TSTP Solution File: COM012+1 by Goeland---1.0.0
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%------------------------------------------------------------------------------
% File : Goeland---1.0.0
% Problem : COM012+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : goeland -dmt -presko -proof %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 6 17:56:51 EDT 2022
% Result : Theorem 223.89s 37.59s
% Output : Proof 223.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM012+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.13 % Command : goeland -dmt -presko -proof %s
% 0.12/0.34 % Computer : n022.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 13:34:26 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.34 [DMT] DMT loaded with preskolemization
% 0.19/0.34 [EQ] equality loaded.
% 0.19/0.34 [0.000038s][1][MAIN] Problem : theBenchmark.p
% 0.19/0.35 Start search
% 0.19/0.35 nb_step : 1 - limit : 10
% 0.19/0.35 Launch Gotab with destructive = true
% 223.89/37.55 % SZS output start Proof for theBenchmark.p
% 223.89/37.58 [0] ALPHA_AND : (! [W04_4] : ((aElement0(W04_4) => $true)) & ! [W05_5] : ((aRewritingSystem0(W05_5) => $true)) & ! [W06_6, W17_7] : (((aElement0(W06_6) & aRewritingSystem0(W17_7)) => ! [W28_8] : ((aReductOfIn0(W28_8, W06_6, W17_7) => aElement0(W28_8))))) & ! [W09_9, W110_10] : (((aElement0(W09_9) & aElement0(W110_10)) => (iLess0(W09_9, W110_10) => $true))) & ! [W011_11, W112_12, W213_13] : ((((aElement0(W011_11) & aRewritingSystem0(W112_12)) & aElement0(W213_13)) => (sdtmndtplgtdt0(W011_11, W112_12, W213_13) => $true))) & ! [W014_14, W115_15, W216_16] : ((((aElement0(W014_14) & aRewritingSystem0(W115_15)) & aElement0(W216_16)) => (sdtmndtplgtdt0(W014_14, W115_15, W216_16) <=> (aReductOfIn0(W216_16, W014_14, W115_15) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, W014_14, W115_15)) & sdtmndtplgtdt0(W317_17, W115_15, W216_16))))))) & ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21)))) & ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24))))) & (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) & ~((sdtmndtasgtdt0(xx, xR, xy) & sdtmndtasgtdt0(xy, xR, xz)) => sdtmndtasgtdt0(xx, xR, xz)))
% 223.89/37.58 -> [1] ! [W04_4] : ((aElement0(W04_4) => $true)), ! [W05_5] : ((aRewritingSystem0(W05_5) => $true)), ! [W06_6, W17_7] : (((aElement0(W06_6) & aRewritingSystem0(W17_7)) => ! [W28_8] : ((aReductOfIn0(W28_8, W06_6, W17_7) => aElement0(W28_8))))), ! [W09_9, W110_10] : (((aElement0(W09_9) & aElement0(W110_10)) => (iLess0(W09_9, W110_10) => $true))), ! [W011_11, W112_12, W213_13] : ((((aElement0(W011_11) & aRewritingSystem0(W112_12)) & aElement0(W213_13)) => (sdtmndtplgtdt0(W011_11, W112_12, W213_13) => $true))), ! [W014_14, W115_15, W216_16] : ((((aElement0(W014_14) & aRewritingSystem0(W115_15)) & aElement0(W216_16)) => (sdtmndtplgtdt0(W014_14, W115_15, W216_16) <=> (aReductOfIn0(W216_16, W014_14, W115_15) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, W014_14, W115_15)) & sdtmndtplgtdt0(W317_17, W115_15, W216_16))))))), ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21)))), ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24))))), (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)), ~((sdtmndtasgtdt0(xx, xR, xy) & sdtmndtasgtdt0(xy, xR, xz)) => sdtmndtasgtdt0(xx, xR, xz))
% 223.89/37.58
% 223.89/37.58 [1] ALPHA_AND : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.58 -> [2] ((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)), aElement0(xz)
% 223.89/37.58
% 223.89/37.58 [2] ALPHA_NOT_IMPLY : ~((sdtmndtasgtdt0(xx, xR, xy) & sdtmndtasgtdt0(xy, xR, xz)) => sdtmndtasgtdt0(xx, xR, xz))
% 223.89/37.58 -> [3] (sdtmndtasgtdt0(xx, xR, xy) & sdtmndtasgtdt0(xy, xR, xz)), ~sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.58
% 223.89/37.58 [3] ALPHA_AND : ((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.58 -> [4] (aElement0(xx) & aRewritingSystem0(xR)), aElement0(xy)
% 223.89/37.58
% 223.89/37.58 [4] ALPHA_AND : (sdtmndtasgtdt0(xx, xR, xy) & sdtmndtasgtdt0(xy, xR, xz))
% 223.89/37.58 -> [5] sdtmndtasgtdt0(xx, xR, xy), sdtmndtasgtdt0(xy, xR, xz)
% 223.89/37.58
% 223.89/37.58 [5] ALPHA_AND : (aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [6] aElement0(xx), aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [6] GAMMA_FORALL : ! [W04_4] : ((aElement0(W04_4) => $true))
% 223.89/37.58 -> [7] (aElement0(xx) => $true)
% 223.89/37.58
% 223.89/37.58 [7] BETA_IMPLY : (aElement0(xx) => $true)
% 223.89/37.58 -> [8] ~aElement0(xx)
% 223.89/37.58 -> [9] $true
% 223.89/37.58
% 223.89/37.58 [8] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [9] GAMMA_FORALL : ! [W05_5] : ((aRewritingSystem0(W05_5) => $true))
% 223.89/37.58 -> [10] (aRewritingSystem0(xR) => $true)
% 223.89/37.58
% 223.89/37.58 [10] BETA_IMPLY : (aRewritingSystem0(xR) => $true)
% 223.89/37.58 -> [11] ~aRewritingSystem0(xR)
% 223.89/37.58 -> [12] $true
% 223.89/37.58
% 223.89/37.58 [11] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [12] GAMMA_FORALL : ! [W06_6, W17_7] : (((aElement0(W06_6) & aRewritingSystem0(W17_7)) => ! [W28_8] : ((aReductOfIn0(W28_8, W06_6, W17_7) => aElement0(W28_8)))))
% 223.89/37.58 -> [13] ((aElement0(xz) & aRewritingSystem0(xR)) => ! [W28_8] : ((aReductOfIn0(W28_8, xz, xR) => aElement0(W28_8))))
% 223.89/37.58
% 223.89/37.58 [13] BETA_IMPLY : ((aElement0(xz) & aRewritingSystem0(xR)) => ! [W28_8] : ((aReductOfIn0(W28_8, xz, xR) => aElement0(W28_8))))
% 223.89/37.58 -> [14] ~(aElement0(xz) & aRewritingSystem0(xR))
% 223.89/37.58 -> [15] ! [W28_8] : ((aReductOfIn0(W28_8, xz, xR) => aElement0(W28_8)))
% 223.89/37.58
% 223.89/37.58 [14] BETA_NOT_AND : ~(aElement0(xz) & aRewritingSystem0(xR))
% 223.89/37.58 -> [16] ~aElement0(xz)
% 223.89/37.58 -> [17] ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [16] CLOSURE : ~aElement0(xz)
% 223.89/37.58
% 223.89/37.58 [17] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [15] GAMMA_FORALL : ! [W09_9, W110_10] : (((aElement0(W09_9) & aElement0(W110_10)) => (iLess0(W09_9, W110_10) => $true)))
% 223.89/37.58 -> [18] ((aElement0(xz) & aElement0(xy)) => (iLess0(xz, xy) => $true))
% 223.89/37.58
% 223.89/37.58 [18] BETA_IMPLY : ((aElement0(xz) & aElement0(xy)) => (iLess0(xz, xy) => $true))
% 223.89/37.58 -> [19] ~(aElement0(xz) & aElement0(xy))
% 223.89/37.58 -> [20] (iLess0(xz, xy) => $true)
% 223.89/37.58
% 223.89/37.58 [19] BETA_NOT_AND : ~(aElement0(xz) & aElement0(xy))
% 223.89/37.58 -> [21] ~aElement0(xz)
% 223.89/37.58 -> [22] ~aElement0(xy)
% 223.89/37.58
% 223.89/37.58 [22] CLOSURE : ~aElement0(xy)
% 223.89/37.58
% 223.89/37.58 [21] CLOSURE : ~aElement0(xz)
% 223.89/37.58
% 223.89/37.58 [20] BETA_IMPLY : (iLess0(xz, xy) => $true)
% 223.89/37.58 -> [23] ~iLess0(xz, xy)
% 223.89/37.58 -> [24] $true
% 223.89/37.58
% 223.89/37.58 [24] GAMMA_FORALL : ! [W011_11, W112_12, W213_13] : ((((aElement0(W011_11) & aRewritingSystem0(W112_12)) & aElement0(W213_13)) => (sdtmndtplgtdt0(W011_11, W112_12, W213_13) => $true)))
% 223.89/37.58 -> [25] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtplgtdt0(xx, xR, xy) => $true))
% 223.89/37.58
% 223.89/37.58 [25] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtplgtdt0(xx, xR, xy) => $true))
% 223.89/37.58 -> [27] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.58 -> [28] (sdtmndtplgtdt0(xx, xR, xy) => $true)
% 223.89/37.58
% 223.89/37.58 [27] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.58 -> [31] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [32] ~aElement0(xy)
% 223.89/37.58
% 223.89/37.58 [32] CLOSURE : ~aElement0(xy)
% 223.89/37.58
% 223.89/37.58 [31] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [83] ~aElement0(xx)
% 223.89/37.58 -> [84] ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [83] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [84] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [28] BETA_IMPLY : (sdtmndtplgtdt0(xx, xR, xy) => $true)
% 223.89/37.58 -> [10534] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.58 -> [10535] $true
% 223.89/37.58
% 223.89/37.58 [10534] GAMMA_FORALL : ! [W014_14, W115_15, W216_16] : ((((aElement0(W014_14) & aRewritingSystem0(W115_15)) & aElement0(W216_16)) => (sdtmndtplgtdt0(W014_14, W115_15, W216_16) <=> (aReductOfIn0(W216_16, W014_14, W115_15) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, W014_14, W115_15)) & sdtmndtplgtdt0(W317_17, W115_15, W216_16)))))))
% 223.89/37.58 -> [10543] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xx)) => (sdtmndtplgtdt0(xx, xR, xx) <=> (aReductOfIn0(xx, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))))
% 223.89/37.58
% 223.89/37.58 [10543] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xx)) => (sdtmndtplgtdt0(xx, xR, xx) <=> (aReductOfIn0(xx, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))))
% 223.89/37.58 -> [10546] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xx))
% 223.89/37.58 -> [10547] (sdtmndtplgtdt0(xx, xR, xx) <=> (aReductOfIn0(xx, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))))
% 223.89/37.58
% 223.89/37.58 [10546] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xx))
% 223.89/37.58 -> [10552] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [10553] ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [10553] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [10552] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [10591] ~aElement0(xx)
% 223.89/37.58 -> [10592] ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [10591] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [10592] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [10547] BETA_EQUIV : (sdtmndtplgtdt0(xx, xR, xx) <=> (aReductOfIn0(xx, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))))
% 223.89/37.58 -> [10857] ~sdtmndtplgtdt0(xx, xR, xx), ~(aReductOfIn0(xx, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.58 -> [10858] sdtmndtplgtdt0(xx, xR, xx), (aReductOfIn0(xx, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.58
% 223.89/37.58 [10857] ALPHA_NOT_OR : ~(aReductOfIn0(xx, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.58 -> [10878] ~aReductOfIn0(xx, xx, xR), ~? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.58
% 223.89/37.58 [10878] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.58 -> [10886] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) & aElement0(xx)) => ((sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xx)) => sdtmndtplgtdt0(xx, xR, xx)))
% 223.89/37.58
% 223.89/37.58 [10886] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) & aElement0(xx)) => ((sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xx)) => sdtmndtplgtdt0(xx, xR, xx)))
% 223.89/37.58 -> [10890] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) & aElement0(xx))
% 223.89/37.58 -> [10891] ((sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xx)) => sdtmndtplgtdt0(xx, xR, xx))
% 223.89/37.58
% 223.89/37.58 [10890] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) & aElement0(xx))
% 223.89/37.58 -> [10894] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.58 -> [10895] ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [10894] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xx))
% 223.89/37.58 -> [10914] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [10915] ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [10914] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [10924] ~aElement0(xx)
% 223.89/37.58 -> [10925] ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [10924] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [10925] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [10915] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [10895] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [10891] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xx)) => sdtmndtplgtdt0(xx, xR, xx))
% 223.89/37.58 -> [11656] ~(sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xx))
% 223.89/37.58 -> [11657] sdtmndtplgtdt0(xx, xR, xx)
% 223.89/37.58
% 223.89/37.58 [11657] CLOSURE : sdtmndtplgtdt0(xx, xR, xx)
% 223.89/37.58
% 223.89/37.58 [11656] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xx))
% 223.89/37.58 -> [11664] ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.58 -> [11665] ~sdtmndtplgtdt0(xz, xR, xx)
% 223.89/37.58
% 223.89/37.58 [11665] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.58 -> [11677] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.58
% 223.89/37.58 [11677] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.58 -> [11681] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.58 -> [11682] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.58
% 223.89/37.58 [11681] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xx))
% 223.89/37.58 -> [11700] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [11701] ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [11700] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [11706] ~aElement0(xx)
% 223.89/37.58 -> [11707] ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [11706] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [11707] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [11701] CLOSURE : ~aElement0(xx)
% 223.89/37.58
% 223.89/37.58 [11682] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.58 -> [11687] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.58 -> [11688] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.58
% 223.89/37.58 [11687] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.58 -> [11711] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.58
% 223.89/37.58 [11711] CLOSURE : ~=(xx, xy)
% 223.89/37.58
% 223.89/37.58 [11688] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.58 -> [12151] =(xx, xy)
% 223.89/37.58 -> [12152] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.58
% 223.89/37.58 [12152] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.58
% 223.89/37.58 [12151] CLOSURE : =
% 223.89/37.58
% 223.89/37.58 [11664] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.58 -> [11680] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.58
% 223.89/37.58 [11680] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.58 -> [11683] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.58 -> [11684] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.58
% 223.89/37.58 [11684] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.58 -> [11685] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.58 -> [11686] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.58
% 223.89/37.58 [11685] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.58 -> [11702] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.58
% 223.89/37.58 [11702] CLOSURE : ~=(xx, xy)
% 223.89/37.58
% 223.89/37.58 [11686] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.58 -> [12170] =(xx, xy)
% 223.89/37.58 -> [12171] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.58
% 223.89/37.58 [12171] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.58
% 223.89/37.58 [12170] CLOSURE : =
% 223.89/37.58
% 223.89/37.58 [11683] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.58 -> [12383] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [12384] ~aElement0(xy)
% 223.89/37.58
% 223.89/37.58 [12384] CLOSURE : ~aElement0(xy)
% 223.89/37.58
% 223.89/37.58 [12383] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.58 -> [12385] ~aElement0(xx)
% 223.89/37.58 -> [12386] ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [12386] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.58
% 223.89/37.58 [12385] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [10858] BETA_OR : (aReductOfIn0(xx, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59 -> [10879] aReductOfIn0(xx, xx, xR)
% 223.89/37.59 -> [10880] ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.59
% 223.89/37.59 [10880] DELTA_EXISTS : ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.59 -> [10881] ((aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xx, xR)) & sdtmndtplgtdt0(skolem_W31717, xR, xx))
% 223.89/37.59
% 223.89/37.59 [10881] ALPHA_AND : ((aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xx, xR)) & sdtmndtplgtdt0(skolem_W31717, xR, xx))
% 223.89/37.59 -> [10884] (aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xx, xR)), sdtmndtplgtdt0(skolem_W31717, xR, xx)
% 223.89/37.59
% 223.89/37.59 [10884] ALPHA_AND : (aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xx, xR))
% 223.89/37.59 -> [10907] aElement0(skolem_W31717), aReductOfIn0(skolem_W31717, xx, xR)
% 223.89/37.59
% 223.89/37.59 [10907] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [10913] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xy)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xy)) => sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [10913] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xy)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xy)) => sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [10920] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xy))
% 223.89/37.59 -> [10921] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xy)) => sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [10920] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xy))
% 223.89/37.59 -> [10942] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [10943] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [10943] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [10942] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [11052] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11053] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11053] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11052] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11087] ~aElement0(xx)
% 223.89/37.59 -> [11088] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11087] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [11088] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [10921] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xy)) => sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [11137] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xy))
% 223.89/37.59 -> [11138] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11138] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11137] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xy))
% 223.89/37.59 -> [11142] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [11143] ~sdtmndtplgtdt0(xy, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11143] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [11183] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [11183] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [11184] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [11185] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [11184] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [11195] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11196] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11196] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11195] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11268] ~aElement0(xx)
% 223.89/37.59 -> [11269] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11268] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [11269] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11185] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [11189] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [11190] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [11189] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [11201] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11201] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11190] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [11880] =(xx, xy)
% 223.89/37.59 -> [11881] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11881] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11880] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [11142] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [11158] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [11158] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [11162] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [11163] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [11163] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [11167] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [11168] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [11167] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [11188] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11188] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11168] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [11768] =(xx, xy)
% 223.89/37.59 -> [11769] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11769] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [11768] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [11162] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [11980] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11981] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11981] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11980] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11982] ~aElement0(xx)
% 223.89/37.59 -> [11983] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11983] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11982] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [10879] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [10929] ((((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xy)) => ((sdtmndtplgtdt0(xz, xR, xy) & sdtmndtplgtdt0(xy, xR, xy)) => sdtmndtplgtdt0(xz, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [10929] BETA_IMPLY : ((((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xy)) => ((sdtmndtplgtdt0(xz, xR, xy) & sdtmndtplgtdt0(xy, xR, xy)) => sdtmndtplgtdt0(xz, xR, xy)))
% 223.89/37.59 -> [10936] ~(((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xy))
% 223.89/37.59 -> [10937] ((sdtmndtplgtdt0(xz, xR, xy) & sdtmndtplgtdt0(xy, xR, xy)) => sdtmndtplgtdt0(xz, xR, xy))
% 223.89/37.59
% 223.89/37.59 [10936] BETA_NOT_AND : ~(((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xy))
% 223.89/37.59 -> [10940] ~((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [10941] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [10941] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [10940] BETA_NOT_AND : ~((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [11012] ~(aElement0(xz) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11013] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11013] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11012] BETA_NOT_AND : ~(aElement0(xz) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11112] ~aElement0(xz)
% 223.89/37.59 -> [11113] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11112] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [11113] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [10937] BETA_IMPLY : ((sdtmndtplgtdt0(xz, xR, xy) & sdtmndtplgtdt0(xy, xR, xy)) => sdtmndtplgtdt0(xz, xR, xy))
% 223.89/37.59 -> [12153] ~(sdtmndtplgtdt0(xz, xR, xy) & sdtmndtplgtdt0(xy, xR, xy))
% 223.89/37.59 -> [12154] sdtmndtplgtdt0(xz, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12154] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [12190] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [12190] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [12193] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [12194] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [12193] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [12206] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [12207] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [12207] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [12206] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [12317] ~aElement0(xx)
% 223.89/37.59 -> [12318] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [12318] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [12317] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [12194] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [12198] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12199] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [12198] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12227] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12227] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12199] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12515] =(xx, xy)
% 223.89/37.59 -> [12516] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12516] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12515] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [12153] BETA_NOT_AND : ~(sdtmndtplgtdt0(xz, xR, xy) & sdtmndtplgtdt0(xy, xR, xy))
% 223.89/37.59 -> [12161] ~sdtmndtplgtdt0(xz, xR, xy)
% 223.89/37.59 -> [12162] ~sdtmndtplgtdt0(xy, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12162] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [12181] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [12181] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [12184] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [12185] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [12185] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [12191] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12192] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [12191] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12222] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12222] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12192] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12289] =(xx, xy)
% 223.89/37.59 -> [12290] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12290] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12289] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [12184] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [12517] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [12518] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [12518] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [12517] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [12524] ~aElement0(xx)
% 223.89/37.59 -> [12525] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [12525] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [12524] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [12161] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [12195] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [12195] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [12200] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [12201] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [12201] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [12202] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12203] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [12202] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12231] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12231] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12203] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [12606] =(xx, xy)
% 223.89/37.59 -> [12607] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12607] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [12606] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [12200] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [12744] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [12745] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [12745] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [12744] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [12751] ~aElement0(xx)
% 223.89/37.59 -> [12752] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [12752] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [12751] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [10535] GAMMA_FORALL : ! [W014_14, W115_15, W216_16] : ((((aElement0(W014_14) & aRewritingSystem0(W115_15)) & aElement0(W216_16)) => (sdtmndtplgtdt0(W014_14, W115_15, W216_16) <=> (aReductOfIn0(W216_16, W014_14, W115_15) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, W014_14, W115_15)) & sdtmndtplgtdt0(W317_17, W115_15, W216_16)))))))
% 223.89/37.59 -> [10536] (((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xx)) => (sdtmndtplgtdt0(xz, xR, xx) <=> (aReductOfIn0(xx, xz, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))))
% 223.89/37.59
% 223.89/37.59 [10536] BETA_IMPLY : (((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xx)) => (sdtmndtplgtdt0(xz, xR, xx) <=> (aReductOfIn0(xx, xz, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))))
% 223.89/37.59 -> [10537] ~((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xx))
% 223.89/37.59 -> [10538] (sdtmndtplgtdt0(xz, xR, xx) <=> (aReductOfIn0(xx, xz, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))))
% 223.89/37.59
% 223.89/37.59 [10537] BETA_NOT_AND : ~((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xx))
% 223.89/37.59 -> [10539] ~(aElement0(xz) & aRewritingSystem0(xR))
% 223.89/37.59 -> [10540] ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [10539] BETA_NOT_AND : ~(aElement0(xz) & aRewritingSystem0(xR))
% 223.89/37.59 -> [10544] ~aElement0(xz)
% 223.89/37.59 -> [10545] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [10545] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [10544] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [10540] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [10538] BETA_EQUIV : (sdtmndtplgtdt0(xz, xR, xx) <=> (aReductOfIn0(xx, xz, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))))
% 223.89/37.59 -> [14483] ~sdtmndtplgtdt0(xz, xR, xx), ~(aReductOfIn0(xx, xz, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59 -> [14484] sdtmndtplgtdt0(xz, xR, xx), (aReductOfIn0(xx, xz, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59
% 223.89/37.59 [14483] ALPHA_NOT_OR : ~(aReductOfIn0(xx, xz, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59 -> [14497] ~aReductOfIn0(xx, xz, xR), ~? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.59
% 223.89/37.59 [14497] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [14529] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [14529] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [14532] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [14533] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [14533] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14534] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [14535] sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14534] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [14544] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [14545] ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14544] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [14657] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [14657] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [14658] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [14659] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [14659] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [14661] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [14662] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [14661] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [14690] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [14690] CLOSURE : ~=(xx, xy)
% 223.89/37.59
% 223.89/37.59 [14662] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [14878] =(xx, xy)
% 223.89/37.59 -> [14879] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [14879] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [14878] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [14658] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [15251] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15252] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [15252] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [15251] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15257] ~aElement0(xx)
% 223.89/37.59 -> [15258] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15258] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15257] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [14584] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59 -> [15289] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [15290] (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [15290] BETA_EQUIV : (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59 -> [15291] ~sdtmndtasgtdt0(xy, xR, xz), ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [15292] sdtmndtasgtdt0(xy, xR, xz), (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59
% 223.89/37.59 [15291] ALPHA_NOT_OR : ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [15302] ~=(xy, xz), ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15302] CLOSURE : ~=(xy, xz)
% 223.89/37.59
% 223.89/37.59 [15292] BETA_OR : (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [15659] =(xy, xz)
% 223.89/37.59 -> [15660] sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15660] CLOSURE : sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15659] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [15289] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [15899] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15900] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [15900] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [15899] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15901] ~aElement0(xy)
% 223.89/37.59 -> [15902] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15902] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15901] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [14535] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [15914] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [15914] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59 -> [15917] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [15918] (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [15918] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [15919] ~sdtmndtasgtdt0(xx, xR, xz), ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [15920] sdtmndtasgtdt0(xx, xR, xz), (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [15920] CLOSURE : sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15919] ALPHA_NOT_OR : ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [15923] ~=(xx, xz), ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15923] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15917] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [16046] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16047] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16047] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16046] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16048] ~aElement0(xx)
% 223.89/37.59 -> [16049] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16048] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [16049] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14532] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [16730] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [16731] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16731] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16730] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [16734] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16735] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16735] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16734] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16736] ~aElement0(xx)
% 223.89/37.59 -> [16737] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16737] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16736] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [14484] BETA_OR : (aReductOfIn0(xx, xz, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59 -> [14490] aReductOfIn0(xx, xz, xR)
% 223.89/37.59 -> [14491] ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.59
% 223.89/37.59 [14490] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [14507] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [14507] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [14509] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [14510] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [14510] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14513] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [14514] sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14514] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [14539] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [14539] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59 -> [14540] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [14541] (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [14540] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [14559] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14560] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14560] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14559] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14641] ~aElement0(xx)
% 223.89/37.59 -> [14642] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14642] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14641] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [14541] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [14762] ~sdtmndtasgtdt0(xx, xR, xz), ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14763] sdtmndtasgtdt0(xx, xR, xz), (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [14763] CLOSURE : sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14762] ALPHA_NOT_OR : ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14768] ~=(xx, xz), ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14768] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14513] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [15105] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [15106] ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15105] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [15112] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [15112] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [15113] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [15114] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [15114] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [15118] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [15119] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [15118] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [15144] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [15144] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [15119] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [15321] =(xx, xy)
% 223.89/37.59 -> [15322] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [15322] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [15321] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [15113] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [15569] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15570] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [15570] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [15569] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15575] ~aElement0(xx)
% 223.89/37.59 -> [15576] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15575] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [15576] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15106] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [15120] (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [15120] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59 -> [15121] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [15122] (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [15122] BETA_EQUIV : (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59 -> [15125] ~sdtmndtasgtdt0(xy, xR, xz), ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [15126] sdtmndtasgtdt0(xy, xR, xz), (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59
% 223.89/37.59 [15125] ALPHA_NOT_OR : ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [15143] ~=(xy, xz), ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15143] CLOSURE : ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15126] BETA_OR : (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [15710] =(xy, xz)
% 223.89/37.59 -> [15711] sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15711] CLOSURE : sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [15710] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [15121] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [16027] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16028] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16028] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16027] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16029] ~aElement0(xy)
% 223.89/37.59 -> [16030] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16030] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16029] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [14509] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [16905] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [16906] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16906] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16905] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [16912] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16913] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16913] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16912] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16914] ~aElement0(xx)
% 223.89/37.59 -> [16915] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16915] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16914] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [14491] DELTA_EXISTS : ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xz, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.59 -> [14494] ((aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xz, xR)) & sdtmndtplgtdt0(skolem_W31717, xR, xx))
% 223.89/37.59
% 223.89/37.59 [14494] ALPHA_AND : ((aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xz, xR)) & sdtmndtplgtdt0(skolem_W31717, xR, xx))
% 223.89/37.59 -> [14495] (aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xz, xR)), sdtmndtplgtdt0(skolem_W31717, xR, xx)
% 223.89/37.59
% 223.89/37.59 [14495] ALPHA_AND : (aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xz, xR))
% 223.89/37.59 -> [14501] aElement0(skolem_W31717), aReductOfIn0(skolem_W31717, xz, xR)
% 223.89/37.59
% 223.89/37.59 [14501] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [14508] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [14508] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [14511] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [14512] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [14512] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14561] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [14562] sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14562] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [14575] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [14575] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59 -> [14578] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [14579] (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [14579] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [14580] ~sdtmndtasgtdt0(xx, xR, xz), ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14581] sdtmndtasgtdt0(xx, xR, xz), (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [14580] ALPHA_NOT_OR : ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14631] ~=(xx, xz), ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14631] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14581] CLOSURE : sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14578] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [15147] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15148] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [15148] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [15147] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15149] ~aElement0(xx)
% 223.89/37.59 -> [15150] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15150] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15149] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [14561] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16347] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [16348] ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16347] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [16395] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [16395] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [16396] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [16397] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [16396] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [16404] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16405] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16405] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16404] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16482] ~aElement0(xx)
% 223.89/37.59 -> [16483] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16482] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [16483] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16397] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [16745] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [16746] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [16745] CLOSURE : ~sdtmndtasgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [16746] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [16759] =(xx, xy)
% 223.89/37.59 -> [16760] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [16760] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [16759] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [16348] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [16432] (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [16432] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59 -> [16433] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [16434] (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [16434] BETA_EQUIV : (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59 -> [16435] ~sdtmndtasgtdt0(xy, xR, xz), ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16436] sdtmndtasgtdt0(xy, xR, xz), (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59
% 223.89/37.59 [16435] ALPHA_NOT_OR : ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16473] ~=(xy, xz), ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16473] CLOSURE : ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16436] BETA_OR : (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16935] =(xy, xz)
% 223.89/37.59 -> [16936] sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16936] CLOSURE : sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16935] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [16433] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [17051] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17052] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17052] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17051] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17056] ~aElement0(xy)
% 223.89/37.59 -> [17057] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17057] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17056] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [14511] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [17480] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17481] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17481] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17480] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17485] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17486] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17486] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17485] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17487] ~aElement0(xx)
% 223.89/37.59 -> [17488] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17488] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17487] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [23] GAMMA_FORALL : ! [W011_11, W112_12, W213_13] : ((((aElement0(W011_11) & aRewritingSystem0(W112_12)) & aElement0(W213_13)) => (sdtmndtplgtdt0(W011_11, W112_12, W213_13) => $true)))
% 223.89/37.59 -> [26] (((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtplgtdt0(xz, xR, xz) => $true))
% 223.89/37.59
% 223.89/37.59 [26] BETA_IMPLY : (((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtplgtdt0(xz, xR, xz) => $true))
% 223.89/37.59 -> [29] ~((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [30] (sdtmndtplgtdt0(xz, xR, xz) => $true)
% 223.89/37.59
% 223.89/37.59 [29] BETA_NOT_AND : ~((aElement0(xz) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [35] ~(aElement0(xz) & aRewritingSystem0(xR))
% 223.89/37.59 -> [36] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [36] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [35] BETA_NOT_AND : ~(aElement0(xz) & aRewritingSystem0(xR))
% 223.89/37.59 -> [94] ~aElement0(xz)
% 223.89/37.59 -> [95] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [94] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [95] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [30] BETA_IMPLY : (sdtmndtplgtdt0(xz, xR, xz) => $true)
% 223.89/37.59 -> [11321] ~sdtmndtplgtdt0(xz, xR, xz)
% 223.89/37.59 -> [11322] $true
% 223.89/37.59
% 223.89/37.59 [11321] GAMMA_FORALL : ! [W014_14, W115_15, W216_16] : ((((aElement0(W014_14) & aRewritingSystem0(W115_15)) & aElement0(W216_16)) => (sdtmndtplgtdt0(W014_14, W115_15, W216_16) <=> (aReductOfIn0(W216_16, W014_14, W115_15) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, W014_14, W115_15)) & sdtmndtplgtdt0(W317_17, W115_15, W216_16)))))))
% 223.89/37.59 -> [11359] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtplgtdt0(xx, xR, xy) <=> (aReductOfIn0(xy, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy))))))
% 223.89/37.59
% 223.89/37.59 [11359] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtplgtdt0(xx, xR, xy) <=> (aReductOfIn0(xy, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy))))))
% 223.89/37.59 -> [11363] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [11364] (sdtmndtplgtdt0(xx, xR, xy) <=> (aReductOfIn0(xy, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy)))))
% 223.89/37.59
% 223.89/37.59 [11364] BETA_EQUIV : (sdtmndtplgtdt0(xx, xR, xy) <=> (aReductOfIn0(xy, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy)))))
% 223.89/37.59 -> [11417] ~sdtmndtplgtdt0(xx, xR, xy), ~(aReductOfIn0(xy, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy))))
% 223.89/37.59 -> [11418] sdtmndtplgtdt0(xx, xR, xy), (aReductOfIn0(xy, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [11417] ALPHA_NOT_OR : ~(aReductOfIn0(xy, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy))))
% 223.89/37.59 -> [11472] ~aReductOfIn0(xy, xx, xR), ~? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [11472] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [11477] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) & aElement0(xy)) => ((sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xy)) => sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [11477] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) & aElement0(xy)) => ((sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xy)) => sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [11483] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) & aElement0(xy))
% 223.89/37.59 -> [11484] ((sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xy)) => sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [11483] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) & aElement0(xy))
% 223.89/37.59 -> [11491] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [11492] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11492] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11491] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [11739] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11740] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [11740] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [11739] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11815] ~aElement0(xx)
% 223.89/37.59 -> [11816] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11816] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11815] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [11484] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xy)) => sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [13323] ~(sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xy))
% 223.89/37.59 -> [13324] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13324] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13323] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xz) & sdtmndtplgtdt0(xz, xR, xy))
% 223.89/37.59 -> [13328] ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59 -> [13329] ~sdtmndtplgtdt0(xz, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13328] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [13333] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [13333] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [13337] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [13338] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [13337] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [13348] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [13349] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [13349] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [13348] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [13388] ~aElement0(xx)
% 223.89/37.59 -> [13389] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [13389] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [13388] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [13338] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [13439] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [13440] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [13439] CLOSURE : ~sdtmndtasgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13440] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [13445] =(xx, xy)
% 223.89/37.59 -> [13446] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13446] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13445] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [13329] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [13334] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [13334] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [13339] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [13340] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [13340] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [13345] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [13346] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [13345] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [13360] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13360] CLOSURE : ~=(xx, xy)
% 223.89/37.59
% 223.89/37.59 [13346] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [13431] =(xx, xy)
% 223.89/37.59 -> [13432] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13432] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13431] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [13339] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [13621] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [13622] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [13622] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [13621] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [13624] ~aElement0(xx)
% 223.89/37.59 -> [13625] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [13625] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [13624] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [11418] BETA_OR : (aReductOfIn0(xy, xx, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy))))
% 223.89/37.59 -> [13649] aReductOfIn0(xy, xx, xR)
% 223.89/37.59 -> [13650] ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [13650] DELTA_EXISTS : ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xx, xR)) & sdtmndtplgtdt0(W317_17, xR, xy)))
% 223.89/37.59 -> [13651] ((aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xx, xR)) & sdtmndtplgtdt0(skolem_W31717, xR, xy))
% 223.89/37.59
% 223.89/37.59 [13651] ALPHA_AND : ((aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xx, xR)) & sdtmndtplgtdt0(skolem_W31717, xR, xy))
% 223.89/37.59 -> [13652] (aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xx, xR)), sdtmndtplgtdt0(skolem_W31717, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13652] ALPHA_AND : (aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xx, xR))
% 223.89/37.59 -> [13656] aElement0(skolem_W31717), aReductOfIn0(skolem_W31717, xx, xR)
% 223.89/37.59
% 223.89/37.59 [13656] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [13670] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [13670] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [13673] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [13674] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [13674] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [13678] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [13679] sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13678] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [13685] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [13686] ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13685] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13686] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [13716] (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [13716] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59 -> [13717] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [13718] (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [13718] BETA_EQUIV : (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59 -> [13721] ~sdtmndtasgtdt0(xy, xR, xz), ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [13722] sdtmndtasgtdt0(xy, xR, xz), (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59
% 223.89/37.59 [13721] ALPHA_NOT_OR : ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [13732] ~=(xy, xz), ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13732] CLOSURE : ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13722] BETA_OR : (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [13868] =(xy, xz)
% 223.89/37.59 -> [13869] sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13869] CLOSURE : sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13868] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [13717] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [13962] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [13963] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [13963] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [13962] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [13964] ~aElement0(xy)
% 223.89/37.59 -> [13965] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [13965] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [13964] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [13679] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [13975] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [13975] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59 -> [13977] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [13978] (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [13978] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [13981] ~sdtmndtasgtdt0(xx, xR, xz), ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [13982] sdtmndtasgtdt0(xx, xR, xz), (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [13982] CLOSURE : sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13981] ALPHA_NOT_OR : ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [13985] ~=(xx, xz), ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13985] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13977] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [14037] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14038] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14038] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14037] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14040] ~aElement0(xx)
% 223.89/37.59 -> [14041] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14040] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [14041] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [13673] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [14733] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [14734] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14734] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14733] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [14735] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14736] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [14736] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [14735] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14737] ~aElement0(xx)
% 223.89/37.59 -> [14738] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14738] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14737] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [13649] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [13655] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [13655] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [13657] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [13658] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [13658] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [13664] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [13665] sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13664] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [13668] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [13669] ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13668] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [13669] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [13992] (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [13992] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59 -> [13993] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [13994] (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [13994] BETA_EQUIV : (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59 -> [13997] ~sdtmndtasgtdt0(xy, xR, xz), ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [13998] sdtmndtasgtdt0(xy, xR, xz), (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59
% 223.89/37.59 [13997] ALPHA_NOT_OR : ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [14001] ~=(xy, xz), ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14001] CLOSURE : ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [13998] BETA_OR : (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [14400] =(xy, xz)
% 223.89/37.59 -> [14401] sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14401] CLOSURE : sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14400] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [13993] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [14750] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14751] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14751] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14750] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14756] ~aElement0(xy)
% 223.89/37.59 -> [14757] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14757] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14756] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [13665] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [14782] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [14782] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59 -> [14785] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [14786] (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [14786] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [14789] ~sdtmndtasgtdt0(xx, xR, xz), ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14790] sdtmndtasgtdt0(xx, xR, xz), (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [14790] CLOSURE : sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14789] ALPHA_NOT_OR : ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [14813] ~=(xx, xz), ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14813] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [14785] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [14850] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14851] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14851] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [14850] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [14855] ~aElement0(xx)
% 223.89/37.59 -> [14856] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14856] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [14855] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [13657] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [15354] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [15355] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [15355] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [15354] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [15362] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15363] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [15363] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [15362] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [15378] ~aElement0(xx)
% 223.89/37.59 -> [15379] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15379] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [15378] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [11363] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17625] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17626] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17626] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17625] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17632] ~aElement0(xx)
% 223.89/37.59 -> [17633] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17633] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17632] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [11322] GAMMA_FORALL : ! [W014_14, W115_15, W216_16] : ((((aElement0(W014_14) & aRewritingSystem0(W115_15)) & aElement0(W216_16)) => (sdtmndtplgtdt0(W014_14, W115_15, W216_16) <=> (aReductOfIn0(W216_16, W014_14, W115_15) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, W014_14, W115_15)) & sdtmndtplgtdt0(W317_17, W115_15, W216_16)))))))
% 223.89/37.59 -> [11327] (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xx)) => (sdtmndtplgtdt0(xy, xR, xx) <=> (aReductOfIn0(xx, xy, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))))
% 223.89/37.59
% 223.89/37.59 [11327] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xx)) => (sdtmndtplgtdt0(xy, xR, xx) <=> (aReductOfIn0(xx, xy, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))))
% 223.89/37.59 -> [11328] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xx))
% 223.89/37.59 -> [11329] (sdtmndtplgtdt0(xy, xR, xx) <=> (aReductOfIn0(xx, xy, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))))
% 223.89/37.59
% 223.89/37.59 [11328] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xx))
% 223.89/37.59 -> [11351] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11352] ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [11352] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [11351] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [11369] ~aElement0(xy)
% 223.89/37.59 -> [11370] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11369] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [11370] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [11329] BETA_EQUIV : (sdtmndtplgtdt0(xy, xR, xx) <=> (aReductOfIn0(xx, xy, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))))
% 223.89/37.59 -> [16480] ~sdtmndtplgtdt0(xy, xR, xx), ~(aReductOfIn0(xx, xy, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59 -> [16481] sdtmndtplgtdt0(xy, xR, xx), (aReductOfIn0(xx, xy, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59
% 223.89/37.59 [16480] ALPHA_NOT_OR : ~(aReductOfIn0(xx, xy, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59 -> [16497] ~aReductOfIn0(xx, xy, xR), ~? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.59
% 223.89/37.59 [16497] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [16625] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [16625] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [16651] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [16652] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [16652] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [16655] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16656] sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16655] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16661] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [16662] ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16662] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [16678] (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [16678] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59 -> [16681] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [16682] (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [16682] BETA_EQUIV : (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59 -> [16683] ~sdtmndtasgtdt0(xy, xR, xz), ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16684] sdtmndtasgtdt0(xy, xR, xz), (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59
% 223.89/37.59 [16683] ALPHA_NOT_OR : ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16796] ~=(xy, xz), ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16796] CLOSURE : ~=(xy, xz)
% 223.89/37.59
% 223.89/37.59 [16684] BETA_OR : (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16803] =(xy, xz)
% 223.89/37.59 -> [16804] sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16804] CLOSURE : sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16803] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [16681] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [17186] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17187] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17187] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17186] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17188] ~aElement0(xy)
% 223.89/37.59 -> [17189] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17189] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17188] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16685] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [17208] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17209] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [17209] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [17215] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17216] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [17215] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17228] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17228] CLOSURE : ~=(xx, xy)
% 223.89/37.59
% 223.89/37.59 [17216] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17259] =(xx, xy)
% 223.89/37.59 -> [17260] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17260] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17259] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [17208] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17379] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17380] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17380] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17379] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17383] ~aElement0(xx)
% 223.89/37.59 -> [17384] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17384] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17383] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [16656] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [17411] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [17411] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59 -> [17413] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [17414] (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [17414] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [17420] ~sdtmndtasgtdt0(xx, xR, xz), ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [17421] sdtmndtasgtdt0(xx, xR, xz), (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [17421] CLOSURE : sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17420] ALPHA_NOT_OR : ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [17433] ~=(xx, xz), ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17433] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17413] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [17516] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17517] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17517] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17516] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17518] ~aElement0(xx)
% 223.89/37.59 -> [17519] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17519] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17518] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [16651] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [17813] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17814] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17814] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17813] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17815] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17816] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17816] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17815] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17818] ~aElement0(xx)
% 223.89/37.59 -> [17819] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17819] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17818] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [16481] BETA_OR : (aReductOfIn0(xx, xy, xR) | ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx))))
% 223.89/37.59 -> [16492] aReductOfIn0(xx, xy, xR)
% 223.89/37.59 -> [16493] ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.59
% 223.89/37.59 [16492] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [16502] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [16502] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [16503] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [16504] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [16503] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [16505] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [16506] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16506] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16505] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [16580] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16581] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16581] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [16580] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16715] ~aElement0(xx)
% 223.89/37.59 -> [16716] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16715] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [16716] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16504] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [16507] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16508] sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16508] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [16530] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [16530] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59 -> [16531] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [16532] (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [16532] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [16536] ~sdtmndtasgtdt0(xx, xR, xz), ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [16537] sdtmndtasgtdt0(xx, xR, xz), (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [16536] ALPHA_NOT_OR : ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [16573] ~=(xx, xz), ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16573] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16537] CLOSURE : sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16531] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [16853] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16854] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16854] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16853] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16855] ~aElement0(xx)
% 223.89/37.59 -> [16856] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16856] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16855] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [16507] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [17171] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [17172] ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17172] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [17181] (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [17181] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59 -> [17182] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [17183] (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [17183] BETA_EQUIV : (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59 -> [17184] ~sdtmndtasgtdt0(xy, xR, xz), ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [17185] sdtmndtasgtdt0(xy, xR, xz), (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59
% 223.89/37.59 [17184] ALPHA_NOT_OR : ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [17225] ~=(xy, xz), ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17225] CLOSURE : ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17185] BETA_OR : (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [17362] =(xy, xz)
% 223.89/37.59 -> [17363] sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17363] CLOSURE : sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17362] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [17182] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [17489] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17490] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17490] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [17489] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17491] ~aElement0(xy)
% 223.89/37.59 -> [17492] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17491] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17492] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17171] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [17194] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [17194] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [17195] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17196] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [17196] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [17200] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17201] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [17200] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17241] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17241] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17201] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17381] =(xx, xy)
% 223.89/37.59 -> [17382] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17382] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17381] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [17195] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17747] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17748] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17748] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [17747] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [17751] ~aElement0(xx)
% 223.89/37.59 -> [17752] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17751] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [17752] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16493] DELTA_EXISTS : ? [W317_17] : (((aElement0(W317_17) & aReductOfIn0(W317_17, xy, xR)) & sdtmndtplgtdt0(W317_17, xR, xx)))
% 223.89/37.59 -> [16496] ((aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xy, xR)) & sdtmndtplgtdt0(skolem_W31717, xR, xx))
% 223.89/37.59
% 223.89/37.59 [16496] ALPHA_AND : ((aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xy, xR)) & sdtmndtplgtdt0(skolem_W31717, xR, xx))
% 223.89/37.59 -> [16498] (aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xy, xR)), sdtmndtplgtdt0(skolem_W31717, xR, xx)
% 223.89/37.59
% 223.89/37.59 [16498] ALPHA_AND : (aElement0(skolem_W31717) & aReductOfIn0(skolem_W31717, xy, xR))
% 223.89/37.59 -> [16574] aElement0(skolem_W31717), aReductOfIn0(skolem_W31717, xy, xR)
% 223.89/37.59
% 223.89/37.59 [16574] GAMMA_FORALL : ! [W018_18, W119_19, W220_20, W321_21] : (((((aElement0(W018_18) & aRewritingSystem0(W119_19)) & aElement0(W220_20)) & aElement0(W321_21)) => ((sdtmndtplgtdt0(W018_18, W119_19, W220_20) & sdtmndtplgtdt0(W220_20, W119_19, W321_21)) => sdtmndtplgtdt0(W018_18, W119_19, W321_21))))
% 223.89/37.59 -> [16609] ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [16609] BETA_IMPLY : ((((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz)) => ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [16613] ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [16614] ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [16614] BETA_IMPLY : ((sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz)) => sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [16621] ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [16622] sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16622] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [16718] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [16718] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))))
% 223.89/37.59 -> [16720] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [16721] (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [16721] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xz) <=> (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz)))
% 223.89/37.59 -> [16724] ~sdtmndtasgtdt0(xx, xR, xz), ~(=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59 -> [16725] sdtmndtasgtdt0(xx, xR, xz), (=(xx, xz) | sdtmndtplgtdt0(xx, xR, xz))
% 223.89/37.59
% 223.89/37.59 [16725] CLOSURE : sdtmndtasgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16747] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xz)
% 223.89/37.59
% 223.89/37.59 [16720] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [16890] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16891] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16891] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [16890] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [16894] ~aElement0(xx)
% 223.89/37.59 -> [16895] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16895] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16894] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [16621] BETA_NOT_AND : ~(sdtmndtplgtdt0(xx, xR, xy) & sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [17888] ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59 -> [17889] ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17889] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [17893] (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59
% 223.89/37.59 [17893] BETA_IMPLY : (((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz)) => (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))))
% 223.89/37.59 -> [17898] ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [17899] (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59
% 223.89/37.59 [17899] BETA_EQUIV : (sdtmndtasgtdt0(xy, xR, xz) <=> (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz)))
% 223.89/37.59 -> [17904] ~sdtmndtasgtdt0(xy, xR, xz), ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [17905] sdtmndtasgtdt0(xy, xR, xz), (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59
% 223.89/37.59 [17904] ALPHA_NOT_OR : ~(=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [17909] ~=(xy, xz), ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17909] CLOSURE : ~sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17905] BETA_OR : (=(xy, xz) | sdtmndtplgtdt0(xy, xR, xz))
% 223.89/37.59 -> [17975] =(xy, xz)
% 223.89/37.59 -> [17976] sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17976] CLOSURE : sdtmndtplgtdt0(xy, xR, xz)
% 223.89/37.59
% 223.89/37.59 [17975] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [17898] BETA_NOT_AND : ~((aElement0(xy) & aRewritingSystem0(xR)) & aElement0(xz))
% 223.89/37.59 -> [18001] ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [18002] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [18002] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [18001] BETA_NOT_AND : ~(aElement0(xy) & aRewritingSystem0(xR))
% 223.89/37.59 -> [18003] ~aElement0(xy)
% 223.89/37.59 -> [18004] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [18003] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [18004] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [17888] GAMMA_FORALL : ! [W022_22, W123_23, W224_24] : ((((aElement0(W022_22) & aRewritingSystem0(W123_23)) & aElement0(W224_24)) => (sdtmndtasgtdt0(W022_22, W123_23, W224_24) <=> (=(W022_22, W224_24) | sdtmndtplgtdt0(W022_22, W123_23, W224_24)))))
% 223.89/37.59 -> [17890] (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59
% 223.89/37.59 [17890] BETA_IMPLY : (((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) => (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))))
% 223.89/37.59 -> [17891] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [17892] (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59
% 223.89/37.59 [17892] BETA_EQUIV : (sdtmndtasgtdt0(xx, xR, xy) <=> (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy)))
% 223.89/37.59 -> [17896] ~sdtmndtasgtdt0(xx, xR, xy), ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17897] sdtmndtasgtdt0(xx, xR, xy), (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59
% 223.89/37.59 [17896] ALPHA_NOT_OR : ~(=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17906] ~=(xx, xy), ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17906] CLOSURE : ~sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17897] BETA_OR : (=(xx, xy) | sdtmndtplgtdt0(xx, xR, xy))
% 223.89/37.59 -> [17977] =(xx, xy)
% 223.89/37.59 -> [17978] sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17978] CLOSURE : sdtmndtplgtdt0(xx, xR, xy)
% 223.89/37.59
% 223.89/37.59 [17977] CLOSURE : =
% 223.89/37.59
% 223.89/37.59 [17891] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [18048] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [18049] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [18049] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [18048] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [18050] ~aElement0(xx)
% 223.89/37.59 -> [18051] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [18050] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [18051] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [16613] BETA_NOT_AND : ~(((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy)) & aElement0(xz))
% 223.89/37.59 -> [18261] ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [18262] ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [18262] CLOSURE : ~aElement0(xz)
% 223.89/37.59
% 223.89/37.59 [18261] BETA_NOT_AND : ~((aElement0(xx) & aRewritingSystem0(xR)) & aElement0(xy))
% 223.89/37.59 -> [18264] ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [18265] ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [18265] CLOSURE : ~aElement0(xy)
% 223.89/37.59
% 223.89/37.59 [18264] BETA_NOT_AND : ~(aElement0(xx) & aRewritingSystem0(xR))
% 223.89/37.59 -> [18266] ~aElement0(xx)
% 223.89/37.59 -> [18267] ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 [18266] CLOSURE : ~aElement0(xx)
% 223.89/37.59
% 223.89/37.59 [18267] CLOSURE : ~aRewritingSystem0(xR)
% 223.89/37.59
% 223.89/37.59 % SZS output end Proof for theBenchmark.p
% 223.89/37.59 [37.242866s][1][Res] 385667 goroutines created
% 223.89/37.59 ==== Result ====
% 223.89/37.59 [37.242905s][1][Res] VALID
% 223.89/37.59 % SZS status Theorem for theBenchmark.p
%------------------------------------------------------------------------------