%----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, db2: !>[X0: $tType]:(X0)).
thf(func_def_25, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_27, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_28, type, vOR: ($o > $o > $o)).
thf(func_def_29, type, vNOT: ($o > $o)).
thf(func_def_30, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_31, type, db3: !>[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, db5: !>[X0: $tType]:(X0)).
thf(func_def_37, type, sK0: ($i > d_unsorted)).
thf(func_def_38, type, sK1: ($i > $o)).
thf(func_def_39, type, sK2: ($i > $o)).
thf(func_def_41, type, sK4: ($i > $i)).
thf(func_def_42, type, sK5: ($i > $i)).
thf(func_def_43, type, sK6: ($i > $i)).
thf(func_def_44, type, sK7: ($i > $i)).
thf(func_def_45, type, sK8: ($i > $i)).
thf(func_def_46, type, sK9: ($i > $i)).
thf(func_def_47, type, sK10: ($i > $i)).
thf(func_def_48, type, sK11: ($i > $i)).
thf(func_def_49, type, sK12: ($i > $i)).
thf(func_def_50, type, sK13: ($i > $i)).
thf(f1,axiom,(
  ((^[X6 : ($i > $o), X9 : ($i > $o), X5 : $i] : (~ ! [X8 : $i] : ((X9 @ X8) | ~(irel @ X5 @ X8)) | ! [X8 : $i] : ((X6 @ X8) | ~(irel @ X5 @ X8)))) = iimplied) & ((^[X6 : ($i > $o), X9 : ($i > $o), X5 : $i] : (~ ! [X13 : $i,X8 : $i,X12 : $i] : (~(irel @ X5 @ X8) | ((~(irel @ X8 @ X13) | ~ ! [X14 : $i] : (~(irel @ X8 @ X14) | (X9 @ X14)) | (X6 @ X13)) & ((X9 @ X12) | ~(irel @ X8 @ X12) | ~ ! [X15 : $i] : ((X6 @ X15) | ~(irel @ X8 @ X15))))))) = ixor) & (iatom = (^[X6 : ($i > $o), X5 : $i] : ((X6 @ X5)))) & ((^[X10 : ($i > $o)] : (! [X11 : $i] : (X10 @ X11))) = ivalid) & ((^[X7 : ($i > $o), X0 : $i] : (~(X7 @ X0))) = mnot) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (isatisfiable = (^[X10 : ($i > $o)] : (~ ! [X11 : $i] : ~(X10 @ X11)))) & (mand = (^[X7 : ($i > $o), X8 : ($i > $o), X0 : $i] : ((X7 @ X0) & (X8 @ X0)))) & (mbox_s4 = (^[X6 : ($i > $o), X7 : $i] : (! [X8 : $i] : ((X6 @ X8) | ~(irel @ X7 @ X8))))) & (iimplies = (^[X6 : ($i > $o), X9 : ($i > $o), X5 : $i] : (~ ! [X8 : $i] : (~(irel @ X5 @ X8) | (X6 @ X8)) | ! [X8 : $i] : ((X9 @ X8) | ~(irel @ X5 @ X8))))) & ((^[X10 : ($i > $o)] : (! [X11 : $i] : ~(X10 @ X11))) = iinvalid) & ((^[X6 : ($i > $o), X5 : $i] : (~ ! [X8 : $i] : ((X6 @ X8) | ~(irel @ X5 @ X8)))) = inot) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1))) & ((^[X10 : ($i > $o)] : (~ ! [X11 : $i] : (X10 @ X11))) = icountersatisfiable) & ((^[X7 : ($i > $o), X8 : ($i > $o), X0 : $i] : ((X7 @ X0) | (X8 @ X0))) = mor) & ! [X3 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ((^[X6 : ($i > $o), X9 : ($i > $o), X5 : $i] : ((~ ! [X8 : $i] : ((X6 @ X8) | ~(irel @ X5 @ X8)) | ! [X8 : $i] : ((X9 @ X8) | ~(irel @ X5 @ X8))) & (! [X8 : $i] : (~(irel @ X5 @ X8) | (X6 @ X8)) | ~ ! [X8 : $i] : (~(irel @ X5 @ X8) | (X9 @ X8))))) = iequiv) & (ior = (^[X6 : ($i > $o), X9 : ($i > $o), X5 : $i] : (! [X8 : $i] : (~(irel @ X5 @ X8) | (X6 @ X8)) | ! [X8 : $i] : (~(irel @ X5 @ X8) | (X9 @ X8))))) & ((^[X0 : ($i > $o), X4 : ($i > $o), X5 : $i] : (~(X0 @ X5) | (X4 @ X5))) = mimplies) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ((^[X6 : ($i > $o), X9 : ($i > $o), X5 : $i] : ((X9 @ X5) & (X6 @ X5))) = iand)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcl695_1)).
thf(f2,conjecture,(
  (ixor = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((inot @ (iequiv @ X0 @ X1)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ixor)).
thf(f3,negated_conjecture,(
  ~ (ixor = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((inot @ (iequiv @ X0 @ X1)))))),
  inference(negated_conjecture,[status(cth)],[f2])).
thf(f4,plain,(
  ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : (~ ! [X3 : $i] : ((X1 @ X3) | ~(irel @ X2 @ X3)) | ! [X4 : $i] : ((X0 @ X4) | ~(irel @ X2 @ X4)))) = iimplied) & ((^[X5 : ($i > $o), X6 : ($i > $o), X7 : $i] : (~ ! [X8 : $i,X9 : $i,X10 : $i] : (~(irel @ X7 @ X9) | ((~(irel @ X9 @ X8) | ~ ! [X11 : $i] : (~(irel @ X9 @ X11) | (X6 @ X11)) | (X5 @ X8)) & ((X6 @ X10) | ~(irel @ X9 @ X10) | ~ ! [X12 : $i] : ((X5 @ X12) | ~(irel @ X9 @ X12))))))) = ixor) & (iatom = (^[X13 : ($i > $o), X14 : $i] : ((X13 @ X14)))) & ((^[X15 : ($i > $o)] : (! [X16 : $i] : (X15 @ X16))) = ivalid) & ((^[X17 : ($i > $o), X18 : $i] : (~(X17 @ X18))) = mnot) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (isatisfiable = (^[X19 : ($i > $o)] : (~ ! [X20 : $i] : ~(X19 @ X20)))) & (mand = (^[X21 : ($i > $o), X22 : ($i > $o), X23 : $i] : ((X21 @ X23) & (X22 @ X23)))) & (mbox_s4 = (^[X24 : ($i > $o), X25 : $i] : (! [X26 : $i] : ((X24 @ X26) | ~(irel @ X25 @ X26))))) & (iimplies = (^[X27 : ($i > $o), X28 : ($i > $o), X29 : $i] : (~ ! [X30 : $i] : (~(irel @ X29 @ X30) | (X27 @ X30)) | ! [X31 : $i] : ((X28 @ X31) | ~(irel @ X29 @ X31))))) & ((^[X32 : ($i > $o)] : (! [X33 : $i] : ~(X32 @ X33))) = iinvalid) & ((^[X34 : ($i > $o), X35 : $i] : (~ ! [X36 : $i] : ((X34 @ X36) | ~(irel @ X35 @ X36)))) = inot) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & ! [X37 : $i] : ? [X38 : d_unsorted] : (((d2unsorted @ X38)) = X37) & ((^[X39 : ($i > $o)] : (~ ! [X40 : $i] : (X39 @ X40))) = icountersatisfiable) & ((^[X41 : ($i > $o), X42 : ($i > $o), X43 : $i] : ((X41 @ X43) | (X42 @ X43))) = mor) & ! [X44 : d_unsorted,X45 : d_unsorted] : ((((d2unsorted @ X45)) = ((d2unsorted @ X44))) => (X44 = X45)) & ((^[X46 : ($i > $o), X47 : ($i > $o), X48 : $i] : ((~ ! [X49 : $i] : ((X46 @ X49) | ~(irel @ X48 @ X49)) | ! [X50 : $i] : ((X47 @ X50) | ~(irel @ X48 @ X50))) & (! [X51 : $i] : (~(irel @ X48 @ X51) | (X46 @ X51)) | ~ ! [X52 : $i] : (~(irel @ X48 @ X52) | (X47 @ X52))))) = iequiv) & (ior = (^[X53 : ($i > $o), X54 : ($i > $o), X55 : $i] : (! [X56 : $i] : (~(irel @ X55 @ X56) | (X53 @ X56)) | ! [X57 : $i] : (~(irel @ X55 @ X57) | (X54 @ X57))))) & ((^[X58 : ($i > $o), X59 : ($i > $o), X60 : $i] : (~(X58 @ X60) | (X59 @ X60))) = mimplies) & ! [X61 : d_unsorted] : (d_unsorted_0 = X61) & ((^[X62 : ($i > $o), X63 : ($i > $o), X64 : $i] : ((X63 @ X64) & (X62 @ X64))) = iand)),
  inference(rectify,[],[f1])).
thf(f5,plain,(
  (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)))))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X37 : $i] : ? [X38 : d_unsorted] : (((d2unsorted @ X38)) = X37) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ! [X44 : d_unsorted,X45 : d_unsorted] : ((((d2unsorted @ X45)) = ((d2unsorted @ X44))) => (X44 = X45)) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $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)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & ! [X61 : d_unsorted] : (d_unsorted_0 = X61) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
  inference(fool_elimination,[],[f4])).
thf(f6,plain,(
  ~ (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
  inference(fool_elimination,[],[f3])).
thf(f7,plain,(
  (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)))))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ! [X3 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $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)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
  inference(rectify,[],[f5])).
thf(f8,plain,(
  (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & ! [X3 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))) & (((itrue @ (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]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))),
  inference(flattening,[],[f7])).
thf(f9,plain,(
  (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
  inference(flattening,[],[f6])).
thf(f10,plain,(
  ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ 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)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (((ifalse @ (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]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & ! [X3 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (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)))))))))))))),
  inference(ennf_transformation,[],[f8])).
thf(f11,plain,(
  ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ 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)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (((ifalse @ (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]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & ! [X1 : $i] : ? [X2 : d_unsorted] : (((d2unsorted @ X2)) = X1) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X3)) != ((d2unsorted @ X4))) | (X3 = X4)) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (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)))))))))))))),
  inference(rectify,[],[f10])).
thf(f12,plain,(
  ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ 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)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (((ifalse @ (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]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4)))))))))))))))) & ! [X1 : $i] : (((d2unsorted @ (sK0 @ X1))) = X1) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X3)) != ((d2unsorted @ X4))) | (X3 = X4)) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X2,$thf(sK0 @ X1))],[f11])).
thf(f15,plain,(
  (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)),
  inference(cnf_transformation,[],[f12])).
thf(f19,plain,(
  ( ! [X1 : $i] : ((((d2unsorted @ (sK0 @ X1))) = X1)) )),
  inference(cnf_transformation,[],[f12])).
thf(f20,plain,(
  (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4))))))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f26,plain,(
  (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f32,plain,(
  (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f35,plain,(
  ( ! [X0 : d_unsorted] : ((d_unsorted_0 = X0)) )),
  inference(cnf_transformation,[],[f12])).
thf(f36,plain,(
  (ixor != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (inot @ (iequiv @ Y0 @ Y1))))))),
  inference(cnf_transformation,[],[f9])).
thf(f39,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4))))))))))))))) != (^[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]: ((Y3 @ Y5) | (~ (irel @ Y4 @ Y5)))))) | (!! @ $i @ (^[Y5 : $i]: ((Y2 @ Y5) | (~ (irel @ Y4 @ Y5)))))) & ((!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y3 @ Y5)))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y2 @ Y5)))))))))))) @ Y0 @ Y1))))))),
  inference(definition_unfolding,[],[f36,f20,f32,f26])).
thf(f40,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4))))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (((~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (irel @ Y3 @ Y4)))))) | (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) | (~ (irel @ Y3 @ Y4)))))) & ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))))))))))))))))),
  inference(beta-eta_normalization,[],[f39])).
thf(f51,plain,(
  ( ! [X1 : $i] : ((((d2unsorted @ d_unsorted_0)) = X1)) )),
  inference(forward_demodulation,[],[f19,f35])).
thf(f55,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
  inference(constrained_superposition,[],[f51,f51])).
thf(f81,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ X0 @ X0)))) )),
  inference(constrained_superposition,[],[f15,f51])).
thf(f84,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y4 @ Y6)) | (Y0 @ Y6))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)) & (((Y0 @ Y5) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y1 @ Y6) | (~ (irel @ Y4 @ Y6))))))) | (~ (irel @ Y4 @ Y5)))) | (~ (irel @ Y2 @ Y4))))))))))))))) @ sK1)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (((~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (irel @ Y3 @ Y4)))))) | (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4) | (~ (irel @ Y3 @ Y4)))))) & ((!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y1 @ Y4)))) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y0 @ Y4)))))))))))))))) @ sK1)))),
  inference(negative_extensionality,[],[f40])).
thf(f85,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK1 @ Y3)))))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK1 @ Y5))))) | (~ (irel @ Y3 @ Y2))) | (Y0 @ Y2)) & (((sK1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5))))))) | (~ (irel @ Y3 @ Y4)))) | (~ (irel @ Y1 @ Y3))))))))))))))),
  inference(beta-eta_normalization,[],[f84])).
thf(f86,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((((~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (sK1 @ Y5))))) | (~ (irel @ Y3 @ Y2))) | (Y0 @ Y2)) & (((sK1 @ Y4) | (~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5))))))) | (~ (irel @ Y3 @ Y4)))) | (~ (irel @ Y1 @ Y3))))))))))))) @ sK2)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (((~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((sK1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (sK1 @ Y3)))))))))))))) @ sK2)))),
  inference(negative_extensionality,[],[f85])).
thf(f87,plain,(
  ((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK1 @ Y4))))) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) & (((sK1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4) | (~ (irel @ Y2 @ Y4))))))) | (~ (irel @ Y2 @ Y3)))) | (~ (irel @ Y0 @ Y2))))))))))) != (^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (((~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) & ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))))))))))))),
  inference(beta-eta_normalization,[],[f86])).
thf(f88,plain,(
  ((((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (((~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) & ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))))))))))) @ sK3)) != (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK1 @ Y4))))) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) & (((sK1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4) | (~ (irel @ Y2 @ Y4))))))) | (~ (irel @ Y2 @ Y3)))) | (~ (irel @ Y0 @ Y2))))))))))) @ sK3)))),
  inference(negative_extensionality,[],[f87])).
thf(f89,plain,(
  ($true = (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK1 @ Y4))))) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) & (((sK1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4) | (~ (irel @ Y2 @ Y4))))))) | (~ (irel @ Y2 @ Y3)))) | (~ (irel @ Y0 @ Y2))))))))))) @ sK3))) | ((((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (((~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) & ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))))))))))) @ sK3)) = $true)),
  inference(xor_proxy_clausification,[],[f88])).
thf(f90,plain,(
  ((((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (((~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y1 @ Y2)))))) | (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2)))))) & ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))))))))))) @ sK3)) = $false) | ($false = (((^[Y0 : $i]: (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((((~ (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y2 @ Y4)) | (sK1 @ Y4))))) | (~ (irel @ Y2 @ Y1))) | (sK2 @ Y1)) & (((sK1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((sK2 @ Y4) | (~ (irel @ Y2 @ Y4))))))) | (~ (irel @ Y2 @ Y3)))) | (~ (irel @ Y0 @ Y2))))))))))) @ sK3)))),
  inference(xor_proxy_clausification,[],[f88])).
thf(f91,plain,(
  ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1))))))))))))),
  inference(beta-eta_normalization,[],[f90])).
thf(f92,plain,(
  ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))))))))) | ($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1))))))))))))),
  inference(not_proxy_clausification,[],[f91])).
thf(f93,plain,(
  ( ! [X1 : $i] : (($false = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))))))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))))) @ X1)))) )),
  inference(pi_proxy_clausification,[],[f92])).
thf(f94,plain,(
  ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))))) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))))) @ X1)))) )),
  inference(not_proxy_clausification,[],[f93])).
thf(f95,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ X2)) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))))) @ X1)))) )),
  inference(pi_proxy_clausification,[],[f94])).
thf(f96,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((~ (irel @ sK3 @ X1)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))))))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))))) )),
  inference(beta-eta_normalization,[],[f95])).
thf(f97,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0))))))))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0)))))))) = $true) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(or_proxy_clausification,[],[f96])).
thf(f98,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0)))))))) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(pi_proxy_clausification,[],[f97])).
thf(f99,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0)))))))) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(and_proxy_clausification,[],[f98])).
thf(f100,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))))))) | (((~ (irel @ sK3 @ X1))) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true)) )),
  inference(and_proxy_clausification,[],[f98])).
thf(f101,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0))))))) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))))))) )),
  inference(or_proxy_clausification,[],[f100])).
thf(f102,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))))))) )),
  inference(not_proxy_clausification,[],[f101])).
thf(f103,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0))))))) | (((irel @ sK3 @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))))))) )),
  inference(not_proxy_clausification,[],[f102])).
thf(f104,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ sK3 @ X1)) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0))))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))) @ (sK4 @ X1))) = $false)) )),
  inference(sigma_proxy_clausification,[],[f103])).
thf(f105,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ sK3 @ X1)) = $false) | ($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ X1 @ Y0)))) @ X4))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X1 @ Y0)))) @ (sK4 @ X1))) = $false)) )),
  inference(pi_proxy_clausification,[],[f104])).
thf(f106,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ sK3 @ X1)) = $false) | ((((sK1 @ X4) | (~ (irel @ X1 @ X4)))) = $true) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))))) = $true) | ($false = (((sK2 @ (sK4 @ X1)) | (~ (irel @ X1 @ (sK4 @ X1))))))) )),
  inference(beta-eta_normalization,[],[f105])).
thf(f107,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK1 @ X4))) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))))) = $true) | (((irel @ sK3 @ X1)) = $false) | (((~ (irel @ X1 @ X4))) = $true) | ($false = (((sK2 @ (sK4 @ X1)) | (~ (irel @ X1 @ (sK4 @ X1))))))) )),
  inference(or_proxy_clausification,[],[f106])).
thf(f108,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((~ (irel @ X1 @ X4))) = $true) | (((irel @ sK3 @ X1)) = $false) | ($false = (((sK2 @ (sK4 @ X1)) | (~ (irel @ X1 @ (sK4 @ X1)))))) | ($true = ((sK1 @ X4))) | ($true = (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))) @ X5)))) )),
  inference(pi_proxy_clausification,[],[f107])).
thf(f109,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((irel @ X1 @ X4)) = $false) | ($false = (((sK2 @ (sK4 @ X1)) | (~ (irel @ X1 @ (sK4 @ X1)))))) | ($true = (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))) @ X5))) | ($true = ((sK1 @ X4))) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(not_proxy_clausification,[],[f108])).
thf(f111,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((sK1 @ X4))) | ($true = (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))) @ X5))) | (((sK2 @ (sK4 @ X1))) = $false) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false)) )),
  inference(or_proxy_clausification,[],[f109])).
thf(f112,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((sK1 @ X4))) | (((sK2 @ (sK4 @ X1))) = $false) | ($true = ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X5)))) | (~ (irel @ sK3 @ X3))))) | (((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(beta-eta_normalization,[],[f111])).
thf(f113,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK1 @ X4))) | ($true = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X5)))))) | (((~ (irel @ sK3 @ X3))) = $true) | (((sK2 @ (sK4 @ X1))) = $false)) )),
  inference(or_proxy_clausification,[],[f112])).
thf(f114,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((irel @ X1 @ X4)) = $false) | (((~ (irel @ sK3 @ X3))) = $true) | (((irel @ sK3 @ X1)) = $false) | (((sK2 @ (sK4 @ X1))) = $false) | ($true = ((sK1 @ X4))) | (((((sK1 @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X5)))) = $true)) )),
  inference(and_proxy_clausification,[],[f113])).
thf(f126,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((sK1 @ X4))) | (((sK2 @ (sK4 @ X1))) = $false) | (((irel @ X1 @ X4)) = $false) | (((((sK1 @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X5)))) = $true) | (((irel @ sK3 @ X3)) = $false) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(not_proxy_clausification,[],[f114])).
thf(f127,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((((sK1 @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0)))))))) = $true) | (((~ (irel @ X3 @ X5))) = $true) | (((irel @ sK3 @ X1)) = $false) | (((irel @ sK3 @ X3)) = $false) | (((sK2 @ (sK4 @ X1))) = $false) | ($true = ((sK1 @ X4))) | (((irel @ X1 @ X4)) = $false)) )),
  inference(or_proxy_clausification,[],[f126])).
thf(f128,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((irel @ sK3 @ X3)) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0)))))))) | (((sK2 @ (sK4 @ X1))) = $false) | ($true = ((sK1 @ X4))) | ($true = ((sK1 @ X5))) | (((~ (irel @ X3 @ X5))) = $true) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false)) )),
  inference(or_proxy_clausification,[],[f127])).
thf(f129,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((irel @ X1 @ X4)) = $false) | ($true = ((sK1 @ X4))) | (((irel @ sK3 @ X1)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (((~ (irel @ X3 @ X5))) = $true) | ($true = ((sK1 @ X5))) | (((sK2 @ (sK4 @ X1))) = $false) | (((irel @ sK3 @ X3)) = $false)) )),
  inference(not_proxy_clausification,[],[f128])).
thf(f130,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((irel @ sK3 @ X3)) = $false) | ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0)))) @ (sK6 @ X3))) = $false) | (((~ (irel @ X3 @ X5))) = $true) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK1 @ X4))) | (((sK2 @ (sK4 @ X1))) = $false) | ($true = ((sK1 @ X5))) | (((irel @ X1 @ X4)) = $false)) )),
  inference(sigma_proxy_clausification,[],[f129])).
thf(f131,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0)))) @ (sK6 @ X3))) = $false) | (((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X3)) = $false) | (((sK2 @ (sK4 @ X1))) = $false) | (((irel @ X3 @ X5)) = $false) | ($true = ((sK1 @ X5))) | ($true = ((sK1 @ X4))) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(not_proxy_clausification,[],[f130])).
thf(f132,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((sK2 @ (sK4 @ X1))) = $false) | (((irel @ X3 @ X5)) = $false) | ((((sK2 @ (sK6 @ X3)) | (~ (irel @ X3 @ (sK6 @ X3))))) = $false) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false) | ($true = ((sK1 @ X4))) | (((irel @ sK3 @ X3)) = $false) | ($true = ((sK1 @ X5)))) )),
  inference(beta-eta_normalization,[],[f131])).
thf(f134,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((sK2 @ (sK6 @ X3)))) | (((irel @ sK3 @ X3)) = $false) | (((irel @ X1 @ X4)) = $false) | ($true = ((sK1 @ X5))) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK1 @ X4))) | (((irel @ X3 @ X5)) = $false) | (((sK2 @ (sK4 @ X1))) = $false)) )),
  inference(or_proxy_clausification,[],[f132])).
thf(f160,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0)))))) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) = $true)) )),
  inference(or_proxy_clausification,[],[f99])).
thf(f161,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))))) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))))))) )),
  inference(not_proxy_clausification,[],[f160])).
thf(f162,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0)))))) | ((((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))) @ X4)) = $true) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(pi_proxy_clausification,[],[f161])).
thf(f163,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | ((((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))) @ (sK9 @ X1))) = $false) | ((((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))) @ X4)) = $true) | (((~ (irel @ sK3 @ X1))) = $true)) )),
  inference(sigma_proxy_clausification,[],[f162])).
thf(f164,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK2 @ Y0))) @ X4)) = $true) | ((((^[Y0 : $i]: ((~ (irel @ X1 @ Y0)) | (sK1 @ Y0))) @ (sK9 @ X1))) = $false) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ X3)) = $true) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(not_proxy_clausification,[],[f163])).
thf(f165,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ sK3 @ X1)) = $false) | ($true = (((~ (irel @ X1 @ X4)) | (sK2 @ X4)))) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))))) = $true) | ((((~ (irel @ X1 @ (sK9 @ X1))) | (sK1 @ (sK9 @ X1)))) = $false)) )),
  inference(beta-eta_normalization,[],[f164])).
thf(f166,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((~ (irel @ X1 @ (sK9 @ X1))) | (sK1 @ (sK9 @ X1)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))))) = $true) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK2 @ X4))) | (((~ (irel @ X1 @ X4))) = $true)) )),
  inference(or_proxy_clausification,[],[f165])).
thf(f167,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK1 @ (sK9 @ X1))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))))) = $true) | (((~ (irel @ X1 @ X4))) = $true) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK2 @ X4)))) )),
  inference(or_proxy_clausification,[],[f166])).
thf(f195,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((sK1 @ (sK9 @ X1))) = $false) | (((irel @ sK3 @ X1)) = $false) | (((~ (irel @ X1 @ X4))) = $true) | ($true = (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))) @ X5))) | ($true = ((sK2 @ X4)))) )),
  inference(pi_proxy_clausification,[],[f167])).
thf(f196,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((irel @ X1 @ X4)) = $false) | ($true = ((sK2 @ X4))) | ($true = (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ X3 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ X3 @ Y1))))))) | (~ (irel @ X3 @ Y0)))) | (~ (irel @ sK3 @ X3)))) @ X5))) | (((sK1 @ (sK9 @ X1))) = $false) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(not_proxy_clausification,[],[f195])).
thf(f197,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((sK2 @ X4))) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false) | (((sK1 @ (sK9 @ X1))) = $false) | ($true = ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X5)))) | (~ (irel @ sK3 @ X3)))))) )),
  inference(beta-eta_normalization,[],[f196])).
thf(f198,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((sK1 @ (sK9 @ X1))) = $false) | ($true = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2)) & (((sK1 @ X5) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ X3 @ Y0))))))) | (~ (irel @ X3 @ X5)))))) | ($true = ((sK2 @ X4))) | (((~ (irel @ sK3 @ X3))) = $true) | (((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(or_proxy_clausification,[],[f197])).
thf(f200,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK1 @ (sK9 @ X1))) = $false) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false) | ($true = ((sK2 @ X4))) | (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ X3 @ X2))) | (sK2 @ X2))) = $true) | (((~ (irel @ sK3 @ X3))) = $true)) )),
  inference(and_proxy_clausification,[],[f198])).
thf(f201,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ X3 @ X2)))) = $true) | (((irel @ X1 @ X4)) = $false) | (((~ (irel @ sK3 @ X3))) = $true) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK2 @ X2))) | (((sK1 @ (sK9 @ X1))) = $false) | ($true = ((sK2 @ X4)))) )),
  inference(or_proxy_clausification,[],[f200])).
thf(f202,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | (((sK1 @ (sK9 @ X1))) = $false) | ($true = ((sK2 @ X4))) | (((~ (irel @ sK3 @ X3))) = $true) | ($true = ((sK2 @ X2))) | (((irel @ sK3 @ X1)) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))))) | ($true = ((~ (irel @ X3 @ X2))))) )),
  inference(or_proxy_clausification,[],[f201])).
thf(f203,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((~ (irel @ X3 @ X2)))) | ($true = ((sK2 @ X4))) | (((irel @ sK3 @ X3)) = $false) | (((sK1 @ (sK9 @ X1))) = $false) | ($true = ((sK2 @ X2))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))))) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false)) )),
  inference(not_proxy_clausification,[],[f202])).
thf(f204,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X1)) = $false) | (((irel @ sK3 @ X3)) = $false) | (((sK1 @ (sK9 @ X1))) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))))) | (((irel @ X3 @ X2)) = $false) | ($true = ((sK2 @ X4))) | ($true = ((sK2 @ X2)))) )),
  inference(not_proxy_clausification,[],[f203])).
thf(f205,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK2 @ X4))) | (((irel @ sK3 @ X3)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))))) = $false) | (((irel @ X3 @ X2)) = $false) | (((sK1 @ (sK9 @ X1))) = $false) | ($true = ((sK2 @ X2))) | (((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(not_proxy_clausification,[],[f204])).
thf(f206,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false) | (((sK1 @ (sK9 @ X1))) = $false) | ((((^[Y0 : $i]: ((~ (irel @ X3 @ Y0)) | (sK1 @ Y0))) @ (sK12 @ X3))) = $false) | (((irel @ X3 @ X2)) = $false) | ($true = ((sK2 @ X4))) | (((irel @ sK3 @ X3)) = $false) | ($true = ((sK2 @ X2)))) )),
  inference(sigma_proxy_clausification,[],[f205])).
thf(f207,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((~ (irel @ X3 @ (sK12 @ X3))) | (sK1 @ (sK12 @ X3)))) = $false) | ($true = ((sK2 @ X4))) | (((irel @ X1 @ X4)) = $false) | ($true = ((sK2 @ X2))) | (((sK1 @ (sK9 @ X1))) = $false) | (((irel @ sK3 @ X3)) = $false) | (((irel @ X3 @ X2)) = $false) | (((irel @ sK3 @ X1)) = $false)) )),
  inference(beta-eta_normalization,[],[f206])).
thf(f208,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK1 @ (sK12 @ X3))) = $false) | (((irel @ X1 @ X4)) = $false) | ($true = ((sK2 @ X4))) | (((irel @ sK3 @ X3)) = $false) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X3 @ X2)) = $false) | (((sK1 @ (sK9 @ X1))) = $false) | ($true = ((sK2 @ X2)))) )),
  inference(or_proxy_clausification,[],[f207])).
thf(f221,plain,(
  ($true = ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))))))) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))))))))))),
  inference(beta-eta_normalization,[],[f89])).
thf(f222,plain,(
  ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))))))))) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))))) = $false)),
  inference(not_proxy_clausification,[],[f221])).
thf(f223,plain,(
  (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))))) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))))))))),
  inference(not_proxy_clausification,[],[f222])).
thf(f224,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))))))))) | ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ sK14)) = $false)),
  inference(sigma_proxy_clausification,[],[f223])).
thf(f225,plain,(
  ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y1 @ Y3)) | (sK1 @ Y3))))) | (~ (irel @ Y1 @ Y0))) | (sK2 @ Y0)) & (((sK1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((sK2 @ Y3) | (~ (irel @ Y1 @ Y3))))))) | (~ (irel @ Y1 @ Y2)))) | (~ (irel @ sK3 @ Y1)))))))) @ sK14)) = $false) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (((~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1)))))) & ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1))))))))) @ sK15)))),
  inference(sigma_proxy_clausification,[],[f224])).
thf(f226,plain,(
  ((((~ (irel @ sK3 @ sK15)) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0)))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0))))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))) = $false)),
  inference(beta-eta_normalization,[],[f225])).
thf(f227,plain,(
  (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))))) = $false) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0)))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0)))))))))),
  inference(or_proxy_clausification,[],[f226])).
thf(f287,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0)))))) & ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0)))))))))),
  inference(sigma_proxy_clausification,[],[f227])).
thf(f288,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18))) | ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0))))))) = $false) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0))))))))),
  inference(and_proxy_clausification,[],[f287])).
thf(f289,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18))) | ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0)))))))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0)))))) = $false)),
  inference(or_proxy_clausification,[],[f288])).
thf(f290,plain,(
  ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0)))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18)))),
  inference(or_proxy_clausification,[],[f288])).
thf(f291,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18)))),
  inference(or_proxy_clausification,[],[f290])).
thf(f411,plain,(
  ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0)))) @ sK21)) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))))) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18)))),
  inference(sigma_proxy_clausification,[],[f291])).
thf(f412,plain,(
  ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK15 @ Y0)))) @ sK21)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK2 @ Y0))) @ sK22)) = $false)),
  inference(sigma_proxy_clausification,[],[f411])).
thf(f413,plain,(
  ($false = (((~ (irel @ sK15 @ sK22)) | (sK2 @ sK22)))) | ((((sK1 @ sK21) | (~ (irel @ sK15 @ sK21)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))))) = $false)),
  inference(beta-eta_normalization,[],[f412])).
thf(f414,plain,(
  ((((sK1 @ sK21) | (~ (irel @ sK15 @ sK21)))) = $false) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))))) = $false) | (((sK2 @ sK22)) = $false)),
  inference(or_proxy_clausification,[],[f413])).
thf(f528,plain,(
  (((sK2 @ sK22)) = $false) | (((sK1 @ sK21)) = $false) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))))) = $false)),
  inference(or_proxy_clausification,[],[f414])).
thf(f529,plain,(
  ($false = (((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))) @ sK24))) | (((sK1 @ sK21)) = $false) | (((sK2 @ sK22)) = $false)),
  inference(sigma_proxy_clausification,[],[f528])).
thf(f530,plain,(
  (((sK2 @ sK22)) = $false) | (((sK1 @ sK21)) = $false) | (((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ sK24) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0))))))) | (~ (irel @ sK18 @ sK24)))) | (~ (irel @ sK3 @ sK18)))) = $false)),
  inference(beta-eta_normalization,[],[f529])).
thf(f532,plain,(
  ((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ sK24) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0))))))) | (~ (irel @ sK18 @ sK24))))) = $false) | (((sK2 @ sK22)) = $false) | (((sK1 @ sK21)) = $false)),
  inference(or_proxy_clausification,[],[f530])).
thf(f533,plain,(
  (((sK1 @ sK21)) = $false) | (((((sK1 @ sK24) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0))))))) | (~ (irel @ sK18 @ sK24)))) = $false) | (((sK2 @ sK22)) = $false) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14))))),
  inference(and_proxy_clausification,[],[f532])).
thf(f535,plain,(
  ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)))) | (((sK2 @ sK22)) = $false) | (((sK1 @ sK21)) = $false) | ((((sK1 @ sK24) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0)))))))) = $false)),
  inference(or_proxy_clausification,[],[f533])).
thf(f536,plain,(
  (((sK1 @ sK21)) = $false) | ((((sK1 @ sK24) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0)))))))) = $false) | (((sK2 @ sK22)) = $false) | (((sK2 @ sK14)) = $false)),
  inference(or_proxy_clausification,[],[f535])).
thf(f565,plain,(
  (((sK1 @ sK24)) = $false) | (((sK2 @ sK22)) = $false) | (((sK2 @ sK14)) = $false) | (((sK1 @ sK21)) = $false)),
  inference(or_proxy_clausification,[],[f536])).
thf(f637,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0)))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0))))))) = $false)),
  inference(or_proxy_clausification,[],[f289])).
thf(f638,plain,(
  (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0))))) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18)))),
  inference(not_proxy_clausification,[],[f637])).
thf(f639,plain,(
  (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0))))) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18)))),
  inference(not_proxy_clausification,[],[f638])).
thf(f640,plain,(
  ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0))))) = $true) | ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))) @ X1)) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18)))) )),
  inference(pi_proxy_clausification,[],[f639])).
thf(f641,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK15 @ Y0)))) @ X1)) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((((~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y0 @ Y2)) | (sK1 @ Y2))))) | (~ (irel @ Y0 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y1) | (~ (!! @ $i @ (^[Y2 : $i]: ((sK2 @ Y2) | (~ (irel @ Y0 @ Y2))))))) | (~ (irel @ Y0 @ Y1)))) | (~ (irel @ sK3 @ Y0)))))) @ sK18))) | ((((^[Y0 : $i]: ((~ (irel @ sK15 @ Y0)) | (sK1 @ Y0))) @ X2)) = $true)) )),
  inference(pi_proxy_clausification,[],[f640])).
thf(f642,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((~ (irel @ sK15 @ X2)) | (sK1 @ X2))) = $true) | ((((sK2 @ X1) | (~ (irel @ sK15 @ X1)))) = $true) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))))) = $false)) )),
  inference(beta-eta_normalization,[],[f641])).
thf(f643,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK1 @ X2)) = $true) | (((~ (irel @ sK15 @ X2))) = $true) | ((((sK2 @ X1) | (~ (irel @ sK15 @ X1)))) = $true) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))))) = $false)) )),
  inference(or_proxy_clausification,[],[f642])).
thf(f644,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK15 @ X2))) | (((!! @ $i @ (^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))))) = $false) | ((((sK2 @ X1) | (~ (irel @ sK15 @ X1)))) = $true) | (((sK1 @ X2)) = $true)) )),
  inference(not_proxy_clausification,[],[f643])).
thf(f645,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))) @ sK26)) = $false) | (((sK1 @ X2)) = $true) | ($false = ((irel @ sK15 @ X2))) | ((((sK2 @ X1) | (~ (irel @ sK15 @ X1)))) = $true)) )),
  inference(sigma_proxy_clausification,[],[f644])).
thf(f646,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK2 @ X1)) = $true) | ((((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))) @ sK26)) = $false) | (((sK1 @ X2)) = $true) | ($true = ((~ (irel @ sK15 @ X1)))) | ($false = ((irel @ sK15 @ X2)))) )),
  inference(or_proxy_clausification,[],[f645])).
thf(f647,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((sK2 @ X1)) = $true) | (((sK1 @ X2)) = $true) | ($false = ((irel @ sK15 @ X1))) | ($false = ((irel @ sK15 @ X2))) | ((((^[Y0 : $i]: (((((~ (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ sK18 @ Y1)) | (sK1 @ Y1))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ Y0) | (~ (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ sK18 @ Y1))))))) | (~ (irel @ sK18 @ Y0)))) | (~ (irel @ sK3 @ sK18)))) @ sK26)) = $false)) )),
  inference(not_proxy_clausification,[],[f646])).
thf(f648,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK15 @ X2))) | (((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X1))) | (((sK1 @ X2)) = $true) | (((((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ sK26) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0))))))) | (~ (irel @ sK18 @ sK26)))) | (~ (irel @ sK3 @ sK18)))) = $false)) )),
  inference(beta-eta_normalization,[],[f647])).
thf(f650,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK15 @ X2))) | (((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X1))) | (((sK1 @ X2)) = $true) | ($false = (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)) & (((sK1 @ sK26) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0))))))) | (~ (irel @ sK18 @ sK26))))))) )),
  inference(or_proxy_clausification,[],[f648])).
thf(f651,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK15 @ X2))) | ($false = ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14))) | (sK2 @ sK14)))) | (((((sK1 @ sK26) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0))))))) | (~ (irel @ sK18 @ sK26)))) = $false) | ($false = ((irel @ sK15 @ X1))) | (((sK1 @ X2)) = $true) | (((sK2 @ X1)) = $true)) )),
  inference(and_proxy_clausification,[],[f650])).
thf(f653,plain,(
  ( ! [X2 : $i,X1 : $i] : ((((((sK1 @ sK26) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0))))))) | (~ (irel @ sK18 @ sK26)))) = $false) | ($false = ((irel @ sK15 @ X1))) | ($false = ((irel @ sK15 @ X2))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14)))) = $false) | (((sK1 @ X2)) = $true) | (((sK2 @ X1)) = $true)) )),
  inference(or_proxy_clausification,[],[f651])).
thf(f655,plain,(
  ( ! [X2 : $i,X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) | (~ (irel @ sK18 @ sK14)))) = $false) | ($false = ((irel @ sK15 @ X1))) | (((sK1 @ X2)) = $true) | (((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X2))) | ((((sK1 @ sK26) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0)))))))) = $false)) )),
  inference(or_proxy_clausification,[],[f653])).
thf(f657,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK15 @ X1))) | ($false = ((irel @ sK15 @ X2))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0)))))) = $false) | ((((sK1 @ sK26) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0)))))))) = $false) | (((sK1 @ X2)) = $true) | (((sK2 @ X1)) = $true)) )),
  inference(or_proxy_clausification,[],[f655])).
thf(f658,plain,(
  ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ sK15 @ X1))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))))) = $true) | ($false = ((irel @ sK15 @ X2))) | (((sK1 @ X2)) = $true) | (((sK2 @ X1)) = $true) | ((((sK1 @ sK26) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0)))))))) = $false)) )),
  inference(not_proxy_clausification,[],[f657])).
thf(f659,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ sK15 @ X2))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X3))) | (((sK1 @ X2)) = $true) | (((sK2 @ X1)) = $true) | ((((sK1 @ sK26) | (~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0)))))))) = $false) | ($false = ((irel @ sK15 @ X1)))) )),
  inference(pi_proxy_clausification,[],[f658])).
thf(f660,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK2 @ X1)) = $true) | (((sK1 @ X2)) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X3))) | ($false = ((irel @ sK15 @ X1))) | ($false = ((irel @ sK15 @ X2))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0))))))) = $false)) )),
  inference(or_proxy_clausification,[],[f659])).
thf(f665,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0)))))) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X3))) | (((sK1 @ X2)) = $true) | ($false = ((irel @ sK15 @ X1))) | (((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X2)))) )),
  inference(not_proxy_clausification,[],[f660])).
thf(f666,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK1 @ X2)) = $true) | ($false = ((irel @ sK15 @ X2))) | ($false = ((irel @ sK15 @ X1))) | ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK18 @ Y0)))) @ X4)) = $true) | (((sK2 @ X1)) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK18 @ Y0)) | (sK1 @ Y0))) @ X3)))) )),
  inference(pi_proxy_clausification,[],[f665])).
thf(f667,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((sK2 @ X4) | (~ (irel @ sK18 @ X4)))) = $true) | ($false = ((irel @ sK15 @ X2))) | (((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X1))) | (((sK1 @ X2)) = $true) | ((((~ (irel @ sK18 @ X3)) | (sK1 @ X3))) = $true)) )),
  inference(beta-eta_normalization,[],[f666])).
thf(f668,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK2 @ X4))) | (((sK1 @ X2)) = $true) | ((((~ (irel @ sK18 @ X3)) | (sK1 @ X3))) = $true) | (((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X2))) | ($false = ((irel @ sK15 @ X1))) | (((~ (irel @ sK18 @ X4))) = $true)) )),
  inference(or_proxy_clausification,[],[f667])).
thf(f669,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((~ (irel @ sK18 @ X3))) = $true) | (((~ (irel @ sK18 @ X4))) = $true) | ($true = ((sK2 @ X4))) | ($false = ((irel @ sK15 @ X2))) | (((sK1 @ X2)) = $true) | ($true = ((sK1 @ X3))) | ($false = ((irel @ sK15 @ X1))) | (((sK2 @ X1)) = $true)) )),
  inference(or_proxy_clausification,[],[f668])).
thf(f670,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((irel @ sK18 @ X3))) | (((~ (irel @ sK18 @ X4))) = $true) | (((sK1 @ X2)) = $true) | (((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X2))) | ($false = ((irel @ sK15 @ X1))) | ($true = ((sK2 @ X4))) | ($true = ((sK1 @ X3)))) )),
  inference(not_proxy_clausification,[],[f669])).
thf(f671,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((sK2 @ X4))) | (((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X2))) | ($false = ((irel @ sK18 @ X4))) | ($false = ((irel @ sK15 @ X1))) | ($true = ((sK1 @ X3))) | ($false = ((irel @ sK18 @ X3))) | (((sK1 @ X2)) = $true)) )),
  inference(not_proxy_clausification,[],[f670])).
thf(f817,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((sK1 @ X5))) | ($true = ((sK1 @ X4))) | (((irel @ X3 @ X5)) = $false) | (((sK2 @ (sK4 @ X1))) = $false) | (((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X1)) = $false) | (((irel @ sK3 @ X3)) = $false) | (((sK2 @ (d2unsorted @ d_unsorted_0))) = $false)) )),
  inference(forward_demodulation,[],[f134,f51])).
thf(f828,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ sK3 @ X3)) = $false) | (((irel @ X3 @ X2)) = $false) | ($true = ((sK2 @ X4))) | (((sK1 @ (d2unsorted @ d_unsorted_0))) = $false) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK2 @ X2))) | (((irel @ X1 @ X4)) = $false) | (((sK1 @ (sK9 @ X1))) = $false)) )),
  inference(forward_demodulation,[],[f208,f51])).
thf(f854,definition,(
  spl29_6 <=> (((sK2 @ sK14)) = $false)),
  introduced(definition,[new_symbols(definition,[spl29_6])],[avatar_definition])).
thf(f855,plain,(
  (((sK2 @ sK14)) != $false) | spl29_6),
  inference(avatar_component_clause,[],[f854])).
thf(f856,plain,(
  (((sK2 @ sK14)) = $false) | ~spl29_6),
  inference(avatar_component_clause,[],[f854])).
thf(f876,definition,(
  spl29_10 <=> ! [X2 : $i] : ((((sK1 @ X2)) = $true) | (((irel @ sK18 @ X2)) = $false))),
  introduced(definition,[new_symbols(definition,[spl29_10])],[avatar_definition])).
thf(f877,plain,(
  ( ! [X2 : $i] : ((((sK1 @ X2)) = $true) | (((irel @ sK18 @ X2)) = $false)) ) | ~spl29_10),
  inference(avatar_component_clause,[],[f876])).
thf(f883,definition,(
  spl29_12 <=> ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X1))))),
  introduced(definition,[new_symbols(definition,[spl29_12])],[avatar_definition])).
thf(f884,plain,(
  ( ! [X1 : $i] : ((((sK2 @ X1)) = $true) | ($false = ((irel @ sK15 @ X1)))) ) | ~spl29_12),
  inference(avatar_component_clause,[],[f883])).
thf(f887,definition,(
  spl29_13 <=> ! [X3 : $i] : ((((sK2 @ X3)) = $true) | ($false = ((irel @ sK18 @ X3))))),
  introduced(definition,[new_symbols(definition,[spl29_13])],[avatar_definition])).
thf(f888,plain,(
  ( ! [X3 : $i] : ((((sK2 @ X3)) = $true) | ($false = ((irel @ sK18 @ X3)))) ) | ~spl29_13),
  inference(avatar_component_clause,[],[f887])).
thf(f906,definition,(
  spl29_16 <=> (((irel @ sK3 @ sK18)) = $true)),
  introduced(definition,[new_symbols(definition,[spl29_16])],[avatar_definition])).
thf(f907,plain,(
  (((irel @ sK3 @ sK18)) != $true) | spl29_16),
  inference(avatar_component_clause,[],[f906])).
thf(f908,plain,(
  (((irel @ sK3 @ sK18)) = $true) | ~spl29_16),
  inference(avatar_component_clause,[],[f906])).
thf(f929,definition,(
  spl29_19 <=> (((sK1 @ sK21)) = $false)),
  introduced(definition,[new_symbols(definition,[spl29_19])],[avatar_definition])).
thf(f931,plain,(
  (((sK1 @ sK21)) = $false) | ~spl29_19),
  inference(avatar_component_clause,[],[f929])).
thf(f965,definition,(
  spl29_23 <=> (((sK2 @ sK22)) = $false)),
  introduced(definition,[new_symbols(definition,[spl29_23])],[avatar_definition])).
thf(f967,plain,(
  (((sK2 @ sK22)) = $false) | ~spl29_23),
  inference(avatar_component_clause,[],[f965])).
thf(f969,definition,(
  spl29_24 <=> (((sK1 @ sK24)) = $false)),
  introduced(definition,[new_symbols(definition,[spl29_24])],[avatar_definition])).
thf(f971,plain,(
  (((sK1 @ sK24)) = $false) | ~spl29_24),
  inference(avatar_component_clause,[],[f969])).
thf(f976,plain,(
  spl29_23 | spl29_6 | spl29_19 | spl29_24),
  inference(avatar_split_clause,[],[f565,f969,f929,f854,f965])).
thf(f1005,definition,(
  spl29_28 <=> ! [X2 : $i] : (($false = ((irel @ sK15 @ X2))) | (((sK1 @ X2)) = $true))),
  introduced(definition,[new_symbols(definition,[spl29_28])],[avatar_definition])).
thf(f1006,plain,(
  ( ! [X2 : $i] : (($false = ((irel @ sK15 @ X2))) | (((sK1 @ X2)) = $true)) ) | ~spl29_28),
  inference(avatar_component_clause,[],[f1005])).
thf(f1012,plain,(
  spl29_28 | spl29_10 | spl29_13 | spl29_12),
  inference(avatar_split_clause,[],[f671,f883,f887,f876,f1005])).
thf(f1063,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : ((((irel @ sK3 @ X1)) = $false) | ($true = ((sK1 @ X4))) | ($true = ((sK1 @ X5))) | (((irel @ X3 @ X5)) = $false) | (((sK2 @ (d2unsorted @ d_unsorted_0))) = $false) | (((sK2 @ (d2unsorted @ d_unsorted_0))) = $false) | (((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X3)) = $false)) )),
  inference(forward_demodulation,[],[f817,f51])).
thf(f1064,plain,(
  ( ! [X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($true = ((sK1 @ X4))) | ($true = ((sK1 @ X5))) | (((irel @ sK3 @ X3)) = $false) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false) | (((sK2 @ (d2unsorted @ d_unsorted_0))) = $false) | (((irel @ X3 @ X5)) = $false)) )),
  inference(duplicate_literal_removal,[],[f1063])).
thf(f1075,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK1 @ (d2unsorted @ d_unsorted_0))) = $false) | (((irel @ sK3 @ X3)) = $false) | (((sK1 @ (d2unsorted @ d_unsorted_0))) = $false) | ($true = ((sK2 @ X4))) | (((irel @ X3 @ X2)) = $false) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false) | ($true = ((sK2 @ X2)))) )),
  inference(forward_demodulation,[],[f828,f51])).
thf(f1076,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ sK3 @ X3)) = $false) | (((irel @ X3 @ X2)) = $false) | (((sK1 @ (d2unsorted @ d_unsorted_0))) = $false) | (((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK2 @ X4))) | ($true = ((sK2 @ X2)))) )),
  inference(duplicate_literal_removal,[],[f1075])).
thf(f1080,definition,(
  spl29_35 <=> ! [X4 : $i,X1 : $i] : (($true = ((sK1 @ X4))) | (((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false))),
  introduced(definition,[new_symbols(definition,[spl29_35])],[avatar_definition])).
thf(f1081,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((irel @ sK3 @ X1)) = $false) | (((irel @ X1 @ X4)) = $false) | ($true = ((sK1 @ X4)))) ) | ~spl29_35),
  inference(avatar_component_clause,[],[f1080])).
thf(f1086,definition,(
  spl29_37 <=> (((sK2 @ (d2unsorted @ d_unsorted_0))) = $false)),
  introduced(definition,[new_symbols(definition,[spl29_37])],[avatar_definition])).
thf(f1088,plain,(
  (((sK2 @ (d2unsorted @ d_unsorted_0))) = $false) | ~spl29_37),
  inference(avatar_component_clause,[],[f1086])).
thf(f1091,definition,(
  spl29_38 <=> (((sK1 @ (d2unsorted @ d_unsorted_0))) = $false)),
  introduced(definition,[new_symbols(definition,[spl29_38])],[avatar_definition])).
thf(f1093,plain,(
  (((sK1 @ (d2unsorted @ d_unsorted_0))) = $false) | ~spl29_38),
  inference(avatar_component_clause,[],[f1091])).
thf(f1095,definition,(
  spl29_39 <=> ! [X2 : $i,X3 : $i] : ((((irel @ X3 @ X2)) = $false) | ($true = ((sK2 @ X2))) | (((irel @ sK3 @ X3)) = $false))),
  introduced(definition,[new_symbols(definition,[spl29_39])],[avatar_definition])).
thf(f1096,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((irel @ X3 @ X2)) = $false) | (((irel @ sK3 @ X3)) = $false) | ($true = ((sK2 @ X2)))) ) | ~spl29_39),
  inference(avatar_component_clause,[],[f1095])).
thf(f1098,plain,(
  spl29_37 | spl29_35 | spl29_35),
  inference(avatar_split_clause,[],[f1064,f1080,f1080,f1086])).
thf(f1112,plain,(
  spl29_38 | spl29_39 | spl29_39),
  inference(avatar_split_clause,[],[f1076,f1095,f1095,f1091])).
thf(f1118,plain,(
  ( ! [X0 : $i] : ((((sK1 @ X0)) = $false)) ) | ~spl29_38),
  inference(constrained_superposition,[],[f1093,f51])).
thf(f1123,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl29_6),
  inference(constrained_superposition,[],[f856,f55])).
thf(f1131,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((irel @ sK3 @ X1)) = $false) | ($true = $false) | (((irel @ X1 @ X4)) = $false)) ) | (~spl29_35 | ~spl29_38)),
  inference(forward_demodulation,[],[f1081,f1118])).
thf(f1132,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | (((irel @ sK3 @ X1)) = $false)) ) | (~spl29_35 | ~spl29_38)),
  inference(trivial_inequality_removal,[],[f1131])).
thf(f1133,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ sK3 @ X0)))) ) | ~spl29_16),
  inference(constrained_superposition,[],[f908,f55])).
thf(f1135,plain,(
  ( ! [X0 : $i] : ((((irel @ X0 @ sK18)) = $true)) ) | ~spl29_16),
  inference(constrained_superposition,[],[f908,f55])).
thf(f1145,plain,(
  ( ! [X1 : $i,X4 : $i] : (($true = $false) | (((irel @ X1 @ X4)) = $false)) ) | (~spl29_16 | ~spl29_35 | ~spl29_38)),
  inference(forward_demodulation,[],[f1132,f1133])).
thf(f1146,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false)) ) | (~spl29_16 | ~spl29_35 | ~spl29_38)),
  inference(trivial_inequality_removal,[],[f1145])).
thf(f1159,plain,(
  ($true = $false) | (~spl29_16 | ~spl29_35 | ~spl29_38)),
  inference(constrained_superposition,[],[f1135,f1146])).
thf(f1183,plain,(
  $false | (~spl29_16 | ~spl29_35 | ~spl29_38)),
  inference(trivial_inequality_removal,[],[f1159])).
thf(f1184,plain,(
  ~spl29_16 | ~spl29_35 | ~spl29_38),
  inference(avatar_contradiction_clause,[],[f1183])).
thf(f1185,plain,(
  ( ! [X2 : $i] : (($false = ((irel @ sK15 @ X2))) | ($true = $false)) ) | (~spl29_28 | ~spl29_38)),
  inference(forward_demodulation,[],[f1006,f1118])).
thf(f1186,plain,(
  ( ! [X2 : $i] : (($false = ((irel @ sK15 @ X2)))) ) | (~spl29_28 | ~spl29_38)),
  inference(trivial_inequality_removal,[],[f1185])).
thf(f1187,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK15 @ X1))) | ($true = $false)) ) | (~spl29_6 | ~spl29_12)),
  inference(forward_demodulation,[],[f884,f1123])).
thf(f1188,plain,(
  ( ! [X1 : $i] : (($false = ((irel @ sK15 @ X1)))) ) | (~spl29_6 | ~spl29_12)),
  inference(trivial_inequality_removal,[],[f1187])).
thf(f1189,plain,(
  ( ! [X0 : $i] : (($true != ((irel @ sK3 @ X0)))) ) | spl29_16),
  inference(constrained_superposition,[],[f907,f55])).
thf(f1197,plain,(
  ($true != $true) | spl29_16),
  inference(constrained_superposition,[],[f1189,f81])).
thf(f1203,plain,(
  $false | spl29_16),
  inference(trivial_inequality_removal,[],[f1197])).
thf(f1204,plain,(
  spl29_16),
  inference(avatar_contradiction_clause,[],[f1203])).
thf(f1205,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ sK3 @ X0)))) ) | ~spl29_16),
  inference(constrained_superposition,[],[f908,f55])).
thf(f1209,plain,(
  ( ! [X0 : $i,X1 : $i] : (($true = ((irel @ X0 @ X1)))) ) | ~spl29_16),
  inference(constrained_superposition,[],[f1205,f55])).
thf(f1219,plain,(
  ($true = $false) | (~spl29_16 | ~spl29_28 | ~spl29_38)),
  inference(forward_demodulation,[],[f1186,f1209])).
thf(f1220,plain,(
  $false | (~spl29_16 | ~spl29_28 | ~spl29_38)),
  inference(trivial_inequality_removal,[],[f1219])).
thf(f1221,plain,(
  ~spl29_16 | ~spl29_28 | ~spl29_38),
  inference(avatar_contradiction_clause,[],[f1220])).
thf(f1222,plain,(
  ($true = $false) | (~spl29_6 | ~spl29_12 | ~spl29_16)),
  inference(forward_demodulation,[],[f1188,f1209])).
thf(f1223,plain,(
  $false | (~spl29_6 | ~spl29_12 | ~spl29_16)),
  inference(trivial_inequality_removal,[],[f1222])).
thf(f1224,plain,(
  ~spl29_6 | ~spl29_12 | ~spl29_16),
  inference(avatar_contradiction_clause,[],[f1223])).
thf(f1225,plain,(
  ( ! [X2 : $i] : ((((irel @ sK18 @ X2)) = $false) | ($true = $false)) ) | (~spl29_10 | ~spl29_38)),
  inference(forward_demodulation,[],[f877,f1118])).
thf(f1226,plain,(
  ( ! [X2 : $i] : ((((irel @ sK18 @ X2)) = $false)) ) | (~spl29_10 | ~spl29_38)),
  inference(trivial_inequality_removal,[],[f1225])).
thf(f1227,plain,(
  ($true = $false) | (~spl29_10 | ~spl29_16 | ~spl29_38)),
  inference(forward_demodulation,[],[f1226,f1209])).
thf(f1228,plain,(
  $false | (~spl29_10 | ~spl29_16 | ~spl29_38)),
  inference(trivial_inequality_removal,[],[f1227])).
thf(f1229,plain,(
  ~spl29_10 | ~spl29_16 | ~spl29_38),
  inference(avatar_contradiction_clause,[],[f1228])).
thf(f1230,plain,(
  ( ! [X3 : $i] : (($false = ((irel @ sK18 @ X3))) | ($true = $false)) ) | (~spl29_6 | ~spl29_13)),
  inference(forward_demodulation,[],[f888,f1123])).
thf(f1231,plain,(
  ( ! [X3 : $i] : (($false = ((irel @ sK18 @ X3)))) ) | (~spl29_6 | ~spl29_13)),
  inference(trivial_inequality_removal,[],[f1230])).
thf(f1232,plain,(
  ($true = $false) | (~spl29_6 | ~spl29_13 | ~spl29_16)),
  inference(forward_demodulation,[],[f1231,f1209])).
thf(f1233,plain,(
  $false | (~spl29_6 | ~spl29_13 | ~spl29_16)),
  inference(trivial_inequality_removal,[],[f1232])).
thf(f1234,plain,(
  ~spl29_6 | ~spl29_13 | ~spl29_16),
  inference(avatar_contradiction_clause,[],[f1233])).
thf(f1243,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl29_37),
  inference(constrained_superposition,[],[f1088,f51])).
thf(f1249,plain,(
  ($false != $false) | (spl29_6 | ~spl29_37)),
  inference(constrained_superposition,[],[f855,f1243])).
thf(f1251,plain,(
  $false | (spl29_6 | ~spl29_37)),
  inference(trivial_inequality_removal,[],[f1249])).
thf(f1252,plain,(
  spl29_6 | ~spl29_37),
  inference(avatar_contradiction_clause,[],[f1251])).
thf(f1262,plain,(
  ( ! [X1 : $i,X4 : $i] : ((((irel @ X1 @ X4)) = $false) | ($true = ((sK1 @ X4))) | ($true = $false)) ) | (~spl29_16 | ~spl29_35)),
  inference(forward_demodulation,[],[f1081,f1209])).
thf(f1263,plain,(
  ( ! [X1 : $i,X4 : $i] : (($true = ((sK1 @ X4))) | (((irel @ X1 @ X4)) = $false)) ) | (~spl29_16 | ~spl29_35)),
  inference(trivial_inequality_removal,[],[f1262])).
thf(f1266,plain,(
  ( ! [X2 : $i,X3 : $i] : (($true = $false) | (((irel @ sK3 @ X3)) = $false) | ($true = ((sK2 @ X2)))) ) | (~spl29_16 | ~spl29_39)),
  inference(forward_demodulation,[],[f1096,f1209])).
thf(f1267,plain,(
  ( ! [X2 : $i,X3 : $i] : ((((irel @ sK3 @ X3)) = $false) | ($true = ((sK2 @ X2)))) ) | (~spl29_16 | ~spl29_39)),
  inference(trivial_inequality_removal,[],[f1266])).
thf(f1268,plain,(
  ( ! [X4 : $i] : (($true = $false) | ($true = ((sK1 @ X4)))) ) | (~spl29_16 | ~spl29_35)),
  inference(forward_demodulation,[],[f1263,f1209])).
thf(f1269,plain,(
  ( ! [X4 : $i] : (($true = ((sK1 @ X4)))) ) | (~spl29_16 | ~spl29_35)),
  inference(trivial_inequality_removal,[],[f1268])).
thf(f1270,plain,(
  ( ! [X2 : $i] : (($true = ((sK2 @ X2))) | ($true = $false)) ) | (~spl29_16 | ~spl29_39)),
  inference(forward_demodulation,[],[f1267,f1209])).
thf(f1271,plain,(
  ( ! [X2 : $i] : (($true = ((sK2 @ X2)))) ) | (~spl29_16 | ~spl29_39)),
  inference(trivial_inequality_removal,[],[f1270])).
thf(f1272,plain,(
  ($true = $false) | (~spl29_6 | ~spl29_16 | ~spl29_39)),
  inference(forward_demodulation,[],[f856,f1271])).
thf(f1273,plain,(
  $false | (~spl29_6 | ~spl29_16 | ~spl29_39)),
  inference(trivial_inequality_removal,[],[f1272])).
thf(f1274,plain,(
  ~spl29_6 | ~spl29_16 | ~spl29_39),
  inference(avatar_contradiction_clause,[],[f1273])).
thf(f1293,plain,(
  ($true = $false) | (~spl29_16 | ~spl29_19 | ~spl29_35)),
  inference(forward_demodulation,[],[f931,f1269])).
thf(f1294,plain,(
  $false | (~spl29_16 | ~spl29_19 | ~spl29_35)),
  inference(trivial_inequality_removal,[],[f1293])).
thf(f1295,plain,(
  ~spl29_16 | ~spl29_19 | ~spl29_35),
  inference(avatar_contradiction_clause,[],[f1294])).
thf(f1297,plain,(
  ($true = $false) | (~spl29_16 | ~spl29_23 | ~spl29_39)),
  inference(forward_demodulation,[],[f967,f1271])).
thf(f1298,plain,(
  $false | (~spl29_16 | ~spl29_23 | ~spl29_39)),
  inference(trivial_inequality_removal,[],[f1297])).
thf(f1299,plain,(
  ~spl29_16 | ~spl29_23 | ~spl29_39),
  inference(avatar_contradiction_clause,[],[f1298])).
thf(f1301,plain,(
  ($true = $false) | (~spl29_16 | ~spl29_24 | ~spl29_35)),
  inference(forward_demodulation,[],[f971,f1269])).
thf(f1302,plain,(
  $false | (~spl29_16 | ~spl29_24 | ~spl29_35)),
  inference(trivial_inequality_removal,[],[f1301])).
thf(f1303,plain,(
  ~spl29_16 | ~spl29_24 | ~spl29_35),
  inference(avatar_contradiction_clause,[],[f1302])).
cnf(s55, plain, spl29_6 | spl29_19 | spl29_23 | spl29_24, inference(sat_conversion,[],[f976])).
cnf(s72, plain, spl29_10 | spl29_12 | spl29_13 | spl29_28, inference(sat_conversion,[],[f1012])).
cnf(s103, plain, spl29_35 | spl29_35 | spl29_37, inference(sat_conversion,[],[f1098])).
cnf(s104, plain, spl29_35 | spl29_37, inference(rat,[],[s103])).
cnf(s117, plain, spl29_39 | spl29_38 | spl29_39, inference(sat_conversion,[],[f1112])).
cnf(s118, plain, spl29_38 | spl29_39, inference(rat,[],[s117])).
cnf(s132, plain, ~spl29_16 | ~spl29_35 | ~spl29_38, inference(sat_conversion,[],[f1184])).
cnf(s134, plain, spl29_16, inference(sat_conversion,[],[f1204])).
cnf(s135, plain, ~spl29_16 | ~spl29_28 | ~spl29_38, inference(sat_conversion,[],[f1221])).
cnf(s136, plain, ~spl29_6 | ~spl29_12 | ~spl29_16, inference(sat_conversion,[],[f1224])).
cnf(s137, plain, ~spl29_10 | ~spl29_16 | ~spl29_38, inference(sat_conversion,[],[f1229])).
cnf(s138, plain, ~spl29_6 | ~spl29_13 | ~spl29_16, inference(sat_conversion,[],[f1234])).
cnf(s139, plain, spl29_6 | ~spl29_37, inference(sat_conversion,[],[f1252])).
cnf(s141, plain, ~spl29_6 | ~spl29_16 | ~spl29_39, inference(sat_conversion,[],[f1274])).
cnf(s146, plain, ~spl29_16 | ~spl29_19 | ~spl29_35, inference(sat_conversion,[],[f1295])).
cnf(s147, plain, ~spl29_16 | ~spl29_23 | ~spl29_39, inference(sat_conversion,[],[f1299])).
cnf(s148, plain, ~spl29_16 | ~spl29_24 | ~spl29_35, inference(sat_conversion,[],[f1303])).
cnf(s149, plain, ~spl29_35 | ~spl29_38, inference(rat,[],[s132,s134])).
cnf(s161, plain, spl29_6, inference(rat,[],[s147,s118,s55,s149,s146,s148,s104,s139,s134])).
cnf(s162, plain, ~spl29_39, inference(rat,[],[s141,s134,s161])).
cnf(s163, plain, ~spl29_13, inference(rat,[],[s138,s134,s161])).
cnf(s164, plain, ~spl29_12, inference(rat,[],[s136,s134,s161])).
cnf(s165, plain, spl29_38, inference(rat,[],[s118,s162])).
cnf(s166, plain, ~spl29_10, inference(rat,[],[s137,s134,s165])).
cnf(s167, plain, ~spl29_28, inference(rat,[],[s135,s134,s165])).
cnf(s170, plain, $false, inference(rat,[],[s72,s164,s163,s166,s167])).
thf(f1304,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s170])).
% SZS output end Proof for theBenchmark