%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWX173^1 : 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 : n011.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 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX173^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n011.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:09:46 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.30 % (274789)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (274797)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=446933187: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)
% 0.20/0.30 % (274794)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3743224066:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (274798)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4074113300:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (274795)lrs+10_16_si=on:nwc=1.5:random_seed=2495179431:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (274796)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1887335588:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (274796)Instruction limit reached!
% 0.20/0.30 % (274796)------------------------------
% 0.20/0.30 % (274796)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (274796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (274796)CaDiCaL version: 2.1.3
% 0.20/0.30 % (274796)Termination reason: Instruction limit
% 0.20/0.30 % (274796)Termination phase: Property scanning
% 0.20/0.30 % (274796)Time elapsed: 0.002 s
% 0.20/0.30 % (274796)Peak memory usage: 10 MB
% 0.20/0.30 % (274796)Instructions burned: 4 (million)
% 0.20/0.30 % (274794) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-274789-274794"...
% 0.20/0.30 % (274795)Instruction limit reached!
% 0.20/0.30 % (274795)------------------------------
% 0.20/0.30 % (274795)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (274795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (274795)CaDiCaL version: 2.1.3
% 0.20/0.30 % (274795)Termination reason: Instruction limit
% 0.20/0.30 % (274795)Termination phase: Saturation
% 0.20/0.30 % (274795)Time elapsed: 0.011 s
% 0.20/0.30 % (274795)Peak memory usage: 12 MB
% 0.20/0.30 % (274795)Instructions burned: 19 (million)
% 0.20/0.30 % (274800)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (274800)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
% 0.20/0.30 % (274798)Instruction limit reached!
% 0.20/0.30 % (274798)------------------------------
% 0.20/0.30 % (274798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (274798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (274798)CaDiCaL version: 2.1.3
% 0.20/0.30 % (274798)Termination reason: Instruction limit
% 0.20/0.30 % (274798)Termination phase: Saturation
% 0.20/0.30 % (274798)Time elapsed: 0.014 s
% 0.20/0.30 % (274798)Peak memory usage: 12 MB
% 0.20/0.30 % (274798)Instructions burned: 24 (million)
% 0.20/0.30 % (274799)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3725645908:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (274794)...printing done.
% 0.20/0.30 % (274800)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=4252819103:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (274794)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, unsorted: $tType).
% 0.20/0.30 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(type_def_7, type, d_unsorted: $tType).
% 0.20/0.30 thf(func_def_0, type, irel: ($i > $i > $o)).
% 0.20/0.30 thf(func_def_1, type, mnot: (($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_2, type, mor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_3, type, mand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_4, type, mimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_5, type, mbox_s4: (($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_6, type, iatom: (($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_7, type, inot: (($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_8, type, itrue: ($i > $o)).
% 0.20/0.30 thf(func_def_9, type, ifalse: ($i > $o)).
% 0.20/0.30 thf(func_def_10, type, iand: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_11, type, ior: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_12, type, iimplies: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_13, type, iimplied: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_14, type, iequiv: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_15, type, ixor: (($i > $o) > ($i > $o) > $i > $o)).
% 0.20/0.30 thf(func_def_16, type, ivalid: (($i > $o) > $o)).
% 0.20/0.30 thf(func_def_17, type, isatisfiable: (($i > $o) > $o)).
% 0.20/0.30 thf(func_def_18, type, icountersatisfiable: (($i > $o) > $o)).
% 0.20/0.30 thf(func_def_19, type, iinvalid: (($i > $o) > $o)).
% 0.20/0.30 thf(func_def_20, type, d2unsorted: (d_unsorted > $i)).
% 0.20/0.30 thf(func_def_21, type, d_unsorted_0: d_unsorted).
% 0.20/0.30 thf(func_def_23, type, vOR: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_24, type, vNOT: ($o > $o)).
% 0.20/0.30 thf(func_def_25, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_26, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_27, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_28, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_29, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.30 thf(func_def_30, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_33, type, vAND: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_34, type, db5: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_35, type, db6: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_36, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_37, type, sK0: ($i > d_unsorted)).
% 0.20/0.30 thf(func_def_38, type, sK1: ($i > $o)).
% 0.20/0.30 thf(func_def_39, type, sK2: ($i > $o)).
% 0.20/0.30 thf(f1,axiom,(
% 0.20/0.30 ((^[X4 : ($i > $o), X5 : ($i > $o), X0 : $i] : ((X5 @ X0) & (X4 @ X0))) = mand) & ((^[X8 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)))) = inot) & ! [X0 : $i] : ? [X1 : d_unsorted] : (X0 = ((d2unsorted @ X1))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)))) = iimplies) & (ivalid = (^[X14 : ($i > $o)] : (! [X15 : $i] : (X14 @ X15)))) & (itrue @ (d2unsorted @ d_unsorted_0)) & (ior = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)) | ! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (mor = (^[X4 : ($i > $o), X5 : ($i > $o), X0 : $i] : ((X4 @ X0) | (X5 @ X0)))) & (ixor = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (~ ! [X11 : $i,X10 : $i,X5 : $i] : (~(irel @ X7 @ X5) | (((X9 @ X10) | ~ ! [X12 : $i] : (~(irel @ X5 @ X12) | (X8 @ X12)) | ~(irel @ X5 @ X10)) & ((X8 @ X11) | ~ ! [X13 : $i] : ((X9 @ X13) | ~(irel @ X5 @ X13)) | ~(irel @ X5 @ X11))))))) & ((^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : ((X8 @ X7) & (X9 @ X7))) = iand) & ((^[X8 : ($i > $o), X4 : $i] : (! [X5 : $i] : (~(irel @ X4 @ X5) | (X8 @ X5)))) = mbox_s4) & (iequiv = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : ((! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ~ ! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5))) & (! [X5 : $i] : (~(irel @ X7 @ X5) | (X9 @ X5)) | ~ ! [X5 : $i] : ((X8 @ X5) | ~(irel @ X7 @ X5)))))) & ((^[X14 : ($i > $o)] : (~ ! [X15 : $i] : (X14 @ X15))) = icountersatisfiable) & (mnot = (^[X4 : ($i > $o), X0 : $i] : (~(X4 @ X0)))) & (iinvalid = (^[X14 : ($i > $o)] : (! [X15 : $i] : ~(X14 @ X15)))) & ((^[X8 : ($i > $o), X7 : $i] : ((X8 @ X7))) = iatom) & ! [X2 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ! [X1 : d_unsorted] : (X1 = d_unsorted_0) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ((^[X0 : ($i > $o), X6 : ($i > $o), X7 : $i] : (~(X0 @ X7) | (X6 @ X7))) = mimplies) & ((^[X14 : ($i > $o)] : (~ ! [X15 : $i] : ~(X14 @ X15))) = isatisfiable) & (iimplied = (^[X8 : ($i > $o), X9 : ($i > $o), X7 : $i] : (! [X5 : $i] : (~(irel @ X7 @ X5) | (X8 @ X5)) | ~ ! [X5 : $i] : ((X9 @ X5) | ~(irel @ X7 @ X5)))))),
% 0.20/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lcl695_1)).
% 0.20/0.30 thf(f2,conjecture,(
% 0.20/0.30 ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = ior)),
% 0.20/0.30 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ior)).
% 0.20/0.30 thf(f3,negated_conjecture,(
% 0.20/0.30 ~ ((^[X0 : ($i > $o), X1 : ($i > $o)] : ((mor @ (mbox_s4 @ X0) @ (mbox_s4 @ X1)))) = ior)),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f2])).
% 0.20/0.30 thf(f4,plain,(
% 0.20/0.30 ((^[X0 : ($i > $o), X1 : ($i > $o), X2 : $i] : ((X1 @ X2) & (X0 @ X2))) = mand) & ((^[X3 : ($i > $o), X4 : $i] : (~ ! [X5 : $i] : (~(irel @ X4 @ X5) | (X3 @ X5)))) = inot) & ! [X6 : $i] : ? [X7 : d_unsorted] : (((d2unsorted @ X7)) = X6) & ((^[X8 : ($i > $o), X9 : ($i > $o), X10 : $i] : (~ ! [X11 : $i] : (~(irel @ X10 @ X11) | (X8 @ X11)) | ! [X12 : $i] : (~(irel @ X10 @ X12) | (X9 @ X12)))) = iimplies) & (ivalid = (^[X13 : ($i > $o)] : (! [X14 : $i] : (X13 @ X14)))) & (itrue @ (d2unsorted @ d_unsorted_0)) & (ior = (^[X15 : ($i > $o), X16 : ($i > $o), X17 : $i] : (! [X18 : $i] : ((X16 @ X18) | ~(irel @ X17 @ X18)) | ! [X19 : $i] : (~(irel @ X17 @ X19) | (X15 @ X19))))) & (irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0)) & (mor = (^[X20 : ($i > $o), X21 : ($i > $o), X22 : $i] : ((X20 @ X22) | (X21 @ X22)))) & (ixor = (^[X23 : ($i > $o), X24 : ($i > $o), X25 : $i] : (~ ! [X26 : $i,X27 : $i,X28 : $i] : (~(irel @ X25 @ X28) | (((X24 @ X27) | ~ ! [X29 : $i] : (~(irel @ X28 @ X29) | (X23 @ X29)) | ~(irel @ X28 @ X27)) & ((X23 @ X26) | ~ ! [X30 : $i] : ((X24 @ X30) | ~(irel @ X28 @ X30)) | ~(irel @ X28 @ X26))))))) & ((^[X31 : ($i > $o), X32 : ($i > $o), X33 : $i] : ((X31 @ X33) & (X32 @ X33))) = iand) & ((^[X34 : ($i > $o), X35 : $i] : (! [X36 : $i] : (~(irel @ X35 @ X36) | (X34 @ X36)))) = mbox_s4) & (iequiv = (^[X37 : ($i > $o), X38 : ($i > $o), X39 : $i] : ((! [X40 : $i] : (~(irel @ X39 @ X40) | (X37 @ X40)) | ~ ! [X41 : $i] : (~(irel @ X39 @ X41) | (X38 @ X41))) & (! [X42 : $i] : (~(irel @ X39 @ X42) | (X38 @ X42)) | ~ ! [X43 : $i] : ((X37 @ X43) | ~(irel @ X39 @ X43)))))) & ((^[X44 : ($i > $o)] : (~ ! [X45 : $i] : (X44 @ X45))) = icountersatisfiable) & (mnot = (^[X46 : ($i > $o), X47 : $i] : (~(X46 @ X47)))) & (iinvalid = (^[X48 : ($i > $o)] : (! [X49 : $i] : ~(X48 @ X49)))) & ((^[X50 : ($i > $o), X51 : $i] : ((X50 @ X51))) = iatom) & ! [X52 : d_unsorted,X53 : d_unsorted] : ((((d2unsorted @ X52)) = ((d2unsorted @ X53))) => (X52 = X53)) & ! [X54 : d_unsorted] : (d_unsorted_0 = X54) & ~(ifalse @ (d2unsorted @ d_unsorted_0)) & ((^[X55 : ($i > $o), X56 : ($i > $o), X57 : $i] : (~(X55 @ X57) | (X56 @ X57))) = mimplies) & ((^[X58 : ($i > $o)] : (~ ! [X59 : $i] : ~(X58 @ X59))) = isatisfiable) & (iimplied = (^[X60 : ($i > $o), X61 : ($i > $o), X62 : $i] : (! [X63 : $i] : (~(irel @ X62 @ X63) | (X60 @ X63)) | ~ ! [X64 : $i] : ((X61 @ X64) | ~(irel @ X62 @ X64)))))),
% 0.20/0.30 inference(rectify,[],[f1])).
% 0.20/0.30 thf(f5,plain,(
% 0.20/0.30 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & ! [X6 : $i] : ? [X7 : d_unsorted] : (((d2unsorted @ X7)) = X6) & (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))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (irel @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y3 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y5)) & (((~ (irel @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (Y1 @ Y4))) | (~ (irel @ Y2 @ Y3)))))))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ! [X52 : d_unsorted,X53 : d_unsorted] : ((((d2unsorted @ X52)) = ((d2unsorted @ X53))) => (X52 = X53)) & ! [X54 : d_unsorted] : (d_unsorted_0 = X54) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 0.20/0.30 inference(fool_elimination,[],[f4])).
% 0.20/0.30 thf(f6,plain,(
% 0.20/0.30 ~ (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.30 inference(fool_elimination,[],[f3])).
% 0.20/0.30 thf(f7,plain,(
% 0.20/0.30 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (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))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (irel @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y3 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y5)) & (((~ (irel @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (Y1 @ Y4))) | (~ (irel @ Y2 @ Y3)))))))))))))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & ! [X3 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & ~ (((ifalse @ (d2unsorted @ d_unsorted_0))) = $true) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 0.20/0.30 inference(rectify,[],[f5])).
% 0.20/0.30 thf(f8,plain,(
% 0.20/0.30 (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & ! [X3 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X2)) = ((d2unsorted @ X3))) => (X2 = X3)) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (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))))))))))))) & (ixor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((((~ (irel @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y3 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y5)) & (((~ (irel @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (Y1 @ Y4))) | (~ (irel @ Y2 @ Y3)))))))))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2)))))))) & (icountersatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true)),
% 0.20/0.30 inference(flattening,[],[f7])).
% 0.20/0.30 thf(f9,plain,(
% 0.20/0.30 (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.30 inference(flattening,[],[f6])).
% 0.20/0.30 thf(f10,plain,(
% 0.20/0.30 (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (icountersatisfiable = (^[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]: (((((~ (irel @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y3 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y5)) & (((~ (irel @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (Y1 @ Y4))) | (~ (irel @ Y2 @ Y3)))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (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]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X3 : d_unsorted,X2 : d_unsorted] : ((((d2unsorted @ X2)) != ((d2unsorted @ X3))) | (X2 = X3)) & ! [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))))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))),
% 0.20/0.30 inference(ennf_transformation,[],[f8])).
% 0.20/0.30 thf(f11,plain,(
% 0.20/0.30 (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (icountersatisfiable = (^[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]: (((((~ (irel @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y3 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y5)) & (((~ (irel @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (Y1 @ Y4))) | (~ (irel @ Y2 @ Y3)))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (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]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) != ((d2unsorted @ X0))) | (X0 = X1)) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (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))))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & ! [X3 : $i] : ? [X4 : d_unsorted] : (((d2unsorted @ X4)) = X3) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))),
% 0.20/0.30 inference(rectify,[],[f10])).
% 0.20/0.30 thf(f12,plain,(
% 0.20/0.30 (((itrue @ (d2unsorted @ d_unsorted_0))) = $true) & (iand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) & (Y0 @ Y2)))))))) & (((ifalse @ (d2unsorted @ d_unsorted_0))) != $true) & (iatom = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (Y0 @ Y1))))) & (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) & (Y1 @ Y2)))))))) & (iimplied = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3)))))))))))) & (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (~ (Y0 @ Y2))))))))) & (inot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))) & (icountersatisfiable = (^[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]: (((((~ (irel @ Y3 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (irel @ Y3 @ Y6)) | (Y1 @ Y6)))))) | (Y0 @ Y5)) & (((~ (irel @ Y3 @ Y4)) | (~ (!! @ $i @ (^[Y6 : $i]: ((Y0 @ Y6) | (~ (irel @ Y3 @ Y6))))))) | (Y1 @ Y4))) | (~ (irel @ Y2 @ Y3)))))))))))))))) & (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1))))) & (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (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]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3))))))))))) & (iinvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1)))))) & (((irel @ (d2unsorted @ d_unsorted_0) @ (d2unsorted @ d_unsorted_0))) = $true) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X1)) != ((d2unsorted @ X0))) | (X0 = X1)) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (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))))))))))))) & (isatisfiable = (^[Y0 : $i > $o]: (~ (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1))))))) & (iequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y0 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) & ((~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3)))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))) & ! [X3 : $i] : (((d2unsorted @ (sK0 @ X3))) = X3) & (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X4,sK0 @ X3)],[f11])).
% 0.20/0.30 thf(f13,plain,(
% 0.20/0.30 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2)))))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f12])).
% 0.20/0.30 thf(f14,plain,(
% 0.20/0.30 ( ! [X3 : $i] : ((((d2unsorted @ (sK0 @ X3))) = X3)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f12])).
% 0.20/0.30 thf(f18,plain,(
% 0.20/0.30 ( ! [X2 : d_unsorted] : ((d_unsorted_0 = X2)) )),
% 0.20/0.30 inference(cnf_transformation,[],[f12])).
% 0.20/0.30 thf(f22,plain,(
% 0.20/0.30 (ior = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f12])).
% 0.20/0.30 thf(f23,plain,(
% 0.20/0.30 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f12])).
% 0.20/0.30 thf(f36,plain,(
% 0.20/0.30 (ior != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f9])).
% 0.20/0.30 thf(f39,plain,(
% 0.20/0.30 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) != (^[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]: ((Y2 @ Y4) | (~ (irel @ Y3 @ Y4)))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (irel @ Y3 @ Y4)))))))) @ Y1))))))),
% 0.20/0.30 inference(definition_unfolding,[],[f36,f22,f23,f13,f13])).
% 0.20/0.30 thf(f40,plain,(
% 0.20/0.30 ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))))),
% 0.20/0.30 inference(beta-eta_normalization,[],[f39])).
% 0.20/0.30 thf(f41,plain,(
% 0.20/0.30 ( ! [X3 : $i] : ((((d2unsorted @ d_unsorted_0)) = X3)) )),
% 0.20/0.30 inference(forward_demodulation,[],[f14,f18])).
% 0.20/0.30 thf(f43,plain,(
% 0.20/0.30 ((((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))))))))) @ sK1)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: ((Y0 @ Y3) | (~ (irel @ Y2 @ Y3))))) | (!! @ $i @ (^[Y3 : $i]: ((~ (irel @ Y2 @ Y3)) | (Y1 @ Y3)))))))))) @ sK1)))),
% 0.20/0.30 inference(negative_extensionality,[],[f40])).
% 0.20/0.30 thf(f44,plain,(
% 0.20/0.30 ((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) != (^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))))))),
% 0.20/0.30 inference(beta-eta_normalization,[],[f43])).
% 0.20/0.30 thf(f50,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
% 0.20/0.30 inference(constrained_superposition,[],[f41,f41])).
% 0.20/0.30 thf(f110,plain,(
% 0.20/0.30 ((((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))))))) @ sK2)) != (((^[Y0 : $i > $o]: ((^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((sK1 @ Y2) | (~ (irel @ Y1 @ Y2))))) | (!! @ $i @ (^[Y2 : $i]: ((~ (irel @ Y1 @ Y2)) | (Y0 @ Y2)))))))) @ sK2)))),
% 0.20/0.30 inference(negative_extensionality,[],[f44])).
% 0.20/0.30 thf(f111,plain,(
% 0.20/0.30 ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))))) != (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))))),
% 0.20/0.30 inference(beta-eta_normalization,[],[f110])).
% 0.20/0.30 thf(f112,plain,(
% 0.20/0.30 ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3)) != (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))))) @ sK3)))),
% 0.20/0.30 inference(negative_extensionality,[],[f111])).
% 0.20/0.30 thf(f113,plain,(
% 0.20/0.30 ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))))) @ sK3)) = $true) | ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3)) = $true)),
% 0.20/0.30 inference(xor_proxy_clausification,[],[f112])).
% 0.20/0.30 thf(f114,plain,(
% 0.20/0.30 ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK2 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))))) @ sK3)) = $false) | ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) | (~ (irel @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (irel @ Y0 @ Y1)) | (sK2 @ Y1)))))) @ sK3)) = $false)),
% 0.20/0.30 inference(xor_proxy_clausification,[],[f112])).
% 0.20/0.30 thf(f115,plain,(
% 0.20/0.30 ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))))) | ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))))))),
% 0.20/0.30 inference(beta-eta_normalization,[],[f114])).
% 0.20/0.30 thf(f116,plain,(
% 0.20/0.30 ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))))) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $false)),
% 0.20/0.30 inference(or_proxy_clausification,[],[f115])).
% 0.20/0.30 thf(f117,plain,(
% 0.20/0.30 ($false = (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))))) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $false)),
% 0.20/0.30 inference(or_proxy_clausification,[],[f115])).
% 0.20/0.30 thf(f118,plain,(
% 0.20/0.30 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))))) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $false)),
% 0.20/0.30 inference(or_proxy_clausification,[],[f117])).
% 0.20/0.30 thf(f133,plain,(
% 0.20/0.30 (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $false) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK6)))),
% 0.20/0.30 inference(sigma_proxy_clausification,[],[f118])).
% 0.20/0.30 thf(f134,plain,(
% 0.20/0.30 ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK7)) = $false) | ($false = (((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ sK6)))),
% 0.20/0.30 inference(sigma_proxy_clausification,[],[f133])).
% 0.20/0.30 thf(f135,plain,(
% 0.20/0.30 ($false = (((~ (irel @ sK3 @ sK6)) | (sK2 @ sK6)))) | ((((sK2 @ sK7) | (~ (irel @ sK3 @ sK7)))) = $false)),
% 0.20/0.30 inference(beta-eta_normalization,[],[f134])).
% 0.20/0.30 thf(f136,plain,(
% 0.20/0.30 ((((sK2 @ sK7) | (~ (irel @ sK3 @ sK7)))) = $false) | (((sK2 @ sK6)) = $false)),
% 0.20/0.30 inference(or_proxy_clausification,[],[f135])).
% 0.20/0.30 thf(f143,plain,(
% 0.20/0.30 (((sK2 @ sK7)) = $false) | (((sK2 @ sK6)) = $false)),
% 0.20/0.30 inference(or_proxy_clausification,[],[f136])).
% 0.20/0.30 thf(f146,plain,(
% 0.20/0.30 (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $false)),
% 0.20/0.30 inference(or_proxy_clausification,[],[f116])).
% 0.20/0.30 thf(f147,plain,(
% 0.20/0.30 ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK8)) = $false) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK8)) = $false)),
% 0.20/0.30 inference(sigma_proxy_clausification,[],[f146])).
% 0.20/0.30 thf(f148,plain,(
% 0.20/0.30 ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ sK8)) = $false)),
% 0.20/0.30 inference(duplicate_literal_removal,[],[f147])).
% 0.20/0.30 thf(f149,plain,(
% 0.20/0.30 ((((sK1 @ sK8) | (~ (irel @ sK3 @ sK8)))) = $false)),
% 0.20/0.30 inference(beta-eta_normalization,[],[f148])).
% 0.20/0.30 thf(f150,plain,(
% 0.20/0.30 ($false = ((~ (irel @ sK3 @ sK8))))),
% 0.20/0.30 inference(or_proxy_clausification,[],[f149])).
% 0.20/0.30 thf(f151,plain,(
% 0.20/0.30 ($false = ((sK1 @ sK8)))),
% 0.20/0.30 inference(or_proxy_clausification,[],[f149])).
% 0.20/0.30 thf(f152,plain,(
% 0.20/0.30 (((irel @ sK3 @ sK8)) = $true)),
% 0.20/0.30 inference(not_proxy_clausification,[],[f150])).
% 0.20/0.30 thf(f165,plain,(
% 0.20/0.30 ((((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))))) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) = $true)),
% 0.20/0.30 inference(beta-eta_normalization,[],[f113])).
% 0.20/0.30 thf(f166,plain,(
% 0.20/0.30 (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))))),
% 0.20/0.30 inference(or_proxy_clausification,[],[f165])).
% 0.20/0.30 thf(f167,plain,(
% 0.20/0.30 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1)) = $true) | ((((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0))))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f166])).
% 0.20/0.30 thf(f168,plain,(
% 0.20/0.30 ( ! [X1 : $i] : (((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $true) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))))))) )),
% 0.20/0.30 inference(or_proxy_clausification,[],[f167])).
% 0.20/0.30 thf(f169,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0)))))) | ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X2)) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $true) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1)) = $true)) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f168])).
% 0.20/0.30 thf(f170,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))))) = $true) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true) | ((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X2)) = $true) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1)) = $true)) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f169])).
% 0.20/0.30 thf(f171,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((^[Y0 : $i]: ((sK2 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X2)) = $true) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X1)) = $true) | ((((^[Y0 : $i]: ((sK1 @ Y0) | (~ (irel @ sK3 @ Y0)))) @ X4)) = $true) | ((((^[Y0 : $i]: ((~ (irel @ sK3 @ Y0)) | (sK2 @ Y0))) @ X3)) = $true)) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f170])).
% 0.20/0.30 thf(f172,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((~ (irel @ sK3 @ X3)) | (sK2 @ X3))) = $true) | ((((sK1 @ X1) | (~ (irel @ sK3 @ X1)))) = $true) | ((((sK1 @ X4) | (~ (irel @ sK3 @ X4)))) = $true) | ((((sK2 @ X2) | (~ (irel @ sK3 @ X2)))) = $true)) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f171])).
% 0.20/0.30 thf(f173,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK2 @ X3)) = $true) | ((((sK1 @ X4) | (~ (irel @ sK3 @ X4)))) = $true) | ((((sK2 @ X2) | (~ (irel @ sK3 @ X2)))) = $true) | ($true = ((~ (irel @ sK3 @ X3)))) | ((((sK1 @ X1) | (~ (irel @ sK3 @ X1)))) = $true)) )),
% 0.20/0.30 inference(or_proxy_clausification,[],[f172])).
% 0.20/0.30 thf(f174,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((~ (irel @ sK3 @ X4)))) | (((sK2 @ X3)) = $true) | ($true = ((~ (irel @ sK3 @ X3)))) | ((((sK1 @ X1) | (~ (irel @ sK3 @ X1)))) = $true) | ((((sK2 @ X2) | (~ (irel @ sK3 @ X2)))) = $true) | (((sK1 @ X4)) = $true)) )),
% 0.20/0.30 inference(or_proxy_clausification,[],[f173])).
% 0.20/0.30 thf(f175,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((~ (irel @ sK3 @ X3)))) | (((irel @ sK3 @ X4)) = $false) | ((((sK2 @ X2) | (~ (irel @ sK3 @ X2)))) = $true) | ((((sK1 @ X1) | (~ (irel @ sK3 @ X1)))) = $true) | (((sK1 @ X4)) = $true) | (((sK2 @ X3)) = $true)) )),
% 0.20/0.30 inference(not_proxy_clausification,[],[f174])).
% 0.20/0.30 thf(f176,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((((sK1 @ X1) | (~ (irel @ sK3 @ X1)))) = $true) | (((irel @ sK3 @ X3)) = $false) | (((sK2 @ X3)) = $true) | ((((sK2 @ X2) | (~ (irel @ sK3 @ X2)))) = $true) | (((irel @ sK3 @ X4)) = $false) | (((sK1 @ X4)) = $true)) )),
% 0.20/0.30 inference(not_proxy_clausification,[],[f175])).
% 0.20/0.30 thf(f177,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK1 @ X1)) = $true) | ((((sK2 @ X2) | (~ (irel @ sK3 @ X2)))) = $true) | (((irel @ sK3 @ X4)) = $false) | (((~ (irel @ sK3 @ X1))) = $true) | (((irel @ sK3 @ X3)) = $false) | (((sK2 @ X3)) = $true) | (((sK1 @ X4)) = $true)) )),
% 0.20/0.30 inference(or_proxy_clausification,[],[f176])).
% 0.20/0.30 thf(f178,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((sK2 @ X2)) = $true) | (((~ (irel @ sK3 @ X1))) = $true) | (((~ (irel @ sK3 @ X2))) = $true) | (((irel @ sK3 @ X4)) = $false) | (((sK1 @ X1)) = $true) | (((sK2 @ X3)) = $true) | (((irel @ sK3 @ X3)) = $false) | (((sK1 @ X4)) = $true)) )),
% 0.20/0.30 inference(or_proxy_clausification,[],[f177])).
% 0.20/0.30 thf(f179,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ sK3 @ X1)) = $false) | (((sK1 @ X4)) = $true) | (((sK1 @ X1)) = $true) | (((sK2 @ X2)) = $true) | (((sK2 @ X3)) = $true) | (((irel @ sK3 @ X4)) = $false) | (((~ (irel @ sK3 @ X2))) = $true) | (((irel @ sK3 @ X3)) = $false)) )),
% 0.20/0.30 inference(not_proxy_clausification,[],[f178])).
% 0.20/0.30 thf(f180,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((irel @ sK3 @ X1)) = $false) | (((sK2 @ X3)) = $true) | (((sK2 @ X2)) = $true) | (((irel @ sK3 @ X4)) = $false) | (((irel @ sK3 @ X2)) = $false) | (((sK1 @ X4)) = $true) | (((irel @ sK3 @ X3)) = $false) | (((sK1 @ X1)) = $true)) )),
% 0.20/0.30 inference(not_proxy_clausification,[],[f179])).
% 0.20/0.30 thf(f202,definition,(
% 0.20/0.30 spl11_5 <=> (((sK2 @ sK7)) = $false)),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition])).
% 0.20/0.30 thf(f204,plain,(
% 0.20/0.30 (((sK2 @ sK7)) = $false) | ~spl11_5),
% 0.20/0.30 inference(avatar_component_clause,[],[f202])).
% 0.20/0.30 thf(f216,definition,(
% 0.20/0.30 spl11_8 <=> (((sK2 @ sK6)) = $false)),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition])).
% 0.20/0.30 thf(f218,plain,(
% 0.20/0.30 (((sK2 @ sK6)) = $false) | ~spl11_8),
% 0.20/0.30 inference(avatar_component_clause,[],[f216])).
% 0.20/0.30 thf(f219,plain,(
% 0.20/0.30 spl11_8 | spl11_5),
% 0.20/0.30 inference(avatar_split_clause,[],[f143,f202,f216])).
% 0.20/0.30 thf(f242,definition,(
% 0.20/0.30 spl11_13 <=> ! [X3 : $i] : ((((sK2 @ X3)) = $true) | (((irel @ sK3 @ X3)) = $false))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition])).
% 0.20/0.30 thf(f243,plain,(
% 0.20/0.30 ( ! [X3 : $i] : ((((irel @ sK3 @ X3)) = $false) | (((sK2 @ X3)) = $true)) ) | ~spl11_13),
% 0.20/0.30 inference(avatar_component_clause,[],[f242])).
% 0.20/0.30 thf(f245,definition,(
% 0.20/0.30 spl11_14 <=> ! [X4 : $i] : ((((irel @ sK3 @ X4)) = $false) | (((sK1 @ X4)) = $true))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition])).
% 0.20/0.30 thf(f246,plain,(
% 0.20/0.30 ( ! [X4 : $i] : ((((sK1 @ X4)) = $true) | (((irel @ sK3 @ X4)) = $false)) ) | ~spl11_14),
% 0.20/0.30 inference(avatar_component_clause,[],[f245])).
% 0.20/0.30 thf(f247,plain,(
% 0.20/0.30 spl11_13 | spl11_14 | spl11_13 | spl11_14),
% 0.20/0.30 inference(avatar_split_clause,[],[f180,f245,f242,f245,f242])).
% 0.20/0.30 thf(f249,plain,(
% 0.20/0.30 ( ! [X0 : $i] : (($false = ((sK1 @ X0)))) )),
% 0.20/0.30 inference(constrained_superposition,[],[f151,f50])).
% 0.20/0.30 thf(f252,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl11_5),
% 0.20/0.30 inference(constrained_superposition,[],[f204,f50])).
% 0.20/0.30 thf(f257,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((((irel @ sK3 @ X0)) = $true)) )),
% 0.20/0.30 inference(constrained_superposition,[],[f152,f50])).
% 0.20/0.30 thf(f273,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $true)) )),
% 0.20/0.30 inference(constrained_superposition,[],[f257,f50])).
% 0.20/0.30 thf(f283,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $false) | ($true = ((sK2 @ X1)))) ) | ~spl11_13),
% 0.20/0.30 inference(constrained_superposition,[],[f243,f50])).
% 0.20/0.30 thf(f296,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((((sK2 @ X0)) = $true) | ($false = $true)) ) | ~spl11_13),
% 0.20/0.30 inference(constrained_superposition,[],[f257,f243])).
% 0.20/0.30 thf(f327,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((((sK2 @ X0)) = $true)) ) | ~spl11_13),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f296])).
% 0.20/0.30 thf(f378,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : (($false = $true) | (((irel @ X0 @ X1)) = $false)) ) | (~spl11_5 | ~spl11_13)),
% 0.20/0.30 inference(forward_demodulation,[],[f283,f252])).
% 0.20/0.30 thf(f379,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : ((((irel @ X0 @ X1)) = $false)) ) | (~spl11_5 | ~spl11_13)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f378])).
% 0.20/0.30 thf(f401,plain,(
% 0.20/0.30 ($false = $true) | (~spl11_5 | ~spl11_13)),
% 0.20/0.30 inference(forward_demodulation,[],[f379,f273])).
% 0.20/0.30 thf(f402,plain,(
% 0.20/0.30 $false | (~spl11_5 | ~spl11_13)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f401])).
% 0.20/0.30 thf(f403,plain,(
% 0.20/0.30 ~spl11_5 | ~spl11_13),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f402])).
% 0.20/0.30 thf(f408,plain,(
% 0.20/0.30 ( ! [X0 : $i] : ((((sK2 @ X0)) = $false)) ) | ~spl11_8),
% 0.20/0.30 inference(constrained_superposition,[],[f218,f50])).
% 0.20/0.30 thf(f413,plain,(
% 0.20/0.30 ($false = $true) | (~spl11_8 | ~spl11_13)),
% 0.20/0.30 inference(forward_demodulation,[],[f408,f327])).
% 0.20/0.30 thf(f414,plain,(
% 0.20/0.30 $false | (~spl11_8 | ~spl11_13)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f413])).
% 0.20/0.30 thf(f415,plain,(
% 0.20/0.30 ~spl11_8 | ~spl11_13),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f414])).
% 0.20/0.30 thf(f416,plain,(
% 0.20/0.30 ( ! [X4 : $i] : ((((irel @ sK3 @ X4)) = $false) | ($false = $true)) ) | ~spl11_14),
% 0.20/0.30 inference(forward_demodulation,[],[f246,f249])).
% 0.20/0.30 thf(f417,plain,(
% 0.20/0.30 ( ! [X4 : $i] : ((((irel @ sK3 @ X4)) = $false)) ) | ~spl11_14),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f416])).
% 0.20/0.30 thf(f418,plain,(
% 0.20/0.30 ($false = $true) | ~spl11_14),
% 0.20/0.30 inference(forward_demodulation,[],[f417,f273])).
% 0.20/0.30 thf(f419,plain,(
% 0.20/0.30 $false | ~spl11_14),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f418])).
% 0.20/0.30 thf(f420,plain,(
% 0.20/0.30 ~spl11_14),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f419])).
% 0.20/0.30 cnf(s7, plain, spl11_5 | spl11_8, inference(sat_conversion,[],[f219])).
% 0.20/0.30 cnf(s13, plain, spl11_13 | spl11_14 | spl11_13 | spl11_14, inference(sat_conversion,[],[f247])).
% 0.20/0.30 cnf(s14, plain, spl11_13 | spl11_14, inference(rat,[],[s13])).
% 0.20/0.30 cnf(s38, plain, ~spl11_5 | ~spl11_13, inference(sat_conversion,[],[f403])).
% 0.20/0.30 cnf(s40, plain, ~spl11_8 | ~spl11_13, inference(sat_conversion,[],[f415])).
% 0.20/0.30 cnf(s41, plain, ~spl11_14, inference(sat_conversion,[],[f420])).
% 0.20/0.30 cnf(s42, plain, spl11_13, inference(rat,[],[s14,s41])).
% 0.20/0.30 cnf(s43, plain, ~spl11_8, inference(rat,[],[s40,s42])).
% 0.20/0.30 cnf(s44, plain, ~spl11_5, inference(rat,[],[s38,s42])).
% 0.20/0.30 cnf(s46, plain, $false, inference(rat,[],[s7,s43,s44])).
% 0.20/0.30 thf(f421,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(avatar_sat_refutation,[],[s46])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (274794)------------------------------
% 0.20/0.30 % (274794)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (274794)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (274794)CaDiCaL version: 2.1.3
% 0.20/0.30 % (274794)Termination reason: Refutation
% 0.20/0.30 % (274794)Time elapsed: 0.018 s
% 0.20/0.30 % (274794)Peak memory usage: 13 MB
% 0.20/0.30 % (274794)Instructions burned: 34 (million)
% 0.20/0.30 % (274789)Success in time 0.051 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------