%----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, db2: !>[X0: $tType]:(X0)). thf(func_def_30, type, db3: !>[X0: $tType]:(X0)). thf(func_def_31, type, vAND: ($o > $o > $o)). thf(func_def_32, type, db5: !>[X0: $tType]:(X0)). thf(func_def_33, type, db4: !>[X0: $tType]:(X0)). thf(func_def_34, type, db6: !>[X0: $tType]:(X0)). thf(func_def_37, type, sK0: ($i > d_unsorted)). thf(f1,conjecture,( ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = iimplies)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iimplies)). thf(f2,negated_conjecture,( ~ ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = iimplies)), inference(negated_conjecture,[status(cth)],[f1])). thf(f3,axiom,( (mand = (^[X1 : ($i > $o), X3 : ($i > $o), X2 : $i] : ((X1 @ X2) & (X3 @ X2)))) & ! [X2 : $i] : ? [X0 : d_unsorted] : (X2 = ((d2unsorted @ X0))) & ((^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (! [X3 : $i] : ((X6 @ X3) | ~(irel @ X5 @ X3)) | ~ ! [X3 : $i] : ((X4 @ X3) | ~(irel @ X5 @ X3)))) = iimplies) & ((^[X7 : ($i > $o)] : (! [X8 : $i] : (X7 @ X8))) = ivalid) & (isatisfiable = (^[X7 : ($i > $o)] : (~ ! [X8 : $i] : ~(X7 @ X8)))) & ((^[X1 : ($i > $o), X2 : $i] : (~(X1 @ X2))) = mnot) & (mimplies = (^[X2 : ($i > $o), X13 : ($i > $o), X5 : $i] : ((X13 @ X5) | ~(X2 @ X5)))) & ((^[X7 : ($i > $o)] : (! [X8 : $i] : ~(X7 @ X8))) = iinvalid) & ! [X0 : d_unsorted] : (X0 = d_unsorted_0) & (mbox_s4 = (^[X4 : ($i > $o), X1 : $i] : (! [X3 : $i] : ((X4 @ X3) | ~(irel @ X1 @ X3))))) & ! [X14 : d_unsorted,X15 : d_unsorted] : ((((d2unsorted @ X14)) = ((d2unsorted @ X15))) => (X14 = X15)) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ((^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : ((X6 @ X5) & (X4 @ X5))) = iand) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & (mor = (^[X1 : ($i > $o), X3 : ($i > $o), X2 : $i] : ((X3 @ X2) | (X1 @ X2)))) & ((^[X4 : ($i > $o), X5 : $i] : ((X4 @ X5))) = iatom) & ((^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (! [X3 : $i] : (~(irel @ X5 @ X3) | (X4 @ X3)) | ! [X3 : $i] : ((X6 @ X3) | ~(irel @ X5 @ X3)))) = ior) & (iequiv = (^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : ((~ ! [X3 : $i] : ((X6 @ X3) | ~(irel @ X5 @ X3)) | ! [X3 : $i] : (~(irel @ X5 @ X3) | (X4 @ X3))) & (! [X3 : $i] : (~(irel @ X5 @ X3) | (X6 @ X3)) | ~ ! [X3 : $i] : ((X4 @ X3) | ~(irel @ X5 @ X3)))))) & (ixor = (^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (~ ! [X3 : $i,X10 : $i,X9 : $i] : (~(irel @ X5 @ X3) | ((~ ! [X11 : $i] : (~(irel @ X3 @ X11) | (X4 @ X11)) | (X6 @ X9) | ~(irel @ X3 @ X9)) & (~(irel @ X3 @ X10) | (X4 @ X10) | ~ ! [X12 : $i] : ((X6 @ X12) | ~(irel @ X3 @ X12)))))))) & (iimplied = (^[X4 : ($i > $o), X6 : ($i > $o), X5 : $i] : (! [X3 : $i] : (~(irel @ X5 @ X3) | (X4 @ X3)) | ~ ! [X3 : $i] : (~(irel @ X5 @ X3) | (X6 @ X3))))) & (icountersatisfiable = (^[X7 : ($i > $o)] : (~ ! [X8 : $i] : (X7 @ X8)))) & ((^[X4 : ($i > $o), X5 : $i] : (~ ! [X3 : $i] : (~(irel @ X5 @ X3) | (X4 @ X3)))) = inot)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lcl695_1)). thf(f4,plain,( ~ (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))), inference(fool_elimination,[],[f2])). thf(f5,plain,( (mand = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) & (X1 @ X2)))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & ((^[X5 : ($i > $o), X6 : ($i > $o), X7 : $i] : (! [X8 : $i] : ((X6 @ X8) | ~(irel @ X7 @ X8)) | ~ ! [X9 : $i] : ((X5 @ X9) | ~(irel @ X7 @ X9)))) = iimplies) & ((^[X10 : ($i > $o)] : (! [X11 : $i] : (X10 @ X11))) = ivalid) & (isatisfiable = (^[X12 : ($i > $o)] : (~ ! [X13 : $i] : ~(X12 @ X13)))) & ((^[X14 : ($i > $o), X15 : $i] : (~(X14 @ X15))) = mnot) & (mimplies = (^[X16 : ($i > $o), X17 : ($i > $o), X18 : $i] : ((X17 @ X18) | ~(X16 @ X18)))) & ((^[X19 : ($i > $o)] : (! [X20 : $i] : ~(X19 @ X20))) = iinvalid) & ! [X21 : d_unsorted] : (d_unsorted_0 = X21) & (mbox_s4 = (^[X22 : ($i > $o), X23 : $i] : (! [X24 : $i] : ((X22 @ X24) | ~(irel @ X23 @ X24))))) & ! [X25 : d_unsorted,X26 : d_unsorted] : ((((d2unsorted @ X26)) = ((d2unsorted @ X25))) => (X25 = X26)) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ((^[X27 : ($i > $o), X28 : ($i > $o), X29 : $i] : ((X28 @ X29) & (X27 @ X29))) = iand) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & (mor = (^[X30 : ($i > $o), X31 : ($i > $o), X32 : $i] : ((X31 @ X32) | (X30 @ X32)))) & ((^[X33 : ($i > $o), X34 : $i] : ((X33 @ X34))) = iatom) & ((^[X35 : ($i > $o), X36 : ($i > $o), X37 : $i] : (! [X38 : $i] : (~(irel @ X37 @ X38) | (X35 @ X38)) | ! [X39 : $i] : ((X36 @ X39) | ~(irel @ X37 @ X39)))) = ior) & (iequiv = (^[X40 : ($i > $o), X41 : ($i > $o), X42 : $i] : ((~ ! [X43 : $i] : ((X41 @ X43) | ~(irel @ X42 @ X43)) | ! [X44 : $i] : (~(irel @ X42 @ X44) | (X40 @ X44))) & (! [X45 : $i] : (~(irel @ X42 @ X45) | (X41 @ X45)) | ~ ! [X46 : $i] : ((X40 @ X46) | ~(irel @ X42 @ X46)))))) & (ixor = (^[X47 : ($i > $o), X48 : ($i > $o), X49 : $i] : (~ ! [X50 : $i,X51 : $i,X52 : $i] : (~(irel @ X49 @ X50) | ((~ ! [X53 : $i] : (~(irel @ X50 @ X53) | (X47 @ X53)) | (X48 @ X52) | ~(irel @ X50 @ X52)) & (~(irel @ X50 @ X51) | (X47 @ X51) | ~ ! [X54 : $i] : ((X48 @ X54) | ~(irel @ X50 @ X54)))))))) & (iimplied = (^[X55 : ($i > $o), X56 : ($i > $o), X57 : $i] : (! [X58 : $i] : (~(irel @ X57 @ X58) | (X55 @ X58)) | ~ ! [X59 : $i] : (~(irel @ X57 @ X59) | (X56 @ X59))))) & (icountersatisfiable = (^[X60 : ($i > $o)] : (~ ! [X61 : $i] : (X60 @ X61)))) & ((^[X62 : ($i > $o), X63 : $i] : (~ ! [X64 : $i] : (~(irel @ X63 @ X64) | (X62 @ X64)))) = inot)), inference(rectify,[],[f3])). thf(f6,plain,( (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X21 : d_unsorted] : (d_unsorted_0 = X21) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X25 : d_unsorted,X26 : d_unsorted] : ((((d2unsorted @ X26)) = ((d2unsorted @ X25))) => (X25 = X26)) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ 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 @ Y5 @ Y6)) | (Y1 @ Y6))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) & (((~ (irel @ Y5 @ Y3)) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))), inference(fool_elimination,[],[f5])). thf(f7,plain,( (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))), inference(flattening,[],[f4])). thf(f8,plain,( (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X3)) = ((d2unsorted @ X4))) => (X3 = X4)) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ 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 @ Y5 @ Y6)) | (Y1 @ Y6))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) & (((~ (irel @ Y5 @ Y3)) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))), inference(rectify,[],[f6])). thf(f9,plain,( (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X3)) = ((d2unsorted @ X4))) => (X3 = X4)) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[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) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((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 @ Y5 @ Y6)) | (Y1 @ Y6))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) & (((~ (irel @ Y5 @ Y3)) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (ior = (^[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(flattening,[],[f8])). thf(f10,plain,( (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) & (((~ (irel @ Y5 @ Y3)) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((X3 = X4) | (((d2unsorted @ X3)) != ((d2unsorted @ X4)))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (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)))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)), inference(ennf_transformation,[],[f9])). thf(f11,plain,( (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) & (((~ (irel @ Y5 @ Y3)) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X1 : d_unsorted,X2 : d_unsorted] : ((X1 = X2) | (((d2unsorted @ X1)) != ((d2unsorted @ X2)))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (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)))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)), inference(rectify,[],[f10])). thf(f12,plain,( (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X0 : d_unsorted] : (d_unsorted_0 = X0) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6))))) | (Y0 @ Y4)) | (~ (irel @ Y5 @ Y4))) & (((~ (irel @ Y5 @ Y3)) | (Y1 @ Y3)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6)))))))) | (~ (irel @ Y2 @ Y5)))))))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X1 : d_unsorted,X2 : d_unsorted] : ((X1 = X2) | (((d2unsorted @ X1)) != ((d2unsorted @ X2)))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (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)))))))) & ! [X3 : $i] : (((d2unsorted @ (sK0 @ X3))) = X3) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)), inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,$thf(sK0 @ X3))],[f11])). thf(f18,plain,( (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))), inference(cnf_transformation,[],[f12])). thf(f28,plain,( (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2))))))))), inference(cnf_transformation,[],[f12])). thf(f33,plain,( (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))), inference(cnf_transformation,[],[f12])). thf(f36,plain,( (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))), inference(cnf_transformation,[],[f7])). thf(f39,plain,( ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ 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]: ((~ (irel @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (irel @ Y3 @ Y4)) | (Y2 @ Y4))))))) @ Y1))))))), inference(definition_unfolding,[],[f36,f18,f28,f33,f33])). thf(f40,plain,( ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))), inference(beta-eta_normalization,[],[f39])). thf(f41,plain,( $false), inference(trivial_inequality_removal,[],[f40])). % SZS output end Proof for theBenchmark