%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX176^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 08:40:39 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX176^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n006.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:09:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 % (921317)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (921328)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.27 % (921328)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.27 % (921328)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3314056541:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.27 % (921328) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-921317-921328"...
% 0.20/0.27 % (921322)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=273214200:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.27 % (921324)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=969189497:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (921323)lrs+10_16_si=on:nwc=1.5:random_seed=1584736287:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.27 % (921327)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3627439845:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.27 % (921326)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1938191623:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.27 % (921325)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=778893588:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.27 % (921324)Instruction limit reached!
% 0.20/0.27 % (921324)------------------------------
% 0.20/0.27 % (921324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (921324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (921324)CaDiCaL version: 2.1.3
% 0.20/0.27 % (921324)Termination reason: Instruction limit
% 0.20/0.27 % (921324)Termination phase: Preprocessing 3
% 0.20/0.27 % (921324)Time elapsed: 0.002 s
% 0.20/0.27 % (921324)Peak memory usage: 10 MB
% 0.20/0.27 % (921324)Instructions burned: 4 (million)
% 0.20/0.27 % (921328)...printing done.
% 0.20/0.27 % (921328)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% 0.20/0.27 thf(type_def_5, type, unsorted: $tType).
% 0.20/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.27 thf(type_def_7, type, d_unsorted: $tType).
% 0.20/0.27 thf(func_def_0, type, irel: ($i > $i > $o)).
% 0.20/0.27 thf(func_def_1, type, mnot: (($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_2, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_3, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_4, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_5, type, mbox_s4: (($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_6, type, iatom: (($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_7, type, inot: (($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_8, type, itrue: ($i > $o)).
% 0.20/0.27 thf(func_def_9, type, ifalse: ($i > $o)).
% 0.20/0.27 thf(func_def_10, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_11, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_12, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_13, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_14, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_15, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.27 thf(func_def_16, type, ivalid: (($i > $o) > $o)).
% 0.20/0.27 thf(func_def_17, type, isatisfiable: (($i > $o) > $o)).
% 0.20/0.27 thf(func_def_18, type, icountersatisfiable: (($i > $o) > $o)).
% 0.20/0.27 thf(func_def_19, type, iinvalid: (($i > $o) > $o)).
% 0.20/0.27 thf(func_def_20, type, d2unsorted: (d_unsorted > $i)).
% 0.20/0.27 thf(func_def_21, type, d_unsorted_0: d_unsorted).
% 0.20/0.27 thf(func_def_23, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_24, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_25, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.27 thf(func_def_28, type, vOR: ($o > $o > $o)).
% 0.20/0.27 thf(func_def_29, type, vNOT: ($o > $o)).
% 0.20/0.27 thf(func_def_30, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.27 thf(func_def_31, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_32, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_33, type, vAND: ($o > $o > $o)).
% 0.20/0.27 thf(func_def_34, type, db5: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_35, type, db8: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_36, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_37, type, db6: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_38, type, db7: !>[X0: $tType]:(X0)).
% 0.20/0.27 thf(func_def_39, type, sK0: ($i > d_unsorted)).
% 0.20/0.27 thf(func_def_40, type, sK1: ($i > $o)).
% 0.20/0.27 thf(func_def_41, type, sK2: ($i > $o)).
% 0.20/0.27 thf(f1,axiom,(
% 0.20/0.27 ((^[X4 : ($i > $o), X5 : ($i > $o), X0 : $i] : ((X4 @ X0) | (X5 @ X0))) = mor) & (ior = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (isatisfiable = (^[X18 : ($i > $o)] : (~ ! [X19 : $i] : ~(X18 @ X19)))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) & ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)))) = iand) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)))) = iimplies) & (icountersatisfiable = (^[X18 : ($i > $o)] : (~ ! [X19 : $i] : (X18 @ X19)))) & (ivalid = (^[X18 : ($i > $o)] : (! [X19 : $i] : (X18 @ X19)))) & ((^[X8 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)))) = inot) & ((^[X0 : ($i > $o), X6 : ($i > $o), X7 : $i] : (~(X0 @ X7) | (X6 @ X7))) = mimplies) & (mbox_s4 = (^[X8 : ($i > $o), X4 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X4 @ X5))))) & (mnot = (^[X4 : ($i > $o), X0 : $i] : (~(X4 @ X0)))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & (iequiv = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X12 : $i,X5 : $i] : (~ ! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | ~(irel @ X5 @ X12) | ~(irel @ X7 @ X5) | (X8 @ X12)) & ! [X10 : $i,X5 : $i] : (~(irel @ X5 @ X10) | (X9 @ X10) | ~(irel @ X7 @ X5) | ~ ! [X11 : $i] : (~(irel @ X5 @ X11) | (X8 @ X11)))))) & ((^[X18 : ($i > $o)] : (! [X19 : $i] : ~(X18 @ X19))) = iinvalid) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X15 : $i,X5 : $i,X16 : $i,X14 : $i,X17 : $i] : (((~ ! [X13 : $i] : ((X9 @ X13) | ~(irel @ X16 @ X13)) | ~(irel @ X16 @ X17) | ~(irel @ X5 @ X16) | (X8 @ X17)) & (~(irel @ X5 @ X14) | (X9 @ X15) | ~(irel @ X14 @ X15) | ~ ! [X11 : $i] : (~(irel @ X14 @ X11) | (X8 @ X11)))) | ~(irel @ X7 @ X5)))) = ixor) & (mand = (^[X4 : ($i > $o), X5 : ($i > $o), X0 : $i] : ((X5 @ X0) & (X4 @ X0)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (iimplied = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)) | ~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))))) & (itrue @ (d2unsorted @ d_unsorted_0)) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ((^[X8 : ($i > $o), X7 : $i] : ((X8 @ X7))) = iatom)),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lcl696_1)).
% 0.20/0.27 thf(f2,conjecture,(
% 0.20/0.27 (ior = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))))),
% 0.20/0.27 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ior)).
% 0.20/0.27 thf(f3,negated_conjecture,(
% 0.20/0.27 ~ (ior = (^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))))),
% 0.20/0.27 inference(negated_conjecture,[status(cth)],[f2])).
% 0.20/0.27 thf(f4,plain,(
% 0.20/0.27 ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor) & (ior = (^[X3 : ($i > $o), X4 : ($i > $o), X5 : $i] : (! [X6 : $i] : ((X3 @ X6) | ~(irel @ X5 @ X6)) | ! [X7 : $i] : (~(irel @ X5 @ X7) | (X4 @ X7))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (isatisfiable = (^[X8 : ($i > $o)] : (~ ! [X9 : $i] : ~(X8 @ X9)))) & ((^[X10 : ($i > $o), X11 : ($i > $o), X12 : $i] : (! [X13 : $i] : (~(irel @ X12 @ X13) | (X11 @ X13)) & ! [X14 : $i] : (~(irel @ X12 @ X14) | (X10 @ X14)))) = iand) & ! [X15 : $i] : ? [X16 : d_unsorted] : (((d2unsorted @ X16)) = X15) & ((^[X17 : ($i > $o), X18 : ($i > $o), X19 : $i] : (~ ! [X20 : $i] : ((X17 @ X20) | ~(irel @ X19 @ X20)) | ! [X21 : $i] : ((X18 @ X21) | ~(irel @ X19 @ X21)))) = iimplies) & (icountersatisfiable = (^[X22 : ($i > $o)] : (~ ! [X23 : $i] : (X22 @ X23)))) & (ivalid = (^[X24 : ($i > $o)] : (! [X25 : $i] : (X24 @ X25)))) & ((^[X26 : ($i > $o), X27 : $i] : (~ ! [X28 : $i] : (~(irel @ X27 @ X28) | (X26 @ X28)))) = inot) & ((^[X29 : ($i > $o), X30 : ($i > $o), X31 : $i] : (~(X29 @ X31) | (X30 @ X31))) = mimplies) & (mbox_s4 = (^[X32 : ($i > $o), X33 : $i] : (! [X34 : $i] : ((X32 @ X34) | ~(irel @ X33 @ X34))))) & (mnot = (^[X35 : ($i > $o), X36 : $i] : (~(X35 @ X36)))) & ! [X37 : d_unsorted,X38 : d_unsorted] : ((((d2unsorted @ X38)) = ((d2unsorted @ X37))) => (X37 = X38)) & (iequiv = (^[X39 : ($i > $o), X40 : ($i > $o), X41 : $i] : (! [X42 : $i,X43 : $i] : (~ ! [X44 : $i] : ((X40 @ X44) | ~(irel @ X43 @ X44)) | ~(irel @ X43 @ X42) | ~(irel @ X41 @ X43) | (X39 @ X42)) & ! [X45 : $i,X46 : $i] : (~(irel @ X46 @ X45) | (X40 @ X45) | ~(irel @ X41 @ X46) | ~ ! [X47 : $i] : (~(irel @ X46 @ X47) | (X39 @ X47)))))) & ((^[X48 : ($i > $o)] : (! [X49 : $i] : ~(X48 @ X49))) = iinvalid) & ((^[X50 : ($i > $o), X51 : ($i > $o), X52 : $i] : (~ ! [X53 : $i,X54 : $i,X55 : $i,X56 : $i,X57 : $i] : (((~ ! [X58 : $i] : ((X51 @ X58) | ~(irel @ X55 @ X58)) | ~(irel @ X55 @ X57) | ~(irel @ X54 @ X55) | (X50 @ X57)) & (~(irel @ X54 @ X56) | (X51 @ X53) | ~(irel @ X56 @ X53) | ~ ! [X59 : $i] : (~(irel @ X56 @ X59) | (X50 @ X59)))) | ~(irel @ X52 @ X54)))) = ixor) & (mand = (^[X60 : ($i > $o), X61 : ($i > $o), X62 : $i] : ((X61 @ X62) & (X60 @ X62)))) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & (iimplied = (^[X63 : ($i > $o), X64 : ($i > $o), X65 : $i] : (! [X66 : $i] : ((X63 @ X66) | ~(irel @ X65 @ X66)) | ~ ! [X67 : $i] : (~(irel @ X65 @ X67) | (X64 @ X67))))) & (itrue @ (d2unsorted @ d_unsorted_0)) & ! [X68 : d_unsorted] : (d_unsorted_0 = X68) & ((^[X69 : ($i > $o), X70 : $i] : ((X69 @ X70))) = iatom)),
% 0.20/0.27 inference(rectify,[],[f1])).
% 0.20/0.27 thf(f5,plain,(
% 0.20/0.27 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X15 : $i] : ? [X16 : d_unsorted] : (((d2unsorted @ X16)) = X15) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X37 : d_unsorted,X38 : d_unsorted] : ((((d2unsorted @ X38)) = ((d2unsorted @ X37))) => (X37 = X38)) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5))))))))))))))))) & (iinvalid = (^[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 @ Y6)) | (((((~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y4 @ Y8)))))) | (~ (irel @ Y4 @ Y7))) | (Y1 @ Y7)) | (~ (irel @ Y6 @ Y4))) & ((((Y0 @ Y3) | (~ (irel @ Y6 @ Y5))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y5 @ Y8)) | (Y1 @ Y8))))))))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (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))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X68 : d_unsorted] : (d_unsorted_0 = X68) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.27 inference(fool_elimination,[],[f4])).
% 0.20/0.27 thf(f6,plain,(
% 0.20/0.27 ~ (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.27 inference(fool_elimination,[],[f3])).
% 0.20/0.27 thf(f7,plain,(
% 0.20/0.27 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5))))))))))))))))) & (iinvalid = (^[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 @ Y6)) | (((((~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y4 @ Y8)))))) | (~ (irel @ Y4 @ Y7))) | (Y1 @ Y7)) | (~ (irel @ Y6 @ Y4))) & ((((Y0 @ Y3) | (~ (irel @ Y6 @ Y5))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y5 @ Y8)) | (Y1 @ Y8))))))))))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (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))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.27 inference(rectify,[],[f5])).
% 0.20/0.27 thf(f8,plain,(
% 0.20/0.27 (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]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mor = (^[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))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5))))))))))))))))) & (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 @ Y6)) | (((((~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y4 @ Y8)))))) | (~ (irel @ Y4 @ Y7))) | (Y1 @ Y7)) | (~ (irel @ Y6 @ Y4))) & ((((Y0 @ Y3) | (~ (irel @ Y6 @ Y5))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y5 @ Y8)) | (Y1 @ Y8))))))))))))))))))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2)))))))))),
% 0.20/0.27 inference(flattening,[],[f7])).
% 0.20/0.27 thf(f9,plain,(
% 0.20/0.27 (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.27 inference(flattening,[],[f6])).
% 0.20/0.27 thf(f10,plain,(
% 0.20/0.27 (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((X2 = X3) | (((d2unsorted @ X2)) != ((d2unsorted @ X3)))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ 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]: ((~ (irel @ Y2 @ Y6)) | (((((~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y4 @ Y8)))))) | (~ (irel @ Y4 @ Y7))) | (Y1 @ Y7)) | (~ (irel @ Y6 @ Y4))) & ((((Y0 @ Y3) | (~ (irel @ Y6 @ Y5))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y5 @ Y8)) | (Y1 @ Y8))))))))))))))))))))))))) & (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))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))),
% 0.20/0.27 inference(ennf_transformation,[],[f8])).
% 0.20/0.27 thf(f11,plain,(
% 0.20/0.27 (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1) | (((d2unsorted @ X1)) != ((d2unsorted @ X0)))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ 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]: ((~ (irel @ Y2 @ Y6)) | (((((~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y4 @ Y8)))))) | (~ (irel @ Y4 @ Y7))) | (Y1 @ Y7)) | (~ (irel @ Y6 @ Y4))) & ((((Y0 @ Y3) | (~ (irel @ Y6 @ Y5))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y5 @ Y8)) | (Y1 @ Y8))))))))))))))))))))))))) & (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))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : (((d2unsorted @ X3)) = X2) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))),
% 0.20/0.27 inference(rectify,[],[f10])).
% 0.20/0.27 thf(f12,plain,(
% 0.20/0.27 (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((X0 = X1) | (((d2unsorted @ X1)) != ((d2unsorted @ X0)))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ 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]: ((~ (irel @ Y2 @ Y6)) | (((((~ (!! @ $i @ (^[Y8 : $i]: ((Y0 @ Y8) | (~ (irel @ Y4 @ Y8)))))) | (~ (irel @ Y4 @ Y7))) | (Y1 @ Y7)) | (~ (irel @ Y6 @ Y4))) & ((((Y0 @ Y3) | (~ (irel @ Y6 @ Y5))) | (~ (irel @ Y5 @ Y3))) | (~ (!! @ $i @ (^[Y8 : $i]: ((~ (irel @ Y5 @ Y8)) | (Y1 @ Y8))))))))))))))))))))))))) & (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))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))) & ! [X2 : $i] : (((d2unsorted @ (sK0 @ X2))) = X2) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) & (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((~ (!! @ $i @ (^[Y5 : $i]: ((Y0 @ Y5) | (~ (irel @ Y3 @ Y5)))))) | (~ (irel @ Y2 @ Y3))) | (Y1 @ Y4)) | (~ (irel @ Y3 @ Y4))))))) & (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((Y0 @ Y4) | (~ (irel @ Y2 @ Y3))) | (~ (irel @ Y3 @ Y4))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (irel @ Y3 @ Y5)) | (Y1 @ Y5))))))))))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))),
% 0.20/0.27 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,sK0 @ X2)],[f11])).
% 0.20/0.27 thf(f13,plain,(
% 0.20/0.27 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f14,plain,(
% 0.20/0.27 ( ! [X4 : d_unsorted] : ((d_unsorted_0 = X4)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f15,plain,(
% 0.20/0.27 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f21,plain,(
% 0.20/0.27 ( ! [X2 : $i] : ((((d2unsorted @ (sK0 @ X2))) = X2)) )),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f29,plain,(
% 0.20/0.27 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f32,plain,(
% 0.20/0.27 (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true)),
% 0.20/0.27 inference(cnf_transformation,[],[f12])).
% 0.20/0.27 thf(f36,plain,(
% 0.20/0.27 (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.27 inference(cnf_transformation,[],[f9])).
% 0.20/0.27 thf(f39,plain,(
% 0.20/0.27 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ 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))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))),
% 0.20/0.27 inference(definition_unfolding,[],[f36,f13,f15,f29,f29])).
% 0.20/0.27 thf(f40,plain,(
% 0.20/0.27 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f39])).
% 0.20/0.27 thf(f54,plain,(
% 0.20/0.27 ( ! [X2 : $i] : ((((d2unsorted @ d_unsorted_0)) = X2)) )),
% 0.20/0.27 inference(forward_demodulation,[],[f21,f14])).
% 0.20/0.27 thf(f58,plain,(
% 0.20/0.27 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 0.20/0.27 inference(constrained_superposition,[],[f54,f54])).
% 0.20/0.27 thf(f81,plain,(
% 0.20/0.27 ( ! [X0 : $i] : ((((irel @ X0 @ X0)) = $true)) )),
% 0.20/0.27 inference(constrained_superposition,[],[f32,f54])).
% 0.20/0.27 thf(f84,plain,(
% 0.20/0.27 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))) @ sK1)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3)))))))))) @ sK1)))),
% 0.20/0.27 inference(negative_extensionality,[],[f40])).
% 0.20/0.27 thf(f85,plain,(
% 0.20/0.27 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))))))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f84])).
% 0.20/0.27 thf(f86,plain,(
% 0.20/0.27 ((((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))) | (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))))))) @ sK2)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (sK1 @ Y2)))))))) @ sK2)))),
% 0.20/0.27 inference(negative_extensionality,[],[f85])).
% 0.20/0.27 thf(f87,plain,(
% 0.20/0.27 ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))) != (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f86])).
% 0.20/0.27 thf(f88,plain,(
% 0.20/0.27 ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))) @ sK3)) != (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))) @ sK3)))),
% 0.20/0.27 inference(negative_extensionality,[],[f87])).
% 0.20/0.27 thf(f89,plain,(
% 0.20/0.27 ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))) @ sK3)) = $true) | ($true = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))) @ sK3)))),
% 0.20/0.27 inference(xor_proxy_clausification,[],[f88])).
% 0.20/0.27 thf(f90,plain,(
% 0.20/0.27 ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))) @ sK3)) = $false) | ($false = (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK1 @ Y1)))))) @ sK3)))),
% 0.20/0.27 inference(xor_proxy_clausification,[],[f88])).
% 0.20/0.27 thf(f91,plain,(
% 0.20/0.27 ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0)))))) = $false) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0)))))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f90])).
% 0.20/0.27 thf(f92,plain,(
% 0.20/0.27 ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $false)),
% 0.20/0.27 inference(or_proxy_clausification,[],[f91])).
% 0.20/0.27 thf(f93,plain,(
% 0.20/0.27 ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))))),
% 0.20/0.27 inference(or_proxy_clausification,[],[f91])).
% 0.20/0.27 thf(f95,plain,(
% 0.20/0.27 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))),
% 0.20/0.27 inference(or_proxy_clausification,[],[f93])).
% 0.20/0.27 thf(f96,plain,(
% 0.20/0.27 ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK4))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))))),
% 0.20/0.27 inference(sigma_proxy_clausification,[],[f95])).
% 0.20/0.27 thf(f97,plain,(
% 0.20/0.27 ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK5)) = $false) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK4)))),
% 0.20/0.27 inference(sigma_proxy_clausification,[],[f96])).
% 0.20/0.27 thf(f98,plain,(
% 0.20/0.27 ((((~ (irel @ sK3 @ sK4)) | (sK2 @ sK4))) = $false) | ($false = (((sK2 @ sK5) | (~ (irel @ sK3 @ sK5)))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f97])).
% 0.20/0.27 thf(f99,plain,(
% 0.20/0.27 ($false = (((sK2 @ sK5) | (~ (irel @ sK3 @ sK5))))) | ($false = ((sK2 @ sK4)))),
% 0.20/0.27 inference(or_proxy_clausification,[],[f98])).
% 0.20/0.27 thf(f107,plain,(
% 0.20/0.27 (((sK2 @ sK5)) = $false) | ($false = ((sK2 @ sK4)))),
% 0.20/0.27 inference(or_proxy_clausification,[],[f99])).
% 0.20/0.27 thf(f121,plain,(
% 0.20/0.27 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $false)),
% 0.20/0.27 inference(or_proxy_clausification,[],[f92])).
% 0.20/0.27 thf(f136,plain,(
% 0.20/0.27 ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ sK10))) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ sK10)))),
% 0.20/0.27 inference(sigma_proxy_clausification,[],[f121])).
% 0.20/0.27 thf(f137,plain,(
% 0.20/0.27 ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ sK10)))),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f136])).
% 0.20/0.27 thf(f138,plain,(
% 0.20/0.27 ($false = (((~ (irel @ sK3 @ sK10)) | (sK1 @ sK10))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f137])).
% 0.20/0.27 thf(f139,plain,(
% 0.20/0.27 ($false = ((sK1 @ sK10)))),
% 0.20/0.27 inference(or_proxy_clausification,[],[f138])).
% 0.20/0.27 thf(f142,plain,(
% 0.20/0.27 ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0)))))) = $true) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0)))))))),
% 0.20/0.27 inference(beta-eta_normalization,[],[f89])).
% 0.20/0.27 thf(f143,plain,(
% 0.20/0.27 ($true = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))))) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))) = $true)),
% 0.20/0.27 inference(or_proxy_clausification,[],[f142])).
% 0.20/0.27 thf(f144,plain,(
% 0.20/0.27 (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $true)),
% 0.20/0.27 inference(or_proxy_clausification,[],[f143])).
% 0.20/0.27 thf(f145,plain,(
% 0.20/0.27 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $true) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1)) = $true)) )),
% 0.20/0.27 inference(pi_proxy_clausification,[],[f144])).
% 0.20/0.27 thf(f146,plain,(
% 0.20/0.27 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ X2))) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $true) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ X2))) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1)) = $true)) )),
% 0.20/0.27 inference(pi_proxy_clausification,[],[f145])).
% 0.20/0.27 thf(f147,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ X2))) | ($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ X2))) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1)) = $true) | ($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X3)))) )),
% 0.20/0.27 inference(pi_proxy_clausification,[],[f146])).
% 0.20/0.27 thf(f148,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK1 @ Y0))) @ X2))) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X1)) = $true) | ($true = (((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X3)))) )),
% 0.20/0.27 inference(duplicate_literal_removal,[],[f147])).
% 0.20/0.27 thf(f149,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((sK2 @ X3) | (~ (irel @ sK3 @ X3)))) = $true) | ($true = (((~ (irel @ sK3 @ X2)) | (sK1 @ X2)))) | ($true = (((~ (irel @ sK3 @ X1)) | (sK2 @ X1))))) )),
% 0.20/0.27 inference(beta-eta_normalization,[],[f148])).
% 0.20/0.27 thf(f150,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((~ (irel @ sK3 @ X2)) | (sK1 @ X2)))) | (((~ (irel @ sK3 @ X3))) = $true) | (((sK2 @ X3)) = $true) | ($true = (((~ (irel @ sK3 @ X1)) | (sK2 @ X1))))) )),
% 0.20/0.27 inference(or_proxy_clausification,[],[f149])).
% 0.20/0.27 thf(f151,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((sK1 @ X2)) = $true) | (((sK2 @ X3)) = $true) | (((~ (irel @ sK3 @ X3))) = $true) | (((~ (irel @ sK3 @ X2))) = $true) | ($true = (((~ (irel @ sK3 @ X1)) | (sK2 @ X1))))) )),
% 0.20/0.27 inference(or_proxy_clausification,[],[f150])).
% 0.20/0.27 thf(f152,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((~ (irel @ sK3 @ X2))) = $true) | ($false = ((irel @ sK3 @ X3))) | (((sK2 @ X3)) = $true) | ($true = (((~ (irel @ sK3 @ X1)) | (sK2 @ X1)))) | (((sK1 @ X2)) = $true)) )),
% 0.20/0.27 inference(not_proxy_clausification,[],[f151])).
% 0.20/0.27 thf(f153,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ sK3 @ X3))) | (((irel @ sK3 @ X2)) = $false) | ($true = (((~ (irel @ sK3 @ X1)) | (sK2 @ X1)))) | (((sK1 @ X2)) = $true) | (((sK2 @ X3)) = $true)) )),
% 0.20/0.27 inference(not_proxy_clausification,[],[f152])).
% 0.20/0.27 thf(f154,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((~ (irel @ sK3 @ X1)))) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ sK3 @ X3))) | (((sK2 @ X3)) = $true) | (((sK1 @ X2)) = $true) | (((sK2 @ X1)) = $true)) )),
% 0.20/0.27 inference(or_proxy_clausification,[],[f153])).
% 0.20/0.27 thf(f155,plain,(
% 0.20/0.27 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ sK3 @ X1))) | (((sK1 @ X2)) = $true) | (((sK2 @ X3)) = $true) | (((irel @ sK3 @ X2)) = $false) | ($false = ((irel @ sK3 @ X3))) | (((sK2 @ X1)) = $true)) )),
% 0.20/0.27 inference(not_proxy_clausification,[],[f154])).
% 0.20/0.27 thf(f161,definition,(
% 0.20/0.27 spl11_2 <=> (((sK2 @ sK5)) = $false)),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition])).
% 0.20/0.27 thf(f163,plain,(
% 0.20/0.27 (((sK2 @ sK5)) = $false) | ~spl11_2),
% 0.20/0.27 inference(avatar_component_clause,[],[f161])).
% 0.20/0.27 thf(f171,definition,(
% 0.20/0.27 spl11_4 <=> ($false = ((sK2 @ sK4)))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition])).
% 0.20/0.27 thf(f173,plain,(
% 0.20/0.27 ($false = ((sK2 @ sK4))) | ~spl11_4),
% 0.20/0.27 inference(avatar_component_clause,[],[f171])).
% 0.20/0.27 thf(f174,plain,(
% 0.20/0.27 spl11_4 | spl11_2),
% 0.20/0.27 inference(avatar_split_clause,[],[f107,f161,f171])).
% 0.20/0.27 thf(f217,definition,(
% 0.20/0.27 spl11_13 <=> ! [X1 : $i] : (($false = ((irel @ sK3 @ X1))) | (((sK2 @ X1)) = $true))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition])).
% 0.20/0.27 thf(f218,plain,(
% 0.20/0.27 ( ! [X1 : $i] : (($false = ((irel @ sK3 @ X1))) | (((sK2 @ X1)) = $true)) ) | ~spl11_13),
% 0.20/0.27 inference(avatar_component_clause,[],[f217])).
% 0.20/0.27 thf(f220,definition,(
% 0.20/0.27 spl11_14 <=> ! [X2 : $i] : ((((sK1 @ X2)) = $true) | (((irel @ sK3 @ X2)) = $false))),
% 0.20/0.27 introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition])).
% 0.20/0.27 thf(f221,plain,(
% 0.20/0.27 ( ! [X2 : $i] : ((((irel @ sK3 @ X2)) = $false) | (((sK1 @ X2)) = $true)) ) | ~spl11_14),
% 0.20/0.27 inference(avatar_component_clause,[],[f220])).
% 0.20/0.27 thf(f222,plain,(
% 0.20/0.27 spl11_13 | spl11_13 | spl11_14),
% 0.20/0.27 inference(avatar_split_clause,[],[f155,f220,f217,f217])).
% 0.20/0.27 thf(f225,plain,(
% 0.20/0.27 ($false = $true) | (((sK2 @ sK3)) = $true) | ~spl11_13),
% 0.20/0.27 inference(constrained_superposition,[],[f218,f81])).
% 0.20/0.27 thf(f228,plain,(
% 0.20/0.27 (((sK2 @ sK3)) = $true) | ~spl11_13),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f225])).
% 0.20/0.27 thf(f231,plain,(
% 0.20/0.27 ( ! [X0 : $i] : ((((sK2 @ X0)) = $true)) ) | ~spl11_13),
% 0.20/0.27 inference(constrained_superposition,[],[f228,f58])).
% 0.20/0.27 thf(f237,plain,(
% 0.20/0.27 ($false = $true) | (~spl11_2 | ~spl11_13)),
% 0.20/0.27 inference(forward_demodulation,[],[f163,f231])).
% 0.20/0.27 thf(f238,plain,(
% 0.20/0.27 $false | (~spl11_2 | ~spl11_13)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f237])).
% 0.20/0.27 thf(f239,plain,(
% 0.20/0.27 ~spl11_2 | ~spl11_13),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f238])).
% 0.20/0.27 thf(f250,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK3))) | ($false = $true) | ~spl11_14),
% 0.20/0.27 inference(constrained_superposition,[],[f221,f81])).
% 0.20/0.27 thf(f253,plain,(
% 0.20/0.27 ($true = ((sK1 @ sK3))) | ~spl11_14),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f250])).
% 0.20/0.27 thf(f256,plain,(
% 0.20/0.27 ( ! [X0 : $i] : (($true = ((sK1 @ X0)))) ) | ~spl11_14),
% 0.20/0.27 inference(constrained_superposition,[],[f253,f58])).
% 0.20/0.27 thf(f261,plain,(
% 0.20/0.27 ($false = $true) | ~spl11_14),
% 0.20/0.27 inference(constrained_superposition,[],[f139,f256])).
% 0.20/0.27 thf(f266,plain,(
% 0.20/0.27 $false | ~spl11_14),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f261])).
% 0.20/0.27 thf(f267,plain,(
% 0.20/0.27 ~spl11_14),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f266])).
% 0.20/0.27 thf(f287,plain,(
% 0.20/0.27 (((sK2 @ sK3)) = $true) | ($false = $true) | ~spl11_13),
% 0.20/0.27 inference(constrained_superposition,[],[f81,f218])).
% 0.20/0.27 thf(f289,plain,(
% 0.20/0.27 (((sK2 @ sK3)) = $true) | ~spl11_13),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f287])).
% 0.20/0.27 thf(f291,plain,(
% 0.20/0.27 ( ! [X0 : $i] : ((((sK2 @ X0)) = $true)) ) | ~spl11_13),
% 0.20/0.27 inference(constrained_superposition,[],[f289,f58])).
% 0.20/0.27 thf(f293,plain,(
% 0.20/0.27 ($false = $true) | (~spl11_4 | ~spl11_13)),
% 0.20/0.27 inference(constrained_superposition,[],[f291,f173])).
% 0.20/0.27 thf(f304,plain,(
% 0.20/0.27 $false | (~spl11_4 | ~spl11_13)),
% 0.20/0.27 inference(trivial_inequality_removal,[],[f293])).
% 0.20/0.27 thf(f305,plain,(
% 0.20/0.27 ~spl11_4 | ~spl11_13),
% 0.20/0.27 inference(avatar_contradiction_clause,[],[f304])).
% 0.20/0.27 cnf(s3, plain, spl11_2 | spl11_4, inference(sat_conversion,[],[f174])).
% 0.20/0.27 cnf(s13, plain, spl11_13 | spl11_13 | spl11_14, inference(sat_conversion,[],[f222])).
% 0.20/0.27 cnf(s14, plain, spl11_13 | spl11_14, inference(rat,[],[s13])).
% 0.20/0.27 cnf(s15, plain, ~spl11_2 | ~spl11_13, inference(sat_conversion,[],[f239])).
% 0.20/0.27 cnf(s18, plain, ~spl11_14, inference(sat_conversion,[],[f267])).
% 0.20/0.27 cnf(s23, plain, ~spl11_4 | ~spl11_13, inference(sat_conversion,[],[f305])).
% 0.20/0.27 cnf(s24, plain, spl11_13, inference(rat,[],[s14,s18])).
% 0.20/0.27 cnf(s25, plain, ~spl11_4, inference(rat,[],[s23,s24])).
% 0.20/0.27 cnf(s27, plain, ~spl11_2, inference(rat,[],[s15,s24])).
% 0.20/0.27 cnf(s31, plain, $false, inference(rat,[],[s3,s25,s27])).
% 0.20/0.27 thf(f306,plain,(
% 0.20/0.27 $false),
% 0.20/0.27 inference(avatar_sat_refutation,[],[s31])).
% 0.20/0.27 % SZS output end Proof for theBenchmark
% 0.20/0.27 % (921328)------------------------------
% 0.20/0.27 % (921328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (921328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (921328)CaDiCaL version: 2.1.3
% 0.20/0.27 % (921328)Termination reason: Refutation
% 0.20/0.27 % (921328)Time elapsed: 0.009 s
% 0.20/0.27 % (921328)Peak memory usage: 13 MB
% 0.20/0.27 % (921328)Instructions burned: 33 (million)
% 0.20/0.27 % (921317)Success in time 0.035 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------