%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, in: ($i > $i > $o)).
thf(func_def_1, type, powerset: ($i > $i)).
thf(func_def_2, type, binunion: ($i > $i > $i)).
thf(func_def_3, type, binintersect: ($i > $i > $i)).
thf(func_def_4, type, setminus: ($i > $i > $i)).
thf(func_def_5, type, binintersectT_lem: $o).
thf(func_def_7, type, binunionT_lem: $o).
thf(func_def_8, type, complementT_lem: $o).
thf(func_def_9, type, setextT: $o).
thf(func_def_10, type, demorgan1a: $o).
thf(func_def_11, type, demorgan1b: $o).
thf(func_def_30, type, sK16: ($i > $i > $i > $i)).
thf(func_def_31, type, sK17: ($i > $i > $i > $i)).
thf(f1,axiom,(
  (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectT_lem)).
thf(f2,axiom,(
  (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))) = binunionT_lem)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionT_lem)).
thf(f3,axiom,(
  (complementT_lem = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complementT_lem)).
thf(f4,axiom,(
  (setextT = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X2) => (in @ X3 @ X1))) => (X1 = X2))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextT)).
thf(f5,axiom,(
  (! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))) = demorgan1a)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1a)).
thf(f6,axiom,(
  (demorgan1b = ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) => (in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1b)).
thf(f7,conjecture,(
  binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan1a => (demorgan1b => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',demorgan1)).
thf(f8,negated_conjecture,(
  ~(binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan1a => (demorgan1b => ! [X1 : $i,X0 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))))))))),
  inference(negated_conjecture,[status(cth)],[f7])).
thf(f9,plain,(
  (setextT = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (! [X4 : $i] : ((in @ X4 @ X1) => ((in @ X4 @ X2) => (in @ X4 @ X0))) => (X0 = X2))))))),
  inference(rectify,[],[f4])).
thf(f10,plain,(
  (setextT = $true) <=> ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => (! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ X0)) = $true) => (((in @ X3 @ X2)) = $true))) => (! [X4 : $i] : ((((in @ X4 @ X1)) = $true) => (($true = ((in @ X4 @ X2))) => ($true = ((in @ X4 @ X0))))) => (X0 = X2)))))),
  inference(fool_elimination,[],[f9])).
thf(f11,plain,(
  (demorgan1b = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) => (in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))))))))),
  inference(rectify,[],[f6])).
thf(f12,plain,(
  ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) = $true) => (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) = $true))))) <=> (demorgan1b = $true)),
  inference(fool_elimination,[],[f11])).
thf(f13,plain,(
  (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ X1) => ((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))))))) = demorgan1a)),
  inference(rectify,[],[f5])).
thf(f14,plain,(
  (demorgan1a = $true) <=> ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => ! [X3 : $i] : ((((in @ X3 @ X1)) = $true) => ((((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) = $true) => (((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) = $true)))))),
  inference(fool_elimination,[],[f13])).
thf(f15,plain,(
  (binintersectT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binintersect @ X1 @ X2) @ (powerset @ X0)))))),
  inference(rectify,[],[f1])).
thf(f16,plain,(
  (binintersectT_lem = $true) <=> ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0))) = $true)))),
  inference(fool_elimination,[],[f15])).
thf(f17,plain,(
  (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => (in @ (setminus @ X1 @ X0) @ (powerset @ X1))))),
  inference(rectify,[],[f3])).
thf(f18,plain,(
  ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1))))) <=> (complementT_lem = $true)),
  inference(fool_elimination,[],[f17])).
thf(f19,plain,(
  ~(binintersectT_lem => (binunionT_lem => (complementT_lem => (setextT => (demorgan1a => (demorgan1b => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = ((setminus @ X1 @ (binintersect @ X0 @ X2))))))))))))),
  inference(rectify,[],[f8])).
thf(f20,plain,(
  ~((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ! [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => (((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) = ((setminus @ X1 @ (binintersect @ X0 @ X2))))))))))))),
  inference(fool_elimination,[],[f19])).
thf(f21,plain,(
  (! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => (in @ (binunion @ X0 @ X2) @ (powerset @ X1)))) = binunionT_lem)),
  inference(rectify,[],[f2])).
thf(f22,plain,(
  ! [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) => (((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) = $true))) <=> (binunionT_lem = $true)),
  inference(fool_elimination,[],[f21])).
thf(f23,plain,(
  (((((? [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : ((((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) != ((setminus @ X1 @ (binintersect @ X0 @ X2)))) & (((in @ X2 @ (powerset @ X1))) = $true))) & (demorgan1b = $true)) & (demorgan1a = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)),
  inference(ennf_transformation,[],[f20])).
thf(f24,plain,(
  (binintersectT_lem = $true) & (setextT = $true) & (demorgan1b = $true) & (binunionT_lem = $true) & (demorgan1a = $true) & ? [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : ((((binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2))) != ((setminus @ X1 @ (binintersect @ X0 @ X2)))) & (((in @ X2 @ (powerset @ X1))) = $true))) & (complementT_lem = $true)),
  inference(flattening,[],[f23])).
thf(f25,plain,(
  (complementT_lem = $true) <=> ! [X1 : $i,X0 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))))),
  inference(ennf_transformation,[],[f18])).
thf(f26,plain,(
  (demorgan1a = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) = $true) | (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) != $true)) | (((in @ X3 @ X1)) != $true)) | (((in @ X2 @ (powerset @ X1))) != $true)) | ($true != ((in @ X0 @ (powerset @ X1)))))),
  inference(ennf_transformation,[],[f14])).
thf(f27,plain,(
  (demorgan1a = $true) <=> ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) = $true) | (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) != $true) | (((in @ X3 @ X1)) != $true))) | ($true != ((in @ X0 @ (powerset @ X1)))))),
  inference(flattening,[],[f26])).
thf(f28,plain,(
  ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) = $true) | (((in @ X2 @ (powerset @ X1))) != $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) <=> (binunionT_lem = $true)),
  inference(ennf_transformation,[],[f22])).
thf(f29,plain,(
  (setextT = $true) <=> ! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((X0 = X2) | ? [X4 : $i] : ((($true != ((in @ X4 @ X0))) & ($true = ((in @ X4 @ X2)))) & (((in @ X4 @ X1)) = $true))) | ? [X3 : $i] : (((((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X3 @ X1)) = $true))) | (((in @ X2 @ (powerset @ X1))) != $true)) | ($true != ((in @ X0 @ (powerset @ X1)))))),
  inference(ennf_transformation,[],[f10])).
thf(f30,plain,(
  ! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((X0 = X2) | ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) | ? [X4 : $i] : (($true != ((in @ X4 @ X0))) & (((in @ X4 @ X1)) = $true) & ($true = ((in @ X4 @ X2)))) | (((in @ X2 @ (powerset @ X1))) != $true))) <=> (setextT = $true)),
  inference(flattening,[],[f29])).
thf(f31,plain,(
  ! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0))) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) <=> (binintersectT_lem = $true)),
  inference(ennf_transformation,[],[f16])).
thf(f32,plain,(
  ! [X0 : $i,X1 : $i] : (! [X2 : $i] : (! [X3 : $i] : (((((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) = $true) | (((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) != $true)) | (((in @ X3 @ X1)) != $true)) | (((in @ X2 @ (powerset @ X1))) != $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) <=> (demorgan1b = $true)),
  inference(ennf_transformation,[],[f12])).
thf(f33,plain,(
  ! [X1 : $i,X0 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) = $true) | (((in @ X3 @ X1)) != $true)))) <=> (demorgan1b = $true)),
  inference(flattening,[],[f32])).
thf(f34,plain,(
  (binintersectT_lem = $true) & (setextT = $true) & (demorgan1b = $true) & (binunionT_lem = $true) & (demorgan1a = $true) & (($true = ((in @ sK0 @ (powerset @ sK1)))) & ((((setminus @ sK1 @ (binintersect @ sK0 @ sK2))) != ((binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)))) & (((in @ sK2 @ (powerset @ sK1))) = $true))) & (complementT_lem = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X2,$thf(sK2))],[f24])).
thf(f35,plain,(
  (! [X1 : $i,X0 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) = $true) | (((in @ X3 @ X1)) != $true)))) | (demorgan1b != $true)) & ((demorgan1b = $true) | ? [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) & ? [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) = $true) & (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) != $true) & (((in @ X3 @ X1)) = $true)))))),
  inference(nnf_transformation,[],[f33])).
thf(f36,plain,(
  (! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ X0)) != $true)))) | (demorgan1b != $true)) & ((demorgan1b = $true) | ? [X4 : $i,X5 : $i] : (($true = ((in @ X5 @ (powerset @ X4)))) & ? [X6 : $i] : ((((in @ X6 @ (powerset @ X4))) = $true) & ? [X7 : $i] : ((((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6)))) = $true) & ($true != ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))))) & (((in @ X7 @ X4)) = $true)))))),
  inference(rectify,[],[f35])).
thf(f37,plain,(
  (! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ X0)) != $true)))) | (demorgan1b != $true)) & ((demorgan1b = $true) | (($true = ((in @ sK4 @ (powerset @ sK3)))) & ((((in @ sK5 @ (powerset @ sK3))) = $true) & (($true = ((in @ sK6 @ (binunion @ (setminus @ sK3 @ sK4) @ (setminus @ sK3 @ sK5))))) & (((in @ sK6 @ (setminus @ sK3 @ (binintersect @ sK4 @ sK5)))) != $true) & (((in @ sK6 @ sK3)) = $true)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X4,$thf(sK3)),skolemize(X5,$thf(sK4)),skolemize(X6,$thf(sK5)),skolemize(X7,$thf(sK6))],[f36])).
thf(f38,plain,(
  (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0))) = $true)) | (((in @ X1 @ (powerset @ X0))) != $true)) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) & (((in @ (binintersect @ X1 @ X2) @ (powerset @ X0))) != $true)) & (((in @ X1 @ (powerset @ X0))) = $true)))),
  inference(nnf_transformation,[],[f31])).
thf(f39,plain,(
  (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | ($true = ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1))))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true = ((in @ X5 @ (powerset @ X4)))) & (((in @ (binintersect @ X3 @ X5) @ (powerset @ X4))) != $true)) & (((in @ X3 @ (powerset @ X4))) = $true)))),
  inference(rectify,[],[f38])).
thf(f40,plain,(
  (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | ($true = ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1))))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (binintersectT_lem != $true)) & ((binintersectT_lem = $true) | ((($true = ((in @ sK9 @ (powerset @ sK8)))) & ($true != ((in @ (binintersect @ sK7 @ sK9) @ (powerset @ sK8))))) & ($true = ((in @ sK7 @ (powerset @ sK8))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X3,$thf(sK7)),skolemize(X4,$thf(sK8)),skolemize(X5,$thf(sK9))],[f39])).
thf(f41,plain,(
  ((demorgan1a = $true) | ? [X1 : $i,X0 : $i] : (? [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) = $true) & ? [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) != $true) & (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) = $true) & (((in @ X3 @ X1)) = $true))) & ($true = ((in @ X0 @ (powerset @ X1)))))) & (! [X1 : $i,X0 : $i] : (! [X2 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | ! [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X1 @ X0) @ (setminus @ X1 @ X2)))) = $true) | (((in @ X3 @ (setminus @ X1 @ (binintersect @ X0 @ X2)))) != $true) | (((in @ X3 @ X1)) != $true))) | ($true != ((in @ X0 @ (powerset @ X1))))) | (demorgan1a != $true))),
  inference(nnf_transformation,[],[f27])).
thf(f42,plain,(
  ((demorgan1a = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) & ? [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) & (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) & (((in @ X3 @ X0)) = $true))) & (((in @ X1 @ (powerset @ X0))) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : ((((in @ X6 @ (powerset @ X4))) != $true) | ! [X7 : $i] : ((((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6)))) = $true) | ($true != ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))))) | (((in @ X7 @ X4)) != $true))) | ($true != ((in @ X5 @ (powerset @ X4))))) | (demorgan1a != $true))),
  inference(rectify,[],[f41])).
thf(f43,plain,(
  ((demorgan1a = $true) | (((((in @ sK12 @ (powerset @ sK10))) = $true) & ((((in @ sK13 @ (binunion @ (setminus @ sK10 @ sK11) @ (setminus @ sK10 @ sK12)))) != $true) & ($true = ((in @ sK13 @ (setminus @ sK10 @ (binintersect @ sK11 @ sK12))))) & (((in @ sK13 @ sK10)) = $true))) & (((in @ sK11 @ (powerset @ sK10))) = $true))) & (! [X4 : $i,X5 : $i] : (! [X6 : $i] : ((((in @ X6 @ (powerset @ X4))) != $true) | ! [X7 : $i] : ((((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6)))) = $true) | ($true != ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))))) | (((in @ X7 @ X4)) != $true))) | ($true != ((in @ X5 @ (powerset @ X4))))) | (demorgan1a != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12,sK13]),skolemize(X0,$thf(sK10)),skolemize(X1,$thf(sK11)),skolemize(X2,$thf(sK12)),skolemize(X3,$thf(sK13))],[f42])).
thf(f44,plain,(
  ((complementT_lem = $true) | ? [X1 : $i,X0 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ($true != ((in @ (setminus @ X1 @ X0) @ (powerset @ X1)))))) & (! [X1 : $i,X0 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (setminus @ X1 @ X0) @ (powerset @ X1))))) | (complementT_lem != $true))),
  inference(nnf_transformation,[],[f25])).
thf(f45,plain,(
  ((complementT_lem = $true) | ? [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) & (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) != $true))) & (! [X2 : $i,X3 : $i] : ((((in @ X3 @ (powerset @ X2))) != $true) | ($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2))))) | (complementT_lem != $true))),
  inference(rectify,[],[f44])).
thf(f46,plain,(
  ((complementT_lem = $true) | ((((in @ sK15 @ (powerset @ sK14))) = $true) & ($true != ((in @ (setminus @ sK14 @ sK15) @ (powerset @ sK14)))))) & (! [X2 : $i,X3 : $i] : ((((in @ X3 @ (powerset @ X2))) != $true) | ($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2))))) | (complementT_lem != $true))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15]),skolemize(X0,$thf(sK14)),skolemize(X1,$thf(sK15))],[f45])).
thf(f47,plain,(
  (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((X0 = X2) | ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) | ? [X4 : $i] : (($true != ((in @ X4 @ X0))) & (((in @ X4 @ X1)) = $true) & ($true = ((in @ X4 @ X2)))) | (((in @ X2 @ (powerset @ X1))) != $true))) | (setextT != $true)) & ((setextT = $true) | ? [X0 : $i,X1 : $i] : (($true = ((in @ X0 @ (powerset @ X1)))) & ? [X2 : $i] : ((X0 != X2) & ! [X3 : $i] : ((((in @ X3 @ X1)) != $true) | (((in @ X3 @ X2)) = $true) | (((in @ X3 @ X0)) != $true)) & ! [X4 : $i] : (($true = ((in @ X4 @ X0))) | (((in @ X4 @ X1)) != $true) | ($true != ((in @ X4 @ X2)))) & (((in @ X2 @ (powerset @ X1))) = $true))))),
  inference(nnf_transformation,[],[f30])).
thf(f48,plain,(
  (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((X0 = X2) | ? [X3 : $i] : ((((in @ X3 @ X1)) = $true) & (((in @ X3 @ X2)) != $true) & (((in @ X3 @ X0)) = $true)) | ? [X4 : $i] : (($true != ((in @ X4 @ X0))) & (((in @ X4 @ X1)) = $true) & ($true = ((in @ X4 @ X2)))) | (((in @ X2 @ (powerset @ X1))) != $true))) | (setextT != $true)) & ((setextT = $true) | ? [X5 : $i,X6 : $i] : (($true = ((in @ X5 @ (powerset @ X6)))) & ? [X7 : $i] : ((X5 != X7) & ! [X8 : $i] : (($true != ((in @ X8 @ X6))) | ($true = ((in @ X8 @ X7))) | (((in @ X8 @ X5)) != $true)) & ! [X9 : $i] : (($true = ((in @ X9 @ X5))) | ($true != ((in @ X9 @ X6))) | ($true != ((in @ X9 @ X7)))) & ($true = ((in @ X7 @ (powerset @ X6)))))))),
  inference(rectify,[],[f47])).
thf(f49,plain,(
  (! [X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ! [X2 : $i] : ((X0 = X2) | (($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))) & (((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true) & ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0)))) | ((((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true) & ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1))) & ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2)))) | (((in @ X2 @ (powerset @ X1))) != $true))) | (setextT != $true)) & ((setextT = $true) | (($true = ((in @ sK18 @ (powerset @ sK19)))) & ((sK20 != sK18) & ! [X8 : $i] : (($true != ((in @ X8 @ sK19))) | ($true = ((in @ X8 @ sK20))) | ($true != ((in @ X8 @ sK18)))) & ! [X9 : $i] : (($true = ((in @ X9 @ sK18))) | ($true != ((in @ X9 @ sK19))) | ($true != ((in @ X9 @ sK20)))) & ($true = ((in @ sK20 @ (powerset @ sK19)))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP,sK18,sK19,sK20]),skolemize(X4,$thf(sK17 @ X2 @ X1 @ X0)),skolemize(X4,$thf(sK17 @ X2 @ X1 @ X0)),skolemize(X5,$thf(sK18)),skolemize(X6,$thf(sK19)),skolemize(X7,$thf(sK20))],[f48])).
thf(f50,plain,(
  (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) = $true) | (((in @ X2 @ (powerset @ X1))) != $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) != $true) & (((in @ X2 @ (powerset @ X1))) = $true)) & ($true = ((in @ X0 @ (powerset @ X1))))))),
  inference(nnf_transformation,[],[f28])).
thf(f51,plain,(
  (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) = $true) | (((in @ X2 @ (powerset @ X1))) != $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | ? [X3 : $i,X4 : $i] : (? [X5 : $i] : (($true != ((in @ (binunion @ X3 @ X5) @ (powerset @ X4)))) & ($true = ((in @ X5 @ (powerset @ X4))))) & (((in @ X3 @ (powerset @ X4))) = $true)))),
  inference(rectify,[],[f50])).
thf(f52,plain,(
  (! [X0 : $i,X1 : $i] : (! [X2 : $i] : ((((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) = $true) | (((in @ X2 @ (powerset @ X1))) != $true)) | ($true != ((in @ X0 @ (powerset @ X1))))) | (binunionT_lem != $true)) & ((binunionT_lem = $true) | (((((in @ (binunion @ sK21 @ sK23) @ (powerset @ sK22))) != $true) & (((in @ sK23 @ (powerset @ sK22))) = $true)) & (((in @ sK21 @ (powerset @ sK22))) = $true)))),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22,sK23]),skolemize(X3,$thf(sK21)),skolemize(X4,$thf(sK22)),skolemize(X5,$thf(sK23))],[f51])).
thf(f53,plain,(
  (complementT_lem = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f54,plain,(
  (((in @ sK2 @ (powerset @ sK1))) = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f55,plain,(
  (((setminus @ sK1 @ (binintersect @ sK0 @ sK2))) != ((binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2))))),
  inference(cnf_transformation,[],[f34])).
thf(f56,plain,(
  ($true = ((in @ sK0 @ (powerset @ sK1))))),
  inference(cnf_transformation,[],[f34])).
thf(f57,plain,(
  (demorgan1a = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f58,plain,(
  (binunionT_lem = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f59,plain,(
  (demorgan1b = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f60,plain,(
  (setextT = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f61,plain,(
  (binintersectT_lem = $true)),
  inference(cnf_transformation,[],[f34])).
thf(f67,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (demorgan1b != $true) | (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true)) )),
  inference(cnf_transformation,[],[f37])).
thf(f71,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true) | (binintersectT_lem != $true) | ($true = ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1))))) )),
  inference(cnf_transformation,[],[f40])).
thf(f72,plain,(
  ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6)))) = $true) | ($true != ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))))) | (demorgan1a != $true) | ($true != ((in @ X5 @ (powerset @ X4)))) | (((in @ X7 @ X4)) != $true) | (((in @ X6 @ (powerset @ X4))) != $true)) )),
  inference(cnf_transformation,[],[f43])).
thf(f78,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((in @ X3 @ (powerset @ X2))) != $true) | (complementT_lem != $true) | ($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2))))) )),
  inference(cnf_transformation,[],[f46])).
thf(f86,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | (setextT != $true) | (X0 = X2) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true)) )),
  inference(cnf_transformation,[],[f49])).
thf(f87,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1))) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true) | (setextT != $true)) )),
  inference(cnf_transformation,[],[f49])).
thf(f88,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | (setextT != $true) | (((in @ X2 @ (powerset @ X1))) != $true)) )),
  inference(cnf_transformation,[],[f49])).
thf(f89,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | (((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (setextT != $true) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2)))) )),
  inference(cnf_transformation,[],[f49])).
thf(f90,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true) | (X0 = X2) | ($true != ((in @ X0 @ (powerset @ X1)))) | (setextT != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1)))) )),
  inference(cnf_transformation,[],[f49])).
thf(f91,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (X0 = X2) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | (setextT != $true)) )),
  inference(cnf_transformation,[],[f49])).
thf(f92,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2))) | (setextT != $true) | (X0 = X2) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true)) )),
  inference(cnf_transformation,[],[f49])).
thf(f93,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true != ((in @ X0 @ (powerset @ X1)))) | (setextT != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1)))) )),
  inference(cnf_transformation,[],[f49])).
thf(f94,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (X0 = X2) | (setextT != $true)) )),
  inference(cnf_transformation,[],[f49])).
thf(f98,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) = $true) | (binunionT_lem != $true)) )),
  inference(cnf_transformation,[],[f52])).
thf(f101,definition,(
  spl24_1 <=> (setextT = $true)),
  introduced(definition,[new_symbols(definition,[spl24_1])],[avatar_definition])).
thf(f109,definition,(
  spl24_3 <=> (demorgan1a = $true)),
  introduced(definition,[new_symbols(definition,[spl24_3])],[avatar_definition])).
thf(f113,definition,(
  spl24_4 <=> ! [X5 : $i,X4 : $i,X7 : $i,X6 : $i] : ((((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6)))) = $true) | (((in @ X6 @ (powerset @ X4))) != $true) | (((in @ X7 @ X4)) != $true) | ($true != ((in @ X5 @ (powerset @ X4)))) | ($true != ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))))))),
  introduced(definition,[new_symbols(definition,[spl24_4])],[avatar_definition])).
thf(f114,plain,(
  ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((in @ X7 @ (binunion @ (setminus @ X4 @ X5) @ (setminus @ X4 @ X6)))) = $true) | ($true != ((in @ X5 @ (powerset @ X4)))) | ($true != ((in @ X7 @ (setminus @ X4 @ (binintersect @ X5 @ X6))))) | (((in @ X6 @ (powerset @ X4))) != $true) | (((in @ X7 @ X4)) != $true)) ) | ~spl24_4),
  inference(avatar_component_clause,[],[f113])).
thf(f115,plain,(
  ~spl24_3 | spl24_4),
  inference(avatar_split_clause,[],[f72,f113,f109])).
thf(f117,definition,(
  spl24_5 <=> (binintersectT_lem = $true)),
  introduced(definition,[new_symbols(definition,[spl24_5])],[avatar_definition])).
thf(f126,definition,(
  spl24_7 <=> (binunionT_lem = $true)),
  introduced(definition,[new_symbols(definition,[spl24_7])],[avatar_definition])).
thf(f135,definition,(
  spl24_9 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2))) | (X0 = X2))),
  introduced(definition,[new_symbols(definition,[spl24_9])],[avatar_definition])).
thf(f136,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | (((in @ X2 @ (powerset @ X1))) != $true) | (X0 = X2)) ) | ~spl24_9),
  inference(avatar_component_clause,[],[f135])).
thf(f137,plain,(
  spl24_9 | ~spl24_1),
  inference(avatar_split_clause,[],[f86,f101,f135])).
thf(f139,definition,(
  spl24_10 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true))),
  introduced(definition,[new_symbols(definition,[spl24_10])],[avatar_definition])).
thf(f140,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | (X0 = X2) | ($true != ((in @ X0 @ (powerset @ X1))))) ) | ~spl24_10),
  inference(avatar_component_clause,[],[f139])).
thf(f141,plain,(
  spl24_10 | ~spl24_1),
  inference(avatar_split_clause,[],[f88,f101,f139])).
thf(f143,definition,(
  spl24_11 <=> ! [X0 : $i,X3 : $i,X2 : $i,X1 : $i] : ((((in @ X3 @ X0)) != $true) | (((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) | (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true))),
  introduced(definition,[new_symbols(definition,[spl24_11])],[avatar_definition])).
thf(f144,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X3 @ X0)) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true)) ) | ~spl24_11),
  inference(avatar_component_clause,[],[f143])).
thf(f146,definition,(
  spl24_12 <=> (demorgan1b = $true)),
  introduced(definition,[new_symbols(definition,[spl24_12])],[avatar_definition])).
thf(f149,plain,(
  spl24_11 | ~spl24_12),
  inference(avatar_split_clause,[],[f67,f146,f143])).
thf(f155,definition,(
  spl24_14 <=> (complementT_lem = $true)),
  introduced(definition,[new_symbols(definition,[spl24_14])],[avatar_definition])).
thf(f159,plain,(
  spl24_12),
  inference(avatar_split_clause,[],[f59,f146])).
thf(f171,definition,(
  spl24_17 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true))),
  introduced(definition,[new_symbols(definition,[spl24_17])],[avatar_definition])).
thf(f172,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (binintersect @ X0 @ X2) @ (powerset @ X1)))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true)) ) | ~spl24_17),
  inference(avatar_component_clause,[],[f171])).
thf(f173,plain,(
  spl24_17 | ~spl24_5),
  inference(avatar_split_clause,[],[f71,f117,f171])).
thf(f174,plain,(
  spl24_1),
  inference(avatar_split_clause,[],[f60,f101])).
thf(f195,definition,(
  spl24_22 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1))))),
  introduced(definition,[new_symbols(definition,[spl24_22])],[avatar_definition])).
thf(f196,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (powerset @ X1)))) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X0))) | (((in @ X2 @ (powerset @ X1))) != $true) | (X0 = X2)) ) | ~spl24_22),
  inference(avatar_component_clause,[],[f195])).
thf(f197,plain,(
  ~spl24_1 | spl24_22),
  inference(avatar_split_clause,[],[f87,f195,f101])).
thf(f198,plain,(
  spl24_7),
  inference(avatar_split_clause,[],[f58,f126])).
thf(f204,plain,(
  spl24_14),
  inference(avatar_split_clause,[],[f53,f155])).
thf(f211,definition,(
  spl24_25 <=> ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (X0 = X2) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2))))),
  introduced(definition,[new_symbols(definition,[spl24_25])],[avatar_definition])).
thf(f212,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2))) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (X0 = X2) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1)))) ) | ~spl24_25),
  inference(avatar_component_clause,[],[f211])).
thf(f213,plain,(
  spl24_25 | ~spl24_1),
  inference(avatar_split_clause,[],[f92,f101,f211])).
thf(f215,definition,(
  spl24_26 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true) | (X0 = X2) | ($true != ((in @ X0 @ (powerset @ X1)))))),
  introduced(definition,[new_symbols(definition,[spl24_26])],[avatar_definition])).
thf(f216,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (X0 = X2) | (((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true)) ) | ~spl24_26),
  inference(avatar_component_clause,[],[f215])).
thf(f217,plain,(
  ~spl24_1 | spl24_26),
  inference(avatar_split_clause,[],[f91,f215,f101])).
thf(f218,plain,(
  spl24_5),
  inference(avatar_split_clause,[],[f61,f117])).
thf(f220,definition,(
  spl24_27 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) = $true) | ($true != ((in @ X0 @ (powerset @ X1)))))),
  introduced(definition,[new_symbols(definition,[spl24_27])],[avatar_definition])).
thf(f221,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (binunion @ X0 @ X2) @ (powerset @ X1))) = $true) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1))))) ) | ~spl24_27),
  inference(avatar_component_clause,[],[f220])).
thf(f222,plain,(
  spl24_27 | ~spl24_7),
  inference(avatar_split_clause,[],[f98,f126,f220])).
thf(f224,definition,(
  spl24_28 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1))) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (X0 = X2))),
  introduced(definition,[new_symbols(definition,[spl24_28])],[avatar_definition])).
thf(f225,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true) | (X0 = X2) | (((in @ X2 @ (powerset @ X1))) != $true)) ) | ~spl24_28),
  inference(avatar_component_clause,[],[f224])).
thf(f226,plain,(
  spl24_28 | ~spl24_1),
  inference(avatar_split_clause,[],[f90,f101,f224])).
thf(f228,definition,(
  spl24_29 <=> ! [X2 : $i,X3 : $i] : ((((in @ X3 @ (powerset @ X2))) != $true) | ($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2)))))),
  introduced(definition,[new_symbols(definition,[spl24_29])],[avatar_definition])).
thf(f229,plain,(
  ( ! [X2 : $i,X3 : $i] : (($true = ((in @ (setminus @ X2 @ X3) @ (powerset @ X2)))) | (((in @ X3 @ (powerset @ X2))) != $true)) ) | ~spl24_29),
  inference(avatar_component_clause,[],[f228])).
thf(f230,plain,(
  spl24_29 | ~spl24_14),
  inference(avatar_split_clause,[],[f78,f155,f228])).
thf(f237,definition,(
  spl24_31 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ X2 @ (powerset @ X1))) != $true) | (((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true))),
  introduced(definition,[new_symbols(definition,[spl24_31])],[avatar_definition])).
thf(f238,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X2))) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ (sK16 @ X2 @ X1 @ X0) @ X2)) != $true) | (X0 = X2)) ) | ~spl24_31),
  inference(avatar_component_clause,[],[f237])).
thf(f239,plain,(
  spl24_31 | ~spl24_1),
  inference(avatar_split_clause,[],[f89,f101,f237])).
thf(f240,plain,(
  spl24_3),
  inference(avatar_split_clause,[],[f57,f109])).
thf(f247,definition,(
  spl24_33 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X1))) != $true) | (X0 = X2) | ($true != ((in @ X0 @ (powerset @ X1)))) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))))),
  introduced(definition,[new_symbols(definition,[spl24_33])],[avatar_definition])).
thf(f248,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (X0 = X2) | (((in @ X2 @ (powerset @ X1))) != $true) | (((in @ (sK17 @ X2 @ X1 @ X0) @ X0)) != $true)) ) | ~spl24_33),
  inference(avatar_component_clause,[],[f247])).
thf(f249,plain,(
  ~spl24_1 | spl24_33),
  inference(avatar_split_clause,[],[f94,f247,f101])).
thf(f256,definition,(
  spl24_35 <=> (((setminus @ sK1 @ (binintersect @ sK0 @ sK2))) = ((binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2))))),
  introduced(definition,[new_symbols(definition,[spl24_35])],[avatar_definition])).
thf(f258,plain,(
  (((setminus @ sK1 @ (binintersect @ sK0 @ sK2))) != ((binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)))) | spl24_35),
  inference(avatar_component_clause,[],[f256])).
thf(f259,plain,(
  ~spl24_35),
  inference(avatar_split_clause,[],[f55,f256])).
thf(f276,definition,(
  spl24_39 <=> (((in @ sK2 @ (powerset @ sK1))) = $true)),
  introduced(definition,[new_symbols(definition,[spl24_39])],[avatar_definition])).
thf(f278,plain,(
  (((in @ sK2 @ (powerset @ sK1))) = $true) | ~spl24_39),
  inference(avatar_component_clause,[],[f276])).
thf(f279,plain,(
  spl24_39),
  inference(avatar_split_clause,[],[f54,f276])).
thf(f281,definition,(
  spl24_40 <=> ($true = ((in @ sK0 @ (powerset @ sK1))))),
  introduced(definition,[new_symbols(definition,[spl24_40])],[avatar_definition])).
thf(f283,plain,(
  ($true = ((in @ sK0 @ (powerset @ sK1)))) | ~spl24_40),
  inference(avatar_component_clause,[],[f281])).
thf(f284,plain,(
  spl24_40),
  inference(avatar_split_clause,[],[f56,f281])).
thf(f286,definition,(
  spl24_41 <=> ! [X2 : $i,X0 : $i,X1 : $i] : ((X0 = X2) | ($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1))) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))) | (((in @ X2 @ (powerset @ X1))) != $true) | ($true != ((in @ X0 @ (powerset @ X1)))))),
  introduced(definition,[new_symbols(definition,[spl24_41])],[avatar_definition])).
thf(f287,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK17 @ X2 @ X1 @ X0) @ X1))) | ($true = ((in @ (sK16 @ X2 @ X1 @ X0) @ X1))) | ($true != ((in @ X0 @ (powerset @ X1)))) | (X0 = X2) | (((in @ X2 @ (powerset @ X1))) != $true)) ) | ~spl24_41),
  inference(avatar_component_clause,[],[f286])).
thf(f288,plain,(
  ~spl24_1 | spl24_41),
  inference(avatar_split_clause,[],[f93,f286,f101])).
thf(f334,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ (powerset @ X3))) != $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))) ) | (~spl24_11 | ~spl24_31)),
  inference(superposition,[],[f144,f238])).
thf(f335,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ (powerset @ X3))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X3)) = $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != $true)) ) | (~spl24_11 | ~spl24_25)),
  inference(superposition,[],[f144,f212])).
thf(f336,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ X4 @ (powerset @ X3))) != $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X4)) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | ($true != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true)) ) | (~spl24_9 | ~spl24_11)),
  inference(superposition,[],[f144,f136])).
thf(f343,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X4)) = $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | (((in @ X4 @ (powerset @ X3))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((in @ X1 @ (powerset @ X0))) != $true)) ) | (~spl24_9 | ~spl24_11)),
  inference(trivial_inequality_removal,[],[f336])).
thf(f345,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X3)) = $true) | (((in @ X4 @ (powerset @ X3))) != $true)) ) | (~spl24_11 | ~spl24_25)),
  inference(trivial_inequality_removal,[],[f335])).
thf(f346,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X4 @ (powerset @ X3))) != $true)) ) | (~spl24_11 | ~spl24_31)),
  inference(trivial_inequality_removal,[],[f334])).
thf(f410,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0)) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((in @ X4 @ (powerset @ X3))) != $true) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | ($true != $true)) ) | (~spl24_4 | ~spl24_11 | ~spl24_31)),
  inference(superposition,[],[f346,f114])).
thf(f414,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != $true) | (((in @ X4 @ (powerset @ X3))) != $true) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0)) != $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))))) ) | (~spl24_4 | ~spl24_11 | ~spl24_31)),
  inference(duplicate_literal_removal,[],[f410])).
thf(f415,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : ((((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | (((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))) = X4) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0)) != $true) | (((in @ X4 @ (powerset @ X3))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ X4) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true)) ) | (~spl24_4 | ~spl24_11 | ~spl24_31)),
  inference(trivial_inequality_removal,[],[f414])).
thf(f488,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true)) ) | (~spl24_4 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(superposition,[],[f216,f415])).
thf(f493,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true)) ) | (~spl24_4 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(duplicate_literal_removal,[],[f488])).
thf(f494,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)))) ) | (~spl24_4 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(trivial_inequality_removal,[],[f493])).
thf(f497,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)))) ) | (~spl24_4 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(forward_subsumption_resolution,[],[f494,f114])).
thf(f540,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | ($true != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3))))) ) | (~spl24_4 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(superposition,[],[f497,f140])).
thf(f547,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))))) ) | (~spl24_4 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(duplicate_literal_removal,[],[f540])).
thf(f548,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) ) | (~spl24_4 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(trivial_inequality_removal,[],[f547])).
thf(f654,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(superposition,[],[f548,f343])).
thf(f675,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(duplicate_literal_removal,[],[f654])).
thf(f676,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(trivial_inequality_removal,[],[f675])).
thf(f678,plain,(
  ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X3)))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X3)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_31)),
  inference(forward_subsumption_resolution,[],[f676,f497])).
thf(f688,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_28 | ~spl24_31)),
  inference(superposition,[],[f678,f225])).
thf(f689,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) | ($true != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_26 | ~spl24_31)),
  inference(superposition,[],[f678,f196])).
thf(f693,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_26 | ~spl24_31)),
  inference(duplicate_literal_removal,[],[f689])).
thf(f694,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_26 | ~spl24_31)),
  inference(trivial_inequality_removal,[],[f693])).
thf(f701,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_28 | ~spl24_31)),
  inference(duplicate_literal_removal,[],[f688])).
thf(f702,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_28 | ~spl24_31)),
  inference(trivial_inequality_removal,[],[f701])).
thf(f731,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_28 | ~spl24_31)),
  inference(superposition,[],[f702,f114])).
thf(f732,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | ($true != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_28 | ~spl24_31)),
  inference(duplicate_literal_removal,[],[f731])).
thf(f733,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | ($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2))))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_26 | ~spl24_28 | ~spl24_31)),
  inference(trivial_inequality_removal,[],[f732])).
thf(f734,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_26 | ~spl24_28 | ~spl24_31)),
  inference(forward_subsumption_resolution,[],[f733,f694])).
thf(f745,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33)),
  inference(superposition,[],[f734,f248])).
thf(f748,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33)),
  inference(duplicate_literal_removal,[],[f745])).
thf(f749,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33)),
  inference(trivial_inequality_removal,[],[f748])).
thf(f792,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != $true) | ($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33)),
  inference(superposition,[],[f749,f345])).
thf(f796,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X2 @ (powerset @ X0))) != $true) | ($true != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33)),
  inference(duplicate_literal_removal,[],[f792])).
thf(f797,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X2 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33)),
  inference(trivial_inequality_removal,[],[f796])).
thf(f800,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (sK17 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33)),
  inference(forward_subsumption_resolution,[],[f797,f678])).
thf(f843,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) != $true) | ($true != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | ~spl24_41)),
  inference(superposition,[],[f800,f287])).
thf(f852,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | ($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0))) | (((in @ X1 @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | ~spl24_41)),
  inference(duplicate_literal_removal,[],[f843])).
thf(f853,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | (((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | ($true = ((in @ (sK16 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ X0 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) @ X0)))) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | ~spl24_41)),
  inference(trivial_inequality_removal,[],[f852])).
thf(f854,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((setminus @ X0 @ (binintersect @ X1 @ X2))) = ((binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) | (((in @ X1 @ (powerset @ X0))) != $true) | (((in @ X2 @ (powerset @ X0))) != $true) | ($true != ((in @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)) @ (powerset @ X0)))) | (((in @ (setminus @ X0 @ (binintersect @ X1 @ X2)) @ (powerset @ X0))) != $true)) ) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | ~spl24_41)),
  inference(forward_subsumption_resolution,[],[f853,f734])).
thf(f873,plain,(
  ($true != ((in @ sK0 @ (powerset @ sK1)))) | (((in @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)) @ (powerset @ sK1))) != $true) | (((in @ sK2 @ (powerset @ sK1))) != $true) | (((in @ (binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)) @ (powerset @ sK1))) != $true) | (((setminus @ sK1 @ (binintersect @ sK0 @ sK2))) != ((setminus @ sK1 @ (binintersect @ sK0 @ sK2)))) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | spl24_35 | ~spl24_41)),
  inference(superposition,[],[f258,f854])).
thf(f956,plain,(
  (((in @ sK2 @ (powerset @ sK1))) != $true) | ($true != ((in @ sK0 @ (powerset @ sK1)))) | (((in @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)) @ (powerset @ sK1))) != $true) | (((in @ (binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)) @ (powerset @ sK1))) != $true) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | spl24_35 | ~spl24_41)),
  inference(trivial_inequality_removal,[],[f873])).
thf(f1008,plain,(
  (((in @ (binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)) @ (powerset @ sK1))) != $true) | ($true != ((in @ sK0 @ (powerset @ sK1)))) | (((in @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)) @ (powerset @ sK1))) != $true) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | spl24_35 | ~spl24_39 | ~spl24_41)),
  inference(forward_subsumption_resolution,[],[f956,f278])).
thf(f1009,plain,(
  (((in @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)) @ (powerset @ sK1))) != $true) | (((in @ (binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)) @ (powerset @ sK1))) != $true) | (~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | spl24_35 | ~spl24_39 | ~spl24_40 | ~spl24_41)),
  inference(forward_subsumption_resolution,[],[f1008,f283])).
thf(f1011,definition,(
  spl24_47 <=> (((in @ (binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)) @ (powerset @ sK1))) = $true)),
  introduced(definition,[new_symbols(definition,[spl24_47])],[avatar_definition])).
thf(f1013,plain,(
  (((in @ (binunion @ (setminus @ sK1 @ sK0) @ (setminus @ sK1 @ sK2)) @ (powerset @ sK1))) != $true) | spl24_47),
  inference(avatar_component_clause,[],[f1011])).
thf(f1015,definition,(
  spl24_48 <=> (((in @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)) @ (powerset @ sK1))) = $true)),
  introduced(definition,[new_symbols(definition,[spl24_48])],[avatar_definition])).
thf(f1017,plain,(
  (((in @ (setminus @ sK1 @ (binintersect @ sK0 @ sK2)) @ (powerset @ sK1))) != $true) | spl24_48),
  inference(avatar_component_clause,[],[f1015])).
thf(f1018,plain,(
  ~spl24_47 | ~spl24_48 | ~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | spl24_35 | ~spl24_39 | ~spl24_40 | ~spl24_41),
  inference(avatar_split_clause,[],[f1009,f286,f281,f276,f256,f247,f237,f224,f215,f211,f195,f143,f139,f135,f113,f1015,f1011])).
thf(f1020,plain,(
  ($true != ((in @ (setminus @ sK1 @ sK2) @ (powerset @ sK1)))) | ($true != $true) | ($true != ((in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1)))) | (~spl24_27 | spl24_47)),
  inference(superposition,[],[f1013,f221])).
thf(f1022,plain,(
  ($true != ((in @ (setminus @ sK1 @ sK2) @ (powerset @ sK1)))) | ($true != ((in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1)))) | (~spl24_27 | spl24_47)),
  inference(trivial_inequality_removal,[],[f1020])).
thf(f1024,definition,(
  spl24_49 <=> ($true = ((in @ (setminus @ sK1 @ sK2) @ (powerset @ sK1))))),
  introduced(definition,[new_symbols(definition,[spl24_49])],[avatar_definition])).
thf(f1026,plain,(
  ($true != ((in @ (setminus @ sK1 @ sK2) @ (powerset @ sK1)))) | spl24_49),
  inference(avatar_component_clause,[],[f1024])).
thf(f1028,definition,(
  spl24_50 <=> ($true = ((in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1))))),
  introduced(definition,[new_symbols(definition,[spl24_50])],[avatar_definition])).
thf(f1030,plain,(
  ($true != ((in @ (setminus @ sK1 @ sK0) @ (powerset @ sK1)))) | spl24_50),
  inference(avatar_component_clause,[],[f1028])).
thf(f1031,plain,(
  ~spl24_49 | ~spl24_50 | ~spl24_27 | spl24_47),
  inference(avatar_split_clause,[],[f1022,f1011,f220,f1028,f1024])).
thf(f1048,plain,(
  (((in @ sK2 @ (powerset @ sK1))) != $true) | ($true != $true) | (~spl24_29 | spl24_49)),
  inference(superposition,[],[f1026,f229])).
thf(f1049,plain,(
  (((in @ sK2 @ (powerset @ sK1))) != $true) | (~spl24_29 | spl24_49)),
  inference(trivial_inequality_removal,[],[f1048])).
thf(f1050,plain,(
  $false | (~spl24_29 | ~spl24_39 | spl24_49)),
  inference(forward_subsumption_resolution,[],[f1049,f278])).
thf(f1051,plain,(
  ~spl24_29 | ~spl24_39 | spl24_49),
  inference(avatar_contradiction_clause,[],[f1050])).
thf(f1052,plain,(
  ($true != $true) | ($true != ((in @ sK0 @ (powerset @ sK1)))) | (~spl24_29 | spl24_50)),
  inference(superposition,[],[f1030,f229])).
thf(f1053,plain,(
  ($true != ((in @ sK0 @ (powerset @ sK1)))) | (~spl24_29 | spl24_50)),
  inference(trivial_inequality_removal,[],[f1052])).
thf(f1054,plain,(
  $false | (~spl24_29 | ~spl24_40 | spl24_50)),
  inference(forward_subsumption_resolution,[],[f1053,f283])).
thf(f1055,plain,(
  ~spl24_29 | ~spl24_40 | spl24_50),
  inference(avatar_contradiction_clause,[],[f1054])).
thf(f1075,plain,(
  ($true != $true) | ($true != ((in @ (binintersect @ sK0 @ sK2) @ (powerset @ sK1)))) | (~spl24_29 | spl24_48)),
  inference(superposition,[],[f1017,f229])).
thf(f1076,plain,(
  ($true != ((in @ (binintersect @ sK0 @ sK2) @ (powerset @ sK1)))) | (~spl24_29 | spl24_48)),
  inference(trivial_inequality_removal,[],[f1075])).
thf(f1078,definition,(
  spl24_51 <=> ($true = ((in @ (binintersect @ sK0 @ sK2) @ (powerset @ sK1))))),
  introduced(definition,[new_symbols(definition,[spl24_51])],[avatar_definition])).
thf(f1080,plain,(
  ($true != ((in @ (binintersect @ sK0 @ sK2) @ (powerset @ sK1)))) | spl24_51),
  inference(avatar_component_clause,[],[f1078])).
thf(f1081,plain,(
  ~spl24_51 | ~spl24_29 | spl24_48),
  inference(avatar_split_clause,[],[f1076,f1015,f228,f1078])).
thf(f1085,plain,(
  ($true != $true) | (((in @ sK2 @ (powerset @ sK1))) != $true) | ($true != ((in @ sK0 @ (powerset @ sK1)))) | (~spl24_17 | spl24_51)),
  inference(superposition,[],[f1080,f172])).
thf(f1086,plain,(
  ($true != ((in @ sK0 @ (powerset @ sK1)))) | (((in @ sK2 @ (powerset @ sK1))) != $true) | (~spl24_17 | spl24_51)),
  inference(trivial_inequality_removal,[],[f1085])).
thf(f1087,plain,(
  (((in @ sK2 @ (powerset @ sK1))) != $true) | (~spl24_17 | ~spl24_40 | spl24_51)),
  inference(forward_subsumption_resolution,[],[f1086,f283])).
thf(f1088,plain,(
  $false | (~spl24_17 | ~spl24_39 | ~spl24_40 | spl24_51)),
  inference(forward_subsumption_resolution,[],[f1087,f278])).
thf(f1089,plain,(
  ~spl24_17 | ~spl24_39 | ~spl24_40 | spl24_51),
  inference(avatar_contradiction_clause,[],[f1088])).
cnf(s2, plain, ~spl24_3 | spl24_4, inference(sat_conversion,[],[f115])).
cnf(s5, plain, ~spl24_1 | spl24_9, inference(sat_conversion,[],[f137])).
cnf(s6, plain, ~spl24_1 | spl24_10, inference(sat_conversion,[],[f141])).
cnf(s7, plain, spl24_11 | ~spl24_12, inference(sat_conversion,[],[f149])).
cnf(s9, plain, spl24_12, inference(sat_conversion,[],[f159])).
cnf(s12, plain, ~spl24_5 | spl24_17, inference(sat_conversion,[],[f173])).
cnf(s13, plain, spl24_1, inference(sat_conversion,[],[f174])).
cnf(s18, plain, ~spl24_1 | spl24_22, inference(sat_conversion,[],[f197])).
cnf(s19, plain, spl24_7, inference(sat_conversion,[],[f198])).
cnf(s21, plain, spl24_14, inference(sat_conversion,[],[f204])).
cnf(s23, plain, ~spl24_1 | spl24_25, inference(sat_conversion,[],[f213])).
cnf(s24, plain, ~spl24_1 | spl24_26, inference(sat_conversion,[],[f217])).
cnf(s25, plain, spl24_5, inference(sat_conversion,[],[f218])).
cnf(s26, plain, ~spl24_7 | spl24_27, inference(sat_conversion,[],[f222])).
cnf(s27, plain, ~spl24_1 | spl24_28, inference(sat_conversion,[],[f226])).
cnf(s28, plain, ~spl24_14 | spl24_29, inference(sat_conversion,[],[f230])).
cnf(s30, plain, ~spl24_1 | spl24_31, inference(sat_conversion,[],[f239])).
cnf(s31, plain, spl24_3, inference(sat_conversion,[],[f240])).
cnf(s33, plain, ~spl24_1 | spl24_33, inference(sat_conversion,[],[f249])).
cnf(s35, plain, ~spl24_35, inference(sat_conversion,[],[f259])).
cnf(s39, plain, spl24_39, inference(sat_conversion,[],[f279])).
cnf(s40, plain, spl24_40, inference(sat_conversion,[],[f284])).
cnf(s41, plain, ~spl24_1 | spl24_41, inference(sat_conversion,[],[f288])).
cnf(s47, plain, ~spl24_4 | ~spl24_9 | ~spl24_10 | ~spl24_11 | ~spl24_22 | ~spl24_25 | ~spl24_26 | ~spl24_28 | ~spl24_31 | ~spl24_33 | spl24_35 | ~spl24_39 | ~spl24_40 | ~spl24_41 | ~spl24_47 | ~spl24_48, inference(sat_conversion,[],[f1018])).
cnf(s48, plain, ~spl24_27 | spl24_47 | ~spl24_49 | ~spl24_50, inference(sat_conversion,[],[f1031])).
cnf(s49, plain, ~spl24_29 | ~spl24_39 | spl24_49, inference(sat_conversion,[],[f1051])).
cnf(s50, plain, ~spl24_29 | ~spl24_40 | spl24_50, inference(sat_conversion,[],[f1055])).
cnf(s51, plain, ~spl24_29 | spl24_48 | ~spl24_51, inference(sat_conversion,[],[f1081])).
cnf(s52, plain, ~spl24_17 | ~spl24_39 | ~spl24_40 | spl24_51, inference(sat_conversion,[],[f1089])).
cnf(s53, plain, spl24_29, inference(rat,[],[s28,s21])).
cnf(s54, plain, spl24_50, inference(rat,[],[s50,s40,s53])).
cnf(s55, plain, spl24_49, inference(rat,[],[s49,s39,s53])).
cnf(s56, plain, spl24_27, inference(rat,[],[s26,s19])).
cnf(s57, plain, spl24_47, inference(rat,[],[s48,s54,s55,s56])).
cnf(s58, plain, spl24_41, inference(rat,[],[s41,s13])).
cnf(s59, plain, spl24_33, inference(rat,[],[s33,s13])).
cnf(s60, plain, spl24_31, inference(rat,[],[s30,s13])).
cnf(s61, plain, spl24_28, inference(rat,[],[s27,s13])).
cnf(s62, plain, spl24_26, inference(rat,[],[s24,s13])).
cnf(s63, plain, spl24_25, inference(rat,[],[s23,s13])).
cnf(s64, plain, spl24_22, inference(rat,[],[s18,s13])).
cnf(s65, plain, spl24_17, inference(rat,[],[s12,s25])).
cnf(s66, plain, spl24_51, inference(rat,[],[s52,s39,s40,s65])).
cnf(s67, plain, spl24_48, inference(rat,[],[s51,s53,s66])).
cnf(s68, plain, spl24_11, inference(rat,[],[s7,s9])).
cnf(s69, plain, spl24_10, inference(rat,[],[s6,s13])).
cnf(s70, plain, spl24_9, inference(rat,[],[s5,s13])).
cnf(s71, plain, ~spl24_4, inference(rat,[],[s47,s67,s57,s58,s40,s39,s35,s59,s60,s61,s62,s63,s64,s68,s69,s70])).
cnf(s72, plain, $false, inference(rat,[],[s2,s71,s31])).
thf(f1090,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s72])).
% SZS output end Proof for theBenchmark