%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, unsorted: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(type_def_7, type, d_unsorted: $tType).
thf(func_def_0, type, irel: ($i > $i > $o)).
thf(func_def_1, type, mnot: (($i > $o) > $i > $o)).
thf(func_def_2, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_3, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_4, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_5, type, mbox_s4: (($i > $o) > $i > $o)).
thf(func_def_6, type, iatom: (($i > $o) > $i > $o)).
thf(func_def_7, type, inot: (($i > $o) > $i > $o)).
thf(func_def_8, type, itrue: ($i > $o)).
thf(func_def_9, type, ifalse: ($i > $o)).
thf(func_def_10, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_11, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_12, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_13, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_14, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_15, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_16, type, ivalid: (($i > $o) > $o)).
thf(func_def_17, type, isatisfiable: (($i > $o) > $o)).
thf(func_def_18, type, icountersatisfiable: (($i > $o) > $o)).
thf(func_def_19, type, iinvalid: (($i > $o) > $o)).
thf(func_def_20, type, d2unsorted: (d_unsorted > $i)).
thf(func_def_21, type, d_unsorted_0: d_unsorted).
thf(func_def_23, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_24, type, vOR: ($o > $o > $o)).
thf(func_def_25, type, vNOT: ($o > $o)).
thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_27, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_28, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_29, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_30, type, vAND: ($o > $o > $o)).
thf(func_def_31, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_32, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_33, type, db5: !>[X0: $tType]:(X0)).
thf(func_def_36, type, db7: !>[X0: $tType]:(X0)).
thf(func_def_37, type, db6: !>[X0: $tType]:(X0)).
thf(func_def_38, type, db8: !>[X0: $tType]:(X0)).
thf(func_def_39, type, sK0: ($i > d_unsorted)).
thf(func_def_40, type, sK1: ($i > $o)).
thf(func_def_41, type, sK2: ($i > $o)).
thf(func_def_55, type, sK16: ($i > $i)).
thf(func_def_56, type, sK17: ($i > $i)).
thf(func_def_57, type, sK18: ($i > $i)).
thf(func_def_58, type, sK19: ($i > $i)).
thf(func_def_59, type, sK20: ($i > $i)).
thf(func_def_60, type, sK21: ($i > $i)).
thf(func_def_61, type, sK22: ($i > $i)).
thf(func_def_62, type, sK23: ($i > $i)).
thf(func_def_63, type, sK24: ($i > $i)).
thf(func_def_64, type, sK25: ($i > $i)).
thf(func_def_65, type, sK26: ($i > $i)).
thf(func_def_66, type, sK27: ($i > $i)).
thf(f1,axiom,(
  ((^[X15 : ($i > $o)] : (~ ! [X16 : $i] : ~(X15 @ X16))) = isatisfiable) & (mand = (^[X17 : ($i > $o), X6 : ($i > $o), X1 : $i] : ((X6 @ X1) & (X17 @ X1)))) & (mor = (^[X17 : ($i > $o), X6 : ($i > $o), X1 : $i] : ((X6 @ X1) | (X17 @ X1)))) & (inot = (^[X4 : ($i > $o), X3 : $i] : (~ ! [X6 : $i] : ((X4 @ X6) | ~(irel @ X3 @ X6))))) & (ixor = (^[X4 : ($i > $o), X5 : ($i > $o), X3 : $i] : (~ ! [X13 : $i,X14 : $i,X6 : $i,X11 : $i,X12 : $i] : (((~(irel @ X11 @ X12) | ~ ! [X10 : $i] : ((X4 @ X10) | ~(irel @ X11 @ X10)) | ~(irel @ X6 @ X11) | (X5 @ X12)) & ((X4 @ X14) | ~(irel @ X6 @ X13) | ~ ! [X8 : $i] : ((X5 @ X8) | ~(irel @ X13 @ X8)) | ~(irel @ X13 @ X14))) | ~(irel @ X3 @ X6))))) & (iimplies = (^[X4 : ($i > $o), X5 : ($i > $o), X3 : $i] : (~ ! [X6 : $i] : (~(irel @ X3 @ X6) | (X4 @ X6)) | ! [X6 : $i] : ((X5 @ X6) | ~(irel @ X3 @ X6))))) & ((^[X15 : ($i > $o)] : (! [X16 : $i] : ~(X15 @ X16))) = iinvalid) & ! [X0 : d_unsorted] : (X0 = d_unsorted_0) & ((^[X4 : ($i > $o), X5 : ($i > $o), X3 : $i] : (~ ! [X6 : $i] : (~(irel @ X3 @ X6) | (X5 @ X6)) | ! [X6 : $i] : (~(irel @ X3 @ X6) | (X4 @ X6)))) = iimplied) & (icountersatisfiable = (^[X15 : ($i > $o)] : (~ ! [X16 : $i] : (X15 @ X16)))) & ! [X19 : d_unsorted,X18 : d_unsorted] : ((((d2unsorted @ X18)) = ((d2unsorted @ X19))) => (X18 = X19)) & ((^[X4 : ($i > $o), X3 : $i] : ((X4 @ X3))) = iatom) & ((^[X1 : ($i > $o), X2 : ($i > $o), X3 : $i] : ((X2 @ X3) | ~(X1 @ X3))) = mimplies) & (itrue @ (d2unsorted @ d_unsorted_0)) & (ior = (^[X4 : ($i > $o), X5 : ($i > $o), X3 : $i] : (! [X6 : $i] : (~(irel @ X3 @ X6) | (X5 @ X6)) | ! [X6 : $i] : (~(irel @ X3 @ X6) | (X4 @ X6))))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (iand = (^[X4 : ($i > $o), X5 : ($i > $o), X3 : $i] : (! [X6 : $i] : ((X4 @ X6) | ~(irel @ X3 @ X6)) & ! [X6 : $i] : ((X5 @ X6) | ~(irel @ X3 @ X6))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X17 : ($i > $o), X1 : $i] : (~(X17 @ X1))) = mnot) & ((^[X15 : ($i > $o)] : (! [X16 : $i] : (X15 @ X16))) = ivalid) & (iequiv = (^[X4 : ($i > $o), X5 : ($i > $o), X3 : $i] : (! [X6 : $i,X9 : $i] : (~(irel @ X3 @ X6) | ~(irel @ X6 @ X9) | ~ ! [X10 : $i] : (~(irel @ X6 @ X10) | (X4 @ X10)) | (X5 @ X9)) & ! [X7 : $i,X6 : $i] : (~(irel @ X6 @ X7) | ~(irel @ X3 @ X6) | ~ ! [X8 : $i] : ((X5 @ X8) | ~(irel @ X6 @ X8)) | (X4 @ X7))))) & (mbox_s4 = (^[X4 : ($i > $o), X17 : $i] : (! [X6 : $i] : ((X4 @ X6) | ~(irel @ X17 @ X6))))) & ! [X1 : $i] : ? [X0 : d_unsorted] : (X1 = ((d2unsorted @ X0)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lcl696_1)).
thf(f2,conjecture,(
  (iequiv = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0)))))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iequiv)).
thf(f3,negated_conjecture,(
  ~ (iequiv = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((iand @ (iimplies @ X0 @ X1) @ (iimplies @ X1 @ X0)))))),
  inference(negated_conjecture,[status(cth)],[f2])).
thf(f4,plain,(
  ((^[X0 : ($i > $o)] : (~ ! [X1 : $i] : ~(X0 @ X1))) = isatisfiable) & (mand = (^[X2 : ($i > $o), X3 : ($i > $o), X4 : $i] : ((X3 @ X4) & (X2 @ X4)))) & (mor = (^[X5 : ($i > $o), X6 : ($i > $o), X7 : $i] : ((X6 @ X7) | (X5 @ X7)))) & (inot = (^[X8 : ($i > $o), X9 : $i] : (~ ! [X10 : $i] : ((X8 @ X10) | ~(irel @ X9 @ X10))))) & (ixor = (^[X11 : ($i > $o), X12 : ($i > $o), X13 : $i] : (~ ! [X14 : $i,X15 : $i,X16 : $i,X17 : $i,X18 : $i] : (((~(irel @ X17 @ X18) | ~ ! [X19 : $i] : ((X11 @ X19) | ~(irel @ X17 @ X19)) | ~(irel @ X16 @ X17) | (X12 @ X18)) & ((X11 @ X15) | ~(irel @ X16 @ X14) | ~ ! [X20 : $i] : ((X12 @ X20) | ~(irel @ X14 @ X20)) | ~(irel @ X14 @ X15))) | ~(irel @ X13 @ X16))))) & (iimplies = (^[X21 : ($i > $o), X22 : ($i > $o), X23 : $i] : (~ ! [X24 : $i] : (~(irel @ X23 @ X24) | (X21 @ X24)) | ! [X25 : $i] : ((X22 @ X25) | ~(irel @ X23 @ X25))))) & ((^[X26 : ($i > $o)] : (! [X27 : $i] : ~(X26 @ X27))) = iinvalid) & ! [X28 : d_unsorted] : (d_unsorted_0 = X28) & ((^[X29 : ($i > $o), X30 : ($i > $o), X31 : $i] : (~ ! [X32 : $i] : (~(irel @ X31 @ X32) | (X30 @ X32)) | ! [X33 : $i] : (~(irel @ X31 @ X33) | (X29 @ X33)))) = iimplied) & (icountersatisfiable = (^[X34 : ($i > $o)] : (~ ! [X35 : $i] : (X34 @ X35)))) & ! [X36 : d_unsorted,X37 : d_unsorted] : ((((d2unsorted @ X36)) = ((d2unsorted @ X37))) => (X36 = X37)) & ((^[X38 : ($i > $o), X39 : $i] : ((X38 @ X39))) = iatom) & ((^[X40 : ($i > $o), X41 : ($i > $o), X42 : $i] : ((X41 @ X42) | ~(X40 @ X42))) = mimplies) & (itrue @ (d2unsorted @ d_unsorted_0)) & (ior = (^[X43 : ($i > $o), X44 : ($i > $o), X45 : $i] : (! [X46 : $i] : (~(irel @ X45 @ X46) | (X44 @ X46)) | ! [X47 : $i] : (~(irel @ X45 @ X47) | (X43 @ X47))))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (iand = (^[X48 : ($i > $o), X49 : ($i > $o), X50 : $i] : (! [X51 : $i] : ((X48 @ X51) | ~(irel @ X50 @ X51)) & ! [X52 : $i] : ((X49 @ X52) | ~(irel @ X50 @ X52))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X53 : ($i > $o), X54 : $i] : (~(X53 @ X54))) = mnot) & ((^[X55 : ($i > $o)] : (! [X56 : $i] : (X55 @ X56))) = ivalid) & (iequiv = (^[X57 : ($i > $o), X58 : ($i > $o), X59 : $i] : (! [X60 : $i,X61 : $i] : (~(irel @ X59 @ X60) | ~(irel @ X60 @ X61) | ~ ! [X62 : $i] : (~(irel @ X60 @ X62) | (X57 @ X62)) | (X58 @ X61)) & ! [X63 : $i,X64 : $i] : (~(irel @ X64 @ X63) | ~(irel @ X59 @ X64) | ~ ! [X65 : $i] : ((X58 @ X65) | ~(irel @ X64 @ X65)) | (X57 @ X63))))) & (mbox_s4 = (^[X66 : ($i > $o), X67 : $i] : (! [X68 : $i] : ((X66 @ X68) | ~(irel @ X67 @ X68))))) & ! [X69 : $i] : ? [X70 : d_unsorted] : (((d2unsorted @ X70)) = X69)),
  inference(rectify,[],[f1])).
thf(f5,plain,(
  (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y5)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y5 @ Y7))) | (Y0 @ Y6)) & ((((Y1 @ Y3) | (~ (irel @ Y5 @ Y4))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y3)))))))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X28 : d_unsorted] : (d_unsorted_0 = X28) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X36 : d_unsorted,X37 : d_unsorted] : ((((d2unsorted @ X36)) = ((d2unsorted @ X37))) => (X36 = X37)) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X69 : $i] : ? [X70 : d_unsorted] : (((d2unsorted @ X70)) = X69)),
  inference(fool_elimination,[],[f4])).
thf(f6,plain,(
  ~ (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
  inference(fool_elimination,[],[f3])).
thf(f7,plain,(
  (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y5)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y5 @ Y7))) | (Y0 @ Y6)) & ((((Y1 @ Y3) | (~ (irel @ Y5 @ Y4))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y3)))))))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X2 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X1))) => (X1 = X2)) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3)),
  inference(rectify,[],[f5])).
thf(f8,plain,(
  (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y5)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y5 @ Y7))) | (Y0 @ Y6)) & ((((Y1 @ Y3) | (~ (irel @ Y5 @ Y4))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y3)))))))))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ! [X2 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X1))) => (X1 = X2))),
  inference(flattening,[],[f7])).
thf(f9,plain,(
  (iequiv != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
  inference(flattening,[],[f6])).
thf(f10,plain,(
  (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y5)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y5 @ Y7))) | (Y0 @ Y6)) & ((((Y1 @ Y3) | (~ (irel @ Y5 @ Y4))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y3)))))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X2 : d_unsorted,X1 : d_unsorted] : ((X1 = X2) | (((d2unsorted @ X2)) != ((d2unsorted @ X1)))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
  inference(ennf_transformation,[],[f8])).
thf(f11,plain,(
  (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y5)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y5 @ Y7))) | (Y0 @ Y6)) & ((((Y1 @ Y3) | (~ (irel @ Y5 @ Y4))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y3)))))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X4)) != ((d2unsorted @ X3)))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
  inference(rectify,[],[f10])).
thf(f12,plain,(
  (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : $i] : (((d2unsorted @ (sK0 @ X0))) = X0) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y5)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y5 @ Y7))) | (Y0 @ Y6)) & ((((Y1 @ Y3) | (~ (irel @ Y5 @ Y4))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y3)))))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4)))))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X4)) != ((d2unsorted @ X3)))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f11])).
thf(f13,plain,(
  (iequiv != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (iand @ (iimplies @ Y0 @ Y1) @ (iimplies @ Y1 @ Y0))))))),
  inference(cnf_transformation,[],[f9])).
thf(f15,plain,(
  (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f22,plain,(
  (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)),
  inference(cnf_transformation,[],[f12])).
thf(f24,plain,(
  ( ! [X2 : d_unsorted] : ((d_unsorted_0 = X2)) )),
  inference(cnf_transformation,[],[f12])).
thf(f26,plain,(
  (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4))))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f29,plain,(
  ( ! [X0 : $i] : ((((d2unsorted @ (sK0 @ X0))) = X0)) )),
  inference(cnf_transformation,[],[f12])).
thf(f31,plain,(
  (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f38,definition,(
  ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
  introduced(theory,[fool_exhaustiveness_axiom])).
thf(f39,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y3 @ Y5)))) & (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y2 @ Y5)))))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y3 @ Y5)))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y3 @ Y5)))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y5) | (~ (irel @ Y4 @ Y5)))))))))))) @ Y1 @ Y0))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4))))))))))))))),
  inference(definition_unfolding,[],[f13,f26,f31,f15,f15])).
thf(f40,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4))))))))))))))),
  inference(beta-eta_normalization,[],[f39])).
thf(f56,plain,(
  ( ! [X0 : $i] : ((((d2unsorted @ d_unsorted_0)) = X0)) )),
  inference(forward_demodulation,[],[f29,f24])).
thf(f60,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
  inference(constrained_superposition,[],[f56,f56])).
thf(f81,plain,(
  ( ! [X0 : $i] : ((((irel @ X0 @ X0)) = $true)) )),
  inference(constrained_superposition,[],[f22,f56])).
thf(f84,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) | (~ (irel @ Y3 @ Y4)))))))))))))))) @ sK1)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (~ (irel @ Y4 @ Y3))) | (~ (irel @ Y2 @ Y4))))))))))))) @ sK1)))),
  inference(negative_extensionality,[],[f40])).
thf(f85,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((sK1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (Y0 @ Y4)))))) | (~ (irel @ Y1 @ Y2))) | (~ (irel @ Y2 @ Y3))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((Y0 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4))))))) | (~ (irel @ Y3 @ Y2))) | (~ (irel @ Y1 @ Y3))))))))))))),
  inference(beta-eta_normalization,[],[f84])).
thf(f86,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((sK1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (Y0 @ Y4)))))) | (~ (irel @ Y1 @ Y2))) | (~ (irel @ Y2 @ Y3))))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((Y0 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4))))))) | (~ (irel @ Y3 @ Y2))) | (~ (irel @ Y1 @ Y3))))))))))) @ sK2)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))) @ sK2)))),
  inference(negative_extensionality,[],[f85])).
thf(f87,plain,(
  ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) != (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2))))))))))),
  inference(beta-eta_normalization,[],[f86])).
thf(f88,plain,(
  ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) @ sK3)) != (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2))))))))) @ sK3)))),
  inference(negative_extensionality,[],[f87])).
thf(f89,plain,(
  ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2))))))))) @ sK3)) = $true) | ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) @ sK3)) = $true)),
  inference(xor_proxy_clausification,[],[f88])).
thf(f90,plain,(
  ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3)))))) | (~ (irel @ Y0 @ Y1))) | (~ (irel @ Y1 @ Y2))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((sK2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (~ (irel @ Y2 @ Y1))) | (~ (irel @ Y0 @ Y2))))))))) @ sK3))) | ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))))) @ sK3)))),
  inference(xor_proxy_clausification,[],[f88])).
thf(f91,plain,(
  ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1)))))))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))))))),
  inference(beta-eta_normalization,[],[f90])).
thf(f92,plain,(
  ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1)))))))))),
  inference(and_proxy_clausification,[],[f91])).
thf(f93,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))),
  inference(and_proxy_clausification,[],[f92])).
thf(f94,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1)))))) @ sK4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))),
  inference(sigma_proxy_clausification,[],[f93])).
thf(f95,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1)))))) @ sK4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))))) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ sK5))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))),
  inference(sigma_proxy_clausification,[],[f94])).
thf(f96,plain,(
  ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ sK5))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1)))))) @ sK6))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1)))))) @ sK4)))),
  inference(sigma_proxy_clausification,[],[f95])).
thf(f97,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1)))))) @ sK6))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1)))))) @ sK4))) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ sK7))) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ sK5)))),
  inference(sigma_proxy_clausification,[],[f96])).
thf(f98,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0))))))) | ($false = (((~ (irel @ sK3 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0))))))) | ($false = (((~ (irel @ sK3 @ sK7)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0))))))))))),
  inference(beta-eta_normalization,[],[f97])).
thf(f99,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0))))))) | ($false = (((~ (irel @ sK3 @ sK7)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0)))))))))) | ($false = (((~ (irel @ sK3 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))))))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8)))),
  inference(sigma_proxy_clausification,[],[f98])).
thf(f100,plain,(
  ($false = (((~ (irel @ sK3 @ sK7)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0)))))))))) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((~ (irel @ sK3 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))))))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8)))),
  inference(sigma_proxy_clausification,[],[f99])).
thf(f101,plain,(
  ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0))))))))) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((~ (irel @ sK3 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))))))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8)))),
  inference(or_proxy_clausification,[],[f100])).
thf(f445,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((~ (irel @ sK3 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))))))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0))))))))),
  inference(or_proxy_clausification,[],[f101])).
thf(f446,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = (((~ (irel @ sK3 @ sK5)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0))))))),
  inference(or_proxy_clausification,[],[f101])).
thf(f447,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0)))))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8)))),
  inference(or_proxy_clausification,[],[f446])).
thf(f614,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0)))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0))))))))),
  inference(or_proxy_clausification,[],[f447])).
thf(f615,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0))))))),
  inference(or_proxy_clausification,[],[f447])).
thf(f616,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0))) @ sK12))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0))))))),
  inference(sigma_proxy_clausification,[],[f615])).
thf(f617,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0))) @ sK12))) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0))) @ sK13)))),
  inference(sigma_proxy_clausification,[],[f616])).
thf(f618,plain,(
  ((((~ (irel @ sK5 @ sK12)) | (sK1 @ sK12))) = $false) | ($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | ($false = (((~ (irel @ sK7 @ sK13)) | (sK2 @ sK13)))) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8)))))),
  inference(beta-eta_normalization,[],[f617])).
thf(f619,plain,(
  ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8))))) | ($false = (((~ (irel @ sK7 @ sK13)) | (sK2 @ sK13)))) | ($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | ($false = ((sK1 @ sK12)))),
  inference(or_proxy_clausification,[],[f618])).
thf(f800,plain,(
  ($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | ($false = (((~ (irel @ sK7 @ sK13)) | (sK2 @ sK13)))) | ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))))) | ($false = ((sK1 @ sK12)))),
  inference(or_proxy_clausification,[],[f619])).
thf(f802,plain,(
  ($false = (((~ (irel @ sK7 @ sK13)) | (sK2 @ sK13)))) | ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))))) | ($false = ((sK1 @ sK12))) | ($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6)))))),
  inference(or_proxy_clausification,[],[f800])).
thf(f803,plain,(
  ($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))))) | (((sK2 @ sK13)) = $false) | ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))))) | ($false = ((sK1 @ sK12)))),
  inference(or_proxy_clausification,[],[f802])).
thf(f860,plain,(
  ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))))) | ($false = ((sK1 @ sK12))) | (((sK2 @ sK13)) = $false) | ($false = (((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0))))))))),
  inference(or_proxy_clausification,[],[f803])).
thf(f862,plain,(
  ($false = (((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))))) | ($false = ((sK1 @ sK12))) | ($false = (((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))))) | (((sK2 @ sK13)) = $false)),
  inference(or_proxy_clausification,[],[f860])).
thf(f864,plain,(
  (((sK2 @ sK13)) = $false) | ($false = ((sK2 @ sK4))) | ($false = ((sK1 @ sK12))) | ($false = (((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0))))))))),
  inference(or_proxy_clausification,[],[f862])).
thf(f866,plain,(
  ($false = ((sK2 @ sK4))) | ($false = ((sK1 @ sK9))) | (((sK2 @ sK13)) = $false) | ($false = ((sK1 @ sK12)))),
  inference(or_proxy_clausification,[],[f864])).
thf(f967,plain,(
  ((((^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0))) @ sK14)) = $false) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0))))))))),
  inference(sigma_proxy_clausification,[],[f614])).
thf(f968,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))) = $true) | ((((^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0))) @ sK14)) = $false)),
  inference(not_proxy_clausification,[],[f967])).
thf(f969,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))) @ X1)) = $true) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ((((^[Y0 : $i]: ((~ (irel @ sK7 @ Y0)) | (sK2 @ Y0))) @ sK14)) = $false) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9)))) )),
  inference(pi_proxy_clausification,[],[f968])).
thf(f970,plain,(
  ( ! [X1 : $i] : (($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | ($false = (((~ (irel @ sK7 @ sK14)) | (sK2 @ sK14)))) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8))))) | ((((sK2 @ X1) | (~ (irel @ sK5 @ X1)))) = $true)) )),
  inference(beta-eta_normalization,[],[f969])).
thf(f972,plain,(
  ( ! [X1 : $i] : (((((sK2 @ X1) | (~ (irel @ sK5 @ X1)))) = $true) | ($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))))) | ($false = (((~ (irel @ sK7 @ sK14)) | (sK2 @ sK14)))) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8)))))) )),
  inference(or_proxy_clausification,[],[f970])).
thf(f973,plain,(
  ( ! [X1 : $i] : (($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))))) | (((~ (irel @ sK5 @ X1))) = $true) | (((sK2 @ X1)) = $true) | ($false = (((~ (irel @ sK7 @ sK14)) | (sK2 @ sK14)))) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8)))))) )),
  inference(or_proxy_clausification,[],[f972])).
thf(f975,plain,(
  ( ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8))))) | ($false = (((~ (irel @ sK7 @ sK14)) | (sK2 @ sK14)))) | (((~ (irel @ sK5 @ X1))) = $true) | ($false = (((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0))))))))) )),
  inference(or_proxy_clausification,[],[f973])).
thf(f977,plain,(
  ( ! [X1 : $i] : (($false = (((~ (irel @ sK7 @ sK14)) | (sK2 @ sK14)))) | ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))))) | ($false = (((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))))) | (((sK2 @ X1)) = $true) | (((~ (irel @ sK5 @ X1))) = $true)) )),
  inference(or_proxy_clausification,[],[f975])).
thf(f978,plain,(
  ( ! [X1 : $i] : (($false = (((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))))) | ($false = ((sK2 @ sK14))) | (((sK2 @ X1)) = $true) | (((~ (irel @ sK5 @ X1))) = $true) | ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4)))))) )),
  inference(or_proxy_clausification,[],[f977])).
thf(f1022,plain,(
  ( ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))))) | ($false = ((sK2 @ sK14))) | (((~ (irel @ sK5 @ X1))) = $true) | ($false = ((sK1 @ sK9)))) )),
  inference(or_proxy_clausification,[],[f978])).
thf(f1024,plain,(
  ( ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = (((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))))) | ($false = ((sK2 @ sK14))) | ($false = ((sK1 @ sK9))) | (((~ (irel @ sK5 @ X1))) = $true)) )),
  inference(or_proxy_clausification,[],[f1022])).
thf(f1026,plain,(
  ( ! [X1 : $i] : (($false = ((sK2 @ sK14))) | ($false = ((sK1 @ sK9))) | (((sK2 @ X1)) = $true) | ($false = ((sK2 @ sK4))) | (((~ (irel @ sK5 @ X1))) = $true)) )),
  inference(or_proxy_clausification,[],[f1024])).
thf(f1027,plain,(
  ( ! [X1 : $i] : (($false = ((sK1 @ sK9))) | ($false = ((sK2 @ sK4))) | ($false = ((sK2 @ sK14))) | ($false = ((irel @ sK5 @ X1))) | (((sK2 @ X1)) = $true)) )),
  inference(not_proxy_clausification,[],[f1026])).
thf(f1161,plain,(
  ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK5 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0))))))))),
  inference(or_proxy_clausification,[],[f445])).
thf(f1249,plain,(
  ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0))))))))),
  inference(or_proxy_clausification,[],[f1161])).
thf(f1428,plain,(
  ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0)))))))) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))) = $true) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8)))),
  inference(not_proxy_clausification,[],[f1249])).
thf(f1429,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0)))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))) = $true) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8)))),
  inference(not_proxy_clausification,[],[f1428])).
thf(f1430,plain,(
  ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9))) | ($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0)))) @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))))) = $true)) )),
  inference(pi_proxy_clausification,[],[f1429])).
thf(f1431,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK5 @ Y0)))) @ X2)) = $true) | ($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK7 @ Y0)))) @ X1))) | ($false = (((^[Y0 : $i]: ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ sK4))) | (~ (irel @ sK3 @ Y0)))) @ sK8))) | ($false = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK6 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ Y0)))) @ sK9)))) )),
  inference(pi_proxy_clausification,[],[f1430])).
thf(f1432,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((sK1 @ X1) | (~ (irel @ sK7 @ X1)))) = $true) | ($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8))))) | ($true = (((sK2 @ X2) | (~ (irel @ sK5 @ X2)))))) )),
  inference(beta-eta_normalization,[],[f1431])).
thf(f1433,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((~ (irel @ sK7 @ X1))) = $true) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8))))) | ($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | ($true = (((sK2 @ X2) | (~ (irel @ sK5 @ X2))))) | (((sK1 @ X1)) = $true)) )),
  inference(or_proxy_clausification,[],[f1432])).
thf(f1434,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((sK2 @ X2) | (~ (irel @ sK5 @ X2))))) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8))))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK7 @ X1))) | ($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9)))))) )),
  inference(not_proxy_clausification,[],[f1433])).
thf(f1435,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = (((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))) | (~ (irel @ sK3 @ sK8))))) | ($true = ((sK2 @ X2))) | ($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | ($false = ((irel @ sK7 @ X1))) | (((~ (irel @ sK5 @ X2))) = $true)) )),
  inference(or_proxy_clausification,[],[f1434])).
thf(f1437,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((~ (irel @ sK5 @ X2))) = $true) | ($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK7 @ X1))) | ($true = ((sK2 @ X2))) | ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4)))))) )),
  inference(or_proxy_clausification,[],[f1435])).
thf(f1438,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = (((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))) | (~ (irel @ sK6 @ sK9))))) | ($false = ((irel @ sK5 @ X2))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK7 @ X1))) | ($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))))) | (((sK1 @ X1)) = $true)) )),
  inference(not_proxy_clausification,[],[f1437])).
thf(f1440,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (~ (irel @ sK8 @ sK4))))) | ($false = ((irel @ sK5 @ X2))) | ($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))))) | ($false = ((irel @ sK7 @ X1))) | (((sK1 @ X1)) = $true) | ($true = ((sK2 @ X2)))) )),
  inference(or_proxy_clausification,[],[f1438])).
thf(f1442,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = (((sK2 @ sK4) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK7 @ X1))) | ($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))))) | ($false = ((irel @ sK5 @ X2)))) )),
  inference(or_proxy_clausification,[],[f1440])).
thf(f1443,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | ($false = ((irel @ sK5 @ X2))) | (((sK1 @ X1)) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0)))))))) | ($false = ((irel @ sK7 @ X1))) | ($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6)))))) )),
  inference(or_proxy_clausification,[],[f1442])).
thf(f1444,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((sK2 @ sK4))) | ($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK7 @ X1))) | ($false = ((irel @ sK5 @ X2))) | (((sK1 @ X1)) = $true)) )),
  inference(or_proxy_clausification,[],[f1442])).
thf(f1446,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X1)) = $true) | ($true = ((sK2 @ X2))) | ($false = (((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))))) | ($false = ((sK2 @ sK4))) | ($false = ((irel @ sK5 @ X2))) | ($false = ((irel @ sK7 @ X1)))) )),
  inference(or_proxy_clausification,[],[f1444])).
thf(f1447,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK5 @ X2))) | (((sK1 @ X1)) = $true) | ($true = ((sK2 @ X2))) | ($false = ((sK2 @ sK4))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0))))))) | ($false = ((irel @ sK7 @ X1)))) )),
  inference(or_proxy_clausification,[],[f1446])).
thf(f1449,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK7 @ X1))) | (((sK1 @ X1)) = $true) | ($false = ((sK2 @ sK4))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK5 @ X2)))) )),
  inference(not_proxy_clausification,[],[f1447])).
thf(f1450,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((sK2 @ sK4))) | (((sK1 @ X1)) = $true) | ($true = ((sK2 @ X2))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0))) @ X3))) | ($false = ((irel @ sK7 @ X1))) | ($false = ((irel @ sK5 @ X2)))) )),
  inference(pi_proxy_clausification,[],[f1449])).
thf(f1451,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ sK7 @ X1))) | ($false = ((irel @ sK5 @ X2))) | ($true = ((sK2 @ X2))) | ($false = ((sK2 @ sK4))) | (((sK1 @ X1)) = $true) | ((((~ (irel @ sK6 @ X3)) | (sK2 @ X3))) = $true)) )),
  inference(beta-eta_normalization,[],[f1450])).
thf(f1452,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK2 @ X3)) = $true) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK5 @ X2))) | ($false = ((irel @ sK7 @ X1))) | ($false = ((sK2 @ sK4))) | ($true = ((sK2 @ X2))) | (((~ (irel @ sK6 @ X3))) = $true)) )),
  inference(or_proxy_clausification,[],[f1451])).
thf(f1453,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ sK7 @ X1))) | ($false = ((irel @ sK6 @ X3))) | ($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true) | ($false = ((sK2 @ sK4))) | (((sK2 @ X3)) = $true) | ($false = ((irel @ sK5 @ X2)))) )),
  inference(not_proxy_clausification,[],[f1452])).
thf(f1455,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK7 @ X1))) | ($false = ((irel @ sK5 @ X2))) | ($true = ((sK2 @ X2))) | ($false = ((((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ sK6))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | (((sK1 @ X1)) = $true)) )),
  inference(not_proxy_clausification,[],[f1443])).
thf(f1457,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | ($false = ((irel @ sK7 @ X1))) | (((sK1 @ X1)) = $true) | ($false = (((sK1 @ sK9) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | ($false = ((irel @ sK5 @ X2)))) )),
  inference(or_proxy_clausification,[],[f1455])).
thf(f1458,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X2))) | ($false = ((irel @ sK5 @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0))))))) | ($false = ((irel @ sK7 @ X1))) | (((sK1 @ X1)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0)))))))) )),
  inference(or_proxy_clausification,[],[f1457])).
thf(f1464,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0)))))) | ($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK5 @ X2))) | ($false = ((irel @ sK7 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0)))))))) )),
  inference(not_proxy_clausification,[],[f1458])).
thf(f1465,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0))) @ X3))) | ($false = ((irel @ sK5 @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0))))))) | ($false = ((irel @ sK7 @ X1))) | ($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true)) )),
  inference(pi_proxy_clausification,[],[f1464])).
thf(f1466,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK6 @ Y0)) | (sK2 @ Y0))) @ X3))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK8 @ Y0)))) @ X4)) = $true) | ($false = ((irel @ sK7 @ X1))) | ($false = ((irel @ sK5 @ X2)))) )),
  inference(pi_proxy_clausification,[],[f1465])).
thf(f1467,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((~ (irel @ sK6 @ X3)) | (sK2 @ X3))) = $true) | ((((sK1 @ X4) | (~ (irel @ sK8 @ X4)))) = $true) | ($false = ((irel @ sK5 @ X2))) | ($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK7 @ X1)))) )),
  inference(beta-eta_normalization,[],[f1466])).
thf(f1468,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK2 @ X2))) | (((sK1 @ X1)) = $true) | ((((sK1 @ X4) | (~ (irel @ sK8 @ X4)))) = $true) | (((~ (irel @ sK6 @ X3))) = $true) | ($false = ((irel @ sK7 @ X1))) | (((sK2 @ X3)) = $true) | ($false = ((irel @ sK5 @ X2)))) )),
  inference(or_proxy_clausification,[],[f1467])).
thf(f1469,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK2 @ X3)) = $true) | (((~ (irel @ sK6 @ X3))) = $true) | (((~ (irel @ sK8 @ X4))) = $true) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK5 @ X2))) | ($true = ((sK2 @ X2))) | ($true = ((sK1 @ X4))) | ($false = ((irel @ sK7 @ X1)))) )),
  inference(or_proxy_clausification,[],[f1468])).
thf(f1470,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK6 @ X3))) | ($false = ((irel @ sK7 @ X1))) | ($true = ((sK1 @ X4))) | (((sK2 @ X3)) = $true) | ($false = ((irel @ sK5 @ X2))) | ($true = ((sK2 @ X2))) | (((~ (irel @ sK8 @ X4))) = $true) | (((sK1 @ X1)) = $true)) )),
  inference(not_proxy_clausification,[],[f1469])).
thf(f1471,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK2 @ X3)) = $true) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK5 @ X2))) | (((sK1 @ X1)) = $true) | ($false = ((irel @ sK8 @ X4))) | ($true = ((sK1 @ X4))) | ($false = ((irel @ sK6 @ X3))) | ($false = ((irel @ sK7 @ X1)))) )),
  inference(not_proxy_clausification,[],[f1470])).
thf(f1518,plain,(
  ($true = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1))))))))))),
  inference(beta-eta_normalization,[],[f89])).
thf(f1519,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))) = $true) | ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1))))))))))),
  inference(and_proxy_clausification,[],[f1518])).
thf(f1520,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))))) = $true) | ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1))))))))))),
  inference(and_proxy_clausification,[],[f1518])).
thf(f1521,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ X1))) | ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1))))))))))) )),
  inference(pi_proxy_clausification,[],[f1520])).
thf(f1523,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1)))))))))) )),
  inference(and_proxy_clausification,[],[f1521])).
thf(f1524,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ X1))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1)))))) @ X2)) = $true)) )),
  inference(pi_proxy_clausification,[],[f1523])).
thf(f1525,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((~ (irel @ sK3 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0))))))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ Y0)))))))) )),
  inference(beta-eta_normalization,[],[f1524])).
thf(f1526,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((~ (irel @ sK3 @ X1))) = $true) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ Y0)))))))) )),
  inference(or_proxy_clausification,[],[f1525])).
thf(f1527,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ Y0))))))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(not_proxy_clausification,[],[f1526])).
thf(f1528,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0))))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ Y0))))))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(or_proxy_clausification,[],[f1527])).
thf(f1529,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))))) = $true)) )),
  inference(not_proxy_clausification,[],[f1528])).
thf(f1530,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0))))))) | ($true = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ Y0)))) @ X3))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))))) = $true) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(pi_proxy_clausification,[],[f1529])).
thf(f1531,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))))) = $true) | ($false = ((irel @ sK3 @ X1))) | ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))) @ (sK16 @ X1)))) | ($true = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ Y0)))) @ X3)))) )),
  inference(sigma_proxy_clausification,[],[f1530])).
thf(f1532,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X2 @ Y1)) | (sK2 @ Y1)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ Y0)))) @ X3))) | ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))) @ (sK16 @ X1)))) | ((((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))) @ X4)) = $true) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(pi_proxy_clausification,[],[f1531])).
thf(f1533,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (((sK2 @ (sK16 @ X1)) | (~ (irel @ X1 @ (sK16 @ X1)))))) | ($false = ((irel @ sK3 @ X1))) | ($true = (((~ (irel @ X1 @ X4)) | (sK1 @ X4)))) | ((((((sK1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ X3)))) = $true)) )),
  inference(beta-eta_normalization,[],[f1532])).
thf(f1535,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (irel @ X1 @ X4)) | (sK1 @ X4)))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK2 @ (sK16 @ X1)))) | ((((((sK1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ X3)))) = $true)) )),
  inference(or_proxy_clausification,[],[f1533])).
thf(f1536,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((~ (irel @ X1 @ X4)))) | ((((((sK1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ X3)))) = $true) | ($false = ((sK2 @ (sK16 @ X1)))) | ($true = ((sK1 @ X4)))) )),
  inference(or_proxy_clausification,[],[f1535])).
thf(f1537,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK1 @ X4))) | ($false = ((sK2 @ (sK16 @ X1)))) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X1))) | ((((((sK1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ X2))) | (~ (irel @ X2 @ X3)))) = $true)) )),
  inference(not_proxy_clausification,[],[f1536])).
thf(f1538,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((((sK1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0)))))) | (~ (irel @ sK3 @ X2)))) = $true) | ($true = ((sK1 @ X4))) | (((~ (irel @ X2 @ X3))) = $true) | ($false = ((sK2 @ (sK16 @ X1)))) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(or_proxy_clausification,[],[f1537])).
thf(f1539,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((sK1 @ X3) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0))))))) = $true) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK1 @ X4))) | ($false = ((sK2 @ (sK16 @ X1)))) | ($true = ((~ (irel @ sK3 @ X2)))) | (((irel @ X1 @ X4)) = $false) | (((~ (irel @ X2 @ X3))) = $true)) )),
  inference(or_proxy_clausification,[],[f1538])).
thf(f1540,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0))))))) | ($true = ((sK1 @ X4))) | (((sK1 @ X3)) = $true) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK2 @ (sK16 @ X1)))) | (((irel @ X1 @ X4)) = $false) | (((~ (irel @ X2 @ X3))) = $true) | ($true = ((~ (irel @ sK3 @ X2))))) )),
  inference(or_proxy_clausification,[],[f1539])).
thf(f1541,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | (((~ (irel @ X2 @ X3))) = $true) | (((sK1 @ X3)) = $true) | ($false = ((sK2 @ (sK16 @ X1)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0)))))) | ($true = ((sK1 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((~ (irel @ sK3 @ X2))))) )),
  inference(not_proxy_clausification,[],[f1540])).
thf(f1542,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0)))))) | ($false = ((sK2 @ (sK16 @ X1)))) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK1 @ X4))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($false = ((irel @ X2 @ X3))) | (((sK1 @ X3)) = $true)) )),
  inference(not_proxy_clausification,[],[f1541])).
thf(f1543,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X1))) | ($false = (((^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0))) @ (sK17 @ X2)))) | (((irel @ X1 @ X4)) = $false) | ($true = ((~ (irel @ sK3 @ X2)))) | ($false = ((irel @ X2 @ X3))) | ($true = ((sK1 @ X4))) | (((sK1 @ X3)) = $true) | ($false = ((sK2 @ (sK16 @ X1))))) )),
  inference(sigma_proxy_clausification,[],[f1542])).
thf(f1544,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((sK2 @ (sK16 @ X1)))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X2 @ X3))) | ($true = ((sK1 @ X4))) | (((irel @ X1 @ X4)) = $false) | ($false = (((^[Y0 : $i]: ((~ (irel @ X2 @ Y0)) | (sK2 @ Y0))) @ (sK17 @ X2)))) | (((sK1 @ X3)) = $true) | (((irel @ sK3 @ X2)) = $false)) )),
  inference(not_proxy_clausification,[],[f1543])).
thf(f1545,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | (((sK1 @ X3)) = $true) | ($false = (((~ (irel @ X2 @ (sK17 @ X2))) | (sK2 @ (sK17 @ X2))))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK2 @ (sK16 @ X1)))) | ($false = ((irel @ X2 @ X3))) | (((irel @ sK3 @ X2)) = $false) | ($true = ((sK1 @ X4)))) )),
  inference(beta-eta_normalization,[],[f1544])).
thf(f1546,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK1 @ X4))) | (((sK1 @ X3)) = $true) | ($false = ((sK2 @ (sK16 @ X1)))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X2 @ X3))) | ($false = ((sK2 @ (sK17 @ X2))))) )),
  inference(or_proxy_clausification,[],[f1545])).
thf(f1602,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ X1)) = $true) | ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2)))))) | (~ (irel @ sK3 @ Y0))) | (~ (irel @ Y0 @ Y1))))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1))))))))))) )),
  inference(pi_proxy_clausification,[],[f1519])).
thf(f1603,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ X1)) = $true) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1)))))))) = $true)) )),
  inference(and_proxy_clausification,[],[f1602])).
thf(f1644,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))) @ X1)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((sK2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (~ (irel @ Y1 @ Y0))) | (~ (irel @ sK3 @ Y1)))))) @ X2)) = $true)) )),
  inference(pi_proxy_clausification,[],[f1603])).
thf(f1645,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((~ (irel @ sK3 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0))))))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ X2))) | (~ (irel @ sK3 @ Y0)))))))) )),
  inference(beta-eta_normalization,[],[f1644])).
thf(f1646,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))))))) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ X2))) | (~ (irel @ sK3 @ Y0)))))))) )),
  inference(or_proxy_clausification,[],[f1645])).
thf(f1647,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ X2))) | (~ (irel @ sK3 @ Y0))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0))))))) = $true)) )),
  inference(or_proxy_clausification,[],[f1646])).
thf(f1648,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0))))))) = $true) | ((((^[Y0 : $i]: ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ X2))) | (~ (irel @ sK3 @ Y0)))) @ X3)) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) = $true)) )),
  inference(pi_proxy_clausification,[],[f1647])).
thf(f1649,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((^[Y0 : $i]: ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ X2))) | (~ (irel @ sK3 @ Y0)))) @ X3)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))))))) )),
  inference(not_proxy_clausification,[],[f1648])).
thf(f1650,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((^[Y0 : $i]: ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ X2))) | (~ (irel @ sK3 @ Y0)))) @ X3)) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))) @ X4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0))))))) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(pi_proxy_clausification,[],[f1649])).
thf(f1651,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))) @ (sK25 @ X1)))) | (((~ (irel @ sK3 @ X1))) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))) @ X4))) | ((((^[Y0 : $i]: ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ X2))) | (~ (irel @ sK3 @ Y0)))) @ X3)) = $true)) )),
  inference(sigma_proxy_clausification,[],[f1650])).
thf(f1652,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((^[Y0 : $i]: ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (~ (irel @ Y0 @ X2))) | (~ (irel @ sK3 @ Y0)))) @ X3)) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))) @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))) @ (sK25 @ X1))))) )),
  inference(not_proxy_clausification,[],[f1651])).
thf(f1653,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((((sK2 @ X2) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X2))) | (~ (irel @ sK3 @ X3))))) | ((((~ (irel @ X1 @ X4)) | (sK2 @ X4))) = $true) | ($false = ((irel @ sK3 @ X1))) | ($false = (((sK1 @ (sK25 @ X1)) | (~ (irel @ X1 @ (sK25 @ X1))))))) )),
  inference(beta-eta_normalization,[],[f1652])).
thf(f1654,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((~ (irel @ sK3 @ X3)))) | ((((~ (irel @ X1 @ X4)) | (sK2 @ X4))) = $true) | ($true = ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X2))))) | ($false = (((sK1 @ (sK25 @ X1)) | (~ (irel @ X1 @ (sK25 @ X1))))))) )),
  inference(or_proxy_clausification,[],[f1653])).
thf(f1655,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X1))) | ((((~ (irel @ X1 @ X4)) | (sK2 @ X4))) = $true) | ($false = ((irel @ sK3 @ X3))) | ($true = ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X2))))) | ($false = (((sK1 @ (sK25 @ X1)) | (~ (irel @ X1 @ (sK25 @ X1))))))) )),
  inference(not_proxy_clausification,[],[f1654])).
thf(f1656,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((~ (irel @ X1 @ X4)))) | ($true = ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X2))))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ sK3 @ X3))) | ($false = (((sK1 @ (sK25 @ X1)) | (~ (irel @ X1 @ (sK25 @ X1)))))) | (((sK2 @ X4)) = $true)) )),
  inference(or_proxy_clausification,[],[f1655])).
thf(f1657,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK2 @ X4)) = $true) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X4)) = $false) | ($true = ((((sK2 @ X2) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X2))))) | ($false = ((irel @ sK3 @ X3))) | ($false = (((sK1 @ (sK25 @ X1)) | (~ (irel @ X1 @ (sK25 @ X1))))))) )),
  inference(not_proxy_clausification,[],[f1656])).
thf(f1658,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = (((sK2 @ X2) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))))) | ($true = ((~ (irel @ X3 @ X2)))) | ($false = (((sK1 @ (sK25 @ X1)) | (~ (irel @ X1 @ (sK25 @ X1)))))) | (((sK2 @ X4)) = $true) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X3)))) )),
  inference(or_proxy_clausification,[],[f1657])).
thf(f1659,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X3))) | ($false = (((sK1 @ (sK25 @ X1)) | (~ (irel @ X1 @ (sK25 @ X1)))))) | ($true = ((~ (irel @ X3 @ X2)))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) = $true) | (((sK2 @ X4)) = $true) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK2 @ X2))) | (((irel @ X1 @ X4)) = $false)) )),
  inference(or_proxy_clausification,[],[f1658])).
thf(f1661,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((sK1 @ (sK25 @ X1)))) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X3))) | ($true = ((~ (irel @ X3 @ X2)))) | ($true = ((sK2 @ X2))) | (((sK2 @ X4)) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) = $true) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(or_proxy_clausification,[],[f1659])).
thf(f1662,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((sK1 @ (sK25 @ X1)))) | ($false = ((irel @ X3 @ X2))) | ($false = ((irel @ sK3 @ X3))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X4)) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) = $true) | ($true = ((sK2 @ X2))) | (((sK2 @ X4)) = $true)) )),
  inference(not_proxy_clausification,[],[f1661])).
thf(f1663,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (((sK2 @ X4)) = $true) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X3))) | ($true = ((sK2 @ X2))) | ($false = ((sK1 @ (sK25 @ X1)))) | ($false = ((irel @ X3 @ X2))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(not_proxy_clausification,[],[f1662])).
thf(f1664,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((sK1 @ (sK25 @ X1)))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X3 @ Y0)))) @ (sK26 @ X3)))) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X3))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ X3 @ X2))) | (((sK2 @ X4)) = $true)) )),
  inference(sigma_proxy_clausification,[],[f1663])).
thf(f1665,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ X3 @ X2))) | ($true = ((sK2 @ X2))) | ($false = ((irel @ sK3 @ X1))) | (((sK2 @ X4)) = $true) | (((irel @ X1 @ X4)) = $false) | ($false = (((sK1 @ (sK26 @ X3)) | (~ (irel @ X3 @ (sK26 @ X3)))))) | ($false = ((sK1 @ (sK25 @ X1)))) | ($false = ((irel @ sK3 @ X3)))) )),
  inference(beta-eta_normalization,[],[f1664])).
thf(f1667,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X3))) | ($true = ((sK2 @ X2))) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ X3 @ X2))) | ($false = ((irel @ sK3 @ X1))) | (((sK2 @ X4)) = $true) | ($false = ((sK1 @ (sK25 @ X1)))) | ($false = ((sK1 @ (sK26 @ X3))))) )),
  inference(or_proxy_clausification,[],[f1665])).
thf(f1678,definition,(
  spl28_1 <=> ($false = ((sK2 @ sK4)))),
  introduced(definition,[new_symbols(definition,[spl28_1])],[avatar_definition])).
thf(f1679,plain,(
  ($false != ((sK2 @ sK4))) | spl28_1),
  inference(avatar_component_clause,[],[f1678])).
thf(f1680,plain,(
  ($false = ((sK2 @ sK4))) | ~spl28_1),
  inference(avatar_component_clause,[],[f1678])).
thf(f1682,definition,(
  spl28_2 <=> ($false = ((sK1 @ sK9)))),
  introduced(definition,[new_symbols(definition,[spl28_2])],[avatar_definition])).
thf(f1683,plain,(
  ($false != ((sK1 @ sK9))) | spl28_2),
  inference(avatar_component_clause,[],[f1682])).
thf(f1684,plain,(
  ($false = ((sK1 @ sK9))) | ~spl28_2),
  inference(avatar_component_clause,[],[f1682])).
thf(f1695,definition,(
  spl28_5 <=> ! [X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((irel @ sK8 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl28_5])],[avatar_definition])).
thf(f1696,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK8 @ X1))) | (((sK1 @ X1)) = $true)) ) | ~spl28_5),
  inference(avatar_component_clause,[],[f1695])).
thf(f1699,definition,(
  spl28_6 <=> ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = ((irel @ sK6 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl28_6])],[avatar_definition])).
thf(f1700,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK6 @ X1))) | (((sK2 @ X1)) = $true)) ) | ~spl28_6),
  inference(avatar_component_clause,[],[f1699])).
thf(f1724,definition,(
  spl28_10 <=> (((irel @ sK6 @ sK9)) = $true)),
  introduced(definition,[new_symbols(definition,[spl28_10])],[avatar_definition])).
thf(f1725,plain,(
  (((irel @ sK6 @ sK9)) != $true) | spl28_10),
  inference(avatar_component_clause,[],[f1724])).
thf(f1726,plain,(
  (((irel @ sK6 @ sK9)) = $true) | ~spl28_10),
  inference(avatar_component_clause,[],[f1724])).
thf(f1772,definition,(
  spl28_13 <=> ! [X1 : $i] : (($false = ((irel @ sK5 @ X1))) | (((sK2 @ X1)) = $true))),
  introduced(definition,[new_symbols(definition,[spl28_13])],[avatar_definition])).
thf(f1773,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK5 @ X1))) | (((sK2 @ X1)) = $true)) ) | ~spl28_13),
  inference(avatar_component_clause,[],[f1772])).
thf(f1845,definition,(
  spl28_18 <=> (((sK2 @ sK13)) = $false)),
  introduced(definition,[new_symbols(definition,[spl28_18])],[avatar_definition])).
thf(f1847,plain,(
  (((sK2 @ sK13)) = $false) | ~spl28_18),
  inference(avatar_component_clause,[],[f1845])).
thf(f1875,definition,(
  spl28_19 <=> ($false = ((sK1 @ sK12)))),
  introduced(definition,[new_symbols(definition,[spl28_19])],[avatar_definition])).
thf(f1877,plain,(
  ($false = ((sK1 @ sK12))) | ~spl28_19),
  inference(avatar_component_clause,[],[f1875])).
thf(f1887,plain,(
  spl28_1 | spl28_2 | spl28_18 | spl28_19),
  inference(avatar_split_clause,[],[f866,f1875,f1845,f1682,f1678])).
thf(f1921,definition,(
  spl28_21 <=> ($false = ((sK2 @ sK14)))),
  introduced(definition,[new_symbols(definition,[spl28_21])],[avatar_definition])).
thf(f1923,plain,(
  ($false = ((sK2 @ sK14))) | ~spl28_21),
  inference(avatar_component_clause,[],[f1921])).
thf(f1924,plain,(
  spl28_1 | spl28_2 | spl28_21 | spl28_13),
  inference(avatar_split_clause,[],[f1027,f1772,f1921,f1682,f1678])).
thf(f1951,definition,(
  spl28_22 <=> ! [X1 : $i] : (($false = ((irel @ sK7 @ X1))) | (((sK1 @ X1)) = $true))),
  introduced(definition,[new_symbols(definition,[spl28_22])],[avatar_definition])).
thf(f1952,plain,(
  ( ! [X1 : $i] : ((((sK1 @ X1)) = $true) | ($false = ((irel @ sK7 @ X1)))) ) | ~spl28_22),
  inference(avatar_component_clause,[],[f1951])).
thf(f2010,plain,(
  spl28_6 | spl28_13 | spl28_22 | spl28_1),
  inference(avatar_split_clause,[],[f1453,f1678,f1951,f1772,f1699])).
thf(f2013,plain,(
  spl28_22 | spl28_13 | spl28_5 | spl28_6),
  inference(avatar_split_clause,[],[f1471,f1699,f1695,f1772,f1951])).
thf(f2026,definition,(
  spl28_25 <=> ! [X4 : $i,X1 : $i] : ((((irel @ X1 @ X4)) = $false) | ($true = ((sK1 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK2 @ (sK16 @ X1)))))),
  introduced(definition,[new_symbols(definition,[spl28_25])],[avatar_definition])).
thf(f2027,plain,(
  ( ! [X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((sK1 @ X4))) | ($false = ((sK2 @ (sK16 @ X1)))) | (((irel @ X1 @ X4)) = $false)) ) | ~spl28_25),
  inference(avatar_component_clause,[],[f2026])).
thf(f2033,definition,(
  spl28_27 <=> ! [X2 : $i,X3 : $i] : ((((sK1 @ X3)) = $true) | ($false = ((sK2 @ (sK17 @ X2)))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X2 @ X3))))),
  introduced(definition,[new_symbols(definition,[spl28_27])],[avatar_definition])).
thf(f2034,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((sK1 @ X3)) = $true) | ($false = ((irel @ X2 @ X3))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((sK2 @ (sK17 @ X2))))) ) | ~spl28_27),
  inference(avatar_component_clause,[],[f2033])).
thf(f2035,plain,(
  spl28_27 | spl28_25),
  inference(avatar_split_clause,[],[f1546,f2026,f2033])).
thf(f2092,definition,(
  spl28_43 <=> ! [X4 : $i,X1 : $i] : ((((irel @ X1 @ X4)) = $false) | ($false = ((sK1 @ (sK25 @ X1)))) | (((sK2 @ X4)) = $true) | ($false = ((irel @ sK3 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl28_43])],[avatar_definition])).
thf(f2093,plain,(
  ( ! [X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X1))) | ($false = ((sK1 @ (sK25 @ X1)))) | (((sK2 @ X4)) = $true) | (((irel @ X1 @ X4)) = $false)) ) | ~spl28_43),
  inference(avatar_component_clause,[],[f2092])).
thf(f2095,definition,(
  spl28_44 <=> ! [X2 : $i,X3 : $i] : (($false = ((irel @ sK3 @ X3))) | ($false = ((sK1 @ (sK26 @ X3)))) | ($false = ((irel @ X3 @ X2))) | ($true = ((sK2 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl28_44])],[avatar_definition])).
thf(f2096,plain,(
  ( ! [X2 : $i,X3 : $i] : (($true = ((sK2 @ X2))) | ($false = ((sK1 @ (sK26 @ X3)))) | ($false = ((irel @ X3 @ X2))) | ($false = ((irel @ sK3 @ X3)))) ) | ~spl28_44),
  inference(avatar_component_clause,[],[f2095])).
thf(f2097,plain,(
  spl28_43 | spl28_44),
  inference(avatar_split_clause,[],[f1667,f2095,f2092])).
thf(f2135,definition,(
  spl28_51 <=> ($true = ((sK1 @ sK3)))),
  introduced(definition,[new_symbols(definition,[spl28_51])],[avatar_definition])).
thf(f2136,plain,(
  ($true != ((sK1 @ sK3))) | spl28_51),
  inference(avatar_component_clause,[],[f2135])).
thf(f2137,plain,(
  ($true = ((sK1 @ sK3))) | ~spl28_51),
  inference(avatar_component_clause,[],[f2135])).
thf(f2139,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | ~spl28_2),
  inference(constrained_superposition,[],[f1684,f60])).
thf(f2145,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ sK6 @ X0)))) ) | ~spl28_10),
  inference(constrained_superposition,[],[f1726,f60])).
thf(f2153,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $true)) ) | ~spl28_10),
  inference(constrained_superposition,[],[f2145,f60])).
thf(f2157,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((irel @ sK3 @ X2)) = $false) | ($false = ((sK2 @ (sK17 @ X2)))) | ($false = $true) | ($false = ((irel @ X2 @ X3)))) ) | (~spl28_2 | ~spl28_27)),
  inference(forward_demodulation,[],[f2034,f2139])).
thf(f2158,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ X2 @ X3))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((sK2 @ (sK17 @ X2))))) ) | (~spl28_2 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2157])).
thf(f2163,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((sK2 @ (sK17 @ X2)))) | ($false = $true) | ($false = ((irel @ X2 @ X3)))) ) | (~spl28_2 | ~spl28_10 | ~spl28_27)),
  inference(forward_demodulation,[],[f2158,f2153])).
thf(f2164,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ X2 @ X3))) | ($false = ((sK2 @ (sK17 @ X2))))) ) | (~spl28_2 | ~spl28_10 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2163])).
thf(f2165,plain,(
  ( ! [X2 : $i] : (($false = ((sK2 @ (sK17 @ X2)))) | ($false = $true)) ) | (~spl28_2 | ~spl28_10 | ~spl28_27)),
  inference(forward_demodulation,[],[f2164,f2153])).
thf(f2166,plain,(
  ( ! [X2 : $i] : (($false = ((sK2 @ (sK17 @ X2))))) ) | (~spl28_2 | ~spl28_10 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2165])).
thf(f2167,plain,(
  ( ! [X0 : $i] : (($false = ((sK2 @ X0)))) ) | (~spl28_2 | ~spl28_10 | ~spl28_27)),
  inference(constrained_superposition,[],[f2166,f60])).
thf(f2174,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK6 @ X1))) | ($false = $true)) ) | (~spl28_2 | ~spl28_6 | ~spl28_10 | ~spl28_27)),
  inference(forward_demodulation,[],[f1700,f2167])).
thf(f2175,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK6 @ X1)))) ) | (~spl28_2 | ~spl28_6 | ~spl28_10 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2174])).
thf(f2176,plain,(
  ($false = $true) | (~spl28_2 | ~spl28_6 | ~spl28_10 | ~spl28_27)),
  inference(forward_demodulation,[],[f2175,f2153])).
thf(f2177,plain,(
  $false | (~spl28_2 | ~spl28_6 | ~spl28_10 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2176])).
thf(f2178,plain,(
  ~spl28_2 | ~spl28_6 | ~spl28_10 | ~spl28_27),
  inference(avatar_contradiction_clause,[],[f2177])).
thf(f2183,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK8 @ X1))) | ($false = $true)) ) | (~spl28_2 | ~spl28_5)),
  inference(forward_demodulation,[],[f1696,f2139])).
thf(f2184,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK8 @ X1)))) ) | (~spl28_2 | ~spl28_5)),
  inference(trivial_inequality_removal,[],[f2183])).
thf(f2187,plain,(
  ( ! [X0 : $i] : (($false = ((sK2 @ X0)))) ) | ~spl28_1),
  inference(constrained_superposition,[],[f1680,f60])).
thf(f2193,plain,(
  ( ! [X0 : $i] : (($true != ((irel @ sK6 @ X0)))) ) | spl28_10),
  inference(constrained_superposition,[],[f1725,f60])).
thf(f2205,plain,(
  ($true != $true) | spl28_10),
  inference(constrained_superposition,[],[f2193,f81])).
thf(f2208,plain,(
  $false | spl28_10),
  inference(trivial_inequality_removal,[],[f2205])).
thf(f2209,plain,(
  spl28_10),
  inference(avatar_contradiction_clause,[],[f2208])).
thf(f2213,plain,(
  ($false = $true) | (~spl28_2 | ~spl28_51)),
  inference(forward_demodulation,[],[f2137,f2139])).
thf(f2214,plain,(
  $false | (~spl28_2 | ~spl28_51)),
  inference(trivial_inequality_removal,[],[f2213])).
thf(f2215,plain,(
  ~spl28_2 | ~spl28_51),
  inference(avatar_contradiction_clause,[],[f2214])).
thf(f2236,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ sK6 @ X0)))) ) | ~spl28_10),
  inference(constrained_superposition,[],[f1726,f60])).
thf(f2253,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $true)) ) | ~spl28_10),
  inference(constrained_superposition,[],[f2236,f60])).
thf(f2264,plain,(
  ($false = $true) | (~spl28_2 | ~spl28_5)),
  inference(constrained_superposition,[],[f81,f2184])).
thf(f2280,plain,(
  $false | (~spl28_2 | ~spl28_5)),
  inference(trivial_inequality_removal,[],[f2264])).
thf(f2281,plain,(
  ~spl28_2 | ~spl28_5),
  inference(avatar_contradiction_clause,[],[f2280])).
thf(f2298,plain,(
  ( ! [X1 : $i] : (($false = $true) | (((sK2 @ X1)) = $true)) ) | (~spl28_6 | ~spl28_10)),
  inference(forward_demodulation,[],[f1700,f2236])).
thf(f2299,plain,(
  ( ! [X1 : $i] : ((((sK2 @ X1)) = $true)) ) | (~spl28_6 | ~spl28_10)),
  inference(trivial_inequality_removal,[],[f2298])).
thf(f2300,plain,(
  ($false = $true) | (~spl28_1 | ~spl28_6 | ~spl28_10)),
  inference(forward_demodulation,[],[f2299,f2187])).
thf(f2301,plain,(
  $false | (~spl28_1 | ~spl28_6 | ~spl28_10)),
  inference(trivial_inequality_removal,[],[f2300])).
thf(f2302,plain,(
  ~spl28_1 | ~spl28_6 | ~spl28_10),
  inference(avatar_contradiction_clause,[],[f2301])).
thf(f2318,plain,(
  ( ! [X0 : $i] : (($true = ((sK1 @ X0)))) ) | ~spl28_51),
  inference(constrained_superposition,[],[f2137,f60])).
thf(f2320,plain,(
  ( ! [X0 : $i] : (($false = ((sK2 @ X0)))) ) | ~spl28_1),
  inference(constrained_superposition,[],[f1680,f60])).
thf(f2348,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | ($false = ((sK1 @ (sK25 @ X1)))) | ($false = $true) | (((sK2 @ X4)) = $true)) ) | (~spl28_10 | ~spl28_43)),
  inference(forward_demodulation,[],[f2093,f2253])).
thf(f2349,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((sK2 @ X4)) = $true) | (((irel @ X1 @ X4)) = $false) | ($false = ((sK1 @ (sK25 @ X1))))) ) | (~spl28_10 | ~spl28_43)),
  inference(trivial_inequality_removal,[],[f2348])).
thf(f2350,plain,(
  ( ! [X1 : $i,X4 : $i] : (($false = ((sK1 @ (sK25 @ X1)))) | ($false = $true) | (((irel @ X1 @ X4)) = $false)) ) | (~spl28_1 | ~spl28_10 | ~spl28_43)),
  inference(forward_demodulation,[],[f2349,f2320])).
thf(f2351,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | ($false = ((sK1 @ (sK25 @ X1))))) ) | (~spl28_1 | ~spl28_10 | ~spl28_43)),
  inference(trivial_inequality_removal,[],[f2350])).
thf(f2352,plain,(
  ( ! [X1 : $i] : (($false = ((sK1 @ (sK25 @ X1)))) | ($false = $true)) ) | (~spl28_1 | ~spl28_10 | ~spl28_43)),
  inference(forward_demodulation,[],[f2351,f2253])).
thf(f2353,plain,(
  ( ! [X1 : $i] : (($false = ((sK1 @ (sK25 @ X1))))) ) | (~spl28_1 | ~spl28_10 | ~spl28_43)),
  inference(trivial_inequality_removal,[],[f2352])).
thf(f2354,plain,(
  ($false = $true) | (~spl28_1 | ~spl28_10 | ~spl28_43 | ~spl28_51)),
  inference(forward_demodulation,[],[f2353,f2318])).
thf(f2355,plain,(
  $false | (~spl28_1 | ~spl28_10 | ~spl28_43 | ~spl28_51)),
  inference(trivial_inequality_removal,[],[f2354])).
thf(f2356,plain,(
  ~spl28_1 | ~spl28_10 | ~spl28_43 | ~spl28_51),
  inference(avatar_contradiction_clause,[],[f2355])).
thf(f2357,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = $true) | ($true = ((sK2 @ X2))) | ($false = ((irel @ X3 @ X2))) | ($false = ((irel @ sK3 @ X3)))) ) | (~spl28_44 | ~spl28_51)),
  inference(forward_demodulation,[],[f2096,f2318])).
thf(f2358,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ sK3 @ X3))) | ($false = ((irel @ X3 @ X2))) | ($true = ((sK2 @ X2)))) ) | (~spl28_44 | ~spl28_51)),
  inference(trivial_inequality_removal,[],[f2357])).
thf(f2359,plain,(
  ( ! [X2 : $i,X3 : $i] : (($true = ((sK2 @ X2))) | ($false = $true) | ($false = ((irel @ X3 @ X2)))) ) | (~spl28_10 | ~spl28_44 | ~spl28_51)),
  inference(forward_demodulation,[],[f2358,f2253])).
thf(f2360,plain,(
  ( ! [X2 : $i,X3 : $i] : (($true = ((sK2 @ X2))) | ($false = ((irel @ X3 @ X2)))) ) | (~spl28_10 | ~spl28_44 | ~spl28_51)),
  inference(trivial_inequality_removal,[],[f2359])).
thf(f2361,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ X3 @ X2))) | ($false = $true)) ) | (~spl28_1 | ~spl28_10 | ~spl28_44 | ~spl28_51)),
  inference(forward_demodulation,[],[f2360,f2320])).
thf(f2362,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ X3 @ X2)))) ) | (~spl28_1 | ~spl28_10 | ~spl28_44 | ~spl28_51)),
  inference(trivial_inequality_removal,[],[f2361])).
thf(f2363,plain,(
  ($false = $true) | (~spl28_1 | ~spl28_10 | ~spl28_44 | ~spl28_51)),
  inference(forward_demodulation,[],[f2362,f2253])).
thf(f2364,plain,(
  $false | (~spl28_1 | ~spl28_10 | ~spl28_44 | ~spl28_51)),
  inference(trivial_inequality_removal,[],[f2363])).
thf(f2365,plain,(
  ~spl28_1 | ~spl28_10 | ~spl28_44 | ~spl28_51),
  inference(avatar_contradiction_clause,[],[f2364])).
thf(f2372,plain,(
  ( ! [X0 : $i] : (($true != ((sK1 @ X0)))) ) | spl28_51),
  inference(constrained_superposition,[],[f2136,f60])).
thf(f2376,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0))) | ($true != $true)) ) | spl28_51),
  inference(constrained_superposition,[],[f2372,f38])).
thf(f2377,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | spl28_51),
  inference(trivial_inequality_removal,[],[f2376])).
thf(f2388,plain,(
  $false | (spl28_2 | spl28_51)),
  inference(forward_subsumption_resolution,[],[f1683,f2377])).
thf(f2389,plain,(
  spl28_2 | spl28_51),
  inference(avatar_contradiction_clause,[],[f2388])).
thf(f2390,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK5 @ X1))) | ($false = $true)) ) | (~spl28_1 | ~spl28_13)),
  inference(forward_demodulation,[],[f1773,f2320])).
thf(f2391,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK5 @ X1)))) ) | (~spl28_1 | ~spl28_13)),
  inference(trivial_inequality_removal,[],[f2390])).
thf(f2392,plain,(
  ($false = $true) | (~spl28_1 | ~spl28_10 | ~spl28_13)),
  inference(forward_demodulation,[],[f2391,f2253])).
thf(f2393,plain,(
  $false | (~spl28_1 | ~spl28_10 | ~spl28_13)),
  inference(trivial_inequality_removal,[],[f2392])).
thf(f2394,plain,(
  ~spl28_1 | ~spl28_10 | ~spl28_13),
  inference(avatar_contradiction_clause,[],[f2393])).
thf(f2395,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK7 @ X1)))) ) | (~spl28_22 | spl28_51)),
  inference(forward_subsumption_resolution,[],[f1952,f2372])).
thf(f2396,plain,(
  ($false = $true) | (~spl28_10 | ~spl28_22 | spl28_51)),
  inference(forward_demodulation,[],[f2395,f2253])).
thf(f2397,plain,(
  $false | (~spl28_10 | ~spl28_22 | spl28_51)),
  inference(trivial_inequality_removal,[],[f2396])).
thf(f2398,plain,(
  ~spl28_10 | ~spl28_22 | spl28_51),
  inference(avatar_contradiction_clause,[],[f2397])).
thf(f2399,plain,(
  ( ! [X1 : $i,X4 : $i] : (($false = ((sK2 @ (sK16 @ X1)))) | (((irel @ X1 @ X4)) = $false) | ($false = ((irel @ sK3 @ X1)))) ) | (~spl28_25 | spl28_51)),
  inference(forward_subsumption_resolution,[],[f2027,f2372])).
thf(f2400,plain,(
  ( ! [X1 : $i] : (($false = $true) | (((sK2 @ X1)) = $true)) ) | (~spl28_10 | ~spl28_13)),
  inference(forward_demodulation,[],[f1773,f2253])).
thf(f2401,plain,(
  ( ! [X1 : $i] : ((((sK2 @ X1)) = $true)) ) | (~spl28_10 | ~spl28_13)),
  inference(trivial_inequality_removal,[],[f2400])).
thf(f2404,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK3 @ X1))) | ($false = $true) | ($false = ((sK2 @ (sK16 @ X1))))) ) | (~spl28_10 | ~spl28_25 | spl28_51)),
  inference(forward_demodulation,[],[f2399,f2253])).
thf(f2405,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK3 @ X1))) | ($false = ((sK2 @ (sK16 @ X1))))) ) | (~spl28_10 | ~spl28_25 | spl28_51)),
  inference(trivial_inequality_removal,[],[f2404])).
thf(f2410,plain,(
  ( ! [X1 : $i] : (($false = ((sK2 @ (sK16 @ X1)))) | ($false = $true)) ) | (~spl28_10 | ~spl28_25 | spl28_51)),
  inference(forward_demodulation,[],[f2405,f2253])).
thf(f2411,plain,(
  ( ! [X1 : $i] : (($false = ((sK2 @ (sK16 @ X1))))) ) | (~spl28_10 | ~spl28_25 | spl28_51)),
  inference(trivial_inequality_removal,[],[f2410])).
thf(f2416,plain,(
  ( ! [X0 : $i] : (($false = ((sK2 @ X0)))) ) | (~spl28_10 | ~spl28_25 | spl28_51)),
  inference(constrained_superposition,[],[f2411,f60])).
thf(f2423,plain,(
  $false | (spl28_1 | ~spl28_10 | ~spl28_25 | spl28_51)),
  inference(forward_subsumption_resolution,[],[f1679,f2416])).
thf(f2424,plain,(
  spl28_1 | ~spl28_10 | ~spl28_25 | spl28_51),
  inference(avatar_contradiction_clause,[],[f2423])).
thf(f2425,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ X2 @ X3))) | ($false = ((sK2 @ (sK17 @ X2)))) | (((irel @ sK3 @ X2)) = $false)) ) | (~spl28_27 | spl28_51)),
  inference(forward_subsumption_resolution,[],[f2034,f2372])).
thf(f2426,plain,(
  ( ! [X2 : $i] : (($false = ((sK2 @ (sK17 @ X2)))) | ($false = $true) | (((irel @ sK3 @ X2)) = $false)) ) | (~spl28_10 | ~spl28_27 | spl28_51)),
  inference(forward_demodulation,[],[f2425,f2253])).
thf(f2427,plain,(
  ( ! [X2 : $i] : ((((irel @ sK3 @ X2)) = $false) | ($false = ((sK2 @ (sK17 @ X2))))) ) | (~spl28_10 | ~spl28_27 | spl28_51)),
  inference(trivial_inequality_removal,[],[f2426])).
thf(f2428,plain,(
  ( ! [X2 : $i] : (($false = $true) | ($false = ((sK2 @ (sK17 @ X2))))) ) | (~spl28_10 | ~spl28_27 | spl28_51)),
  inference(forward_demodulation,[],[f2427,f2253])).
thf(f2429,plain,(
  ( ! [X2 : $i] : (($false = ((sK2 @ (sK17 @ X2))))) ) | (~spl28_10 | ~spl28_27 | spl28_51)),
  inference(trivial_inequality_removal,[],[f2428])).
thf(f2430,plain,(
  ( ! [X0 : $i] : (($false != ((sK2 @ X0)))) ) | spl28_1),
  inference(constrained_superposition,[],[f1679,f60])).
thf(f2443,plain,(
  ($false = $true) | (~spl28_10 | ~spl28_13 | ~spl28_18)),
  inference(forward_demodulation,[],[f1847,f2401])).
thf(f2444,plain,(
  $false | (~spl28_10 | ~spl28_13 | ~spl28_18)),
  inference(trivial_inequality_removal,[],[f2443])).
thf(f2445,plain,(
  ~spl28_10 | ~spl28_13 | ~spl28_18),
  inference(avatar_contradiction_clause,[],[f2444])).
thf(f2450,plain,(
  ($false = $true) | (~spl28_10 | ~spl28_13 | ~spl28_27 | spl28_51)),
  inference(forward_demodulation,[],[f2429,f2401])).
thf(f2451,plain,(
  $false | (~spl28_10 | ~spl28_13 | ~spl28_27 | spl28_51)),
  inference(trivial_inequality_removal,[],[f2450])).
thf(f2452,plain,(
  ~spl28_10 | ~spl28_13 | ~spl28_27 | spl28_51),
  inference(avatar_contradiction_clause,[],[f2451])).
thf(f2480,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ X2 @ X3))) | (((irel @ sK3 @ X2)) = $false) | (((sK1 @ X3)) = $true) | ($false = $true)) ) | (~spl28_10 | ~spl28_13 | ~spl28_27)),
  inference(forward_demodulation,[],[f2034,f2401])).
thf(f2481,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((irel @ sK3 @ X2)) = $false) | (((sK1 @ X3)) = $true) | ($false = ((irel @ X2 @ X3)))) ) | (~spl28_10 | ~spl28_13 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2480])).
thf(f2482,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ X2 @ X3))) | (((sK1 @ X3)) = $true) | ($false = $true)) ) | (~spl28_10 | ~spl28_13 | ~spl28_27)),
  inference(forward_demodulation,[],[f2481,f2253])).
thf(f2483,plain,(
  ( ! [X2 : $i,X3 : $i] : (($false = ((irel @ X2 @ X3))) | (((sK1 @ X3)) = $true)) ) | (~spl28_10 | ~spl28_13 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2482])).
thf(f2484,plain,(
  ( ! [X3 : $i] : ((((sK1 @ X3)) = $true) | ($false = $true)) ) | (~spl28_10 | ~spl28_13 | ~spl28_27)),
  inference(forward_demodulation,[],[f2483,f2253])).
thf(f2485,plain,(
  ( ! [X3 : $i] : ((((sK1 @ X3)) = $true)) ) | (~spl28_10 | ~spl28_13 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2484])).
thf(f2489,plain,(
  ($false = $true) | (~spl28_10 | ~spl28_13 | ~spl28_19 | ~spl28_27)),
  inference(forward_demodulation,[],[f1877,f2485])).
thf(f2490,plain,(
  $false | (~spl28_10 | ~spl28_13 | ~spl28_19 | ~spl28_27)),
  inference(trivial_inequality_removal,[],[f2489])).
thf(f2491,plain,(
  ~spl28_10 | ~spl28_13 | ~spl28_19 | ~spl28_27),
  inference(avatar_contradiction_clause,[],[f2490])).
thf(f2492,plain,(
  ( ! [X1 : $i,X4 : $i] : (($false = ((sK2 @ (sK16 @ X1)))) | ($false = $true) | ($true = ((sK1 @ X4))) | (((irel @ X1 @ X4)) = $false)) ) | (~spl28_10 | ~spl28_25)),
  inference(forward_demodulation,[],[f2027,f2253])).
thf(f2493,plain,(
  ( ! [X1 : $i,X4 : $i] : (($false = ((sK2 @ (sK16 @ X1)))) | ($true = ((sK1 @ X4))) | (((irel @ X1 @ X4)) = $false)) ) | (~spl28_10 | ~spl28_25)),
  inference(trivial_inequality_removal,[],[f2492])).
thf(f2494,plain,(
  ( ! [X1 : $i,X4 : $i] : (($true = ((sK1 @ X4))) | (((irel @ X1 @ X4)) = $false) | ($false = $true)) ) | (~spl28_10 | ~spl28_13 | ~spl28_25)),
  inference(forward_demodulation,[],[f2493,f2401])).
thf(f2495,plain,(
  ( ! [X1 : $i,X4 : $i] : (($true = ((sK1 @ X4))) | (((irel @ X1 @ X4)) = $false)) ) | (~spl28_10 | ~spl28_13 | ~spl28_25)),
  inference(trivial_inequality_removal,[],[f2494])).
thf(f2496,plain,(
  ( ! [X4 : $i] : (($true = ((sK1 @ X4))) | ($false = $true)) ) | (~spl28_10 | ~spl28_13 | ~spl28_25)),
  inference(forward_demodulation,[],[f2495,f2253])).
thf(f2497,plain,(
  ( ! [X4 : $i] : (($true = ((sK1 @ X4)))) ) | (~spl28_10 | ~spl28_13 | ~spl28_25)),
  inference(trivial_inequality_removal,[],[f2496])).
thf(f2501,plain,(
  ($false = $true) | (~spl28_10 | ~spl28_13 | ~spl28_19 | ~spl28_25)),
  inference(forward_demodulation,[],[f1877,f2497])).
thf(f2502,plain,(
  $false | (~spl28_10 | ~spl28_13 | ~spl28_19 | ~spl28_25)),
  inference(trivial_inequality_removal,[],[f2501])).
thf(f2503,plain,(
  ~spl28_10 | ~spl28_13 | ~spl28_19 | ~spl28_25),
  inference(avatar_contradiction_clause,[],[f2502])).
thf(f2587,plain,(
  $false | (spl28_1 | ~spl28_21)),
  inference(forward_subsumption_resolution,[],[f1923,f2430])).
thf(f2588,plain,(
  spl28_1 | ~spl28_21),
  inference(avatar_contradiction_clause,[],[f2587])).
cnf(s138, plain, spl28_1 | spl28_2 | spl28_18 | spl28_19, inference(sat_conversion,[],[f1887])).
cnf(s167, plain, spl28_1 | spl28_2 | spl28_13 | spl28_21, inference(sat_conversion,[],[f1924])).
cnf(s242, plain, spl28_1 | spl28_6 | spl28_13 | spl28_22, inference(sat_conversion,[],[f2010])).
cnf(s245, plain, spl28_5 | spl28_6 | spl28_13 | spl28_22, inference(sat_conversion,[],[f2013])).
cnf(s258, plain, spl28_25 | spl28_27, inference(sat_conversion,[],[f2035])).
cnf(s269, plain, spl28_43 | spl28_44, inference(sat_conversion,[],[f2097])).
cnf(s276, plain, ~spl28_2 | ~spl28_6 | ~spl28_10 | ~spl28_27, inference(sat_conversion,[],[f2178])).
cnf(s277, plain, spl28_10, inference(sat_conversion,[],[f2209])).
cnf(s279, plain, ~spl28_2 | ~spl28_51, inference(sat_conversion,[],[f2215])).
cnf(s290, plain, ~spl28_2 | ~spl28_5, inference(sat_conversion,[],[f2281])).
cnf(s293, plain, ~spl28_1 | ~spl28_6 | ~spl28_10, inference(sat_conversion,[],[f2302])).
cnf(s296, plain, ~spl28_1 | ~spl28_10 | ~spl28_43 | ~spl28_51, inference(sat_conversion,[],[f2356])).
cnf(s297, plain, ~spl28_1 | ~spl28_10 | ~spl28_44 | ~spl28_51, inference(sat_conversion,[],[f2365])).
cnf(s298, plain, spl28_2 | spl28_51, inference(sat_conversion,[],[f2389])).
cnf(s299, plain, ~spl28_1 | ~spl28_10 | ~spl28_13, inference(sat_conversion,[],[f2394])).
cnf(s300, plain, ~spl28_10 | ~spl28_22 | spl28_51, inference(sat_conversion,[],[f2398])).
cnf(s301, plain, spl28_1 | ~spl28_10 | ~spl28_25 | spl28_51, inference(sat_conversion,[],[f2424])).
cnf(s304, plain, ~spl28_10 | ~spl28_13 | ~spl28_18, inference(sat_conversion,[],[f2445])).
cnf(s306, plain, ~spl28_10 | ~spl28_13 | ~spl28_27 | spl28_51, inference(sat_conversion,[],[f2452])).
cnf(s310, plain, ~spl28_10 | ~spl28_13 | ~spl28_19 | ~spl28_27, inference(sat_conversion,[],[f2491])).
cnf(s311, plain, ~spl28_10 | ~spl28_13 | ~spl28_19 | ~spl28_25, inference(sat_conversion,[],[f2503])).
cnf(s325, plain, spl28_1 | ~spl28_21, inference(sat_conversion,[],[f2588])).
cnf(s326, plain, ~spl28_2 | ~spl28_6 | ~spl28_27, inference(rat,[],[s276,s277])).
cnf(s327, plain, ~spl28_19 | ~spl28_13, inference(rat,[],[s258,s310,s311,s277])).
cnf(s328, plain, spl28_2 | spl28_21 | spl28_1, inference(rat,[],[s327,s138,s304,s167,s277])).
cnf(s329, plain, spl28_21 | spl28_1, inference(rat,[],[s242,s326,s306,s258,s301,s300,s279,s328,s277])).
cnf(s330, plain, spl28_1, inference(rat,[],[s329,s325])).
cnf(s331, plain, ~spl28_13, inference(rat,[],[s299,s277,s330])).
cnf(s332, plain, ~spl28_6, inference(rat,[],[s293,s277,s330])).
cnf(s333, plain, ~spl28_51, inference(rat,[],[s269,s296,s297,s277,s330])).
cnf(s334, plain, spl28_2, inference(rat,[],[s298,s333])).
cnf(s335, plain, ~spl28_22, inference(rat,[],[s300,s277,s333])).
cnf(s336, plain, ~spl28_5, inference(rat,[],[s290,s334])).
cnf(s338, plain, $false, inference(rat,[],[s245,s332,s331,s336,s335])).
thf(f2589,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s338])).
% SZS output end Proof for theBenchmark