%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, unsorted: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(type_def_7, type, d_unsorted: $tType).
thf(func_def_0, type, irel: ($i > $i > $o)).
thf(func_def_1, type, mnot: (($i > $o) > $i > $o)).
thf(func_def_2, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_3, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_4, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_5, type, mbox_s4: (($i > $o) > $i > $o)).
thf(func_def_6, type, iatom: (($i > $o) > $i > $o)).
thf(func_def_7, type, inot: (($i > $o) > $i > $o)).
thf(func_def_8, type, itrue: ($i > $o)).
thf(func_def_9, type, ifalse: ($i > $o)).
thf(func_def_10, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_11, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_12, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_13, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_14, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_15, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
thf(func_def_16, type, ivalid: (($i > $o) > $o)).
thf(func_def_17, type, isatisfiable: (($i > $o) > $o)).
thf(func_def_18, type, icountersatisfiable: (($i > $o) > $o)).
thf(func_def_19, type, iinvalid: (($i > $o) > $o)).
thf(func_def_20, type, d2unsorted: (d_unsorted > $i)).
thf(func_def_21, type, d_unsorted_0: d_unsorted).
thf(func_def_23, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_24, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_25, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_26, type, vNOT: ($o > $o)).
thf(func_def_27, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_28, type, vOR: ($o > $o > $o)).
thf(func_def_29, type, vAND: ($o > $o > $o)).
thf(func_def_30, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_31, type, db7: !>[X0: $tType]:(X0)).
thf(func_def_32, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_33, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_34, type, db8: !>[X0: $tType]:(X0)).
thf(func_def_35, type, db5: !>[X0: $tType]:(X0)).
thf(func_def_36, type, db6: !>[X0: $tType]:(X0)).
thf(func_def_39, type, sK0: ($i > d_unsorted)).
thf(func_def_40, type, sK1: ($i > $o)).
thf(func_def_41, type, sK2: ($i > $o)).
thf(f1,conjecture,(
  (ior = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',ior)).
thf(f2,negated_conjecture,(
  ~ (ior = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))))),
  inference(negated_conjecture,[status(cth)],[f1])).
thf(f3,axiom,(
  (inot = (^[X4 : ($i > $o), X5 : $i] : (~ ! [X2 : $i] : (~(irel @ X5 @ X2) | (X4 @ X2))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ! [X0 : d_unsorted] : (X0 = d_unsorted_0) & ((^[X1 : ($i > $o), X2 : ($i > $o), X3 : $i] : ((X1 @ X3) & (X2 @ X3))) = mand) & ((^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (! [X2 : $i,X7 : $i] : (~ ! [X8 : $i] : ((X4 @ X8) | ~(irel @ X2 @ X8)) | ~(irel @ X2 @ X7) | ~(irel @ X5 @ X2) | (X6 @ X7)) & ! [X2 : $i,X9 : $i] : (~(irel @ X2 @ X9) | ~ ! [X10 : $i] : ((X6 @ X10) | ~(irel @ X2 @ X10)) | ~(irel @ X5 @ X2) | (X4 @ X9)))) = iequiv) & ! [X3 : $i] : ? [X0 : d_unsorted] : (X3 = ((d2unsorted @ X0))) & (itrue @ (d2unsorted @ d_unsorted_0)) & ((^[X15 : ($i > $o)] : (! [X16 : $i] : (X15 @ X16))) = ivalid) & ((^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (! [X2 : $i] : (~(irel @ X5 @ X2) | (X4 @ X2)) | ! [X2 : $i] : (~(irel @ X5 @ X2) | (X6 @ X2)))) = ior) & (iimplies = (^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (! [X2 : $i] : (~(irel @ X5 @ X2) | (X6 @ X2)) | ~ ! [X2 : $i] : ((X4 @ X2) | ~(irel @ X5 @ X2))))) & ((^[X15 : ($i > $o)] : (~ ! [X16 : $i] : ~(X15 @ X16))) = isatisfiable) & ((^[X1 : ($i > $o), X2 : ($i > $o), X3 : $i] : ((X2 @ X3) | (X1 @ X3))) = mor) & (iatom = (^[X4 : ($i > $o), X5 : $i] : ((X4 @ X5)))) & ((^[X15 : ($i > $o)] : (! [X16 : $i] : ~(X15 @ X16))) = iinvalid) & ((^[X15 : ($i > $o)] : (~ ! [X16 : $i] : (X15 @ X16))) = icountersatisfiable) & (iand = (^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (! [X2 : $i] : (~(irel @ X5 @ X2) | (X4 @ X2)) & ! [X2 : $i] : ((X6 @ X2) | ~(irel @ X5 @ X2))))) & (mbox_s4 = (^[X4 : ($i > $o), X1 : $i] : (! [X2 : $i] : (~(irel @ X1 @ X2) | (X4 @ X2))))) & ((^[X1 : ($i > $o), X3 : $i] : (~(X1 @ X3))) = mnot) & ((^[X3 : ($i > $o), X17 : ($i > $o), X5 : $i] : ((X17 @ X5) | ~(X3 @ X5))) = mimplies) & ((^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (! [X2 : $i] : (~(irel @ X5 @ X2) | (X4 @ X2)) | ~ ! [X2 : $i] : ((X6 @ X2) | ~(irel @ X5 @ X2)))) = iimplied) & ! [X18 : d_unsorted,X19 : d_unsorted] : ((((d2unsorted @ X18)) = ((d2unsorted @ X19))) => (X18 = X19)) & (ixor = (^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (~ ! [X2 : $i,X13 : $i,X12 : $i,X14 : $i,X11 : $i] : (~(irel @ X5 @ X2) | (((X6 @ X12) | ~ ! [X8 : $i] : (~(irel @ X11 @ X8) | (X4 @ X8)) | ~(irel @ X11 @ X12) | ~(irel @ X2 @ X11)) & (~(irel @ X2 @ X13) | (X4 @ X14) | ~(irel @ X13 @ X14) | ~ ! [X10 : $i] : ((X6 @ X10) | ~(irel @ X13 @ X10))))))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcl696_1)).
thf(f4,plain,(
  ~ (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
  inference(fool_elimination,[],[f2])).
thf(f5,plain,(
  (inot = (^[X0 : ($i > $o), X1 : $i] : (~ ! [X2 : $i] : (~(irel @ X1 @ X2) | (X0 @ X2))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ! [X3 : d_unsorted] : (d_unsorted_0 = X3) & ((^[X4 : ($i > $o), X5 : ($i > $o), X6 : $i] : ((X4 @ X6) & (X5 @ X6))) = mand) & ((^[X7 : ($i > $o), X8 : ($i > $o), X9 : $i] : (! [X10 : $i,X11 : $i] : (~ ! [X12 : $i] : ((X7 @ X12) | ~(irel @ X10 @ X12)) | ~(irel @ X10 @ X11) | ~(irel @ X9 @ X10) | (X8 @ X11)) & ! [X13 : $i,X14 : $i] : (~(irel @ X13 @ X14) | ~ ! [X15 : $i] : ((X8 @ X15) | ~(irel @ X13 @ X15)) | ~(irel @ X9 @ X13) | (X7 @ X14)))) = iequiv) & ! [X16 : $i] : ? [X17 : d_unsorted] : (((d2unsorted @ X17)) = X16) & (itrue @ (d2unsorted @ d_unsorted_0)) & ((^[X18 : ($i > $o)] : (! [X19 : $i] : (X18 @ X19))) = ivalid) & ((^[X20 : ($i > $o), X21 : ($i > $o), X22 : $i] : (! [X23 : $i] : (~(irel @ X22 @ X23) | (X20 @ X23)) | ! [X24 : $i] : (~(irel @ X22 @ X24) | (X21 @ X24)))) = ior) & (iimplies = (^[X25 : ($i > $o), X26 : ($i > $o), X27 : $i] : (! [X28 : $i] : (~(irel @ X27 @ X28) | (X26 @ X28)) | ~ ! [X29 : $i] : ((X25 @ X29) | ~(irel @ X27 @ X29))))) & ((^[X30 : ($i > $o)] : (~ ! [X31 : $i] : ~(X30 @ X31))) = isatisfiable) & ((^[X32 : ($i > $o), X33 : ($i > $o), X34 : $i] : ((X33 @ X34) | (X32 @ X34))) = mor) & (iatom = (^[X35 : ($i > $o), X36 : $i] : ((X35 @ X36)))) & ((^[X37 : ($i > $o)] : (! [X38 : $i] : ~(X37 @ X38))) = iinvalid) & ((^[X39 : ($i > $o)] : (~ ! [X40 : $i] : (X39 @ X40))) = icountersatisfiable) & (iand = (^[X41 : ($i > $o), X42 : ($i > $o), X43 : $i] : (! [X44 : $i] : (~(irel @ X43 @ X44) | (X41 @ X44)) & ! [X45 : $i] : ((X42 @ X45) | ~(irel @ X43 @ X45))))) & (mbox_s4 = (^[X46 : ($i > $o), X47 : $i] : (! [X48 : $i] : (~(irel @ X47 @ X48) | (X46 @ X48))))) & ((^[X49 : ($i > $o), X50 : $i] : (~(X49 @ X50))) = mnot) & ((^[X51 : ($i > $o), X52 : ($i > $o), X53 : $i] : ((X52 @ X53) | ~(X51 @ X53))) = mimplies) & ((^[X54 : ($i > $o), X55 : ($i > $o), X56 : $i] : (! [X57 : $i] : (~(irel @ X56 @ X57) | (X54 @ X57)) | ~ ! [X58 : $i] : ((X55 @ X58) | ~(irel @ X56 @ X58)))) = iimplied) & ! [X59 : d_unsorted,X60 : d_unsorted] : ((((d2unsorted @ X60)) = ((d2unsorted @ X59))) => (X59 = X60)) & (ixor = (^[X61 : ($i > $o), X62 : ($i > $o), X63 : $i] : (~ ! [X64 : $i,X65 : $i,X66 : $i,X67 : $i,X68 : $i] : (~(irel @ X63 @ X64) | (((X62 @ X66) | ~ ! [X69 : $i] : (~(irel @ X68 @ X69) | (X61 @ X69)) | ~(irel @ X68 @ X66) | ~(irel @ X64 @ X68)) & (~(irel @ X64 @ X65) | (X61 @ X67) | ~(irel @ X65 @ X67) | ~ ! [X70 : $i] : ((X62 @ X70) | ~(irel @ X65 @ X70))))))))),
  inference(rectify,[],[f3])).
thf(f6,plain,(
  (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X3 : d_unsorted] : (d_unsorted_0 = X3) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5))))))))))))))))) & ! [X16 : $i] : ? [X17 : d_unsorted] : (((d2unsorted @ X17)) = X16) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (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)))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X59 : d_unsorted,X60 : d_unsorted] : ((((d2unsorted @ X60)) = ((d2unsorted @ X59))) => (X59 = X60)) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4)) | (~ (irel @ Y7 @ Y6))) & ((((~ (irel @ Y7 @ Y3)) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y3 @ Y8))))))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y7))))))))))))))))))))),
  inference(fool_elimination,[],[f5])).
thf(f7,plain,(
  (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
  inference(flattening,[],[f4])).
thf(f8,plain,(
  (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5))))))))))))))))) & ! [X1 : $i] : ? [X2 : d_unsorted] : (((d2unsorted @ X2)) = X1) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (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)))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iimplied = (^[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,X3 : d_unsorted] : ((((d2unsorted @ X4)) = ((d2unsorted @ X3))) => (X3 = X4)) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4)) | (~ (irel @ Y7 @ Y6))) & ((((~ (irel @ Y7 @ Y3)) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y3 @ Y8))))))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y7))))))))))))))))))))),
  inference(rectify,[],[f6])).
thf(f9,plain,(
  (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5))))))))))))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X4 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X4)) = ((d2unsorted @ X3))) => (X3 = X4)) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((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)))))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4)) | (~ (irel @ Y7 @ Y6))) & ((((~ (irel @ Y7 @ Y3)) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y3 @ Y8))))))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y7)))))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : $i] : ? [X2 : d_unsorted] : (((d2unsorted @ X2)) = X1)),
  inference(flattening,[],[f8])).
thf(f10,plain,(
  (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (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)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X4)) != ((d2unsorted @ X3)))) & ! [X1 : $i] : ? [X2 : d_unsorted] : (((d2unsorted @ X2)) = X1) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[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)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5))))))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4)) | (~ (irel @ Y7 @ Y6))) & ((((~ (irel @ Y7 @ Y3)) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y3 @ Y8))))))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y7)))))))))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
  inference(ennf_transformation,[],[f9])).
thf(f11,plain,(
  (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (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)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : d_unsorted,X2 : d_unsorted] : ((X1 = X2) | (((d2unsorted @ X2)) != ((d2unsorted @ X1)))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[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)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5))))))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4)) | (~ (irel @ Y7 @ Y6))) & ((((~ (irel @ Y7 @ Y3)) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y3 @ Y8))))))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y7)))))))))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
  inference(rectify,[],[f10])).
thf(f12,plain,(
  (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (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)))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & ! [X1 : d_unsorted,X2 : d_unsorted] : ((X1 = X2) | (((d2unsorted @ X2)) != ((d2unsorted @ X1)))) & ! [X3 : $i] : (((d2unsorted @ (sK0 @ X3))) = X3) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[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)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y1 @ Y3) | (~ (irel @ Y2 @ Y4))) | (~ (irel @ Y4 @ Y3))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5))))))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((((((~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y1 @ Y8))))) | (~ (irel @ Y6 @ Y4))) | (Y0 @ Y4)) | (~ (irel @ Y7 @ Y6))) & ((((~ (irel @ Y7 @ Y3)) | (~ (irel @ Y3 @ Y5))) | (~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y3 @ Y8))))))) | (Y1 @ Y5))) | (~ (irel @ Y2 @ Y7)))))))))))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,$thf(sK0 @ X3))],[f11])).
thf(f13,plain,(
  (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
  inference(cnf_transformation,[],[f7])).
thf(f26,plain,(
  (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f29,plain,(
  ( ! [X3 : $i] : ((((d2unsorted @ (sK0 @ X3))) = X3)) )),
  inference(cnf_transformation,[],[f12])).
thf(f31,plain,(
  ( ! [X0 : d_unsorted] : ((d_unsorted_0 = X0)) )),
  inference(cnf_transformation,[],[f12])).
thf(f33,plain,(
  (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))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f36,plain,(
  (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f39,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (irel @ Y3 @ Y4)))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (irel @ Y3 @ Y4)))))))) @ Y1))))))),
  inference(definition_unfolding,[],[f13,f33,f26,f36,f36])).
thf(f40,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
  inference(beta-eta_normalization,[],[f39])).
thf(f41,plain,(
  ( ! [X3 : $i] : ((((d2unsorted @ d_unsorted_0)) = X3)) )),
  inference(forward_demodulation,[],[f29,f31])).
thf(f43,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))) @ sK1)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))) @ sK1)))),
  inference(negative_extensionality,[],[f40])).
thf(f44,plain,(
  ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))),
  inference(beta-eta_normalization,[],[f43])).
thf(f50,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
  inference(constrained_superposition,[],[f41,f41])).
thf(f84,plain,(
  ((((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) @ sK2)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) @ sK2)))),
  inference(negative_extensionality,[],[f44])).
thf(f85,plain,(
  ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) != (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))))),
  inference(beta-eta_normalization,[],[f84])).
thf(f86,plain,(
  ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3)) != (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3)))),
  inference(negative_extensionality,[],[f85])).
thf(f87,plain,(
  ($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3))) | ($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3)))),
  inference(xor_proxy_clausification,[],[f86])).
thf(f88,plain,(
  ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3))) | ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3)))),
  inference(xor_proxy_clausification,[],[f86])).
thf(f89,plain,(
  ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))))),
  inference(beta-eta_normalization,[],[f88])).
thf(f90,plain,(
  ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))),
  inference(or_proxy_clausification,[],[f89])).
thf(f91,plain,(
  ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))),
  inference(or_proxy_clausification,[],[f89])).
thf(f92,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))),
  inference(or_proxy_clausification,[],[f91])).
thf(f107,plain,(
  ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK6))) | ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK6)))),
  inference(sigma_proxy_clausification,[],[f92])).
thf(f108,plain,(
  ($false = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK6)))),
  inference(duplicate_literal_removal,[],[f107])).
thf(f109,plain,(
  ($false = (((sK1 @ sK6) | (~ (irel @ sK3 @ sK6)))))),
  inference(beta-eta_normalization,[],[f108])).
thf(f110,plain,(
  (((~ (irel @ sK3 @ sK6))) = $false)),
  inference(or_proxy_clausification,[],[f109])).
thf(f111,plain,(
  ($false = ((sK1 @ sK6)))),
  inference(or_proxy_clausification,[],[f109])).
thf(f112,plain,(
  ($true = ((irel @ sK3 @ sK6)))),
  inference(not_proxy_clausification,[],[f110])).
thf(f114,plain,(
  ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))),
  inference(or_proxy_clausification,[],[f90])).
thf(f115,plain,(
  ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7))) | ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7)))),
  inference(sigma_proxy_clausification,[],[f114])).
thf(f116,plain,(
  ($false = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7)))),
  inference(duplicate_literal_removal,[],[f115])).
thf(f117,plain,(
  ($false = (((sK2 @ sK7) | (~ (irel @ sK3 @ sK7)))))),
  inference(beta-eta_normalization,[],[f116])).
thf(f119,plain,(
  (((sK2 @ sK7)) = $false)),
  inference(or_proxy_clausification,[],[f117])).
thf(f134,plain,(
  ($true = (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))))),
  inference(beta-eta_normalization,[],[f87])).
thf(f135,plain,(
  ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))),
  inference(or_proxy_clausification,[],[f134])).
thf(f136,plain,(
  ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) )),
  inference(pi_proxy_clausification,[],[f135])).
thf(f137,plain,(
  ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1)))) )),
  inference(or_proxy_clausification,[],[f136])).
thf(f138,plain,(
  ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))))) | ($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X2)) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) )),
  inference(pi_proxy_clausification,[],[f137])).
thf(f139,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1))) | ($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X3))) | ($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X3))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X2)) = $true)) )),
  inference(pi_proxy_clausification,[],[f138])).
thf(f140,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1))) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X2)) = $true) | ($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X3)))) )),
  inference(duplicate_literal_removal,[],[f139])).
thf(f141,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK1 @ X2) | (~ (irel @ sK3 @ X2)))) = $true) | ($true = (((sK2 @ X3) | (~ (irel @ sK3 @ X3))))) | ((((sK1 @ X1) | (~ (irel @ sK3 @ X1)))) = $true)) )),
  inference(beta-eta_normalization,[],[f140])).
thf(f142,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK1 @ X1) | (~ (irel @ sK3 @ X1)))) = $true) | ($true = ((sK1 @ X2))) | ($true = (((sK2 @ X3) | (~ (irel @ sK3 @ X3))))) | ($true = ((~ (irel @ sK3 @ X2))))) )),
  inference(or_proxy_clausification,[],[f141])).
thf(f143,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK1 @ X2))) | ($true = (((sK2 @ X3) | (~ (irel @ sK3 @ X3))))) | ($true = ((~ (irel @ sK3 @ X1)))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((sK1 @ X1)))) )),
  inference(or_proxy_clausification,[],[f142])).
thf(f144,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK3 @ X1)))) | ($true = ((sK1 @ X1))) | ($true = ((~ (irel @ sK3 @ X3)))) | ($true = ((sK1 @ X2))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((sK2 @ X3)))) )),
  inference(or_proxy_clausification,[],[f143])).
thf(f145,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK1 @ X2))) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK2 @ X3))) | ($true = ((~ (irel @ sK3 @ X3)))) | ($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((sK1 @ X1)))) )),
  inference(not_proxy_clausification,[],[f144])).
thf(f146,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK3 @ X2)))) | ($true = ((sK1 @ X2))) | ($true = ((sK1 @ X1))) | (((irel @ sK3 @ X1)) = $false) | ($true = ((sK2 @ X3))) | ($false = ((irel @ sK3 @ X3)))) )),
  inference(not_proxy_clausification,[],[f145])).
thf(f147,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((sK1 @ X2))) | ($false = ((irel @ sK3 @ X3))) | ($true = ((sK1 @ X1))) | (((irel @ sK3 @ X1)) = $false) | ($false = ((irel @ sK3 @ X2))) | ($true = ((sK2 @ X3)))) )),
  inference(not_proxy_clausification,[],[f146])).
thf(f189,definition,(
  spl10_9 <=> ! [X1 : $i] : (($true = ((sK1 @ X1))) | (((irel @ sK3 @ X1)) = $false))),
  introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition])).
thf(f190,plain,(
  ( ! [X1 : $i] : ((((irel @ sK3 @ X1)) = $false) | ($true = ((sK1 @ X1)))) ) | ~spl10_9),
  inference(avatar_component_clause,[],[f189])).
thf(f192,definition,(
  spl10_10 <=> ! [X3 : $i] : (($false = ((irel @ sK3 @ X3))) | ($true = ((sK2 @ X3))))),
  introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition])).
thf(f193,plain,(
  ( ! [X3 : $i] : (($true = ((sK2 @ X3))) | ($false = ((irel @ sK3 @ X3)))) ) | ~spl10_10),
  inference(avatar_component_clause,[],[f192])).
thf(f194,plain,(
  spl10_9 | spl10_9 | spl10_10),
  inference(avatar_split_clause,[],[f147,f192,f189,f189])).
thf(f196,plain,(
  ( ! [X0 : $i] : ((((sK1 @ X0)) = $false)) )),
  inference(constrained_superposition,[],[f111,f50])).
thf(f197,plain,(
  ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) )),
  inference(constrained_superposition,[],[f119,f50])).
thf(f203,plain,(
  ( ! [X0 : $i] : (($true = ((irel @ sK3 @ X0)))) )),
  inference(constrained_superposition,[],[f112,f50])).
thf(f219,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $true)) )),
  inference(constrained_superposition,[],[f203,f50])).
thf(f229,plain,(
  ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $false) | ($true = ((sK1 @ X1)))) ) | ~spl10_9),
  inference(constrained_superposition,[],[f190,f50])).
thf(f340,plain,(
  ( ! [X1 : $i] : (($true = $false) | ($true = ((sK1 @ X1)))) ) | ~spl10_9),
  inference(forward_demodulation,[],[f229,f219])).
thf(f341,plain,(
  ( ! [X1 : $i] : (($true = ((sK1 @ X1)))) ) | ~spl10_9),
  inference(trivial_inequality_removal,[],[f340])).
thf(f348,plain,(
  ($true = $false) | ~spl10_9),
  inference(forward_demodulation,[],[f341,f196])).
thf(f349,plain,(
  $false | ~spl10_9),
  inference(trivial_inequality_removal,[],[f348])).
thf(f350,plain,(
  ~spl10_9),
  inference(avatar_contradiction_clause,[],[f349])).
thf(f351,plain,(
  ( ! [X3 : $i] : (($false = ((irel @ sK3 @ X3))) | ($true = $false)) ) | ~spl10_10),
  inference(forward_demodulation,[],[f193,f197])).
thf(f352,plain,(
  ( ! [X3 : $i] : (($false = ((irel @ sK3 @ X3)))) ) | ~spl10_10),
  inference(trivial_inequality_removal,[],[f351])).
thf(f353,plain,(
  ($true = $false) | ~spl10_10),
  inference(forward_demodulation,[],[f352,f219])).
thf(f354,plain,(
  $false | ~spl10_10),
  inference(trivial_inequality_removal,[],[f353])).
thf(f355,plain,(
  ~spl10_10),
  inference(avatar_contradiction_clause,[],[f354])).
cnf(s9, plain, spl10_9 | spl10_9 | spl10_10, inference(sat_conversion,[],[f194])).
cnf(s10, plain, spl10_9 | spl10_10, inference(rat,[],[s9])).
cnf(s34, plain, ~spl10_9, inference(sat_conversion,[],[f350])).
cnf(s35, plain, ~spl10_10, inference(sat_conversion,[],[f355])).
cnf(s36, plain, $false, inference(rat,[],[s10,s35,s34])).
thf(f356,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s36])).
% SZS output end Proof for theBenchmark