%----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 > $i)). thf(func_def_21, type, d_unsorted_0: d_unsorted). thf(func_def_23, type, vNOT: ($o > $o)). thf(func_def_24, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))). thf(func_def_25, type, db1: !>[X0: $tType]:(X0)). thf(func_def_26, type, db0: !>[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, db3: !>[X0: $tType]:(X0)). thf(func_def_30, type, db2: !>[X0: $tType]:(X0)). thf(func_def_33, type, vAND: ($o > $o > $o)). thf(func_def_34, type, db5: !>[X0: $tType]:(X0)). thf(func_def_35, type, db4: !>[X0: $tType]:(X0)). thf(func_def_36, type, db6: !>[X0: $tType]:(X0)). thf(func_def_37, type, sK0: ($i > d_unsorted)). thf(f1,axiom,( (mimplies = (^[X4 : ($i > $o), X6 : ($i > $o), X7 : $i] : ((X6 @ X7) | ~(X4 @ X7)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (mor = (^[X3 : ($i > $o), X5 : ($i > $o), X4 : $i] : ((X5 @ X4) | (X3 @ X4)))) & (mbox_s4 = (^[X8 : ($i > $o), X3 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X3 @ X5))))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : ((X9 @ X7) & (X8 @ X7))) = iand) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : ((~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5))) & (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) = iequiv) & ((^[X3 : ($i > $o), X5 : ($i > $o), X4 : $i] : ((X3 @ X4) & (X5 @ X4))) = mand) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)))) = iimplied) & ((^[X14 : ($i > $o)] : (~ ! [X15 : $i] : ~(X14 @ X15))) = isatisfiable) & ((^[X8 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = inot) & (iinvalid = (^[X14 : ($i > $o)] : (! [X15 : $i] : ~(X14 @ X15)))) & ! [X4 : $i] : ? [X0 : d_unsorted] : (X4 = ((d2unsorted @ X0))) & (ixor = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i,X10 : $i,X11 : $i] : (((~(irel @ X5 @ X10) | ~ ! [X12 : $i] : (~(irel @ X5 @ X12) | (X8 @ X12)) | (X9 @ X10)) & (~ ! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | ~(irel @ X5 @ X11) | (X8 @ X11))) | ~(irel @ X7 @ X5))))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)))) = iimplies) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & (ivalid = (^[X14 : ($i > $o)] : (! [X15 : $i] : (X14 @ X15)))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))) = ior) & ! [X2 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X2))) => (X1 = X2)) & ((^[X8 : ($i > $o), X7 : $i] : ((X8 @ X7))) = iatom) & (mnot = (^[X3 : ($i > $o), X4 : $i] : (~(X3 @ X4)))) & (icountersatisfiable = (^[X14 : ($i > $o)] : (~ ! [X15 : $i] : (X14 @ X15)))) & ! [X0 : d_unsorted] : (X0 = d_unsorted_0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcl695_1)). thf(f2,conjecture,( ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = ior)), file('/export/starexec/sandbox/benchmark/theBenchmark.p',ior)). thf(f3,negated_conjecture,( ~ ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = ior)), inference(negated_conjecture,[status(cth)],[f2])). thf(f4,plain,( (mimplies = (^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) | ~(X0 @ X2)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (mor = (^[X3 : ($i > $o), X4 : ($i > $o), X5 : $i] : ((X4 @ X5) | (X3 @ X5)))) & (mbox_s4 = (^[X6 : ($i > $o), X7 : $i] : (! [X8 : $i] : ((X6 @ X8) | ~(irel @ X7 @ X8))))) & ((^[X9 : ($i > $o), X10 : ($i > $o), X11 : $i] : ((X10 @ X11) & (X9 @ X11))) = iand) & ((^[X12 : ($i > $o), X13 : ($i > $o), X14 : $i] : ((~ ! [X15 : $i] : ((X12 @ X15) | ~(irel @ X14 @ X15)) | ! [X16 : $i] : ((X13 @ X16) | ~(irel @ X14 @ X16))) & (! [X17 : $i] : ((X12 @ X17) | ~(irel @ X14 @ X17)) | ~ ! [X18 : $i] : (~(irel @ X14 @ X18) | (X13 @ X18))))) = iequiv) & ((^[X19 : ($i > $o), X20 : ($i > $o), X21 : $i] : ((X19 @ X21) & (X20 @ X21))) = mand) & ((^[X22 : ($i > $o), X23 : ($i > $o), X24 : $i] : (! [X25 : $i] : ((X22 @ X25) | ~(irel @ X24 @ X25)) | ~ ! [X26 : $i] : (~(irel @ X24 @ X26) | (X23 @ X26)))) = iimplied) & ((^[X27 : ($i > $o)] : (~ ! [X28 : $i] : ~(X27 @ X28))) = isatisfiable) & ((^[X29 : ($i > $o), X30 : $i] : (~ ! [X31 : $i] : ((X29 @ X31) | ~(irel @ X30 @ X31)))) = inot) & (iinvalid = (^[X32 : ($i > $o)] : (! [X33 : $i] : ~(X32 @ X33)))) & ! [X34 : $i] : ? [X35 : d_unsorted] : (((d2unsorted @ X35)) = X34) & (ixor = (^[X36 : ($i > $o), X37 : ($i > $o), X38 : $i] : (~ ! [X39 : $i,X40 : $i,X41 : $i] : (((~(irel @ X39 @ X40) | ~ ! [X42 : $i] : (~(irel @ X39 @ X42) | (X36 @ X42)) | (X37 @ X40)) & (~ ! [X43 : $i] : ((X37 @ X43) | ~(irel @ X39 @ X43)) | ~(irel @ X39 @ X41) | (X36 @ X41))) | ~(irel @ X38 @ X39))))) & ((^[X44 : ($i > $o), X45 : ($i > $o), X46 : $i] : (~ ! [X47 : $i] : (~(irel @ X46 @ X47) | (X44 @ X47)) | ! [X48 : $i] : (~(irel @ X46 @ X48) | (X45 @ X48)))) = iimplies) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & (ivalid = (^[X49 : ($i > $o)] : (! [X50 : $i] : (X49 @ X50)))) & ((^[X51 : ($i > $o), X52 : ($i > $o), X53 : $i] : (! [X54 : $i] : ((X52 @ X54) | ~(irel @ X53 @ X54)) | ! [X55 : $i] : ((X51 @ X55) | ~(irel @ X53 @ X55)))) = ior) & ! [X56 : d_unsorted,X57 : d_unsorted] : ((((d2unsorted @ X56)) = ((d2unsorted @ X57))) => (X56 = X57)) & ((^[X58 : ($i > $o), X59 : $i] : ((X58 @ X59))) = iatom) & (mnot = (^[X60 : ($i > $o), X61 : $i] : (~(X60 @ X61)))) & (icountersatisfiable = (^[X62 : ($i > $o)] : (~ ! [X63 : $i] : (X62 @ X63)))) & ! [X64 : d_unsorted] : (d_unsorted_0 = X64)), inference(rectify,[],[f1])). thf(f5,plain,( (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X34 : $i] : ? [X35 : d_unsorted] : (((d2unsorted @ X35)) = X34) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((Y0 @ Y3) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) & (((Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) | (~ (irel @ Y5 @ Y4)))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (((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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & ! [X56 : d_unsorted,X57 : d_unsorted] : ((((d2unsorted @ X56)) = ((d2unsorted @ X57))) => (X56 = X57)) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X64 : d_unsorted] : (d_unsorted_0 = X64)), inference(fool_elimination,[],[f4])). thf(f6,plain,( ~ (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))), inference(fool_elimination,[],[f3])). thf(f7,plain,( (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[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]: ((~ (irel @ Y2 @ Y5)) | ((((Y0 @ Y3) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) & (((Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) | (~ (irel @ Y5 @ Y4)))))))))))))))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (((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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4)), inference(rectify,[],[f5])). thf(f8,plain,( (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((Y0 @ Y3) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) & (((Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) | (~ (irel @ Y5 @ Y4)))))))))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (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]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ 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))))))), inference(flattening,[],[f7])). thf(f9,plain,( (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))), inference(flattening,[],[f6])). thf(f10,plain,( (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X3 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplies = (^[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)))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((Y0 @ Y3) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) & (((Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) | (~ (irel @ Y5 @ Y4)))))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true)), inference(ennf_transformation,[],[f8])). thf(f11,plain,( (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplies = (^[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)))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((Y0 @ Y3) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) & (((Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) | (~ (irel @ Y5 @ Y4)))))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true)), inference(rectify,[],[f10])). thf(f12,plain,( (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : $i] : (((d2unsorted @ (sK0 @ X0))) = X0) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplies = (^[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)))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y2 @ Y5)) | ((((Y0 @ Y3) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y5 @ Y6)) | (Y1 @ Y6)))))) & (((Y1 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y5 @ Y6))))))) | (~ (irel @ Y5 @ Y4)))))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) & ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true)), inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X1,$thf(sK0 @ X0))],[f11])). thf(f13,plain,( (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))), inference(cnf_transformation,[],[f9])). thf(f23,plain,( (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))), inference(cnf_transformation,[],[f12])). thf(f26,plain,( (ior = (^[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(f31,plain,( (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))), inference(cnf_transformation,[],[f12])). 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,[],[f13,f26,f23,f31,f31])). 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