22_12 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f1092])).
thf(f1099,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK4))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true)) ) | (spl22_9 | ~spl22_12 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f1093,f130])).
thf(f1130,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ((^[Y1 : $i]: ((breln @ X1 @ Y0 @ Y1) & (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X1) => (ex1 @ Y0 @ (^[Y3 : $i]: (in @ (kpair @ Y2 @ Y3) @ Y1)))))))))) @ X2)) = ((func @ X1 @ X2)))) ) | ~spl22_41),
  inference(argument_congruence,[],[f474])).
thf(f1131,plain,(
  ( ! [X2 : $i,X1 : $i] : (((^[Y0 : $i]: ((breln @ X1 @ X2 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (ex1 @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) = ((func @ X1 @ X2)))) ) | ~spl22_41),
  inference(beta-eta_normalization,[],[f1130])).
thf(f1233,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((^[Y0 : $i]: ((breln @ X1 @ X2 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (ex1 @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) @ X3)) = ((func @ X1 @ X2 @ X3)))) ) | ~spl22_41),
  inference(argument_congruence,[],[f1131])).
thf(f1234,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((^[Y0 : $i]: ((breln @ X1 @ X2 @ Y0) & (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => (ex1 @ X2 @ (^[Y2 : $i]: (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) @ X3)) = $true) | ($false = ((func @ X1 @ X2 @ X3)))) ) | ~spl22_41),
  inference(iff_proxy_clausification,[],[f1233])).
thf(f1242,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((func @ X1 @ X2 @ X3))) | ($true = (((breln @ X1 @ X2 @ X3) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => (ex1 @ X2 @ (^[Y1 : $i]: (in @ (kpair @ Y0 @ Y1) @ X3)))))))))) ) | ~spl22_41),
  inference(beta-eta_normalization,[],[f1234])).
thf(f1244,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((func @ X1 @ X2 @ X3))) | (((breln @ X1 @ X2 @ X3)) = $true)) ) | ~spl22_41),
  inference(and_proxy_clausification,[],[f1242])).
thf(f1248,plain,(
  ($true = $false) | ($true = ((breln @ sK1 @ sK3 @ sK2))) | (~spl22_36 | ~spl22_41)),
  inference(superposition,[],[f1244,f253])).
thf(f1251,plain,(
  ($true = ((breln @ sK1 @ sK3 @ sK4))) | ($true = $false) | (~spl22_39 | ~spl22_41)),
  inference(superposition,[],[f267,f1244])).
thf(f1252,plain,(
  ($true = ((breln @ sK1 @ sK3 @ sK2))) | (~spl22_36 | ~spl22_41)),
  inference(trivial_inequality_removal,[],[f1248])).
thf(f1253,plain,(
  ($true = ((breln @ sK1 @ sK3 @ sK4))) | (~spl22_39 | ~spl22_41)),
  inference(trivial_inequality_removal,[],[f1251])).
thf(f1258,plain,(
  spl22_54 | ~spl22_39 | ~spl22_41),
  inference(avatar_split_clause,[],[f1253,f274,f265,f914])).
thf(f1274,plain,(
  spl22_50 | ~spl22_36 | ~spl22_41),
  inference(avatar_split_clause,[],[f1252,f274,f251,f898])).
thf(f1379,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK2))) | ($true != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true)) ) | (spl22_9 | ~spl22_12 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f1099,f313])).
thf(f1381,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK2))) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3)))) ) | (spl22_9 | ~spl22_12 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f1379])).
thf(f1382,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (kpair @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ (sK17 @ sK2 @ sK4 @ X0 @ X1)) @ sK2))) | ($true != ((breln @ X1 @ X0 @ sK2))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3)))) ) | (spl22_9 | ~spl22_12 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f1381])).
thf(f1386,plain,(
  ($true != $true) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | (~spl22_7 | spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39 | spl22_51)),
  inference(superposition,[],[f904,f672])).
thf(f1388,plain,(
  ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | (~spl22_7 | spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39 | spl22_51)),
  inference(trivial_inequality_removal,[],[f1386])).
thf(f1389,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (~spl22_7 | spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39 | spl22_51 | ~spl22_54)),
  inference(forward_subsumption_resolution,[],[f1388,f915])).
thf(f1390,plain,(
  ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | (~spl22_7 | spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39 | ~spl22_50 | spl22_51 | ~spl22_54)),
  inference(forward_subsumption_resolution,[],[f1389,f899])).
thf(f1392,definition,(
  spl22_62 <=> ($true = ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)))),
  introduced(definition,[new_symbols(definition,[spl22_62])],[avatar_definition])).
thf(f1393,plain,(
  ($true = ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | ~spl22_62),
  inference(avatar_component_clause,[],[f1392])).
thf(f1394,plain,(
  ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | spl22_62),
  inference(avatar_component_clause,[],[f1392])).
thf(f1396,definition,(
  spl22_63 <=> ($true = ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3)))),
  introduced(definition,[new_symbols(definition,[spl22_63])],[avatar_definition])).
thf(f1398,plain,(
  ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | spl22_63),
  inference(avatar_component_clause,[],[f1396])).
thf(f1399,plain,(
  ~spl22_62 | ~spl22_63 | ~spl22_7 | spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39 | ~spl22_50 | spl22_51 | ~spl22_54),
  inference(avatar_split_clause,[],[f1390,f914,f902,f898,f265,f256,f251,f215,f207,f128,f119,f1396,f1392])).
thf(f1400,plain,(
  ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != $true) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | (sK2 = sK4) | (~spl22_33 | spl22_62)),
  inference(superposition,[],[f1394,f238])).
thf(f1404,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | (sK2 = sK4) | ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (~spl22_33 | spl22_62)),
  inference(trivial_inequality_removal,[],[f1400])).
thf(f1407,plain,(
  ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (sK2 = sK4) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | (~spl22_33 | ~spl22_54 | spl22_62)),
  inference(forward_subsumption_resolution,[],[f1404,f915])).
thf(f1417,plain,(
  ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | (spl22_9 | ~spl22_33 | ~spl22_54 | spl22_62)),
  inference(forward_subsumption_resolution,[],[f1407,f130])).
thf(f1419,plain,(
  ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (spl22_9 | ~spl22_33 | ~spl22_50 | ~spl22_54 | spl22_62)),
  inference(forward_subsumption_resolution,[],[f1417,f899])).
thf(f1421,plain,(
  spl22_51 | spl22_9 | ~spl22_33 | ~spl22_50 | ~spl22_54 | spl22_62),
  inference(avatar_split_clause,[],[f1419,f1392,f914,f898,f237,f128,f902])).
thf(f1529,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((breln @ X1 @ X0 @ sK4)) != $true) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) = $true) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((breln @ X1 @ X0 @ sK2))) | (sK2 = sK4) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((breln @ X1 @ X0 @ sK2)))) ) | (spl22_9 | ~spl22_12 | ~spl22_15 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f1382,f156])).
thf(f1534,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | (sK2 = sK4) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) = $true) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != $true) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3)))) ) | (spl22_9 | ~spl22_12 | ~spl22_15 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f1529])).
thf(f1535,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((in @ (kpair @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ (sK15 @ sK2 @ sK4 @ X0 @ X1)) @ sK4)) = $true) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | (sK2 = sK4)) ) | (spl22_9 | ~spl22_12 | ~spl22_15 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f1534])).
thf(f1544,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true) | (sK2 = sK4) | ($true != ((breln @ X1 @ X0 @ sK2))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | (((breln @ X1 @ X0 @ sK4)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1)))) ) | (spl22_9 | ~spl22_12 | ~spl22_15 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f1535,f1005])).
thf(f1545,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true != ((in @ (sK17 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ X0 @ X1) @ sK3))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ X0 @ X1) @ sK1))) | ($true != ((breln @ X1 @ X0 @ sK2))) | (((breln @ X1 @ X0 @ sK4)) != $true) | (((in @ (sK16 @ sK2 @ sK4 @ X0 @ X1) @ sK1)) != $true)) ) | (spl22_9 | ~spl22_12 | ~spl22_15 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(forward_subsumption_resolution,[],[f1544,f130])).
thf(f1546,plain,(
  ($true != $true) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true = ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | (sK2 = sK4) | (~spl22_27 | spl22_56)),
  inference(superposition,[],[f924,f212])).
thf(f1551,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true = ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | (sK2 = sK4) | (~spl22_27 | spl22_56)),
  inference(trivial_inequality_removal,[],[f1546])).
thf(f1553,plain,(
  ($true = ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | (sK2 = sK4) | (~spl22_27 | ~spl22_50 | spl22_56)),
  inference(forward_subsumption_resolution,[],[f1551,f899])).
thf(f1554,plain,(
  (sK2 = sK4) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | (~spl22_27 | ~spl22_50 | spl22_56 | spl22_62)),
  inference(forward_subsumption_resolution,[],[f1553,f1394])).
thf(f1555,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK4))) | (spl22_9 | ~spl22_27 | ~spl22_50 | spl22_56 | spl22_62)),
  inference(forward_subsumption_resolution,[],[f1554,f130])).
thf(f1556,plain,(
  $false | (spl22_9 | ~spl22_27 | ~spl22_50 | ~spl22_54 | spl22_56 | spl22_62)),
  inference(forward_subsumption_resolution,[],[f1555,f915])).
thf(f1557,plain,(
  spl22_9 | ~spl22_27 | ~spl22_50 | ~spl22_54 | spl22_56 | spl22_62),
  inference(avatar_contradiction_clause,[],[f1556])).
thf(f1597,plain,(
  ( ! [X0 : $i] : (($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ X0) @ sK3))) | ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ X0) @ sK1))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ sK3 @ X0) @ sK1))) | ($true != ((breln @ X0 @ sK3 @ sK2))) | (((breln @ X0 @ sK3 @ sK4)) != $true) | (((breln @ X0 @ sK3 @ sK4)) != $true) | ($true != ((breln @ X0 @ sK3 @ sK2))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ X0) @ sK3))) | ($true != $true) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ sK3 @ X0) @ sK1)))) ) | (~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_15 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f1545,f551])).
thf(f1601,plain,(
  ( ! [X0 : $i] : (($true != $true) | ($true != ((breln @ X0 @ sK3 @ sK2))) | (((breln @ X0 @ sK3 @ sK4)) != $true) | ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ X0) @ sK1))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ X0) @ sK3))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ sK3 @ X0) @ sK1)))) ) | (~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_15 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f1597])).
thf(f1602,plain,(
  ( ! [X0 : $i] : (($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ X0) @ sK1))) | ($true != ((in @ (sK14 @ sK2 @ sK4 @ sK3 @ X0) @ sK1))) | ($true != ((breln @ X0 @ sK3 @ sK2))) | (((breln @ X0 @ sK3 @ sK4)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ X0) @ sK3)))) ) | (~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_15 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f1601])).
thf(f1713,plain,(
  ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != $true) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) != $true) | (~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_14 | ~spl22_15 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(superposition,[],[f1602,f721])).
thf(f1720,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) != $true) | ($true != $true) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | (~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_14 | ~spl22_15 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(duplicate_literal_removal,[],[f1713])).
thf(f1721,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) != $true) | (~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_14 | ~spl22_15 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39)),
  inference(trivial_inequality_removal,[],[f1720])).
thf(f1723,plain,(
  (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) != $true) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_14 | ~spl22_15 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39 | ~spl22_50)),
  inference(forward_subsumption_resolution,[],[f1721,f899])).
thf(f1725,plain,(
  (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) != $true) | ($true != ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_14 | ~spl22_15 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39 | ~spl22_50 | ~spl22_54)),
  inference(forward_subsumption_resolution,[],[f1723,f915])).
thf(f1749,plain,(
  ($true != $true) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | (spl22_9 | ~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42 | spl22_56)),
  inference(superposition,[],[f924,f705])).
thf(f1753,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | (spl22_9 | ~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42 | spl22_56)),
  inference(trivial_inequality_removal,[],[f1749])).
thf(f1754,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | (spl22_9 | ~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42 | ~spl22_50 | spl22_56)),
  inference(forward_subsumption_resolution,[],[f1753,f899])).
thf(f1755,plain,(
  ($true != ((in @ (sK16 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1))) | ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (spl22_9 | ~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42 | ~spl22_50 | ~spl22_54 | spl22_56)),
  inference(forward_subsumption_resolution,[],[f1754,f915])).
thf(f1756,plain,(
  ($true != ((in @ (sK17 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (spl22_9 | ~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42 | ~spl22_50 | ~spl22_54 | spl22_56 | ~spl22_62)),
  inference(forward_subsumption_resolution,[],[f1755,f1393])).
thf(f1757,plain,(
  ~spl22_63 | spl22_9 | ~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42 | ~spl22_50 | ~spl22_54 | spl22_56 | ~spl22_62),
  inference(avatar_split_clause,[],[f1756,f1392,f922,f914,f898,f279,f265,f251,f215,f207,f164,f128,f1396])).
thf(f1758,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != $true) | (sK2 = sK4) | (~spl22_40 | spl22_63)),
  inference(superposition,[],[f1398,f271])).
thf(f1759,plain,(
  (sK2 = sK4) | (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) = $true) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != $true) | (~spl22_24 | spl22_63)),
  inference(superposition,[],[f1398,f198])).
thf(f1763,plain,(
  ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (sK2 = sK4) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | (~spl22_40 | spl22_63)),
  inference(trivial_inequality_removal,[],[f1758])).
thf(f1764,plain,(
  (sK2 = sK4) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) = $true) | (~spl22_24 | spl22_63)),
  inference(trivial_inequality_removal,[],[f1759])).
thf(f1765,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true != ((breln @ sK1 @ sK3 @ sK2))) | (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) = $true) | (spl22_9 | ~spl22_24 | spl22_63)),
  inference(forward_subsumption_resolution,[],[f1764,f130])).
thf(f1766,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK2))) | (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) = $true) | (spl22_9 | ~spl22_24 | ~spl22_54 | spl22_63)),
  inference(forward_subsumption_resolution,[],[f1765,f915])).
thf(f1770,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK2))) | ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | ($true != ((breln @ sK1 @ sK3 @ sK4))) | (spl22_9 | ~spl22_40 | spl22_63)),
  inference(forward_subsumption_resolution,[],[f1763,f130])).
thf(f1772,plain,(
  ~spl22_56 | ~spl22_51 | ~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_14 | ~spl22_15 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39 | ~spl22_50 | ~spl22_54),
  inference(avatar_split_clause,[],[f1725,f914,f898,f265,f251,f242,f233,f215,f207,f168,f155,f150,f146,f142,f128,f101,f902,f922])).
thf(f1774,plain,(
  (((in @ (sK14 @ sK2 @ sK4 @ sK3 @ sK1) @ sK1)) = $true) | (spl22_9 | ~spl22_24 | ~spl22_50 | ~spl22_54 | spl22_63)),
  inference(forward_subsumption_resolution,[],[f1766,f899])).
thf(f1775,plain,(
  ($true != ((breln @ sK1 @ sK3 @ sK4))) | ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (spl22_9 | ~spl22_40 | ~spl22_50 | spl22_63)),
  inference(forward_subsumption_resolution,[],[f1770,f899])).
thf(f1778,plain,(
  spl22_56 | spl22_9 | ~spl22_24 | ~spl22_50 | ~spl22_54 | spl22_63),
  inference(avatar_split_clause,[],[f1774,f1396,f914,f898,f197,f128,f922])).
thf(f1779,plain,(
  ($true = ((in @ (sK15 @ sK2 @ sK4 @ sK3 @ sK1) @ sK3))) | (spl22_9 | ~spl22_40 | ~spl22_50 | ~spl22_54 | spl22_63)),
  inference(forward_subsumption_resolution,[],[f1775,f915])).
thf(f1782,plain,(
  spl22_51 | spl22_9 | ~spl22_40 | ~spl22_50 | ~spl22_54 | spl22_63),
  inference(avatar_split_clause,[],[f1779,f1396,f914,f898,f270,f128,f902])).
cnf(s2, plain, spl22_3 | ~spl22_4, inference(sat_conversion,[],[f107])).
cnf(s4, plain, spl22_4 | ~spl22_6, inference(sat_conversion,[],[f117])).
cnf(s5, plain, ~spl22_4 | spl22_7, inference(sat_conversion,[],[f121])).
cnf(s7, plain, ~spl22_9, inference(sat_conversion,[],[f131])).
cnf(s10, plain, ~spl22_4 | spl22_12, inference(sat_conversion,[],[f144])).
cnf(s11, plain, ~spl22_4 | spl22_13, inference(sat_conversion,[],[f148])).
cnf(s12, plain, ~spl22_4 | spl22_14, inference(sat_conversion,[],[f152])).
cnf(s14, plain, ~spl22_4 | spl22_15, inference(sat_conversion,[],[f157])).
cnf(s16, plain, ~spl22_4 | spl22_17, inference(sat_conversion,[],[f166])).
cnf(s17, plain, ~spl22_4 | spl22_18, inference(sat_conversion,[],[f170])).
cnf(s22, plain, spl22_1, inference(sat_conversion,[],[f195])).
cnf(s23, plain, ~spl22_4 | spl22_24, inference(sat_conversion,[],[f199])).
cnf(s24, plain, spl22_6, inference(sat_conversion,[],[f200])).
cnf(s26, plain, ~spl22_19 | spl22_26, inference(sat_conversion,[],[f209])).
cnf(s27, plain, ~spl22_4 | spl22_27, inference(sat_conversion,[],[f213])).
cnf(s28, plain, ~spl22_1 | spl22_28, inference(sat_conversion,[],[f217])).
cnf(s32, plain, ~spl22_4 | spl22_32, inference(sat_conversion,[],[f235])).
cnf(s33, plain, ~spl22_4 | spl22_33, inference(sat_conversion,[],[f239])).
cnf(s34, plain, spl22_19, inference(sat_conversion,[],[f240])).
cnf(s35, plain, ~spl22_4 | spl22_34, inference(sat_conversion,[],[f244])).
cnf(s37, plain, spl22_36, inference(sat_conversion,[],[f254])).
cnf(s38, plain, ~spl22_4 | spl22_37, inference(sat_conversion,[],[f258])).
cnf(s40, plain, spl22_39, inference(sat_conversion,[],[f268])).
cnf(s41, plain, ~spl22_4 | spl22_40, inference(sat_conversion,[],[f272])).
cnf(s42, plain, spl22_41, inference(sat_conversion,[],[f277])).
cnf(s43, plain, ~spl22_4 | spl22_42, inference(sat_conversion,[],[f281])).
cnf(s53, plain, ~spl22_39 | ~spl22_41 | spl22_54, inference(sat_conversion,[],[f1258])).
cnf(s57, plain, ~spl22_36 | ~spl22_41 | spl22_50, inference(sat_conversion,[],[f1274])).
cnf(s63, plain, ~spl22_7 | spl22_9 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_37 | ~spl22_39 | ~spl22_50 | spl22_51 | ~spl22_54 | ~spl22_62 | ~spl22_63, inference(sat_conversion,[],[f1399])).
cnf(s67, plain, spl22_9 | ~spl22_33 | ~spl22_50 | spl22_51 | ~spl22_54 | spl22_62, inference(sat_conversion,[],[f1421])).
cnf(s71, plain, spl22_9 | ~spl22_27 | ~spl22_50 | ~spl22_54 | spl22_56 | spl22_62, inference(sat_conversion,[],[f1557])).
cnf(s75, plain, spl22_9 | ~spl22_17 | ~spl22_26 | ~spl22_28 | ~spl22_36 | ~spl22_39 | ~spl22_42 | ~spl22_50 | ~spl22_54 | spl22_56 | ~spl22_62 | ~spl22_63, inference(sat_conversion,[],[f1757])).
cnf(s77, plain, ~spl22_3 | spl22_9 | ~spl22_12 | ~spl22_13 | ~spl22_14 | ~spl22_15 | ~spl22_18 | ~spl22_26 | ~spl22_28 | ~spl22_32 | ~spl22_34 | ~spl22_36 | ~spl22_39 | ~spl22_50 | ~spl22_51 | ~spl22_54 | ~spl22_56, inference(sat_conversion,[],[f1772])).
cnf(s78, plain, spl22_9 | ~spl22_24 | ~spl22_50 | ~spl22_54 | spl22_56 | spl22_63, inference(sat_conversion,[],[f1778])).
cnf(s81, plain, spl22_9 | ~spl22_40 | ~spl22_50 | spl22_51 | ~spl22_54 | spl22_63, inference(sat_conversion,[],[f1782])).
cnf(s82, plain, spl22_54, inference(rat,[],[s53,s42,s40])).
cnf(s83, plain, spl22_50, inference(rat,[],[s57,s42,s37])).
cnf(s84, plain, spl22_26, inference(rat,[],[s26,s34])).
cnf(s85, plain, spl22_28, inference(rat,[],[s28,s22])).
cnf(s86, plain, spl22_4, inference(rat,[],[s4,s24])).
cnf(s87, plain, spl22_42, inference(rat,[],[s43,s86])).
cnf(s88, plain, spl22_40, inference(rat,[],[s41,s86])).
cnf(s89, plain, spl22_37, inference(rat,[],[s38,s86])).
cnf(s90, plain, spl22_34, inference(rat,[],[s35,s86])).
cnf(s91, plain, spl22_33, inference(rat,[],[s33,s86])).
cnf(s92, plain, spl22_32, inference(rat,[],[s32,s86])).
cnf(s93, plain, spl22_27, inference(rat,[],[s27,s86])).
cnf(s94, plain, spl22_24, inference(rat,[],[s23,s86])).
cnf(s95, plain, spl22_18, inference(rat,[],[s17,s86])).
cnf(s96, plain, spl22_17, inference(rat,[],[s16,s86])).
cnf(s97, plain, spl22_15, inference(rat,[],[s14,s86])).
cnf(s98, plain, spl22_14, inference(rat,[],[s12,s86])).
cnf(s99, plain, spl22_13, inference(rat,[],[s11,s86])).
cnf(s100, plain, spl22_12, inference(rat,[],[s10,s86])).
cnf(s101, plain, spl22_7, inference(rat,[],[s5,s86])).
cnf(s102, plain, spl22_3, inference(rat,[],[s2,s86])).
cnf(s103, plain, spl22_51, inference(rat,[],[s63,s67,s81,s84,s85,s37,s7,s40,s83,s89,s82,s101,s91,s88])).
cnf(s104, plain, ~spl22_56, inference(rat,[],[s77,s102,s82,s100,s83,s40,s37,s90,s92,s85,s84,s95,s97,s98,s99,s7,s103])).
cnf(s105, plain, spl22_63, inference(rat,[],[s78,s94,s7,s82,s83,s104])).
cnf(s106, plain, spl22_62, inference(rat,[],[s71,s93,s7,s82,s83,s104])).
cnf(s107, plain, $false, inference(rat,[],[s75,s105,s96,s87,s82,s83,s7,s40,s37,s85,s84,s106,s104])).
thf(f1783,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s107])).
% SZS output end Proof for theBenchmark