%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWX177^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:45 AM UTC 2026
% Result : Theorem 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX177^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:11:59 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.26 % (2686979)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (2686988)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3205540579:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.08/0.26 % (2686988)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.26 % (2686988) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2686979-2686988"...
% 0.08/0.26 % (2686985)% WARNING: option uhcvi not known.
% 0.08/0.26 % (2686988)...printing done.
% 0.08/0.26 % (2686988)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% 0.08/0.26 thf(type_def_5, type, unsorted: $tType).
% 0.08/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.08/0.26 thf(type_def_7, type, d_unsorted: $tType).
% 0.08/0.26 thf(func_def_0, type, irel: ($i > $i > $o)).
% 0.08/0.26 thf(func_def_1, type, mnot: (($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_2, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_3, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_4, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_5, type, mbox_s4: (($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_6, type, iatom: (($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_7, type, inot: (($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_8, type, itrue: ($i > $o)).
% 0.08/0.26 thf(func_def_9, type, ifalse: ($i > $o)).
% 0.08/0.26 thf(func_def_10, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_11, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_12, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_13, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_14, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_15, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.08/0.26 thf(func_def_16, type, ivalid: (($i > $o) > $o)).
% 0.08/0.26 thf(func_def_17, type, isatisfiable: (($i > $o) > $o)).
% 0.08/0.26 thf(func_def_18, type, icountersatisfiable: (($i > $o) > $o)).
% 0.08/0.26 thf(func_def_19, type, iinvalid: (($i > $o) > $o)).
% 0.08/0.26 thf(func_def_20, type, d2unsorted: (d_unsorted > $i)).
% 0.08/0.26 thf(func_def_21, type, d_unsorted_0: d_unsorted).
% 0.08/0.26 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.08/0.26 thf(func_def_24, type, db1: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_25, type, db0: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_26, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.08/0.26 thf(func_def_27, type, vOR: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_28, type, db2: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_29, type, vAND: ($o > $o > $o)).
% 0.08/0.26 thf(func_def_30, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.08/0.26 thf(func_def_31, type, db3: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_32, type, db5: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_33, type, db4: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_34, type, db8: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_35, type, db6: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_36, type, db7: !>[X0: $tType]:(X0)).
% 0.08/0.26 thf(func_def_39, type, sK0: ($i > d_unsorted)).
% 0.08/0.26 thf(f1,axiom,(
% 0.08/0.26 ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (iinvalid = (^[X18 : ($i > $o)] : (! [X19 : $i] : ~(X18 @ X19)))) & (icountersatisfiable = (^[X18 : ($i > $o)] : (~ ! [X19 : $i] : (X18 @ X19)))) & (isatisfiable = (^[X18 : ($i > $o)] : (~ ! [X19 : $i] : ~(X18 @ X19)))) & (ivalid = (^[X18 : ($i > $o)] : (! [X19 : $i] : (X18 @ X19)))) & (ixor = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i,X14 : $i,X15 : $i,X16 : $i,X17 : $i] : ((((X8 @ X17) | ~(irel @ X16 @ X17) | ~ ! [X13 : $i] : ((X9 @ X13) | ~(irel @ X16 @ X13)) | ~(irel @ X5 @ X16)) & ((X9 @ X15) | ~(irel @ X14 @ X15) | ~ ! [X11 : $i] : ((X8 @ X11) | ~(irel @ X14 @ X11)) | ~(irel @ X5 @ X14))) | ~(irel @ X7 @ X5))))) & (iequiv = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i,X12 : $i] : ((X8 @ X12) | ~(irel @ X5 @ X12) | ~ ! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | ~(irel @ X7 @ X5)) & ! [X5 : $i,X10 : $i] : ((X9 @ X10) | ~(irel @ X5 @ X10) | ~ ! [X11 : $i] : ((X8 @ X11) | ~(irel @ X5 @ X11)) | ~(irel @ X7 @ X5))))) & (iimplied = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ~ ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5))))) & (iimplies = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & (ior = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & (iand = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) & ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & (inot = (^[X8 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5))))) & (iatom = (^[X8 : ($i > $o), X7 : $i] : ((X8 @ X7)))) & (mbox_s4 = (^[X8 : ($i > $o), X4 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X4 @ X5))))) & (mimplies = (^[X0 : ($i > $o), X6 : ($i > $o), X7 : $i] : ((X6 @ X7) | ~(X0 @ X7)))) & (mand = (^[X4 : ($i > $o), X5 : ($i > $o), X0 : $i] : ((X5 @ X0) & (X4 @ X0)))) & (mor = (^[X4 : ($i > $o), X5 : ($i > $o), X0 : $i] : ((X5 @ X0) | (X4 @ X0)))) & (mnot = (^[X4 : ($i > $o), X0 : $i] : (~(X4 @ X0)))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1)))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',lcl696_1)).
% 0.08/0.26 thf(f2,conjecture,(
% 0.08/0.26 (iimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))))),
% 0.08/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p',iimplies)).
% 0.08/0.26 thf(f3,negated_conjecture,(
% 0.08/0.26 ~ (iimplies = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))))),
% 0.08/0.26 inference(negated_conjecture,[status(cth)],[f2])).
% 0.08/0.26 thf(f4,plain,(
% 0.08/0.26 ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (itrue @ (d2unsorted @ d_unsorted_0)) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (iinvalid = (^[X0 : ($i > $o)] : (! [X1 : $i] : ~(X0 @ X1)))) & (icountersatisfiable = (^[X2 : ($i > $o)] : (~ ! [X3 : $i] : (X2 @ X3)))) & (isatisfiable = (^[X4 : ($i > $o)] : (~ ! [X5 : $i] : ~(X4 @ X5)))) & (ivalid = (^[X6 : ($i > $o)] : (! [X7 : $i] : (X6 @ X7)))) & (ixor = (^[X8 : ($i > $o), X9 : ($i > $o), X10 : $i] : (~ ! [X11 : $i,X12 : $i,X13 : $i,X14 : $i,X15 : $i] : ((((X8 @ X15) | ~(irel @ X14 @ X15) | ~ ! [X16 : $i] : ((X9 @ X16) | ~(irel @ X14 @ X16)) | ~(irel @ X11 @ X14)) & ((X9 @ X13) | ~(irel @ X12 @ X13) | ~ ! [X17 : $i] : ((X8 @ X17) | ~(irel @ X12 @ X17)) | ~(irel @ X11 @ X12))) | ~(irel @ X10 @ X11))))) & (iequiv = (^[X18 : ($i > $o), X19 : ($i > $o), X20 : $i] : (! [X21 : $i,X22 : $i] : ((X18 @ X22) | ~(irel @ X21 @ X22) | ~ ! [X23 : $i] : ((X19 @ X23) | ~(irel @ X21 @ X23)) | ~(irel @ X20 @ X21)) & ! [X24 : $i,X25 : $i] : ((X19 @ X25) | ~(irel @ X24 @ X25) | ~ ! [X26 : $i] : ((X18 @ X26) | ~(irel @ X24 @ X26)) | ~(irel @ X20 @ X24))))) & (iimplied = (^[X27 : ($i > $o), X28 : ($i > $o), X29 : $i] : (! [X30 : $i] : ((X27 @ X30) | ~(irel @ X29 @ X30)) | ~ ! [X31 : $i] : ((X28 @ X31) | ~(irel @ X29 @ X31))))) & (iimplies = (^[X32 : ($i > $o), X33 : ($i > $o), X34 : $i] : (! [X35 : $i] : ((X33 @ X35) | ~(irel @ X34 @ X35)) | ~ ! [X36 : $i] : ((X32 @ X36) | ~(irel @ X34 @ X36))))) & (ior = (^[X37 : ($i > $o), X38 : ($i > $o), X39 : $i] : (! [X40 : $i] : ((X38 @ X40) | ~(irel @ X39 @ X40)) | ! [X41 : $i] : ((X37 @ X41) | ~(irel @ X39 @ X41))))) & (iand = (^[X42 : ($i > $o), X43 : ($i > $o), X44 : $i] : (! [X45 : $i] : ((X43 @ X45) | ~(irel @ X44 @ X45)) & ! [X46 : $i] : ((X42 @ X46) | ~(irel @ X44 @ X46))))) & (inot = (^[X47 : ($i > $o), X48 : $i] : (~ ! [X49 : $i] : ((X47 @ X49) | ~(irel @ X48 @ X49))))) & (iatom = (^[X50 : ($i > $o), X51 : $i] : ((X50 @ X51)))) & (mbox_s4 = (^[X52 : ($i > $o), X53 : $i] : (! [X54 : $i] : ((X52 @ X54) | ~(irel @ X53 @ X54))))) & (mimplies = (^[X55 : ($i > $o), X56 : ($i > $o), X57 : $i] : ((X56 @ X57) | ~(X55 @ X57)))) & (mand = (^[X58 : ($i > $o), X59 : ($i > $o), X60 : $i] : ((X59 @ X60) & (X58 @ X60)))) & (mor = (^[X61 : ($i > $o), X62 : ($i > $o), X63 : $i] : ((X62 @ X63) | (X61 @ X63)))) & (mnot = (^[X64 : ($i > $o), X65 : $i] : (~(X64 @ X65)))) & ! [X66 : d_unsorted,X67 : d_unsorted] : ((((d2unsorted @ X66)) = ((d2unsorted @ X67))) => (X66 = X67)) & ! [X68 : d_unsorted] : (d_unsorted_0 = X68) & ! [X69 : $i] : ? [X70 : d_unsorted] : (((d2unsorted @ X70)) = X69)),
% 0.08/0.26 inference(rectify,[],[f1])).
% 0.08/0.26 thf(f5,plain,(
% 0.08/0.26 ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y6 @ Y5))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y4)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (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))))))))))) & (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))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X66 : d_unsorted,X67 : d_unsorted] : ((((d2unsorted @ X66)) = ((d2unsorted @ X67))) => (X66 = X67)) & ! [X68 : d_unsorted] : (d_unsorted_0 = X68) & ! [X69 : $i] : ? [X70 : d_unsorted] : (((d2unsorted @ X70)) = X69)),
% 0.08/0.26 inference(fool_elimination,[],[f4])).
% 0.08/0.26 thf(f6,plain,(
% 0.08/0.26 ~ (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.08/0.26 inference(fool_elimination,[],[f3])).
% 0.08/0.26 thf(f7,plain,(
% 0.08/0.26 ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y6 @ Y5))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y4)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (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))))))))))) & (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))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X0))) => (X0 = X1)) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3)),
% 0.08/0.26 inference(rectify,[],[f5])).
% 0.08/0.26 thf(f8,plain,(
% 0.08/0.26 (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y6 @ Y5))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y4)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (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))))))))))) & (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))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) = ((d2unsorted @ X0))) => (X0 = X1)) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3)),
% 0.08/0.26 inference(flattening,[],[f7])).
% 0.08/0.26 thf(f9,plain,(
% 0.08/0.26 (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.08/0.26 inference(flattening,[],[f6])).
% 0.08/0.26 thf(f10,plain,(
% 0.08/0.26 (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y6 @ Y5))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y4)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (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))))))))))) & (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))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1) | (((d2unsorted @ X1)) != ((d2unsorted @ X0)))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3)),
% 0.08/0.26 inference(ennf_transformation,[],[f8])).
% 0.08/0.26 thf(f11,plain,(
% 0.08/0.26 (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (irel @ Y2 @ Y7)) | (((((~ (irel @ Y7 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y6 @ Y8)) | (Y0 @ Y8)))))) | (~ (irel @ Y6 @ Y5))) | (Y1 @ Y5)) & ((((~ (irel @ Y7 @ Y4)) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y4 @ Y8)) | (Y1 @ Y8)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y0 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y1 @ Y3)))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (irel @ Y2 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y4 @ Y5)) | (Y1 @ Y5)))))) | (~ (irel @ Y4 @ Y3))) | (Y0 @ Y3))))))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (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))))))))))) & (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))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))) & (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1) | (((d2unsorted @ X1)) != ((d2unsorted @ X0)))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & ! [X3 : $i] : (((d2unsorted @ (sK0 @ X3))) = X3)),
% 0.08/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X3)],[f10])).
% 0.08/0.26 thf(f18,plain,(
% 0.08/0.26 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (Y0 @ Y2)) | (Y1 @ Y2))))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f11])).
% 0.08/0.26 thf(f19,plain,(
% 0.08/0.26 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f11])).
% 0.08/0.26 thf(f24,plain,(
% 0.08/0.26 (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)))))))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f11])).
% 0.08/0.26 thf(f35,plain,(
% 0.08/0.26 (iimplies != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.08/0.26 inference(cnf_transformation,[],[f9])).
% 0.08/0.26 thf(f38,plain,(
% 0.08/0.26 ((^[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))))))),
% 0.08/0.26 inference(definition_unfolding,[],[f35,f24,f18,f19,f19])).
% 0.08/0.26 thf(f39,plain,(
% 0.08/0.26 ((^[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)))))))))))),
% 0.08/0.26 inference(beta-eta_normalization,[],[f38])).
% 0.08/0.26 thf(f40,plain,(
% 0.08/0.26 $false),
% 0.08/0.26 inference(trivial_inequality_removal,[],[f39])).
% 0.08/0.26 % SZS output end Proof for theBenchmark
% 0.08/0.26 % (2686988)------------------------------
% 0.08/0.26 % (2686988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (2686988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (2686988)CaDiCaL version: 2.1.3
% 0.08/0.26 % (2686988)Termination reason: Refutation
% 0.08/0.26 % (2686988)Time elapsed: 0.004 s
% 0.08/0.26 % (2686988)Peak memory usage: 12 MB
% 0.08/0.26 % (2686988)Instructions burned: 16 (million)
% 0.08/0.26 % (2686979)Success in time 0.04 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------