%----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 > $i)).
thf(func_def_21, type, d_unsorted_0: d_unsorted).
thf(func_def_23, type, vAND: ($o > $o > $o)).
thf(func_def_24, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_25, type, vOR: ($o > $o > $o)).
thf(func_def_26, type, vNOT: ($o > $o)).
thf(func_def_27, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_28, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_29, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_30, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_31, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_34, type, db6: !>[X0: $tType]:(X0)).
thf(func_def_35, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_36, type, db8: !>[X0: $tType]:(X0)).
thf(func_def_37, type, db7: !>[X0: $tType]:(X0)).
thf(func_def_38, type, db5: !>[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 > $o)).
thf(func_def_43, type, sK4: ($i > $i)).
thf(func_def_44, type, sK5: ($i > $i)).
thf(func_def_45, type, sK6: ($i > $i)).
thf(func_def_46, type, sK7: ($i > $i)).
thf(func_def_47, type, sK8: ($i > $i)).
thf(func_def_48, type, sK9: ($i > $i)).
thf(func_def_49, type, sK10: ($i > $i)).
thf(func_def_50, type, sK11: ($i > $i)).
thf(func_def_51, type, sK12: ($i > $i)).
thf(func_def_52, type, sK13: ($i > $i)).
thf(f1,conjecture,(
  ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((inot @ (iequiv @ X0 @ X1)))) = ixor)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ixor)).
thf(f2,negated_conjecture,(
  ~ ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((inot @ (iequiv @ X0 @ X1)))) = ixor)),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,axiom,(
  (inot = (^[X8 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i,X18 : $i] : (~(irel @ X5 @ X18) | ~(irel @ X7 @ X5) | (X9 @ X18) | ~ ! [X16 : $i] : (~(irel @ X5 @ X16) | (X8 @ X16))) & ! [X5 : $i,X19 : $i] : ((X8 @ X19) | ~ ! [X17 : $i] : (~(irel @ X5 @ X17) | (X9 @ X17)) | ~(irel @ X7 @ X5) | ~(irel @ X5 @ X19)))) = iequiv) & (mnot = (^[X3 : ($i > $o), X4 : $i] : (~(X3 @ X4)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (mbox_s4 = (^[X8 : ($i > $o), X3 : $i] : (! [X5 : $i] : (~(irel @ X3 @ X5) | (X8 @ X5))))) & (mand = (^[X3 : ($i > $o), X5 : ($i > $o), X4 : $i] : ((X3 @ X4) & (X5 @ X4)))) & (itrue @ (d2unsorted @ d_unsorted_0)) & (iatom = (^[X8 : ($i > $o), X7 : $i] : ((X8 @ X7)))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X13 : $i,X14 : $i,X12 : $i,X15 : $i,X5 : $i] : (~(irel @ X7 @ X5) | ((~(irel @ X14 @ X15) | ~(irel @ X5 @ X14) | (X8 @ X15) | ~ ! [X17 : $i] : ((X9 @ X17) | ~(irel @ X14 @ X17))) & (~(irel @ X12 @ X13) | ~ ! [X16 : $i] : (~(irel @ X12 @ X16) | (X8 @ X16)) | ~(irel @ X5 @ X12) | (X9 @ X13)))))) = ixor) & (iimplies = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5))))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)))) = ior) & (iinvalid = (^[X10 : ($i > $o)] : (! [X11 : $i] : ~(X10 @ X11)))) & ! [X2 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X2))) => (X1 = X2)) & (iimplied = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5))))) & ((^[X10 : ($i > $o)] : (~ ! [X11 : $i] : (X10 @ X11))) = icountersatisfiable) & ((^[X4 : ($i > $o), X6 : ($i > $o), X7 : $i] : (~(X4 @ X7) | (X6 @ X7))) = mimplies) & (ivalid = (^[X10 : ($i > $o)] : (! [X11 : $i] : (X10 @ X11)))) & (mor = (^[X3 : ($i > $o), X5 : ($i > $o), X4 : $i] : ((X3 @ X4) | (X5 @ X4)))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X10 : ($i > $o)] : (~ ! [X11 : $i] : ~(X10 @ X11))) = isatisfiable) & ! [X0 : d_unsorted] : (X0 = d_unsorted_0) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) & ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = iand) & ! [X4 : $i] : ? [X0 : d_unsorted] : (X4 = ((d2unsorted @ X0)))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lcl696_1)).
thf(f4,plain,(
  (inot = (^[X0 : ($i > $o), X1 : $i] : (~ ! [X2 : $i] : ((X0 @ X2) | ~(irel @ X1 @ X2))))) & ((^[X3 : ($i > $o), X4 : ($i > $o), X5 : $i] : (! [X6 : $i,X7 : $i] : (~(irel @ X6 @ X7) | ~(irel @ X5 @ X6) | (X4 @ X7) | ~ ! [X8 : $i] : (~(irel @ X6 @ X8) | (X3 @ X8))) & ! [X9 : $i,X10 : $i] : ((X3 @ X10) | ~ ! [X11 : $i] : (~(irel @ X9 @ X11) | (X4 @ X11)) | ~(irel @ X5 @ X9) | ~(irel @ X9 @ X10)))) = iequiv) & (mnot = (^[X12 : ($i > $o), X13 : $i] : (~(X12 @ X13)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (mbox_s4 = (^[X14 : ($i > $o), X15 : $i] : (! [X16 : $i] : (~(irel @ X15 @ X16) | (X14 @ X16))))) & (mand = (^[X17 : ($i > $o), X18 : ($i > $o), X19 : $i] : ((X17 @ X19) & (X18 @ X19)))) & (itrue @ (d2unsorted @ d_unsorted_0)) & (iatom = (^[X20 : ($i > $o), X21 : $i] : ((X20 @ X21)))) & ((^[X22 : ($i > $o), X23 : ($i > $o), X24 : $i] : (~ ! [X25 : $i,X26 : $i,X27 : $i,X28 : $i,X29 : $i] : (~(irel @ X24 @ X29) | ((~(irel @ X26 @ X28) | ~(irel @ X29 @ X26) | (X22 @ X28) | ~ ! [X30 : $i] : ((X23 @ X30) | ~(irel @ X26 @ X30))) & (~(irel @ X27 @ X25) | ~ ! [X31 : $i] : (~(irel @ X27 @ X31) | (X22 @ X31)) | ~(irel @ X29 @ X27) | (X23 @ X25)))))) = ixor) & (iimplies = (^[X32 : ($i > $o), X33 : ($i > $o), X34 : $i] : (~ ! [X35 : $i] : ((X32 @ X35) | ~(irel @ X34 @ X35)) | ! [X36 : $i] : ((X33 @ X36) | ~(irel @ X34 @ X36))))) & ((^[X37 : ($i > $o), X38 : ($i > $o), X39 : $i] : (! [X40 : $i] : (~(irel @ X39 @ X40) | (X37 @ X40)) | ! [X41 : $i] : (~(irel @ X39 @ X41) | (X38 @ X41)))) = ior) & (iinvalid = (^[X42 : ($i > $o)] : (! [X43 : $i] : ~(X42 @ X43)))) & ! [X44 : d_unsorted,X45 : d_unsorted] : ((((d2unsorted @ X44)) = ((d2unsorted @ X45))) => (X44 = X45)) & (iimplied = (^[X46 : ($i > $o), X47 : ($i > $o), X48 : $i] : (~ ! [X49 : $i] : ((X47 @ X49) | ~(irel @ X48 @ X49)) | ! [X50 : $i] : (~(irel @ X48 @ X50) | (X46 @ X50))))) & ((^[X51 : ($i > $o)] : (~ ! [X52 : $i] : (X51 @ X52))) = icountersatisfiable) & ((^[X53 : ($i > $o), X54 : ($i > $o), X55 : $i] : (~(X53 @ X55) | (X54 @ X55))) = mimplies) & (ivalid = (^[X56 : ($i > $o)] : (! [X57 : $i] : (X56 @ X57)))) & (mor = (^[X58 : ($i > $o), X59 : ($i > $o), X60 : $i] : ((X58 @ X60) | (X59 @ X60)))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X61 : ($i > $o)] : (~ ! [X62 : $i] : ~(X61 @ X62))) = isatisfiable) & ! [X63 : d_unsorted] : (d_unsorted_0 = X63) & ((^[X64 : ($i > $o), X65 : ($i > $o), X66 : $i] : (! [X67 : $i] : ((X65 @ X67) | ~(irel @ X66 @ X67)) & ! [X68 : $i] : ((X64 @ X68) | ~(irel @ X66 @ X68)))) = iand) & ! [X69 : $i] : ? [X70 : d_unsorted] : (((d2unsorted @ X70)) = X69)),
  inference(rectify,[],[f3])).
thf(f5,plain,(
  (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y1 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3)))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3)))))))))))))))))))) & (iimplies = (^[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]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X44 : d_unsorted,X45 : d_unsorted] : ((((d2unsorted @ X44)) = ((d2unsorted @ X45))) => (X44 = X45)) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X63 : d_unsorted] : (d_unsorted_0 = X63) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & ! [X69 : $i] : ? [X70 : d_unsorted] : (((d2unsorted @ X70)) = X69)),
  inference(fool_elimination,[],[f4])).
thf(f6,plain,(
  ~ (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
  inference(fool_elimination,[],[f2])).
thf(f7,plain,(
  (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y1 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3)))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3)))))))))))))))))))) & (iimplies = (^[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]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X1 : d_unsorted,X0 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X0))) => (X0 = X1)) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3)),
  inference(rectify,[],[f5])).
thf(f8,plain,(
  (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3)))))))))))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X1 : d_unsorted,X0 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X0))) => (X0 = X1)) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y1 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))))))))))))))),
  inference(flattening,[],[f7])).
thf(f9,plain,(
  (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
  inference(flattening,[],[f6])).
thf(f10,plain,(
  (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & ! [X1 : d_unsorted,X0 : d_unsorted] : ((((d2unsorted @ X1)) != ((d2unsorted @ X0))) | (X0 = X1)) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y1 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3)))))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3)))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))),
  inference(ennf_transformation,[],[f8])).
thf(f11,plain,(
  (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iimplies = (^[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,X3 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y1 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3)))))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3)))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))),
  inference(rectify,[],[f10])).
thf(f12,plain,(
  (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X0 : $i] : (((d2unsorted @ (sK0 @ X0))) = X0) & (iimplies = (^[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,X3 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y1 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3)))))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3)))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f11])).
thf(f13,plain,(
  (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
  inference(cnf_transformation,[],[f9])).
thf(f15,plain,(
  (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f24,plain,(
  (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3))))))))))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f25,plain,(
  (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)),
  inference(cnf_transformation,[],[f12])).
thf(f26,plain,(
  (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (Y0 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y1 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f31,plain,(
  ( ! [X4 : d_unsorted] : ((d_unsorted_0 = X4)) )),
  inference(cnf_transformation,[],[f12])).
thf(f34,plain,(
  ( ! [X0 : $i] : ((((d2unsorted @ (sK0 @ X0))) = X0)) )),
  inference(cnf_transformation,[],[f12])).
thf(f39,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3))))))))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y2 @ Y4)))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((~ (irel @ Y6 @ Y5)) | (~ (irel @ Y4 @ Y6))) | (~ (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7) | (~ (irel @ Y6 @ Y7))))))) | (Y2 @ Y5)))))) & (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((~ (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y7) | (~ (irel @ Y6 @ Y7)))))) | (Y3 @ Y5)) | (~ (irel @ Y4 @ Y6))) | (~ (irel @ Y6 @ Y5))))))))))))) @ Y0 @ Y1))))))),
  inference(definition_unfolding,[],[f13,f24,f15,f26])).
thf(f40,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (irel @ Y5 @ Y4)) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y5 @ Y6))))))) | (Y0 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y5))) | (~ (irel @ Y5 @ Y4))))))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3))))))))))))))))))))),
  inference(beta-eta_normalization,[],[f39])).
thf(f59,plain,(
  ( ! [X0 : $i] : ((((d2unsorted @ d_unsorted_0)) = X0)) )),
  inference(forward_demodulation,[],[f34,f31])).
thf(f63,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
  inference(constrained_superposition,[],[f59,f59])).
thf(f77,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ X0 @ X0)))) )),
  inference(constrained_superposition,[],[f25,f59])).
thf(f84,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((Y1 @ Y7) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y5 @ Y8))))))) | (~ (irel @ Y5 @ Y7))) & ((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (Y0 @ Y4)) | (~ (irel @ Y3 @ Y6))) | (~ (irel @ Y6 @ Y4)))) | (~ (irel @ Y2 @ Y3))))))))))))))))))) @ sK1)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | ((!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (irel @ Y5 @ Y4)) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y5 @ Y6))))))) | (Y0 @ Y4)))))) & (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y5))) | (~ (irel @ Y5 @ Y4))))))))))))))))) @ sK1)))),
  inference(negative_extensionality,[],[f40])).
thf(f85,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (sK1 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y0 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((((Y0 @ Y6) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y7 : $i]: ((sK1 @ Y7) | (~ (irel @ Y4 @ Y7))))))) | (~ (irel @ Y4 @ Y6))) & ((((~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y5 @ Y7)) | (Y0 @ Y7))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ Y5))) | (~ (irel @ Y5 @ Y3)))) | (~ (irel @ Y1 @ Y2))))))))))))))))))),
  inference(beta-eta_normalization,[],[f84])).
thf(f86,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y4 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y4 @ Y5))))))) | (sK1 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (Y0 @ Y3)) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))))))))))))))) @ sK2)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((((((Y0 @ Y6) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y7 : $i]: ((sK1 @ Y7) | (~ (irel @ Y4 @ Y7))))))) | (~ (irel @ Y4 @ Y6))) & ((((~ (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y5 @ Y7)) | (Y0 @ Y7))))) | (sK1 @ Y3)) | (~ (irel @ Y2 @ Y5))) | (~ (irel @ Y5 @ Y3)))) | (~ (irel @ Y1 @ Y2))))))))))))))))) @ sK2)))),
  inference(negative_extensionality,[],[f85])).
thf(f87,plain,(
  ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((sK2 @ Y5) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((sK1 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (~ (irel @ Y3 @ Y5))) & ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (sK2 @ Y6))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ Y4))) | (~ (irel @ Y4 @ Y2)))) | (~ (irel @ Y0 @ Y1))))))))))))))) != (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y3 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4) | (~ (irel @ Y3 @ Y4))))))) | (sK1 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4)))))) | (sK2 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (irel @ Y3 @ Y2))))))))))))))),
  inference(beta-eta_normalization,[],[f86])).
thf(f88,plain,(
  ((((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((sK2 @ Y5) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((sK1 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (~ (irel @ Y3 @ Y5))) & ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (sK2 @ Y6))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ Y4))) | (~ (irel @ Y4 @ Y2)))) | (~ (irel @ Y0 @ Y1))))))))))))))) @ sK3)) != (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y3 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4) | (~ (irel @ Y3 @ Y4))))))) | (sK1 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4)))))) | (sK2 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (irel @ Y3 @ Y2))))))))))))) @ sK3)))),
  inference(negative_extensionality,[],[f87])).
thf(f89,plain,(
  ($true = (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y3 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4) | (~ (irel @ Y3 @ Y4))))))) | (sK1 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4)))))) | (sK2 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (irel @ Y3 @ Y2))))))))))))) @ sK3))) | ($true = (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((sK2 @ Y5) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((sK1 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (~ (irel @ Y3 @ Y5))) & ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (sK2 @ Y6))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ Y4))) | (~ (irel @ Y4 @ Y2)))) | (~ (irel @ Y0 @ Y1))))))))))))))) @ sK3)))),
  inference(xor_proxy_clausification,[],[f88])).
thf(f90,plain,(
  ($false = (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | ((!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (irel @ Y3 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4) | (~ (irel @ Y3 @ Y4))))))) | (sK1 @ Y2)))))) & (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y3 @ Y4)))))) | (sK2 @ Y2)) | (~ (irel @ Y1 @ Y3))) | (~ (irel @ Y3 @ Y2))))))))))))) @ sK3))) | ($false = (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((sK2 @ Y5) | (~ (irel @ Y1 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((sK1 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (~ (irel @ Y3 @ Y5))) & ((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (sK2 @ Y6))))) | (sK1 @ Y2)) | (~ (irel @ Y1 @ Y4))) | (~ (irel @ Y4 @ Y2)))) | (~ (irel @ Y0 @ Y1))))))))))))))) @ sK3)))),
  inference(xor_proxy_clausification,[],[f88])).
thf(f91,plain,(
  ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1)))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))))))))))),
  inference(beta-eta_normalization,[],[f90])).
thf(f92,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1)))))))))))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))))))))))),
  inference(not_proxy_clausification,[],[f91])).
thf(f93,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1)))))))))) @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))))))))))) )),
  inference(pi_proxy_clausification,[],[f92])).
thf(f94,plain,(
  ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))))))))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1)))))))))) @ X1)))) )),
  inference(not_proxy_clausification,[],[f93])).
thf(f95,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1)))))))))) @ X1)))) )),
  inference(pi_proxy_clausification,[],[f94])).
thf(f96,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((~ (irel @ sK3 @ X1)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (irel @ Y1 @ Y0))))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2)))))))))))))) )),
  inference(beta-eta_normalization,[],[f95])).
thf(f97,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((~ (irel @ sK3 @ X1)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2))))))))))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (irel @ Y1 @ Y0))))))))))) )),
  inference(or_proxy_clausification,[],[f96])).
thf(f98,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (irel @ Y1 @ Y0)))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2)))))))))))))) )),
  inference(not_proxy_clausification,[],[f97])).
thf(f99,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2))))))))))))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (irel @ Y1 @ Y0)))))))))) )),
  inference(and_proxy_clausification,[],[f98])).
thf(f100,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2))))))))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0)))))))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(and_proxy_clausification,[],[f98])).
thf(f101,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0)))))))) | ($false = ((irel @ sK3 @ X1))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2)))))))))) @ X3)))) )),
  inference(pi_proxy_clausification,[],[f100])).
thf(f102,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2)))))))))) @ X3))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0))))) @ X4)) = $true) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(pi_proxy_clausification,[],[f101])).
thf(f103,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ Y0 @ X4)) | (~ (irel @ X1 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (sK1 @ X4)))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y1))) | (~ (irel @ Y1 @ X3)))) | (~ (irel @ sK3 @ X2))))))))))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(beta-eta_normalization,[],[f102])).
thf(f104,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y1))) | (~ (irel @ Y1 @ X3)))) | (~ (irel @ sK3 @ X2))))))))))) | ($true = (((^[Y0 : $i]: ((((~ (irel @ Y0 @ X4)) | (~ (irel @ X1 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (sK1 @ X4))) @ X5))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(pi_proxy_clausification,[],[f103])).
thf(f105,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = (((^[Y0 : $i]: ((((~ (irel @ Y0 @ X4)) | (~ (irel @ X1 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (sK1 @ X4))) @ X5))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y1))) | (~ (irel @ Y1 @ X3)))) | (~ (irel @ sK3 @ X2)))))))) @ X6)))) )),
  inference(pi_proxy_clausification,[],[f104])).
thf(f106,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (((((~ (irel @ X5 @ X4)) | (~ (irel @ X1 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0))))))) | (sK1 @ X4)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2))))))))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(beta-eta_normalization,[],[f105])).
thf(f107,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2))))))))) | ($true = ((sK1 @ X4))) | ($true = ((((~ (irel @ X5 @ X4)) | (~ (irel @ X1 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0)))))))))) )),
  inference(or_proxy_clausification,[],[f106])).
thf(f108,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((((~ (irel @ X5 @ X4)) | (~ (irel @ X1 @ X5))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0))))))))) | ($true = ((sK1 @ X4))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7)))) )),
  inference(pi_proxy_clausification,[],[f107])).
thf(f109,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0)))))))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK1 @ X4))) | ($true = (((~ (irel @ X5 @ X4)) | (~ (irel @ X1 @ X5)))))) )),
  inference(or_proxy_clausification,[],[f108])).
thf(f110,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($true = ((sK1 @ X4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0))))))) | ($true = (((~ (irel @ X5 @ X4)) | (~ (irel @ X1 @ X5)))))) )),
  inference(not_proxy_clausification,[],[f109])).
thf(f111,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((~ (irel @ X5 @ X4)) | (~ (irel @ X1 @ X5))))) | ($false = ((irel @ sK3 @ X1))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0)))) @ (sK4 @ X5)))) | ($true = ((sK1 @ X4)))) )),
  inference(sigma_proxy_clausification,[],[f110])).
thf(f112,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($false = ((irel @ sK3 @ X1))) | (((~ (irel @ X5 @ X4))) = $true) | ($true = ((~ (irel @ X1 @ X5)))) | ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0)))) @ (sK4 @ X5)))) | ($true = ((sK1 @ X4)))) )),
  inference(or_proxy_clausification,[],[f111])).
thf(f113,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0)))) @ (sK4 @ X5)))) | ($true = ((sK1 @ X4))) | ($true = ((~ (irel @ X1 @ X5)))) | ($false = ((irel @ sK3 @ X1))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7)))) )),
  inference(not_proxy_clausification,[],[f112])).
thf(f114,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($true = ((sK1 @ X4))) | ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X5 @ Y0)))) @ (sK4 @ X5)))) | (((irel @ X1 @ X5)) = $false)) )),
  inference(not_proxy_clausification,[],[f113])).
thf(f115,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((((sK2 @ (sK4 @ X5)) | (~ (irel @ X5 @ (sK4 @ X5))))) = $false) | ($false = ((irel @ X5 @ X4))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ X6 @ Y1))))))) | (~ (irel @ X6 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X7 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))) | (~ (irel @ sK3 @ X2))))))) | ($true = ((sK1 @ X4))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X5)) = $false)) )),
  inference(beta-eta_normalization,[],[f114])).
thf(f117,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X1 @ X5)) = $false) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK1 @ X4))) | ($false = ((sK2 @ (sK4 @ X5)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ X6 @ Y1))))))) | (~ (irel @ X6 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X7 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))) | (~ (irel @ sK3 @ X2)))))))) )),
  inference(or_proxy_clausification,[],[f115])).
thf(f118,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((sK1 @ X4))) | ($true = (((^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ X6 @ Y1))))))) | (~ (irel @ X6 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X7 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))) | (~ (irel @ sK3 @ X2)))) @ X8))) | (((irel @ X1 @ X5)) = $false) | ($false = ((sK2 @ (sK4 @ X5)))) | ($false = ((irel @ X5 @ X4)))) )),
  inference(pi_proxy_clausification,[],[f117])).
thf(f119,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK2 @ (sK4 @ X5)))) | ($true = (((((((sK2 @ X8) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | (~ (irel @ X6 @ X8))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))) | (~ (irel @ sK3 @ X2))))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X5)) = $false) | ($true = ((sK1 @ X4))) | ($false = ((irel @ X5 @ X4)))) )),
  inference(beta-eta_normalization,[],[f118])).
thf(f120,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK2 @ (sK4 @ X5)))) | ($true = ((sK1 @ X4))) | ($true = ((~ (irel @ sK3 @ X2)))) | (((irel @ X1 @ X5)) = $false) | ($false = ((irel @ sK3 @ X1))) | ($true = ((((((sK2 @ X8) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | (~ (irel @ X6 @ X8))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))))) | ($false = ((irel @ X5 @ X4)))) )),
  inference(or_proxy_clausification,[],[f119])).
thf(f121,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((sK2 @ (sK4 @ X5)))) | (((irel @ X1 @ X5)) = $false) | ($true = ((((((sK2 @ X8) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | (~ (irel @ X6 @ X8))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))))) | ($false = ((irel @ X5 @ X4))) | ($true = ((sK1 @ X4)))) )),
  inference(not_proxy_clausification,[],[f120])).
thf(f122,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3))))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((sK2 @ (sK4 @ X5)))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X5)) = $false) | ($false = ((irel @ X5 @ X4))) | ($true = ((sK1 @ X4)))) )),
  inference(and_proxy_clausification,[],[f121])).
thf(f135,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($true = ((sK1 @ X4))) | ($false = ((sK2 @ (sK4 @ X5)))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ sK3 @ X2)) = $false) | (((~ (irel @ X7 @ X3))) = $true) | (((irel @ X1 @ X5)) = $false)) )),
  inference(or_proxy_clausification,[],[f122])).
thf(f136,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((sK2 @ (sK4 @ X5)))) | ($true = ((sK1 @ X4))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X3)))) | (((irel @ sK3 @ X2)) = $false) | ($true = ((~ (irel @ X2 @ X7)))) | (((~ (irel @ X7 @ X3))) = $true) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X5 @ X4))) | (((irel @ X1 @ X5)) = $false)) )),
  inference(or_proxy_clausification,[],[f135])).
thf(f137,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ sK3 @ X2)) = $false) | ($true = ((sK1 @ X3))) | (((~ (irel @ X7 @ X3))) = $true) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X5)) = $false) | ($true = ((~ (irel @ X2 @ X7)))) | ($true = ((sK1 @ X4))) | ($false = ((sK2 @ (sK4 @ X5)))) | ($false = ((irel @ X5 @ X4))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0)))))))) )),
  inference(or_proxy_clausification,[],[f136])).
thf(f138,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK1 @ X4))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))))) | ($false = ((irel @ X5 @ X4))) | (((irel @ X1 @ X5)) = $false) | (((irel @ X7 @ X3)) = $false) | ($false = ((irel @ sK3 @ X1))) | (((irel @ sK3 @ X2)) = $false) | ($true = ((~ (irel @ X2 @ X7)))) | ($true = ((sK1 @ X3))) | ($false = ((sK2 @ (sK4 @ X5))))) )),
  inference(not_proxy_clausification,[],[f137])).
thf(f139,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($true = ((~ (irel @ X2 @ X7)))) | ($true = ((sK1 @ X3))) | (((irel @ X1 @ X5)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0)))))) | ($true = ((sK1 @ X4))) | (((irel @ sK3 @ X2)) = $false) | (((irel @ X7 @ X3)) = $false) | ($false = ((sK2 @ (sK4 @ X5)))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(not_proxy_clausification,[],[f138])).
thf(f140,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | (((irel @ sK3 @ X2)) = $false) | ($true = ((sK1 @ X4))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X5)) = $false) | ($false = ((sK2 @ (sK4 @ X5)))) | (((irel @ X7 @ X3)) = $false) | ($true = ((sK1 @ X3))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0)))))) | ($false = ((irel @ X2 @ X7)))) )),
  inference(not_proxy_clausification,[],[f139])).
thf(f141,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X7 @ X3)) = $false) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ X2 @ X7))) | ($false = ((sK2 @ (sK4 @ X5)))) | ((((^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))) @ (sK6 @ X7))) = $false) | (((irel @ sK3 @ X2)) = $false) | (((irel @ X1 @ X5)) = $false) | ($true = ((sK1 @ X3))) | ($true = ((sK1 @ X4)))) )),
  inference(sigma_proxy_clausification,[],[f140])).
thf(f142,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK1 @ X4))) | ($false = ((sK2 @ (sK4 @ X5)))) | (((irel @ X7 @ X3)) = $false) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ X2 @ X7))) | ($true = ((sK1 @ X3))) | (((irel @ X1 @ X5)) = $false) | (((irel @ sK3 @ X2)) = $false) | ((((~ (irel @ X7 @ (sK6 @ X7))) | (sK2 @ (sK6 @ X7)))) = $false) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(beta-eta_normalization,[],[f141])).
thf(f143,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X7 @ X3)) = $false) | (((irel @ X1 @ X5)) = $false) | ($true = ((sK1 @ X3))) | ($false = ((sK2 @ (sK6 @ X7)))) | ($false = ((sK2 @ (sK4 @ X5)))) | ($true = ((sK1 @ X4))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X2 @ X7))) | ($false = ((irel @ X5 @ X4)))) )),
  inference(or_proxy_clausification,[],[f142])).
thf(f175,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2)))))))))) @ X3))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (irel @ Y1 @ Y0)))))))))) )),
  inference(pi_proxy_clausification,[],[f99])).
thf(f176,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ X1 @ Y1))) | (~ (irel @ Y1 @ Y0)))))) @ X4))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ X2 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ X2 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ X2)))))))))) @ X3)))) )),
  inference(pi_proxy_clausification,[],[f175])).
thf(f177,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (sK2 @ X4)) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ X4))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y1))) | (~ (irel @ Y1 @ X3)))) | (~ (irel @ sK3 @ X2))))))))))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(beta-eta_normalization,[],[f176])).
thf(f178,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (sK2 @ X4)) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ X4)))) @ X5))) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y1))) | (~ (irel @ Y1 @ X3)))) | (~ (irel @ sK3 @ X2))))))))))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(pi_proxy_clausification,[],[f177])).
thf(f179,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ X2 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y1))) | (~ (irel @ Y1 @ X3)))) | (~ (irel @ sK3 @ X2)))))))) @ X6))) | ($true = (((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (sK2 @ X4)) | (~ (irel @ X1 @ Y0))) | (~ (irel @ Y0 @ X4)))) @ X5))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(pi_proxy_clausification,[],[f178])).
thf(f180,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2))))))))) | ($false = ((irel @ sK3 @ X1))) | ($true = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0)))))) | (sK2 @ X4)) | (~ (irel @ X1 @ X5))) | (~ (irel @ X5 @ X4)))))) )),
  inference(beta-eta_normalization,[],[f179])).
thf(f181,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($false = ((irel @ sK3 @ X1))) | ($true = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0)))))) | (sK2 @ X4)) | (~ (irel @ X1 @ X5))) | (~ (irel @ X5 @ X4)))))) )),
  inference(pi_proxy_clausification,[],[f180])).
thf(f182,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | (((~ (irel @ X5 @ X4))) = $true) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0)))))) | (sK2 @ X4)) | (~ (irel @ X1 @ X5)))))) )),
  inference(or_proxy_clausification,[],[f181])).
thf(f183,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0)))))) | (sK2 @ X4)) | (~ (irel @ X1 @ X5))))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7)))) )),
  inference(not_proxy_clausification,[],[f182])).
thf(f184,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0)))))) | (sK2 @ X4)))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((~ (irel @ X1 @ X5)))) | ($false = ((irel @ X5 @ X4)))) )),
  inference(or_proxy_clausification,[],[f183])).
thf(f185,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK2 @ X4))) | ($false = ((irel @ X5 @ X4))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0)))))))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((~ (irel @ X1 @ X5)))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7)))) )),
  inference(or_proxy_clausification,[],[f184])).
thf(f186,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0))))))) | ($false = ((irel @ X5 @ X4))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($true = ((sK2 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((~ (irel @ X1 @ X5))))) )),
  inference(not_proxy_clausification,[],[f185])).
thf(f187,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK2 @ X4))) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X5 @ X4))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0)))) @ (sK9 @ X5)))) | ($true = ((~ (irel @ X1 @ X5))))) )),
  inference(sigma_proxy_clausification,[],[f186])).
thf(f188,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X5 @ Y0)))) @ (sK9 @ X5)))) | ($true = ((sK2 @ X4))) | (((irel @ X1 @ X5)) = $false) | ($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ X6 @ Y2))))))) | (~ (irel @ X6 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ X3)) | (~ (irel @ X2 @ Y0))) | (~ (irel @ Y0 @ X3)))) | (~ (irel @ sK3 @ X2)))))) @ X7))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X5 @ X4)))) )),
  inference(not_proxy_clausification,[],[f187])).
thf(f189,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = (((sK1 @ (sK9 @ X5)) | (~ (irel @ X5 @ (sK9 @ X5)))))) | (((irel @ X1 @ X5)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ X6 @ Y1))))))) | (~ (irel @ X6 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X7 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))) | (~ (irel @ sK3 @ X2))))))) | ($true = ((sK2 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X5 @ X4)))) )),
  inference(beta-eta_normalization,[],[f188])).
thf(f191,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ X6 @ Y1))))))) | (~ (irel @ X6 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X7 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))) | (~ (irel @ sK3 @ X2))))))) | ($true = ((sK2 @ X4))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X5)) = $false)) )),
  inference(or_proxy_clausification,[],[f189])).
thf(f192,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($true = ((sK2 @ X4))) | (((irel @ X1 @ X5)) = $false) | ($true = (((^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ X6 @ Y1))))))) | (~ (irel @ X6 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X7 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))) | (~ (irel @ sK3 @ X2)))) @ X8)))) )),
  inference(pi_proxy_clausification,[],[f191])).
thf(f193,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK2 @ X4))) | ($false = ((sK1 @ (sK9 @ X5)))) | (((irel @ X1 @ X5)) = $false) | ($true = (((((((sK2 @ X8) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | (~ (irel @ X6 @ X8))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))) | (~ (irel @ sK3 @ X2)))))) )),
  inference(beta-eta_normalization,[],[f192])).
thf(f194,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X8 : $i,X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($true = ((sK2 @ X4))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X5)) = $false) | ($true = ((((((sK2 @ X8) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | (~ (irel @ X6 @ X8))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X7 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ X3)) | (~ (irel @ X2 @ X7))) | (~ (irel @ X7 @ X3)))))) | ($true = ((~ (irel @ sK3 @ X2))))) )),
  inference(or_proxy_clausification,[],[f193])).
thf(f196,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (((((sK2 @ X8) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | (~ (irel @ X6 @ X8))))) | ($false = ((irel @ X5 @ X4))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((sK2 @ X4))) | ($false = ((sK1 @ (sK9 @ X5)))) | (((irel @ X1 @ X5)) = $false) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(and_proxy_clausification,[],[f194])).
thf(f197,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ X5 @ X4))) | ($true = ((sK2 @ X4))) | (((irel @ X1 @ X5)) = $false) | ($true = ((~ (irel @ X6 @ X8)))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((((sK2 @ X8) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))))) | ($false = ((irel @ sK3 @ X1)))) )),
  inference(or_proxy_clausification,[],[f196])).
thf(f198,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($false = ((irel @ X5 @ X4))) | (((irel @ X1 @ X5)) = $false) | ($true = ((((sK2 @ X8) | (~ (irel @ X2 @ X6))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((sK2 @ X4))) | ($false = ((irel @ X6 @ X8)))) )),
  inference(not_proxy_clausification,[],[f197])).
thf(f199,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))))))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($false = ((irel @ X6 @ X8))) | ($true = (((sK2 @ X8) | (~ (irel @ X2 @ X6))))) | ($false = ((irel @ X5 @ X4))) | ($true = ((sK2 @ X4))) | ($false = ((sK1 @ (sK9 @ X5)))) | (((irel @ X1 @ X5)) = $false)) )),
  inference(or_proxy_clausification,[],[f198])).
thf(f200,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = (((sK2 @ X8) | (~ (irel @ X2 @ X6))))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($true = ((sK2 @ X4))) | ($false = ((irel @ X6 @ X8))) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | (((irel @ X1 @ X5)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | ($true = ((~ (irel @ sK3 @ X2))))) )),
  inference(not_proxy_clausification,[],[f199])).
thf(f201,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0))))))) | (((irel @ X1 @ X5)) = $false) | ($true = ((sK2 @ X8))) | ($false = ((irel @ sK3 @ X1))) | ($true = ((sK2 @ X4))) | ($false = ((irel @ X6 @ X8))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($true = ((~ (irel @ X2 @ X6)))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($false = ((irel @ X5 @ X4)))) )),
  inference(or_proxy_clausification,[],[f200])).
thf(f202,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((irel @ X1 @ X5)) = $false) | ($true = ((sK2 @ X4))) | ($false = ((irel @ X6 @ X8))) | ($true = ((~ (irel @ X2 @ X6)))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((sK2 @ X8))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))) @ (sK10 @ X6)))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X5 @ X4))) | ($false = ((sK1 @ (sK9 @ X5))))) )),
  inference(sigma_proxy_clausification,[],[f201])).
thf(f203,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((sK2 @ X4))) | ($false = ((irel @ X6 @ X8))) | (((irel @ X1 @ X5)) = $false) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))) @ (sK10 @ X6)))) | ($false = ((irel @ X5 @ X4))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((sK2 @ X8))) | ($false = ((irel @ X2 @ X6)))) )),
  inference(not_proxy_clausification,[],[f202])).
thf(f204,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($false = ((sK1 @ (sK9 @ X5)))) | ($true = ((sK2 @ X8))) | ($true = ((sK2 @ X4))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X6 @ X8))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X6 @ Y0)))) @ (sK10 @ X6)))) | (((irel @ X1 @ X5)) = $false) | ($false = ((irel @ X2 @ X6)))) )),
  inference(not_proxy_clausification,[],[f203])).
thf(f205,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((irel @ sK3 @ X2)) = $false) | ($false = ((sK1 @ (sK9 @ X5)))) | ($true = ((sK2 @ X8))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ X6 @ X8))) | (((irel @ X1 @ X5)) = $false) | ($true = ((sK2 @ X4))) | ($false = (((sK1 @ (sK10 @ X6)) | (~ (irel @ X6 @ (sK10 @ X6))))))) )),
  inference(beta-eta_normalization,[],[f204])).
thf(f207,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((irel @ X1 @ X5)) = $false) | ($true = ((sK2 @ X4))) | ($false = ((sK1 @ (sK10 @ X6)))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ X6 @ X8))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($false = ((irel @ X5 @ X4))) | ($true = ((sK2 @ X8)))) )),
  inference(or_proxy_clausification,[],[f205])).
thf(f251,plain,(
  ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1))))))))))))))),
  inference(beta-eta_normalization,[],[f89])).
thf(f252,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1))))))))))))))),
  inference(not_proxy_clausification,[],[f251])).
thf(f253,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))))) @ sK14))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1))))))))))))))),
  inference(sigma_proxy_clausification,[],[f252])).
thf(f254,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1)))))))))))) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))))) @ sK14)))),
  inference(not_proxy_clausification,[],[f253])).
thf(f255,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((sK2 @ Y4) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y5 : $i]: ((sK1 @ Y5) | (~ (irel @ Y2 @ Y5))))))) | (~ (irel @ Y2 @ Y4))) & ((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK2 @ Y5))))) | (sK1 @ Y1)) | (~ (irel @ Y0 @ Y3))) | (~ (irel @ Y3 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))))) @ sK14))) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (irel @ Y2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y2 @ Y3))))))) | (sK1 @ Y1)))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (sK2 @ Y1)) | (~ (irel @ Y0 @ Y2))) | (~ (irel @ Y2 @ Y1)))))))))) @ sK15)))),
  inference(sigma_proxy_clausification,[],[f254])).
thf(f256,plain,(
  ($false = (((~ (irel @ sK3 @ sK15)) | ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (irel @ Y1 @ Y0))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ sK14 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ sK14 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ sK14)))))))))))))),
  inference(beta-eta_normalization,[],[f255])).
thf(f257,plain,(
  ($false = (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0)))))) & (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (irel @ Y1 @ Y0)))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ sK14 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ sK14 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ sK14)))))))))))))),
  inference(or_proxy_clausification,[],[f256])).
thf(f350,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (irel @ Y1 @ Y0))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ sK14 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ sK14 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ sK14))))))))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0))))))))),
  inference(and_proxy_clausification,[],[f257])).
thf(f351,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ sK14 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ sK14 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ sK14))))))))))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (irel @ Y1 @ Y0)))))) @ sK20))) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0))))))))),
  inference(sigma_proxy_clausification,[],[f350])).
thf(f352,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (irel @ Y1 @ Y0)))))) @ sK20))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ sK14 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ sK14 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ sK14)))))))))) @ sK21)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0))))))))),
  inference(sigma_proxy_clausification,[],[f351])).
thf(f353,plain,(
  ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((sK2 @ Y3) | (~ (irel @ sK14 @ Y1))) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK1 @ Y4) | (~ (irel @ Y1 @ Y4))))))) | (~ (irel @ Y1 @ Y3))) & ((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK2 @ Y4))))) | (sK1 @ Y0)) | (~ (irel @ sK14 @ Y2))) | (~ (irel @ Y2 @ Y0)))) | (~ (irel @ sK3 @ sK14)))))))))) @ sK21)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (irel @ Y1 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2))))))) | (sK1 @ Y0))))) @ sK22))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (sK2 @ Y0)) | (~ (irel @ sK15 @ Y1))) | (~ (irel @ Y1 @ Y0)))))) @ sK20)))),
  inference(sigma_proxy_clausification,[],[f352])).
thf(f354,plain,(
  (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y1))) | (~ (irel @ Y1 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ Y0))) | (~ (irel @ Y0 @ sK20))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ Y0 @ sK22)) | (~ (irel @ sK15 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (sK1 @ sK22))))))),
  inference(beta-eta_normalization,[],[f353])).
thf(f355,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y1))) | (~ (irel @ Y1 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) @ sK23))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ Y0))) | (~ (irel @ Y0 @ sK20))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ Y0 @ sK22)) | (~ (irel @ sK15 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (sK1 @ sK22))))))),
  inference(sigma_proxy_clausification,[],[f354])).
thf(f356,plain,(
  ((((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ Y0))) | (~ (irel @ Y0 @ sK20)))) @ sK24)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y1))) | (~ (irel @ Y1 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) @ sK23))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((~ (irel @ Y0 @ sK22)) | (~ (irel @ sK15 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (sK1 @ sK22))))))),
  inference(sigma_proxy_clausification,[],[f355])).
thf(f357,plain,(
  ($false = (((^[Y0 : $i]: ((((~ (irel @ Y0 @ sK22)) | (~ (irel @ sK15 @ Y0))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) | (sK1 @ sK22))) @ sK25))) | ((((^[Y0 : $i]: ((((~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ Y0))) | (~ (irel @ Y0 @ sK20)))) @ sK24)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((sK2 @ Y2) | (~ (irel @ sK14 @ Y0))) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y0 @ Y3))))))) | (~ (irel @ Y0 @ Y2))) & ((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK2 @ Y3))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y1))) | (~ (irel @ Y1 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) @ sK23)))),
  inference(sigma_proxy_clausification,[],[f356])).
thf(f358,plain,(
  ($false = (((((~ (irel @ sK25 @ sK22)) | (~ (irel @ sK15 @ sK25))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0))))))) | (sK1 @ sK22)))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ sK24))) | (~ (irel @ sK24 @ sK20))))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) = $false)),
  inference(beta-eta_normalization,[],[f357])).
thf(f359,plain,(
  ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ sK24))) | (~ (irel @ sK24 @ sK20))))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) = $false) | (((sK1 @ sK22)) = $false)),
  inference(or_proxy_clausification,[],[f358])).
thf(f360,plain,(
  (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) = $false) | ($false = ((((~ (irel @ sK25 @ sK22)) | (~ (irel @ sK15 @ sK25))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0))))))))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ sK24))) | (~ (irel @ sK24 @ sK20)))))),
  inference(or_proxy_clausification,[],[f358])).
thf(f361,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ sK24))) | (~ (irel @ sK24 @ sK20))))) | ($false = ((((~ (irel @ sK25 @ sK22)) | (~ (irel @ sK15 @ sK25))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0)))))))))),
  inference(sigma_proxy_clausification,[],[f360])).
thf(f363,plain,(
  ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ sK24))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26))) | ($false = ((((~ (irel @ sK25 @ sK22)) | (~ (irel @ sK15 @ sK25))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0)))))))))),
  inference(or_proxy_clausification,[],[f361])).
thf(f365,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26))) | ($false = ((((~ (irel @ sK25 @ sK22)) | (~ (irel @ sK15 @ sK25))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0))))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20))))),
  inference(or_proxy_clausification,[],[f363])).
thf(f366,plain,(
  ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0)))))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26)))),
  inference(or_proxy_clausification,[],[f365])).
thf(f723,plain,(
  ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0))))))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20))))),
  inference(not_proxy_clausification,[],[f366])).
thf(f724,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0)))) @ X1))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20))))) )),
  inference(pi_proxy_clausification,[],[f723])).
thf(f726,plain,(
  ( ! [X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))))) | ($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0)))) @ X1))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26)))) )),
  inference(or_proxy_clausification,[],[f724])).
thf(f727,plain,(
  ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0))))))) | ($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0)))) @ X1))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26)))) )),
  inference(not_proxy_clausification,[],[f726])).
thf(f728,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK26))) | ($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))) @ X2))) | ($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK25 @ Y0)))) @ X1)))) )),
  inference(pi_proxy_clausification,[],[f727])).
thf(f729,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((sK2 @ X1) | (~ (irel @ sK25 @ X1))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ sK23 @ Y1))))))) | (~ (irel @ sK23 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK26 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21)))) | (~ (irel @ sK3 @ sK14))))))) | ($true = (((sK1 @ X2) | (~ (irel @ sK24 @ X2)))))) )),
  inference(beta-eta_normalization,[],[f728])).
thf(f730,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((sK1 @ X2) | (~ (irel @ sK24 @ X2))))) | ($true = ((~ (irel @ sK25 @ X1)))) | ($true = ((sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ sK23 @ Y1))))))) | (~ (irel @ sK23 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK26 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) )),
  inference(or_proxy_clausification,[],[f729])).
thf(f731,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((~ (irel @ sK24 @ X2)))) | ($true = ((~ (irel @ sK25 @ X1)))) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ X2))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ sK23 @ Y1))))))) | (~ (irel @ sK23 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK26 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) )),
  inference(or_proxy_clausification,[],[f730])).
thf(f732,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((~ (irel @ sK25 @ X1)))) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK24 @ X2))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ sK23 @ Y1))))))) | (~ (irel @ sK23 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK26 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21)))) | (~ (irel @ sK3 @ sK14))))))) | ($true = ((sK2 @ X1)))) )),
  inference(not_proxy_clausification,[],[f731])).
thf(f733,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X1))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ sK23 @ Y1))))))) | (~ (irel @ sK23 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK26 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21)))) | (~ (irel @ sK3 @ sK14))))))) | ($false = ((irel @ sK25 @ X1))) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK24 @ X2)))) )),
  inference(not_proxy_clausification,[],[f732])).
thf(f734,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ sK23 @ Y1))))))) | (~ (irel @ sK23 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK26 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21)))) | (~ (irel @ sK3 @ sK14)))) @ sK31)) = $false) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK24 @ X2))) | ($true = ((sK2 @ X1))) | ($false = ((irel @ sK25 @ X1)))) )),
  inference(sigma_proxy_clausification,[],[f733])).
thf(f735,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK1 @ X2))) | ($false = ((irel @ sK25 @ X1))) | ($false = ((irel @ sK24 @ X2))) | ($true = ((sK2 @ X1))) | ($false = (((((((sK2 @ sK31) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))) | (~ (irel @ sK23 @ sK31))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) )),
  inference(beta-eta_normalization,[],[f734])).
thf(f737,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK24 @ X2))) | ($true = ((sK2 @ X1))) | ($false = ((irel @ sK25 @ X1))) | ($true = ((sK1 @ X2))) | ($false = ((((((sK2 @ sK31) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))) | (~ (irel @ sK23 @ sK31))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21))))))) )),
  inference(or_proxy_clausification,[],[f735])).
thf(f738,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK24 @ X2))) | ($false = ((irel @ sK25 @ X1))) | ($false = (((((sK2 @ sK31) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))) | (~ (irel @ sK23 @ sK31))))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21))))) | ($true = ((sK1 @ X2))) | ($true = ((sK2 @ X1)))) )),
  inference(and_proxy_clausification,[],[f737])).
thf(f740,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))) | (~ (irel @ sK26 @ sK21))))) | ($false = ((irel @ sK25 @ X1))) | (((((sK2 @ sK31) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))))))) = $false) | ($true = ((sK2 @ X1))) | ($false = ((irel @ sK24 @ X2))) | ($true = ((sK1 @ X2)))) )),
  inference(or_proxy_clausification,[],[f738])).
thf(f742,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK25 @ X1))) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ X2))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK26))))) | (((((sK2 @ sK31) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))))))) = $false) | ($false = ((irel @ sK24 @ X2)))) )),
  inference(or_proxy_clausification,[],[f740])).
thf(f744,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK2 @ X1))) | ($false = ((irel @ sK24 @ X2))) | ($false = ((irel @ sK25 @ X1))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)))) | (((((sK2 @ sK31) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))))))) = $false) | ($true = ((sK1 @ X2)))) )),
  inference(or_proxy_clausification,[],[f742])).
thf(f746,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK24 @ X2))) | ($true = ((sK1 @ X2))) | (((((sK2 @ sK31) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))))))) = $false) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))))) | ($true = ((sK2 @ X1))) | ($false = ((irel @ sK25 @ X1)))) )),
  inference(or_proxy_clausification,[],[f744])).
thf(f747,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK1 @ X2))) | ($true = ((sK2 @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))))) | ($false = ((irel @ sK24 @ X2))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))))))) | ($false = ((irel @ sK25 @ X1)))) )),
  inference(or_proxy_clausification,[],[f746])).
thf(f762,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK25 @ X1))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))))))) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK24 @ X2))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))))))) )),
  inference(not_proxy_clausification,[],[f747])).
thf(f763,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0)))))) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK25 @ X1))) | ($false = ((irel @ sK24 @ X2))) | ($true = ((sK2 @ X1)))) )),
  inference(not_proxy_clausification,[],[f762])).
thf(f764,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0)))))) | ($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))) @ X3))) | ($false = ((irel @ sK25 @ X1))) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK24 @ X2)))) )),
  inference(pi_proxy_clausification,[],[f763])).
thf(f765,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))) @ X3))) | ($true = ((sK1 @ X2))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK26 @ Y0)) | (sK2 @ Y0))) @ X4))) | ($false = ((irel @ sK24 @ X2))) | ($false = ((irel @ sK25 @ X1))) | ($true = ((sK2 @ X1)))) )),
  inference(pi_proxy_clausification,[],[f764])).
thf(f766,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK24 @ X2))) | ($true = (((sK1 @ X3) | (~ (irel @ sK23 @ X3))))) | ($true = ((sK2 @ X1))) | ($true = (((~ (irel @ sK26 @ X4)) | (sK2 @ X4)))) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK25 @ X1)))) )),
  inference(beta-eta_normalization,[],[f765])).
thf(f767,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = (((~ (irel @ sK26 @ X4)) | (sK2 @ X4)))) | (((~ (irel @ sK23 @ X3))) = $true) | ($true = ((sK2 @ X1))) | ($false = ((irel @ sK24 @ X2))) | ($true = ((sK1 @ X2))) | ($true = ((sK1 @ X3))) | ($false = ((irel @ sK25 @ X1)))) )),
  inference(or_proxy_clausification,[],[f766])).
thf(f768,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK1 @ X3))) | ($false = ((irel @ sK25 @ X1))) | ($true = ((sK2 @ X4))) | ($true = ((~ (irel @ sK26 @ X4)))) | ($false = ((irel @ sK24 @ X2))) | (((~ (irel @ sK23 @ X3))) = $true) | ($true = ((sK2 @ X1))) | ($true = ((sK1 @ X2)))) )),
  inference(or_proxy_clausification,[],[f767])).
thf(f769,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK1 @ X3))) | (((~ (irel @ sK23 @ X3))) = $true) | ($true = ((sK2 @ X4))) | ($true = ((sK2 @ X1))) | ($false = ((irel @ sK24 @ X2))) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK26 @ X4))) | ($false = ((irel @ sK25 @ X1)))) )),
  inference(not_proxy_clausification,[],[f768])).
thf(f770,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK1 @ X3))) | ($true = ((sK1 @ X2))) | ($false = ((irel @ sK24 @ X2))) | ($false = ((irel @ sK26 @ X4))) | ($false = ((irel @ sK25 @ X1))) | ($true = ((sK2 @ X1))) | ($false = ((irel @ sK23 @ X3))) | ($true = ((sK2 @ X4)))) )),
  inference(not_proxy_clausification,[],[f769])).
thf(f1441,plain,(
  (((sK1 @ sK22)) = $false) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20)) | (~ (irel @ sK15 @ sK24))))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) = $false)),
  inference(or_proxy_clausification,[],[f359])).
thf(f1443,plain,(
  (((sK1 @ sK22)) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))))) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20))))),
  inference(or_proxy_clausification,[],[f1441])).
thf(f1444,plain,(
  (((sK1 @ sK22)) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK24 @ Y0)))))) | (sK2 @ sK20)))) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK39)))),
  inference(sigma_proxy_clausification,[],[f1443])).
thf(f1445,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((sK2 @ Y1) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ sK23 @ Y2))))))) | (~ (irel @ sK23 @ Y1))) & ((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK2 @ Y2))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ Y0))) | (~ (irel @ Y0 @ sK21)))) | (~ (irel @ sK3 @ sK14)))))) @ sK39))) | (((sK1 @ sK22)) = $false) | ($false = ((sK2 @ sK20)))),
  inference(or_proxy_clausification,[],[f1444])).
thf(f1541,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ sK23 @ Y1))))))) | (~ (irel @ sK23 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK39 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK39))) | (~ (irel @ sK39 @ sK21)))) | (~ (irel @ sK3 @ sK14))))))) | (((sK1 @ sK22)) = $false) | ($false = ((sK2 @ sK20)))),
  inference(beta-eta_normalization,[],[f1445])).
thf(f1542,plain,(
  ($false = (((^[Y0 : $i]: ((((((sK2 @ Y0) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ sK23 @ Y1))))))) | (~ (irel @ sK23 @ Y0))) & ((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK39 @ Y1)) | (sK2 @ Y1))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK39))) | (~ (irel @ sK39 @ sK21)))) | (~ (irel @ sK3 @ sK14)))) @ sK41))) | (((sK1 @ sK22)) = $false) | ($false = ((sK2 @ sK20)))),
  inference(sigma_proxy_clausification,[],[f1541])).
thf(f1543,plain,(
  ($false = (((((((sK2 @ sK41) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))) | (~ (irel @ sK23 @ sK41))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK39 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK39))) | (~ (irel @ sK39 @ sK21)))) | (~ (irel @ sK3 @ sK14))))) | (((sK1 @ sK22)) = $false) | ($false = ((sK2 @ sK20)))),
  inference(beta-eta_normalization,[],[f1542])).
thf(f1545,plain,(
  ($false = ((((((sK2 @ sK41) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))) | (~ (irel @ sK23 @ sK41))) & ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK39 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK39))) | (~ (irel @ sK39 @ sK21)))))) | (((sK1 @ sK22)) = $false) | ($false = ((sK2 @ sK20)))),
  inference(or_proxy_clausification,[],[f1543])).
thf(f1546,plain,(
  ($false = (((((sK2 @ sK41) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))) | (~ (irel @ sK23 @ sK41))))) | ($false = ((sK2 @ sK20))) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK39 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK39))) | (~ (irel @ sK39 @ sK21))))) | (((sK1 @ sK22)) = $false)),
  inference(and_proxy_clausification,[],[f1545])).
thf(f1548,plain,(
  ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK39 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK39))) | (~ (irel @ sK39 @ sK21))))) | ($false = ((((sK2 @ sK41) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))))) | ($false = ((sK2 @ sK20))) | (((sK1 @ sK22)) = $false)),
  inference(or_proxy_clausification,[],[f1546])).
thf(f1550,plain,(
  (((sK1 @ sK22)) = $false) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK39 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)) | (~ (irel @ sK14 @ sK39))))) | ($false = ((sK2 @ sK20))) | ($false = ((((sK2 @ sK41) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0)))))))))),
  inference(or_proxy_clausification,[],[f1548])).
thf(f1552,plain,(
  ($false = ((((sK2 @ sK41) | (~ (irel @ sK14 @ sK23))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK23 @ Y0))))))))) | ($false = ((sK2 @ sK20))) | (((sK1 @ sK22)) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK39 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21))))),
  inference(or_proxy_clausification,[],[f1550])).
thf(f1554,plain,(
  ($false = (((sK2 @ sK41) | (~ (irel @ sK14 @ sK23))))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK39 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)))) | ($false = ((sK2 @ sK20))) | (((sK1 @ sK22)) = $false)),
  inference(or_proxy_clausification,[],[f1552])).
thf(f1556,plain,(
  (((sK1 @ sK22)) = $false) | ($false = ((sK2 @ sK41))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK39 @ Y0)) | (sK2 @ Y0))))) | (sK1 @ sK21)))) | ($false = ((sK2 @ sK20)))),
  inference(or_proxy_clausification,[],[f1554])).
thf(f1557,plain,(
  (((sK1 @ sK22)) = $false) | ($false = ((sK2 @ sK20))) | ($false = ((sK1 @ sK21))) | ($false = ((sK2 @ sK41)))),
  inference(or_proxy_clausification,[],[f1556])).
thf(f1802,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | ($true = ((sK1 @ X4))) | ($false = ((irel @ X2 @ X7))) | (((irel @ X1 @ X5)) = $false) | (((irel @ X7 @ X3)) = $false) | ($false = ((sK2 @ (sK4 @ X5)))) | ($true = ((sK1 @ X3))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X5 @ X4))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0))))) )),
  inference(forward_demodulation,[],[f143,f59])).
thf(f1807,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((sK2 @ X8))) | (((irel @ X1 @ X5)) = $false) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X6 @ X8))) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK2 @ X4))) | ($false = ((sK1 @ (sK9 @ X5)))) | ($false = ((irel @ X2 @ X6)))) )),
  inference(forward_demodulation,[],[f207,f59])).
thf(f1819,definition,(
  spl46_2 <=> ($false = ((sK2 @ sK19)))),
  introduced(definition,[new_symbols(definition,[spl46_2])],[avatar_definition])).
thf(f1820,plain,(
  ($false != ((sK2 @ sK19))) | spl46_2),
  inference(avatar_component_clause,[],[f1819])).
thf(f1821,plain,(
  ($false = ((sK2 @ sK19))) | ~spl46_2),
  inference(avatar_component_clause,[],[f1819])).
thf(f1823,definition,(
  spl46_3 <=> ($true = ((irel @ sK3 @ sK15)))),
  introduced(definition,[new_symbols(definition,[spl46_3])],[avatar_definition])).
thf(f1824,plain,(
  ($true != ((irel @ sK3 @ sK15))) | spl46_3),
  inference(avatar_component_clause,[],[f1823])).
thf(f1825,plain,(
  ($true = ((irel @ sK3 @ sK15))) | ~spl46_3),
  inference(avatar_component_clause,[],[f1823])).
thf(f1866,definition,(
  spl46_10 <=> ($true = ((irel @ sK3 @ sK14)))),
  introduced(definition,[new_symbols(definition,[spl46_10])],[avatar_definition])).
thf(f1867,plain,(
  ($true != ((irel @ sK3 @ sK14))) | spl46_10),
  inference(avatar_component_clause,[],[f1866])).
thf(f1868,plain,(
  ($true = ((irel @ sK3 @ sK14))) | ~spl46_10),
  inference(avatar_component_clause,[],[f1866])).
thf(f1871,definition,(
  spl46_11 <=> ! [X1 : $i] : (($false = ((irel @ sK24 @ X1))) | ($true = ((sK1 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl46_11])],[avatar_definition])).
thf(f1872,plain,(
  ( ! [X1 : $i] : (($true = ((sK1 @ X1))) | ($false = ((irel @ sK24 @ X1)))) ) | ~spl46_11),
  inference(avatar_component_clause,[],[f1871])).
thf(f1874,definition,(
  spl46_12 <=> ! [X2 : $i] : (($true = ((sK2 @ X2))) | (((irel @ sK26 @ X2)) = $false))),
  introduced(definition,[new_symbols(definition,[spl46_12])],[avatar_definition])).
thf(f1875,plain,(
  ( ! [X2 : $i] : (($true = ((sK2 @ X2))) | (((irel @ sK26 @ X2)) = $false)) ) | ~spl46_12),
  inference(avatar_component_clause,[],[f1874])).
thf(f1886,definition,(
  spl46_15 <=> ($false = ((sK1 @ sK21)))),
  introduced(definition,[new_symbols(definition,[spl46_15])],[avatar_definition])).
thf(f1888,plain,(
  ($false = ((sK1 @ sK21))) | ~spl46_15),
  inference(avatar_component_clause,[],[f1886])).
thf(f1903,definition,(
  spl46_18 <=> ! [X2 : $i] : (($true = ((sK1 @ X2))) | ($false = ((irel @ sK23 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl46_18])],[avatar_definition])).
thf(f1904,plain,(
  ( ! [X2 : $i] : (($false = ((irel @ sK23 @ X2))) | ($true = ((sK1 @ X2)))) ) | ~spl46_18),
  inference(avatar_component_clause,[],[f1903])).
thf(f1958,definition,(
  spl46_25 <=> ($false = ((sK2 @ sK20)))),
  introduced(definition,[new_symbols(definition,[spl46_25])],[avatar_definition])).
thf(f1960,plain,(
  ($false = ((sK2 @ sK20))) | ~spl46_25),
  inference(avatar_component_clause,[],[f1958])).
thf(f2012,definition,(
  spl46_30 <=> ! [X1 : $i] : (($true = ((sK2 @ X1))) | ($false = ((irel @ sK25 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl46_30])],[avatar_definition])).
thf(f2013,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK25 @ X1))) | ($true = ((sK2 @ X1)))) ) | ~spl46_30),
  inference(avatar_component_clause,[],[f2012])).
thf(f2016,plain,(
  spl46_12 | spl46_11 | spl46_30 | spl46_18),
  inference(avatar_split_clause,[],[f770,f1903,f2012,f1871,f1874])).
thf(f2226,definition,(
  spl46_50 <=> (((sK1 @ sK22)) = $false)),
  introduced(definition,[new_symbols(definition,[spl46_50])],[avatar_definition])).
thf(f2227,plain,(
  (((sK1 @ sK22)) != $false) | spl46_50),
  inference(avatar_component_clause,[],[f2226])).
thf(f2228,plain,(
  (((sK1 @ sK22)) = $false) | ~spl46_50),
  inference(avatar_component_clause,[],[f2226])).
thf(f2259,definition,(
  spl46_54 <=> ($false = ((sK2 @ sK41)))),
  introduced(definition,[new_symbols(definition,[spl46_54])],[avatar_definition])).
thf(f2261,plain,(
  ($false = ((sK2 @ sK41))) | ~spl46_54),
  inference(avatar_component_clause,[],[f2259])).
thf(f2263,plain,(
  spl46_15 | spl46_25 | spl46_50 | spl46_54),
  inference(avatar_split_clause,[],[f1557,f2259,f2226,f1958,f1886])).
thf(f2358,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : ((((irel @ X7 @ X3)) = $false) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | (((irel @ X1 @ X5)) = $false) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ($true = ((sK1 @ X4))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X2 @ X7))) | ($true = ((sK1 @ X3)))) )),
  inference(forward_demodulation,[],[f1802,f59])).
thf(f2359,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true = ((sK1 @ X4))) | ($true = ((sK1 @ X3))) | ($false = ((irel @ sK3 @ X1))) | ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ X2 @ X7))) | (((irel @ X1 @ X5)) = $false) | (((irel @ sK3 @ X2)) = $false) | (((irel @ X7 @ X3)) = $false)) )),
  inference(duplicate_literal_removal,[],[f2358])).
thf(f2364,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : ((((irel @ sK3 @ X2)) = $false) | ($true = ((sK2 @ X8))) | ($false = ((irel @ X5 @ X4))) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((irel @ X6 @ X8))) | ($true = ((sK2 @ X4))) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | (((irel @ X1 @ X5)) = $false) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X2 @ X6)))) )),
  inference(forward_demodulation,[],[f1807,f59])).
thf(f2365,plain,(
  ( ! [X2 : $i,X1 : $i,X8 : $i,X6 : $i,X4 : $i,X5 : $i] : (($true = ((sK2 @ X8))) | (((irel @ X1 @ X5)) = $false) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X6 @ X8))) | ($true = ((sK2 @ X4))) | ($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ X2 @ X6)))) )),
  inference(duplicate_literal_removal,[],[f2364])).
thf(f2374,definition,(
  spl46_66 <=> ! [X4 : $i,X5 : $i,X1 : $i] : (($true = ((sK1 @ X4))) | (((irel @ X1 @ X5)) = $false) | ($false = ((irel @ X5 @ X4))) | ($false = ((irel @ sK3 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl46_66])],[avatar_definition])).
thf(f2375,plain,(
  ( ! [X1 : $i,X4 : $i,X5 : $i] : (($false = ((irel @ sK3 @ X1))) | ($false = ((irel @ X5 @ X4))) | ($true = ((sK1 @ X4))) | (((irel @ X1 @ X5)) = $false)) ) | ~spl46_66),
  inference(avatar_component_clause,[],[f2374])).
thf(f2377,definition,(
  spl46_67 <=> ($false = ((sK2 @ (d2unsorted @ d_unsorted_0))))),
  introduced(definition,[new_symbols(definition,[spl46_67])],[avatar_definition])).
thf(f2379,plain,(
  ($false = ((sK2 @ (d2unsorted @ d_unsorted_0)))) | ~spl46_67),
  inference(avatar_component_clause,[],[f2377])).
thf(f2381,definition,(
  spl46_68 <=> ! [X6 : $i,X2 : $i,X8 : $i] : (($false = ((irel @ X2 @ X6))) | ($true = ((sK2 @ X8))) | ($false = ((irel @ X6 @ X8))) | (((irel @ sK3 @ X2)) = $false))),
  introduced(definition,[new_symbols(definition,[spl46_68])],[avatar_definition])).
thf(f2382,plain,(
  ( ! [X2 : $i,X8 : $i,X6 : $i] : (($false = ((irel @ X2 @ X6))) | (((irel @ sK3 @ X2)) = $false) | ($true = ((sK2 @ X8))) | ($false = ((irel @ X6 @ X8)))) ) | ~spl46_68),
  inference(avatar_component_clause,[],[f2381])).
thf(f2384,definition,(
  spl46_69 <=> ($false = ((sK1 @ (d2unsorted @ d_unsorted_0))))),
  introduced(definition,[new_symbols(definition,[spl46_69])],[avatar_definition])).
thf(f2386,plain,(
  ($false = ((sK1 @ (d2unsorted @ d_unsorted_0)))) | ~spl46_69),
  inference(avatar_component_clause,[],[f2384])).
thf(f2396,plain,(
  spl46_67 | spl46_66 | spl46_66),
  inference(avatar_split_clause,[],[f2359,f2374,f2374,f2377])).
thf(f2401,plain,(
  spl46_69 | spl46_68 | spl46_68),
  inference(avatar_split_clause,[],[f2365,f2381,f2381,f2384])).
thf(f2423,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl46_25),
  inference(constrained_superposition,[],[f1960,f63])).
thf(f2429,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ sK3 @ X0)))) ) | ~spl46_3),
  inference(constrained_superposition,[],[f1825,f63])).
thf(f2437,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((irel @ X0 @ X1)))) ) | ~spl46_3),
  inference(constrained_superposition,[],[f2429,f63])).
thf(f2449,plain,(
  ( ! [X2 : $i,X8 : $i,X6 : $i] : ((((irel @ sK3 @ X2)) = $false) | ($true = $false) | ($false = ((irel @ X6 @ X8))) | ($false = ((irel @ X2 @ X6)))) ) | (~spl46_25 | ~spl46_68)),
  inference(forward_demodulation,[],[f2382,f2423])).
thf(f2450,plain,(
  ( ! [X2 : $i,X8 : $i,X6 : $i] : (($false = ((irel @ X6 @ X8))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X2 @ X6)))) ) | (~spl46_25 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2449])).
thf(f2451,plain,(
  ( ! [X2 : $i,X8 : $i,X6 : $i] : (($true = $false) | ($false = ((irel @ X2 @ X6))) | ($false = ((irel @ X6 @ X8)))) ) | (~spl46_3 | ~spl46_25 | ~spl46_68)),
  inference(forward_demodulation,[],[f2450,f2429])).
thf(f2452,plain,(
  ( ! [X2 : $i,X8 : $i,X6 : $i] : (($false = ((irel @ X6 @ X8))) | ($false = ((irel @ X2 @ X6)))) ) | (~spl46_3 | ~spl46_25 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2451])).
thf(f2454,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((irel @ X0 @ X1))) | ($true = $false) | ($true = ((sK1 @ X2))) | (((irel @ X1 @ X2)) = $false)) ) | (~spl46_3 | ~spl46_66)),
  inference(constrained_superposition,[],[f2375,f2437])).
thf(f2455,plain,(
  ( ! [X2 : $i,X0 : $i,X1 : $i] : (($false = ((irel @ X0 @ X1))) | (((irel @ X1 @ X2)) = $false) | ($true = ((sK1 @ X2)))) ) | (~spl46_3 | ~spl46_66)),
  inference(trivial_inequality_removal,[],[f2454])).
thf(f2457,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2)) = $false) | ($true = ((sK1 @ X2))) | ($true = $false)) ) | (~spl46_3 | ~spl46_66)),
  inference(forward_demodulation,[],[f2455,f2437])).
thf(f2458,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2)) = $false) | ($true = ((sK1 @ X2)))) ) | (~spl46_3 | ~spl46_66)),
  inference(trivial_inequality_removal,[],[f2457])).
thf(f2461,plain,(
  ( ! [X2 : $i] : (($true = ((sK1 @ X2))) | ($true = $false)) ) | (~spl46_3 | ~spl46_66)),
  inference(forward_demodulation,[],[f2458,f2437])).
thf(f2462,plain,(
  ( ! [X2 : $i] : (($true = ((sK1 @ X2)))) ) | (~spl46_3 | ~spl46_66)),
  inference(trivial_inequality_removal,[],[f2461])).
thf(f2465,plain,(
  ( ! [X2 : $i,X6 : $i] : (($true = $false) | ($false = ((irel @ X2 @ X6)))) ) | (~spl46_3 | ~spl46_25 | ~spl46_68)),
  inference(forward_demodulation,[],[f2452,f2437])).
thf(f2466,plain,(
  ( ! [X2 : $i,X6 : $i] : (($false = ((irel @ X2 @ X6)))) ) | (~spl46_3 | ~spl46_25 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2465])).
thf(f2467,plain,(
  ($true = $false) | (~spl46_3 | ~spl46_25 | ~spl46_68)),
  inference(forward_demodulation,[],[f2466,f2437])).
thf(f2468,plain,(
  $false | (~spl46_3 | ~spl46_25 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2467])).
thf(f2469,plain,(
  ~spl46_3 | ~spl46_25 | ~spl46_68),
  inference(avatar_contradiction_clause,[],[f2468])).
thf(f2470,plain,(
  ($true = $false) | (~spl46_3 | ~spl46_50 | ~spl46_66)),
  inference(forward_demodulation,[],[f2228,f2462])).
thf(f2471,plain,(
  $false | (~spl46_3 | ~spl46_50 | ~spl46_66)),
  inference(trivial_inequality_removal,[],[f2470])).
thf(f2472,plain,(
  ~spl46_3 | ~spl46_50 | ~spl46_66),
  inference(avatar_contradiction_clause,[],[f2471])).
thf(f2475,plain,(
  ($true = $false) | (~spl46_3 | ~spl46_15 | ~spl46_66)),
  inference(forward_demodulation,[],[f1888,f2462])).
thf(f2476,plain,(
  $false | (~spl46_3 | ~spl46_15 | ~spl46_66)),
  inference(trivial_inequality_removal,[],[f2475])).
thf(f2477,plain,(
  ~spl46_3 | ~spl46_15 | ~spl46_66),
  inference(avatar_contradiction_clause,[],[f2476])).
thf(f2478,plain,(
  ( ! [X2 : $i,X8 : $i,X6 : $i] : (($false = ((irel @ X6 @ X8))) | ($true = $false) | (((irel @ sK3 @ X2)) = $false) | ($true = ((sK2 @ X8)))) ) | (~spl46_3 | ~spl46_68)),
  inference(forward_demodulation,[],[f2382,f2437])).
thf(f2479,plain,(
  ( ! [X2 : $i,X8 : $i,X6 : $i] : ((((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ X6 @ X8))) | ($true = ((sK2 @ X8)))) ) | (~spl46_3 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2478])).
thf(f2480,plain,(
  ( ! [X8 : $i,X6 : $i] : (($true = $false) | ($true = ((sK2 @ X8))) | ($false = ((irel @ X6 @ X8)))) ) | (~spl46_3 | ~spl46_68)),
  inference(forward_demodulation,[],[f2479,f2437])).
thf(f2481,plain,(
  ( ! [X8 : $i,X6 : $i] : (($false = ((irel @ X6 @ X8))) | ($true = ((sK2 @ X8)))) ) | (~spl46_3 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2480])).
thf(f2482,plain,(
  ( ! [X8 : $i] : (($true = ((sK2 @ X8))) | ($true = $false)) ) | (~spl46_3 | ~spl46_68)),
  inference(forward_demodulation,[],[f2481,f2437])).
thf(f2483,plain,(
  ( ! [X8 : $i] : (($true = ((sK2 @ X8)))) ) | (~spl46_3 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2482])).
thf(f2485,plain,(
  ( ! [X1 : $i] : (($true = $false) | ($true = ((sK2 @ X1)))) ) | (~spl46_3 | ~spl46_30)),
  inference(forward_demodulation,[],[f2013,f2437])).
thf(f2486,plain,(
  ( ! [X1 : $i] : (($true = ((sK2 @ X1)))) ) | (~spl46_3 | ~spl46_30)),
  inference(trivial_inequality_removal,[],[f2485])).
thf(f2488,plain,(
  ($true = $false) | (~spl46_3 | ~spl46_54 | ~spl46_68)),
  inference(forward_demodulation,[],[f2261,f2483])).
thf(f2489,plain,(
  $false | (~spl46_3 | ~spl46_54 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2488])).
thf(f2490,plain,(
  ~spl46_3 | ~spl46_54 | ~spl46_68),
  inference(avatar_contradiction_clause,[],[f2489])).
thf(f2494,plain,(
  ($true = $false) | (~spl46_3 | ~spl46_67 | ~spl46_68)),
  inference(forward_demodulation,[],[f2379,f2483])).
thf(f2495,plain,(
  $false | (~spl46_3 | ~spl46_67 | ~spl46_68)),
  inference(trivial_inequality_removal,[],[f2494])).
thf(f2496,plain,(
  ~spl46_3 | ~spl46_67 | ~spl46_68),
  inference(avatar_contradiction_clause,[],[f2495])).
thf(f2513,plain,(
  ($true = $false) | (~spl46_3 | ~spl46_30 | ~spl46_67)),
  inference(forward_demodulation,[],[f2379,f2486])).
thf(f2514,plain,(
  $false | (~spl46_3 | ~spl46_30 | ~spl46_67)),
  inference(trivial_inequality_removal,[],[f2513])).
thf(f2515,plain,(
  ~spl46_3 | ~spl46_30 | ~spl46_67),
  inference(avatar_contradiction_clause,[],[f2514])).
thf(f2516,plain,(
  ( ! [X2 : $i] : (($true = ((sK1 @ X2))) | ($true = $false)) ) | (~spl46_3 | ~spl46_18)),
  inference(forward_demodulation,[],[f1904,f2437])).
thf(f2517,plain,(
  ( ! [X2 : $i] : (($true = ((sK1 @ X2)))) ) | (~spl46_3 | ~spl46_18)),
  inference(trivial_inequality_removal,[],[f2516])).
thf(f2518,plain,(
  ( ! [X0 : $i] : (($false != ((sK1 @ X0)))) ) | spl46_50),
  inference(constrained_superposition,[],[f2227,f63])).
thf(f2540,plain,(
  ($true = $false) | (~spl46_3 | ~spl46_18 | ~spl46_69)),
  inference(forward_demodulation,[],[f2386,f2517])).
thf(f2541,plain,(
  $false | (~spl46_3 | ~spl46_18 | ~spl46_69)),
  inference(trivial_inequality_removal,[],[f2540])).
thf(f2542,plain,(
  ~spl46_3 | ~spl46_18 | ~spl46_69),
  inference(avatar_contradiction_clause,[],[f2541])).
thf(f2544,plain,(
  $false | (spl46_50 | ~spl46_69)),
  inference(forward_subsumption_resolution,[],[f2386,f2518])).
thf(f2545,plain,(
  spl46_50 | ~spl46_69),
  inference(avatar_contradiction_clause,[],[f2544])).
thf(f2562,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ sK3 @ X0)))) ) | ~spl46_10),
  inference(constrained_superposition,[],[f1868,f63])).
thf(f2566,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl46_2),
  inference(constrained_superposition,[],[f1821,f63])).
thf(f2576,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((irel @ X0 @ X1)))) ) | ~spl46_10),
  inference(constrained_superposition,[],[f2562,f63])).
thf(f2580,plain,(
  $false | (spl46_3 | ~spl46_10)),
  inference(forward_subsumption_resolution,[],[f1824,f2576])).
thf(f2581,plain,(
  spl46_3 | ~spl46_10),
  inference(avatar_contradiction_clause,[],[f2580])).
thf(f2595,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | ~spl46_69),
  inference(constrained_superposition,[],[f2386,f59])).
thf(f2612,plain,(
  ( ! [X1 : $i] : (($true = ((sK1 @ X1))) | ($true = $false)) ) | (~spl46_10 | ~spl46_11)),
  inference(forward_demodulation,[],[f1872,f2576])).
thf(f2613,plain,(
  ( ! [X1 : $i] : (($true = ((sK1 @ X1)))) ) | (~spl46_10 | ~spl46_11)),
  inference(trivial_inequality_removal,[],[f2612])).
thf(f2614,plain,(
  ($true = $false) | (~spl46_10 | ~spl46_11 | ~spl46_69)),
  inference(forward_demodulation,[],[f2613,f2595])).
thf(f2615,plain,(
  $false | (~spl46_10 | ~spl46_11 | ~spl46_69)),
  inference(trivial_inequality_removal,[],[f2614])).
thf(f2616,plain,(
  ~spl46_10 | ~spl46_11 | ~spl46_69),
  inference(avatar_contradiction_clause,[],[f2615])).
thf(f2619,plain,(
  ( ! [X2 : $i] : ((((irel @ sK26 @ X2)) = $false) | ($true = $false)) ) | (~spl46_2 | ~spl46_12)),
  inference(forward_demodulation,[],[f1875,f2566])).
thf(f2620,plain,(
  ( ! [X2 : $i] : ((((irel @ sK26 @ X2)) = $false)) ) | (~spl46_2 | ~spl46_12)),
  inference(trivial_inequality_removal,[],[f2619])).
thf(f2621,plain,(
  ($true = $false) | (~spl46_2 | ~spl46_10 | ~spl46_12)),
  inference(forward_demodulation,[],[f2620,f2576])).
thf(f2622,plain,(
  $false | (~spl46_2 | ~spl46_10 | ~spl46_12)),
  inference(trivial_inequality_removal,[],[f2621])).
thf(f2623,plain,(
  ~spl46_2 | ~spl46_10 | ~spl46_12),
  inference(avatar_contradiction_clause,[],[f2622])).
thf(f2632,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl46_67),
  inference(constrained_superposition,[],[f2379,f59])).
thf(f2638,plain,(
  ($false != $false) | (spl46_2 | ~spl46_67)),
  inference(constrained_superposition,[],[f1820,f2632])).
thf(f2640,plain,(
  $false | (spl46_2 | ~spl46_67)),
  inference(trivial_inequality_removal,[],[f2638])).
thf(f2641,plain,(
  spl46_2 | ~spl46_67),
  inference(avatar_contradiction_clause,[],[f2640])).
thf(f2648,plain,(
  ( ! [X0 : $i] : (($true != ((irel @ sK3 @ X0)))) ) | spl46_10),
  inference(constrained_superposition,[],[f1867,f63])).
thf(f2656,plain,(
  ($true != $true) | spl46_10),
  inference(constrained_superposition,[],[f2648,f77])).
thf(f2659,plain,(
  $false | spl46_10),
  inference(trivial_inequality_removal,[],[f2656])).
thf(f2660,plain,(
  spl46_10),
  inference(avatar_contradiction_clause,[],[f2659])).
cnf(s88, plain, spl46_11 | spl46_12 | spl46_18 | spl46_30, inference(sat_conversion,[],[f2016])).
cnf(s240, plain, spl46_15 | spl46_25 | spl46_50 | spl46_54, inference(sat_conversion,[],[f2263])).
cnf(s293, plain, spl46_66 | spl46_66 | spl46_67, inference(sat_conversion,[],[f2396])).
cnf(s294, plain, spl46_66 | spl46_67, inference(rat,[],[s293])).
cnf(s300, plain, spl46_68 | spl46_68 | spl46_69, inference(sat_conversion,[],[f2401])).
cnf(s301, plain, spl46_68 | spl46_69, inference(rat,[],[s300])).
cnf(s310, plain, ~spl46_3 | ~spl46_25 | ~spl46_68, inference(sat_conversion,[],[f2469])).
cnf(s311, plain, ~spl46_3 | ~spl46_50 | ~spl46_66, inference(sat_conversion,[],[f2472])).
cnf(s312, plain, ~spl46_3 | ~spl46_15 | ~spl46_66, inference(sat_conversion,[],[f2477])).
cnf(s313, plain, ~spl46_3 | ~spl46_54 | ~spl46_68, inference(sat_conversion,[],[f2490])).
cnf(s314, plain, ~spl46_3 | ~spl46_67 | ~spl46_68, inference(sat_conversion,[],[f2496])).
cnf(s317, plain, ~spl46_3 | ~spl46_30 | ~spl46_67, inference(sat_conversion,[],[f2515])).
cnf(s320, plain, ~spl46_3 | ~spl46_18 | ~spl46_69, inference(sat_conversion,[],[f2542])).
cnf(s321, plain, spl46_50 | ~spl46_69, inference(sat_conversion,[],[f2545])).
cnf(s324, plain, spl46_3 | ~spl46_10, inference(sat_conversion,[],[f2581])).
cnf(s330, plain, ~spl46_10 | ~spl46_11 | ~spl46_69, inference(sat_conversion,[],[f2616])).
cnf(s332, plain, ~spl46_2 | ~spl46_10 | ~spl46_12, inference(sat_conversion,[],[f2623])).
cnf(s333, plain, spl46_2 | ~spl46_67, inference(sat_conversion,[],[f2641])).
cnf(s334, plain, spl46_10, inference(sat_conversion,[],[f2660])).
cnf(s335, plain, ~spl46_2 | ~spl46_12, inference(rat,[],[s332,s334])).
cnf(s336, plain, ~spl46_11 | ~spl46_69, inference(rat,[],[s330,s334])).
cnf(s339, plain, spl46_3, inference(rat,[],[s324,s334])).
cnf(s340, plain, ~spl46_18 | ~spl46_69, inference(rat,[],[s320,s339])).
cnf(s342, plain, ~spl46_30 | ~spl46_67, inference(rat,[],[s317,s339])).
cnf(s345, plain, ~spl46_67 | ~spl46_68, inference(rat,[],[s314,s339])).
cnf(s346, plain, ~spl46_54 | ~spl46_68, inference(rat,[],[s313,s339])).
cnf(s347, plain, ~spl46_15 | ~spl46_66, inference(rat,[],[s312,s339])).
cnf(s348, plain, ~spl46_50 | ~spl46_66, inference(rat,[],[s311,s339])).
cnf(s349, plain, ~spl46_25 | ~spl46_68, inference(rat,[],[s310,s339])).
cnf(s350, plain, ~spl46_66, inference(rat,[],[s240,s349,s346,s301,s321,s348,s347])).
cnf(s351, plain, spl46_67, inference(rat,[],[s294,s350])).
cnf(s352, plain, spl46_2, inference(rat,[],[s333,s351])).
cnf(s353, plain, ~spl46_30, inference(rat,[],[s342,s351])).
cnf(s354, plain, ~spl46_68, inference(rat,[],[s345,s351])).
cnf(s355, plain, ~spl46_12, inference(rat,[],[s335,s352])).
cnf(s357, plain, spl46_69, inference(rat,[],[s301,s354])).
cnf(s359, plain, ~spl46_11, inference(rat,[],[s336,s357])).
cnf(s363, plain, ~spl46_18, inference(rat,[],[s340,s357])).
cnf(s364, plain, $false, inference(rat,[],[s88,s355,s353,s363,s359])).
thf(f2661,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s364])).
% SZS output end Proof for theBenchmark