%----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, db1: !>[X0: $tType]:(X0)).
thf(func_def_24, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_25, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_26, type, vNOT: ($o > $o)).
thf(func_def_27, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_28, type, vOR: ($o > $o > $o)).
thf(func_def_29, type, vAND: ($o > $o > $o)).
thf(func_def_30, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_31, type, db8: !>[X0: $tType]:(X0)).
thf(func_def_32, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_33, type, db6: !>[X0: $tType]:(X0)).
thf(func_def_34, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_35, type, db7: !>[X0: $tType]:(X0)).
thf(func_def_36, 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 > $o)).
thf(f1,axiom,(
  ((^[X2 : ($i > $o), X4 : ($i > $o), X3 : $i] : ((X2 @ X3) | (X4 @ X3))) = mor) & ((^[X16 : ($i > $o)] : (~ ! [X17 : $i] : (X16 @ X17))) = icountersatisfiable) & (iimplied = (^[X5 : ($i > $o), X7 : ($i > $o), X6 : $i] : (~ ! [X4 : $i] : ((X7 @ X4) | ~(irel @ X6 @ X4)) | ! [X4 : $i] : ((X5 @ X4) | ~(irel @ X6 @ X4))))) & ((^[X5 : ($i > $o), X7 : ($i > $o), X6 : $i] : (~ ! [X4 : $i] : (~(irel @ X6 @ X4) | (X5 @ X4)) | ! [X4 : $i] : ((X7 @ X4) | ~(irel @ X6 @ X4)))) = iimplies) & ((^[X3 : ($i > $o), X18 : ($i > $o), X6 : $i] : (~(X3 @ X6) | (X18 @ X6))) = mimplies) & ! [X3 : $i] : ? [X19 : d_unsorted] : (X3 = ((d2unsorted @ X19))) & ((^[X5 : ($i > $o), X7 : ($i > $o), X6 : $i] : (! [X10 : $i,X4 : $i] : (~(irel @ X4 @ X10) | (X7 @ X10) | ~ ! [X11 : $i] : ((X5 @ X11) | ~(irel @ X4 @ X11)) | ~(irel @ X6 @ X4)) & ! [X4 : $i,X8 : $i] : (~(irel @ X6 @ X4) | (X5 @ X8) | ~(irel @ X4 @ X8) | ~ ! [X9 : $i] : (~(irel @ X4 @ X9) | (X7 @ X9))))) = iequiv) & ((^[X16 : ($i > $o)] : (! [X17 : $i] : (X16 @ X17))) = ivalid) & (iand = (^[X5 : ($i > $o), X7 : ($i > $o), X6 : $i] : (! [X4 : $i] : (~(irel @ X6 @ X4) | (X7 @ X4)) & ! [X4 : $i] : (~(irel @ X6 @ X4) | (X5 @ X4))))) & ((^[X16 : ($i > $o)] : (! [X17 : $i] : ~(X16 @ X17))) = iinvalid) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X5 : ($i > $o), X7 : ($i > $o), X6 : $i] : (! [X4 : $i] : ((X5 @ X4) | ~(irel @ X6 @ X4)) | ! [X4 : $i] : (~(irel @ X6 @ X4) | (X7 @ X4)))) = ior) & ((^[X5 : ($i > $o), X2 : $i] : (! [X4 : $i] : ((X5 @ X4) | ~(irel @ X2 @ X4)))) = mbox_s4) & ((^[X16 : ($i > $o)] : (~ ! [X17 : $i] : ~(X16 @ X17))) = isatisfiable) & ! [X19 : d_unsorted] : (X19 = d_unsorted_0) & ((^[X5 : ($i > $o), X6 : $i] : (~ ! [X4 : $i] : (~(irel @ X6 @ X4) | (X5 @ X4)))) = inot) & (mand = (^[X2 : ($i > $o), X4 : ($i > $o), X3 : $i] : ((X2 @ X3) & (X4 @ X3)))) & (mnot = (^[X2 : ($i > $o), X3 : $i] : (~(X2 @ X3)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & (ixor = (^[X5 : ($i > $o), X7 : ($i > $o), X6 : $i] : (~ ! [X14 : $i,X12 : $i,X13 : $i,X4 : $i,X15 : $i] : (~(irel @ X6 @ X4) | ((~ ! [X9 : $i] : ((X7 @ X9) | ~(irel @ X14 @ X9)) | ~(irel @ X4 @ X14) | (X5 @ X15) | ~(irel @ X14 @ X15)) & ((X7 @ X13) | ~(irel @ X4 @ X12) | ~ ! [X11 : $i] : ((X5 @ X11) | ~(irel @ X12 @ X11)) | ~(irel @ X12 @ X13))))))) & (iatom = (^[X5 : ($i > $o), X6 : $i] : ((X5 @ X6)))) & ! [X1 : d_unsorted,X0 : d_unsorted] : ((((d2unsorted @ X0)) = ((d2unsorted @ X1))) => (X0 = X1))),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lcl696_1)).
thf(f2,conjecture,(
  ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = iimplies)),
  file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iimplies)).
thf(f3,negated_conjecture,(
  ~ ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = iimplies)),
  inference(negated_conjecture,[status(cth)],[f2])).
thf(f4,plain,(
  ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor) & ((^[X3 : ($i > $o)] : (~ ! [X4 : $i] : (X3 @ X4))) = icountersatisfiable) & (iimplied = (^[X5 : ($i > $o), X6 : ($i > $o), X7 : $i] : (~ ! [X8 : $i] : ((X6 @ X8) | ~(irel @ X7 @ X8)) | ! [X9 : $i] : ((X5 @ X9) | ~(irel @ X7 @ X9))))) & ((^[X10 : ($i > $o), X11 : ($i > $o), X12 : $i] : (~ ! [X13 : $i] : (~(irel @ X12 @ X13) | (X10 @ X13)) | ! [X14 : $i] : ((X11 @ X14) | ~(irel @ X12 @ X14)))) = iimplies) & ((^[X15 : ($i > $o), X16 : ($i > $o), X17 : $i] : (~(X15 @ X17) | (X16 @ X17))) = mimplies) & ! [X18 : $i] : ? [X19 : d_unsorted] : (((d2unsorted @ X19)) = X18) & ((^[X20 : ($i > $o), X21 : ($i > $o), X22 : $i] : (! [X23 : $i,X24 : $i] : (~(irel @ X24 @ X23) | (X21 @ X23) | ~ ! [X25 : $i] : ((X20 @ X25) | ~(irel @ X24 @ X25)) | ~(irel @ X22 @ X24)) & ! [X26 : $i,X27 : $i] : (~(irel @ X22 @ X26) | (X20 @ X27) | ~(irel @ X26 @ X27) | ~ ! [X28 : $i] : (~(irel @ X26 @ X28) | (X21 @ X28))))) = iequiv) & ((^[X29 : ($i > $o)] : (! [X30 : $i] : (X29 @ X30))) = ivalid) & (iand = (^[X31 : ($i > $o), X32 : ($i > $o), X33 : $i] : (! [X34 : $i] : (~(irel @ X33 @ X34) | (X32 @ X34)) & ! [X35 : $i] : (~(irel @ X33 @ X35) | (X31 @ X35))))) & ((^[X36 : ($i > $o)] : (! [X37 : $i] : ~(X36 @ X37))) = iinvalid) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ((^[X38 : ($i > $o), X39 : ($i > $o), X40 : $i] : (! [X41 : $i] : ((X38 @ X41) | ~(irel @ X40 @ X41)) | ! [X42 : $i] : (~(irel @ X40 @ X42) | (X39 @ X42)))) = ior) & ((^[X43 : ($i > $o), X44 : $i] : (! [X45 : $i] : ((X43 @ X45) | ~(irel @ X44 @ X45)))) = mbox_s4) & ((^[X46 : ($i > $o)] : (~ ! [X47 : $i] : ~(X46 @ X47))) = isatisfiable) & ! [X48 : d_unsorted] : (d_unsorted_0 = X48) & ((^[X49 : ($i > $o), X50 : $i] : (~ ! [X51 : $i] : (~(irel @ X50 @ X51) | (X49 @ X51)))) = inot) & (mand = (^[X52 : ($i > $o), X53 : ($i > $o), X54 : $i] : ((X52 @ X54) & (X53 @ X54)))) & (mnot = (^[X55 : ($i > $o), X56 : $i] : (~(X55 @ X56)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & (ixor = (^[X57 : ($i > $o), X58 : ($i > $o), X59 : $i] : (~ ! [X60 : $i,X61 : $i,X62 : $i,X63 : $i,X64 : $i] : (~(irel @ X59 @ X63) | ((~ ! [X65 : $i] : ((X58 @ X65) | ~(irel @ X60 @ X65)) | ~(irel @ X63 @ X60) | (X57 @ X64) | ~(irel @ X60 @ X64)) & ((X58 @ X62) | ~(irel @ X63 @ X61) | ~ ! [X66 : $i] : ((X57 @ X66) | ~(irel @ X61 @ X66)) | ~(irel @ X61 @ X62))))))) & (iatom = (^[X67 : ($i > $o), X68 : $i] : ((X67 @ X68)))) & ! [X69 : d_unsorted,X70 : d_unsorted] : ((((d2unsorted @ X70)) = ((d2unsorted @ X69))) => (X69 = X70))),
  inference(rectify,[],[f1])).
thf(f5,plain,(
  (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & ! [X18 : $i] : ? [X19 : d_unsorted] : (((d2unsorted @ X19)) = X18) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3)) | (~ (irel @ Y2 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4)))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X48 : d_unsorted] : (d_unsorted_0 = X48) & (inot = (^[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)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (((itrue @ (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]: ((((((~ (irel @ Y6 @ Y5)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y6))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y3)) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y7))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8))))))) | (~ (irel @ Y2 @ Y4)))))))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ! [X69 : d_unsorted,X70 : d_unsorted] : ((((d2unsorted @ X70)) = ((d2unsorted @ X69))) => (X69 = X70))),
  inference(fool_elimination,[],[f4])).
thf(f6,plain,(
  ~ (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
  inference(fool_elimination,[],[f3])).
thf(f7,plain,(
  (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3)) | (~ (irel @ Y2 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4)))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (inot = (^[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)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (((itrue @ (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]: ((((((~ (irel @ Y6 @ Y5)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y6))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y3)) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y7))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8))))))) | (~ (irel @ Y2 @ Y4)))))))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X4)) = ((d2unsorted @ X3))) => (X3 = X4))),
  inference(rectify,[],[f5])).
thf(f8,plain,(
  (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3)) | (~ (irel @ Y2 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4)))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X4)) = ((d2unsorted @ X3))) => (X3 = X4)) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (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]: ((((((~ (irel @ Y6 @ Y5)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y6))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y3)) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y7))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8))))))) | (~ (irel @ Y2 @ Y4)))))))))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2)),
  inference(flattening,[],[f7])).
thf(f9,plain,(
  (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
  inference(flattening,[],[f6])).
thf(f10,plain,(
  (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3)) | (~ (irel @ Y2 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4)))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (irel @ Y6 @ Y5)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y6))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y3)) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y7))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8))))))) | (~ (irel @ Y2 @ Y4)))))))))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplied = (^[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 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X4)) != ((d2unsorted @ X3)))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
  inference(ennf_transformation,[],[f8])).
thf(f11,plain,(
  (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3)) | (~ (irel @ Y2 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4)))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (irel @ Y6 @ Y5)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y6))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y3)) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y7))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8))))))) | (~ (irel @ Y2 @ Y4)))))))))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((X2 = X3) | (((d2unsorted @ X3)) != ((d2unsorted @ X2)))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
  inference(rectify,[],[f10])).
thf(f12,plain,(
  (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : $i] : (((d2unsorted @ (sK0 @ X0))) = X0) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3)) | (~ (irel @ Y2 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y3)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y0 @ Y5)))))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4)))))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (irel @ Y6 @ Y5)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y4 @ Y6))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y3)) | (Y0 @ Y3)) | (~ (irel @ Y4 @ Y7))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y7 @ Y8)) | (Y1 @ Y8))))))) | (~ (irel @ Y2 @ Y4)))))))))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((X2 = X3) | (((d2unsorted @ X3)) != ((d2unsorted @ X2)))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f11])).
thf(f14,plain,(
  (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f15,plain,(
  ( ! [X4 : d_unsorted] : ((d_unsorted_0 = X4)) )),
  inference(cnf_transformation,[],[f12])).
thf(f21,plain,(
  (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)),
  inference(cnf_transformation,[],[f12])).
thf(f27,plain,(
  (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f31,plain,(
  (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2)))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f33,plain,(
  ( ! [X0 : $i] : ((((d2unsorted @ (sK0 @ X0))) = X0)) )),
  inference(cnf_transformation,[],[f12])).
thf(f36,plain,(
  (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
  inference(cnf_transformation,[],[f9])).
thf(f39,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (~ (Y2 @ Y4)))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ Y1))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))),
  inference(definition_unfolding,[],[f36,f14,f31,f27,f27])).
thf(f40,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))),
  inference(beta-eta_normalization,[],[f39])).
thf(f41,plain,(
  ( ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1)) )),
  inference(constrained_superposition,[],[f15,f15])).
thf(f42,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) @ sK1)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) @ sK1)))),
  inference(negative_extensionality,[],[f40])).
thf(f43,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2))))))))))),
  inference(beta-eta_normalization,[],[f42])).
thf(f49,plain,(
  ( ! [X0 : d_unsorted,X1 : $i] : ((((d2unsorted @ X0)) = X1)) )),
  inference(constrained_superposition,[],[f33,f41])).
thf(f53,plain,(
  ( ! [X2 : $i,X0 : $i] : ((X0 = X2)) )),
  inference(constrained_superposition,[],[f49,f49])).
thf(f98,plain,(
  ( ! [X0 : $i] : ((((irel @ X0 @ X0)) = $true)) )),
  inference(constrained_superposition,[],[f21,f53])).
thf(f100,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) @ sK2)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2))))))))) @ sK2)))),
  inference(negative_extensionality,[],[f43])).
thf(f101,plain,(
  ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))) != (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))))),
  inference(beta-eta_normalization,[],[f100])).
thf(f102,plain,(
  ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))) @ sK3)) != (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))) @ sK3)))),
  inference(negative_extensionality,[],[f101])).
thf(f103,plain,(
  ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))) @ sK3)) = $true) | ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))) @ sK3)) = $true)),
  inference(xor_proxy_clausification,[],[f102])).
thf(f104,plain,(
  ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))))) @ sK3))) | ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))) @ sK3)))),
  inference(xor_proxy_clausification,[],[f102])).
thf(f105,plain,(
  ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))))),
  inference(beta-eta_normalization,[],[f104])).
thf(f106,plain,(
  ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))))),
  inference(or_proxy_clausification,[],[f105])).
thf(f107,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))) = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))))),
  inference(or_proxy_clausification,[],[f105])).
thf(f108,plain,(
  ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK4))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))))),
  inference(sigma_proxy_clausification,[],[f107])).
thf(f110,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))) = $false) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK4)))),
  inference(or_proxy_clausification,[],[f108])).
thf(f111,plain,(
  ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK4))) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK5)) = $false)),
  inference(sigma_proxy_clausification,[],[f110])).
thf(f112,plain,(
  ($false = (((~ (irel @ sK3 @ sK5)) | (sK2 @ sK5)))) | ($false = (((~ (irel @ sK3 @ sK4)) | (sK2 @ sK4))))),
  inference(beta-eta_normalization,[],[f111])).
thf(f113,plain,(
  ($false = (((~ (irel @ sK3 @ sK4)) | (sK2 @ sK4)))) | (((sK2 @ sK5)) = $false)),
  inference(or_proxy_clausification,[],[f112])).
thf(f119,plain,(
  (((sK2 @ sK5)) = $false) | (((sK2 @ sK4)) = $false)),
  inference(or_proxy_clausification,[],[f113])).
thf(f131,plain,(
  ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $true)),
  inference(not_proxy_clausification,[],[f106])).
thf(f132,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $true) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))))),
  inference(or_proxy_clausification,[],[f131])).
thf(f142,plain,(
  ( ! [X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ X1)) = $true)) )),
  inference(pi_proxy_clausification,[],[f132])).
thf(f143,plain,(
  ( ! [X1 : $i] : (((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ X1)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) )),
  inference(not_proxy_clausification,[],[f142])).
thf(f144,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ X1)) = $true) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X2)) = $true)) )),
  inference(pi_proxy_clausification,[],[f143])).
thf(f145,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((~ (irel @ sK3 @ X1)) | (sK1 @ X1))) = $true) | ((((sK1 @ X2) | (~ (irel @ sK3 @ X2)))) = $true)) )),
  inference(beta-eta_normalization,[],[f144])).
thf(f146,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((sK1 @ X2) | (~ (irel @ sK3 @ X2)))) = $true) | ($true = ((sK1 @ X1))) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(or_proxy_clausification,[],[f145])).
thf(f147,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X2)) = $true) | (((~ (irel @ sK3 @ X2))) = $true) | ($true = ((sK1 @ X1))) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(or_proxy_clausification,[],[f146])).
thf(f148,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK1 @ X1))) | (((sK1 @ X2)) = $true) | ($false = ((irel @ sK3 @ X2))) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(not_proxy_clausification,[],[f147])).
thf(f149,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((sK1 @ X1))) | (((irel @ sK3 @ X1)) = $false) | (((sK1 @ X2)) = $true) | ($false = ((irel @ sK3 @ X2)))) )),
  inference(not_proxy_clausification,[],[f148])).
thf(f150,plain,(
  ($true = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))))) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) = $true)),
  inference(beta-eta_normalization,[],[f103])).
thf(f151,plain,(
  (((~ (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) = $true)),
  inference(or_proxy_clausification,[],[f150])).
thf(f152,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) = $true)),
  inference(not_proxy_clausification,[],[f151])).
thf(f153,plain,(
  ( ! [X1 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1))) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) = $true)) )),
  inference(pi_proxy_clausification,[],[f152])).
thf(f154,plain,(
  ( ! [X1 : $i] : (((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) = $true) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1)))) )),
  inference(sigma_proxy_clausification,[],[f153])).
thf(f155,plain,(
  ( ! [X1 : $i] : (($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0)))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))) = $true)) )),
  inference(or_proxy_clausification,[],[f154])).
thf(f156,plain,(
  ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $false) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7)))) )),
  inference(not_proxy_clausification,[],[f155])).
thf(f157,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1))) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X2)) = $true) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $false)) )),
  inference(pi_proxy_clausification,[],[f156])).
thf(f158,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1))) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X2)) = $true) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ sK8)) = $false)) )),
  inference(sigma_proxy_clausification,[],[f157])).
thf(f159,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = (((sK1 @ sK7) | (~ (irel @ sK3 @ sK7))))) | ((((~ (irel @ sK3 @ X1)) | (sK2 @ X1))) = $true) | ((((~ (irel @ sK3 @ X2)) | (sK2 @ X2))) = $true) | ($false = (((~ (irel @ sK3 @ sK8)) | (sK1 @ sK8))))) )),
  inference(beta-eta_normalization,[],[f158])).
thf(f161,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((~ (irel @ sK3 @ X1)) | (sK2 @ X1))) = $true) | (((sK1 @ sK7)) = $false) | ((((~ (irel @ sK3 @ X2)) | (sK2 @ X2))) = $true) | ($false = (((~ (irel @ sK3 @ sK8)) | (sK1 @ sK8))))) )),
  inference(or_proxy_clausification,[],[f159])).
thf(f162,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK1 @ sK7)) = $false) | ((((~ (irel @ sK3 @ X2)) | (sK2 @ X2))) = $true) | ($true = ((sK2 @ X1))) | ($false = (((~ (irel @ sK3 @ sK8)) | (sK1 @ sK8)))) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(or_proxy_clausification,[],[f161])).
thf(f163,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = (((~ (irel @ sK3 @ sK8)) | (sK1 @ sK8)))) | (((~ (irel @ sK3 @ X1))) = $true) | ($true = ((sK2 @ X1))) | (((sK2 @ X2)) = $true) | (((~ (irel @ sK3 @ X2))) = $true) | (((sK1 @ sK7)) = $false)) )),
  inference(or_proxy_clausification,[],[f162])).
thf(f164,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK1 @ sK7)) = $false) | (((~ (irel @ sK3 @ X1))) = $true) | ($true = ((sK2 @ X1))) | (((sK2 @ X2)) = $true) | ($false = ((sK1 @ sK8))) | (((~ (irel @ sK3 @ X2))) = $true)) )),
  inference(or_proxy_clausification,[],[f163])).
thf(f169,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((sK1 @ sK8))) | (((sK1 @ sK7)) = $false) | (((~ (irel @ sK3 @ X2))) = $true) | (((sK2 @ X2)) = $true) | ($true = ((sK2 @ X1))) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(not_proxy_clausification,[],[f164])).
thf(f170,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK3 @ X2))) | ($false = ((sK1 @ sK8))) | (((sK1 @ sK7)) = $false) | ($true = ((sK2 @ X1))) | (((irel @ sK3 @ X1)) = $false) | (((sK2 @ X2)) = $true)) )),
  inference(not_proxy_clausification,[],[f169])).
thf(f191,definition,(
  spl9_3 <=> (((sK2 @ sK4)) = $false)),
  introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition])).
thf(f193,plain,(
  (((sK2 @ sK4)) = $false) | ~spl9_3),
  inference(avatar_component_clause,[],[f191])).
thf(f196,definition,(
  spl9_4 <=> (((sK2 @ sK5)) = $false)),
  introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition])).
thf(f197,plain,(
  (((sK2 @ sK5)) != $false) | spl9_4),
  inference(avatar_component_clause,[],[f196])).
thf(f198,plain,(
  (((sK2 @ sK5)) = $false) | ~spl9_4),
  inference(avatar_component_clause,[],[f196])).
thf(f200,plain,(
  spl9_3 | spl9_4),
  inference(avatar_split_clause,[],[f119,f196,f191])).
thf(f202,definition,(
  spl9_5 <=> ! [X1 : $i] : ((((irel @ sK3 @ X1)) = $false) | ($true = ((sK1 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition])).
thf(f203,plain,(
  ( ! [X1 : $i] : ((((irel @ sK3 @ X1)) = $false) | ($true = ((sK1 @ X1)))) ) | ~spl9_5),
  inference(avatar_component_clause,[],[f202])).
thf(f216,plain,(
  spl9_5 | spl9_5),
  inference(avatar_split_clause,[],[f149,f202,f202])).
thf(f218,definition,(
  spl9_8 <=> (((sK1 @ sK7)) = $false)),
  introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition])).
thf(f220,plain,(
  (((sK1 @ sK7)) = $false) | ~spl9_8),
  inference(avatar_component_clause,[],[f218])).
thf(f222,definition,(
  spl9_9 <=> ! [X2 : $i] : ((((sK2 @ X2)) = $true) | ($false = ((irel @ sK3 @ X2))))),
  introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition])).
thf(f223,plain,(
  ( ! [X2 : $i] : (($false = ((irel @ sK3 @ X2))) | (((sK2 @ X2)) = $true)) ) | ~spl9_9),
  inference(avatar_component_clause,[],[f222])).
thf(f230,definition,(
  spl9_11 <=> ($false = ((sK1 @ sK8)))),
  introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition])).
thf(f231,plain,(
  ($false != ((sK1 @ sK8))) | spl9_11),
  inference(avatar_component_clause,[],[f230])).
thf(f232,plain,(
  ($false = ((sK1 @ sK8))) | ~spl9_11),
  inference(avatar_component_clause,[],[f230])).
thf(f233,plain,(
  spl9_11 | spl9_8 | spl9_9 | spl9_9),
  inference(avatar_split_clause,[],[f170,f222,f222,f218,f230])).
thf(f241,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl9_4),
  inference(constrained_superposition,[],[f198,f53])).
thf(f257,plain,(
  (((sK2 @ sK3)) = $true) | ($false = $true) | ~spl9_9),
  inference(constrained_superposition,[],[f98,f223])).
thf(f269,plain,(
  (((sK2 @ sK3)) = $true) | ~spl9_9),
  inference(trivial_inequality_removal,[],[f257])).
thf(f295,plain,(
  ($false = $true) | (~spl9_4 | ~spl9_9)),
  inference(forward_demodulation,[],[f269,f241])).
thf(f296,plain,(
  $false | (~spl9_4 | ~spl9_9)),
  inference(trivial_inequality_removal,[],[f295])).
thf(f297,plain,(
  ~spl9_4 | ~spl9_9),
  inference(avatar_contradiction_clause,[],[f296])).
thf(f312,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | ~spl9_11),
  inference(constrained_superposition,[],[f232,f53])).
thf(f321,plain,(
  ($false = $true) | (((sK1 @ sK3)) = $true) | ~spl9_5),
  inference(constrained_superposition,[],[f98,f203])).
thf(f332,plain,(
  (((sK1 @ sK3)) = $true) | ~spl9_5),
  inference(trivial_inequality_removal,[],[f321])).
thf(f356,plain,(
  ($false = $true) | (~spl9_5 | ~spl9_11)),
  inference(forward_demodulation,[],[f332,f312])).
thf(f357,plain,(
  $false | (~spl9_5 | ~spl9_11)),
  inference(trivial_inequality_removal,[],[f356])).
thf(f358,plain,(
  ~spl9_5 | ~spl9_11),
  inference(avatar_contradiction_clause,[],[f357])).
thf(f381,plain,(
  ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) ) | ~spl9_8),
  inference(constrained_superposition,[],[f220,f53])).
thf(f409,plain,(
  $false | (~spl9_8 | spl9_11)),
  inference(forward_subsumption_resolution,[],[f231,f381])).
thf(f410,plain,(
  ~spl9_8 | spl9_11),
  inference(avatar_contradiction_clause,[],[f409])).
thf(f418,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl9_3),
  inference(constrained_superposition,[],[f193,f53])).
thf(f419,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) != $false)) ) | spl9_4),
  inference(constrained_superposition,[],[f197,f53])).
thf(f423,plain,(
  $false | (~spl9_3 | spl9_4)),
  inference(forward_subsumption_resolution,[],[f419,f418])).
thf(f424,plain,(
  ~spl9_3 | spl9_4),
  inference(avatar_contradiction_clause,[],[f423])).
cnf(s4, plain, spl9_3 | spl9_4, inference(sat_conversion,[],[f200])).
cnf(s9, plain, spl9_5 | spl9_5, inference(sat_conversion,[],[f216])).
cnf(s10, plain, spl9_5, inference(rat,[],[s9])).
cnf(s13, plain, spl9_9 | spl9_8 | spl9_9 | spl9_11, inference(sat_conversion,[],[f233])).
cnf(s14, plain, spl9_8 | spl9_9 | spl9_11, inference(rat,[],[s13])).
cnf(s26, plain, ~spl9_4 | ~spl9_9, inference(sat_conversion,[],[f297])).
cnf(s37, plain, ~spl9_5 | ~spl9_11, inference(sat_conversion,[],[f358])).
cnf(s46, plain, ~spl9_8 | spl9_11, inference(sat_conversion,[],[f410])).
cnf(s48, plain, ~spl9_3 | spl9_4, inference(sat_conversion,[],[f424])).
cnf(s49, plain, ~spl9_11, inference(rat,[],[s37,s10])).
cnf(s50, plain, ~spl9_8, inference(rat,[],[s46,s49])).
cnf(s51, plain, spl9_9, inference(rat,[],[s14,s49,s50])).
cnf(s52, plain, ~spl9_4, inference(rat,[],[s26,s51])).
cnf(s53, plain, ~spl9_3, inference(rat,[],[s48,s52])).
cnf(s54, plain, $false, inference(rat,[],[s4,s52,s53])).
thf(f425,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s54])).
% SZS output end Proof for theBenchmark