TSTP Solution File: RNG085+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : RNG085+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 : 600s
% DateTime : Mon Jul 18 20:25:19 EDT 2022
% Result : Theorem 5.22s 1.87s
% Output : Proof 9.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : RNG085+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon May 30 21:27:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.60 ____ _
% 0.18/0.60 ___ / __ \_____(_)___ ________ __________
% 0.18/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic
% 0.18/0.60 (ePrincess v.1.0)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2015
% 0.18/0.60 (c) Peter Backeman, 2014-2015
% 0.18/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.60 Bug reports to peter@backeman.se
% 0.18/0.60
% 0.18/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.58/0.98 Prover 0: Preprocessing ...
% 2.80/1.33 Prover 0: Warning: ignoring some quantifiers
% 2.80/1.36 Prover 0: Constructing countermodel ...
% 5.22/1.87 Prover 0: proved (1222ms)
% 5.22/1.87
% 5.22/1.87 No countermodel exists, formula is valid
% 5.22/1.87 % SZS status Theorem for theBenchmark
% 5.22/1.87
% 5.22/1.87 Generating proof ... Warning: ignoring some quantifiers
% 8.99/2.77 found it (size 170)
% 8.99/2.77
% 8.99/2.77 % SZS output start Proof for theBenchmark
% 8.99/2.77 Assumed formulas after preprocessing and simplification:
% 8.99/2.77 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (sz10 = sz00) & sdtpldt1(xI, xJ) = v1 & smndt0(sz10) = v0 & aIdeal0(xJ) & aIdeal0(xI) & aElementOf0(v2, v1) & aSet0(v1) & aSet0(xJ) & aSet0(xI) & aElement0(sz10) & aElement0(sz00) & ~ aIdeal0(v1) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtpldt1(v5, v6) = v7) | ~ (sdtpldt0(v9, v10) = v8) | ~ aElementOf0(v10, v6) | ~ aElementOf0(v9, v5) | ~ aSet0(v6) | ~ aSet0(v5) | aElementOf0(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v7, v5) = v9) | ~ (sdtasdt0(v6, v5) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aElement0(v7) | ~ aElement0(v6) | ~ aElement0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v10 & sdtasdt0(v5, v11) = v12 & sdtasdt0(v5, v7) = v14 & sdtasdt0(v5, v6) = v13 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sdtasdt0(v5, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ (sdtpldt0(v8, v9) = v10) | ~ aElement0(v7) | ~ aElement0(v6) | ~ aElement0(v5) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v11, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v11) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v6, v7) = v11)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v7) = v9) | ~ (sdtasdt0(v5, v6) = v8) | ~ aElement0(v7) | ~ aElement0(v6) | ~ aElement0(v5) | ? [v10] : (sdtasdt0(v6, v7) = v10 & sdtasdt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v8, v5) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aElement0(v7) | ~ aElement0(v6) | ~ aElement0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v8) = v10 & sdtasdt0(v5, v7) = v12 & sdtasdt0(v5, v6) = v11 & sdtpldt0(v13, v14) = v9 & sdtpldt0(v11, v12) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v6, v7) = v8) | ~ (sdtasdt0(v5, v8) = v9) | ~ aElement0(v7) | ~ aElement0(v6) | ~ aElement0(v5) | ? [v10] : (sdtasdt0(v10, v7) = v9 & sdtasdt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtasdt0(v5, v8) = v9) | ~ (sdtpldt0(v6, v7) = v8) | ~ aElement0(v7) | ~ aElement0(v6) | ~ aElement0(v5) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (sdtasdt0(v8, v5) = v12 & sdtasdt0(v7, v5) = v14 & sdtasdt0(v6, v5) = v13 & sdtasdt0(v5, v7) = v11 & sdtasdt0(v5, v6) = v10 & sdtpldt0(v13, v14) = v12 & sdtpldt0(v10, v11) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v7) = v9) | ~ (sdtpldt0(v5, v6) = v8) | ~ aElement0(v7) | ~ aElement0(v6) | ~ aElement0(v5) | ? [v10] : (sdtpldt0(v6, v7) = v10 & sdtpldt0(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ (sdtpldt0(v5, v8) = v9) | ~ aElement0(v7) | ~ aElement0(v6) | ~ aElement0(v5) | ? [v10] : (sdtpldt0(v10, v7) = v9 & sdtpldt0(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtasasdt0(v5, v6) = v7) | ~ aSet0(v8) | ~ aSet0(v6) | ~ aSet0(v5) | ? [v9] : (( ~ aElementOf0(v9, v8) | ~ aElementOf0(v9, v6) | ~ aElementOf0(v9, v5)) & (aElementOf0(v9, v8) | (aElementOf0(v9, v6) & aElementOf0(v9, v5))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v7 | ~ (sdtpldt1(v5, v6) = v7) | ~ aSet0(v8) | ~ aSet0(v6) | ~ aSet0(v5) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ aElementOf0(v9, v8) | ! [v13] : ! [v14] : ( ~ (sdtpldt0(v13, v14) = v9) | ~ aElementOf0(v14, v6) | ~ aElementOf0(v13, v5))) & (aElementOf0(v9, v8) | (v12 = v9 & sdtpldt0(v10, v11) = v9 & aElementOf0(v11, v6) & aElementOf0(v10, v5))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtasasdt0(v8, v7) = v6) | ~ (sdtasasdt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt1(v8, v7) = v6) | ~ (sdtpldt1(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtasdt0(v8, v7) = v6) | ~ (sdtasdt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (sdtpldt0(v8, v7) = v6) | ~ (sdtpldt0(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasasdt0(v5, v6) = v7) | ~ aElementOf0(v8, v7) | ~ aSet0(v6) | ~ aSet0(v5) | aElementOf0(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasasdt0(v5, v6) = v7) | ~ aElementOf0(v8, v7) | ~ aSet0(v6) | ~ aSet0(v5) | aElementOf0(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasasdt0(v5, v6) = v7) | ~ aElementOf0(v8, v6) | ~ aElementOf0(v8, v5) | ~ aSet0(v6) | ~ aSet0(v5) | aElementOf0(v8, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt1(v5, v6) = v7) | ~ aElementOf0(v8, v7) | ~ aSet0(v6) | ~ aSet0(v5) | ? [v9] : ? [v10] : (sdtpldt0(v9, v10) = v8 & aElementOf0(v10, v6) & aElementOf0(v9, v5))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtasdt0(v7, v6) = v8) | ~ aIdeal0(v5) | ~ aElementOf0(v6, v5) | ~ aElement0(v7) | aElementOf0(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (sdtpldt0(v6, v7) = v8) | ~ aIdeal0(v5) | ~ aElementOf0(v7, v5) | ~ aElementOf0(v6, v5) | aElementOf0(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtpldt0(v6, v5) = v7) | ~ (smndt0(v5) = v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : ! [v7] : (v7 = sz00 | ~ (sdtpldt0(v5, v6) = v7) | ~ (smndt0(v5) = v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (smndt0(v7) = v6) | ~ (smndt0(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasasdt0(v5, v6) = v7) | ~ aSet0(v6) | ~ aSet0(v5) | aSet0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt1(v5, v6) = v7) | ~ aSet0(v6) | ~ aSet0(v5) | aSet0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) | ~ aElementOf0(v5, xJ) | ~ aElement0(v6) | aElementOf0(v7, xJ)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) | ~ aElementOf0(v5, xI) | ~ aElement0(v6) | aElementOf0(v7, xI)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v6, v5) = v7) | ~ aElement0(v6) | ~ aElement0(v5) | sdtasdt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aElement0(v6) | ~ aElement0(v5) | sdtasdt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtasdt0(v5, v6) = v7) | ~ aElement0(v6) | ~ aElement0(v5) | aElement0(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, v5) = v7) | ~ (smndt0(v5) = v6) | ~ aElement0(v5) | sdtpldt0(v5, v6) = sz00) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v6, v5) = v7) | ~ aElement0(v6) | ~ aElement0(v5) | sdtpldt0(v5, v6) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ (smndt0(v5) = v6) | ~ aElement0(v5) | sdtpldt0(v6, v5) = sz00) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aElementOf0(v6, xJ) | ~ aElementOf0(v5, xJ) | aElementOf0(v7, xJ)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aElementOf0(v6, xI) | ~ aElementOf0(v5, xI) | aElementOf0(v7, xI)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aElement0(v6) | ~ aElement0(v5) | sdtpldt0(v6, v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sdtpldt0(v5, v6) = v7) | ~ aElement0(v6) | ~ aElement0(v5) | aElement0(v7)) & ? [v5] : ! [v6] : ! [v7] : ( ~ aElementOf0(v7, xJ) | ~ aElementOf0(v6, xI) | aElementOf0(v5, v1) | ? [v8] : ( ~ (v8 = v5) & sdtpldt0(v6, v7) = v8)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(v5, sz10) = v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtasdt0(sz10, v5) = v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(v5, sz00) = v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (sdtpldt0(sz00, v5) = v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ aSet0(v6) | ~ aSet0(v5) | ? [v7] : ((aElementOf0(v7, v6) & ~ aElementOf0(v7, v5)) | (aElementOf0(v7, v5) & ~ aElementOf0(v7, v6)))) & ! [v5] : ! [v6] : (v6 = sz00 | v5 = sz00 | ~ (sdtasdt0(v5, v6) = sz00) | ~ aElement0(v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(v5, sz00) = v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : (v6 = sz00 | ~ (sdtasdt0(sz00, v5) = v6) | ~ aElement0(v5)) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, v0) = v6) | ~ aElement0(v5) | (sdtasdt0(v0, v5) = v6 & smndt0(v5) = v6)) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz10) = v6) | ~ aElement0(v5) | sdtasdt0(sz10, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v5, sz00) = v6) | ~ aElement0(v5) | sdtasdt0(sz00, v5) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(v0, v5) = v6) | ~ aElement0(v5) | (sdtasdt0(v5, v0) = v6 & smndt0(v5) = v6)) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz10, v5) = v6) | ~ aElement0(v5) | sdtasdt0(v5, sz10) = v5) & ! [v5] : ! [v6] : ( ~ (sdtasdt0(sz00, v5) = v6) | ~ aElement0(v5) | sdtasdt0(v5, sz00) = sz00) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(v5, sz00) = v6) | ~ aElement0(v5) | sdtpldt0(sz00, v5) = v5) & ! [v5] : ! [v6] : ( ~ (sdtpldt0(sz00, v5) = v6) | ~ aElement0(v5) | sdtpldt0(v5, sz00) = v5) & ! [v5] : ! [v6] : ( ~ (smndt0(v5) = v6) | ~ aElement0(v5) | aElement0(v6)) & ! [v5] : ! [v6] : ( ~ (smndt0(v5) = v6) | ~ aElement0(v5) | (sdtasdt0(v5, v0) = v6 & sdtasdt0(v0, v5) = v6)) & ! [v5] : ! [v6] : ( ~ aElementOf0(v6, v5) | ~ aSet0(v5) | aElement0(v6)) & ! [v5] : ( ~ aIdeal0(v5) | aSet0(v5)) & ! [v5] : ( ~ aElementOf0(v5, v1) | ? [v6] : ? [v7] : (sdtpldt0(v6, v7) = v5 & aElementOf0(v7, xJ) & aElementOf0(v6, xI))) & ! [v5] : ( ~ aSet0(v5) | aIdeal0(v5) | ? [v6] : ? [v7] : ? [v8] : (aElementOf0(v6, v5) & ((sdtasdt0(v7, v6) = v8 & aElement0(v7) & ~ aElementOf0(v8, v5)) | (sdtpldt0(v6, v7) = v8 & aElementOf0(v7, v5) & ~ aElementOf0(v8, v5))))) & ((sdtasdt0(v3, v2) = v4 & aElement0(v3) & ~ aElementOf0(v4, v1)) | (sdtpldt0(v2, v3) = v4 & aElementOf0(v3, v1) & ~ aElementOf0(v4, v1))))
% 9.51/2.82 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 9.51/2.82 | (1) ~ (sz10 = sz00) & sdtpldt1(xI, xJ) = all_0_3_3 & smndt0(sz10) = all_0_4_4 & aIdeal0(xJ) & aIdeal0(xI) & aElementOf0(all_0_2_2, all_0_3_3) & aSet0(all_0_3_3) & aSet0(xJ) & aSet0(xI) & aElement0(sz10) & aElement0(sz00) & ~ aIdeal0(all_0_3_3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtasasdt0(v0, v1) = v2) | ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : (( ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v4, v0)) & (aElementOf0(v4, v3) | (aElementOf0(v4, v1) & aElementOf0(v4, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ aElementOf0(v4, v3) | ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, v1) & aElementOf0(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3, v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : ? [v5] : (sdtpldt0(v4, v5) = v3 & aElementOf0(v5, v1) & aElementOf0(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, v1) = v3) | ~ aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1, v0) | aElementOf0(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v0, v1) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | aElementOf0(v2, xJ)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) | aElementOf0(v2, xI)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtasdt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0) | sdtpldt0(v0, v1) = sz00) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtpldt0(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0) | sdtpldt0(v1, v0) = sz00) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, xJ) | aElementOf0(v2, xJ)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | aElementOf0(v2, xI)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2)) & ? [v0] : ! [v1] : ! [v2] : ( ~ aElementOf0(v2, xJ) | ~ aElementOf0(v1, xI) | aElementOf0(v0, all_0_3_3) | ? [v3] : ( ~ (v3 = v0) & sdtpldt0(v1, v2) = v3)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ aSet0(v1) | ~ aSet0(v0) | ? [v2] : ((aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)) | (aElementOf0(v2, v0) & ~ aElementOf0(v2, v1)))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aElement0(v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aElement0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, all_0_4_4) = v1) | ~ aElement0(v0) | (sdtasdt0(all_0_4_4, v0) = v1 & smndt0(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aElement0(v0) | sdtasdt0(sz10, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aElement0(v0) | sdtasdt0(sz00, v0) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(all_0_4_4, v0) = v1) | ~ aElement0(v0) | (sdtasdt0(v0, all_0_4_4) = v1 & smndt0(v0) = v1)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aElement0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aElement0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aElement0(v0) | sdtpldt0(sz00, v0) = v0) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aElement0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aElement0(v0) | aElement0(v1)) & ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aElement0(v0) | (sdtasdt0(v0, all_0_4_4) = v1 & sdtasdt0(all_0_4_4, v0) = v1)) & ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1)) & ! [v0] : ( ~ aIdeal0(v0) | aSet0(v0)) & ! [v0] : ( ~ aElementOf0(v0, all_0_3_3) | ? [v1] : ? [v2] : (sdtpldt0(v1, v2) = v0 & aElementOf0(v2, xJ) & aElementOf0(v1, xI))) & ! [v0] : ( ~ aSet0(v0) | aIdeal0(v0) | ? [v1] : ? [v2] : ? [v3] : (aElementOf0(v1, v0) & ((sdtasdt0(v2, v1) = v3 & aElement0(v2) & ~ aElementOf0(v3, v0)) | (sdtpldt0(v1, v2) = v3 & aElementOf0(v2, v0) & ~ aElementOf0(v3, v0))))) & ((sdtasdt0(all_0_1_1, all_0_2_2) = all_0_0_0 & aElement0(all_0_1_1) & ~ aElementOf0(all_0_0_0, all_0_3_3)) | (sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0 & aElementOf0(all_0_1_1, all_0_3_3) & ~ aElementOf0(all_0_0_0, all_0_3_3)))
% 9.51/2.84 |
% 9.51/2.84 | Applying alpha-rule on (1) yields:
% 9.51/2.84 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2))
% 9.51/2.84 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ (sdtpldt0(v4, v5) = v3) | ~ aElementOf0(v5, v1) | ~ aElementOf0(v4, v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 9.51/2.84 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (smndt0(v2) = v1) | ~ (smndt0(v2) = v0))
% 9.51/2.84 | (5) ! [v0] : ( ~ aIdeal0(v0) | aSet0(v0))
% 9.51/2.84 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtasdt0(v0, v1) = v2)
% 9.51/2.84 | (7) smndt0(sz10) = all_0_4_4
% 9.51/2.84 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v8, v9) = v4 & sdtpldt0(v6, v7) = v5))
% 9.51/2.84 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtasdt0(v1, v0) = v2)
% 9.51/2.84 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v0))
% 9.51/2.84 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aElement0(v0))
% 9.51/2.84 | (12) aElement0(sz00)
% 9.51/2.84 | (13) aSet0(all_0_3_3)
% 9.51/2.84 | (14) aSet0(xI)
% 9.51/2.84 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ aIdeal0(v0) | ~ aElementOf0(v2, v0) | ~ aElementOf0(v1, v0) | aElementOf0(v3, v0))
% 9.51/2.84 | (16) sdtpldt1(xI, xJ) = all_0_3_3
% 9.51/2.84 | (17) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aElement0(v0) | sdtasdt0(v0, sz00) = sz00)
% 9.51/2.84 | (18) ~ aIdeal0(all_0_3_3)
% 9.51/2.84 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v1, xI) | ~ aElementOf0(v0, xI) | aElementOf0(v2, xI))
% 9.51/2.84 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtpldt1(v0, v1) = v2) | ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ aElementOf0(v4, v3) | ! [v8] : ! [v9] : ( ~ (sdtpldt0(v8, v9) = v4) | ~ aElementOf0(v9, v1) | ~ aElementOf0(v8, v0))) & (aElementOf0(v4, v3) | (v7 = v4 & sdtpldt0(v5, v6) = v4 & aElementOf0(v6, v1) & aElementOf0(v5, v0)))))
% 9.51/2.84 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v1) | ~ aElementOf0(v3, v0) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2))
% 9.51/2.84 | (22) ! [v0] : ! [v1] : ( ~ (sdtasdt0(all_0_4_4, v0) = v1) | ~ aElement0(v0) | (sdtasdt0(v0, all_0_4_4) = v1 & smndt0(v0) = v1))
% 9.51/2.84 | (23) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, all_0_4_4) = v1) | ~ aElement0(v0) | (sdtasdt0(all_0_4_4, v0) = v1 & smndt0(v0) = v1))
% 9.51/2.84 | (24) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aElement0(v0) | sdtasdt0(v0, sz10) = v0)
% 9.51/2.84 | (25) aElement0(sz10)
% 9.51/2.84 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 9.51/2.84 | (27) ~ (sz10 = sz00)
% 9.51/2.84 | (28) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ~ aElement0(v0) | sdtasdt0(sz00, v0) = sz00)
% 9.51/2.84 | (29) ? [v0] : ! [v1] : ! [v2] : ( ~ aElementOf0(v2, xJ) | ~ aElementOf0(v1, xI) | aElementOf0(v0, all_0_3_3) | ? [v3] : ( ~ (v3 = v0) & sdtpldt0(v1, v2) = v3))
% 9.51/2.84 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v3, v0) = v7 & sdtasdt0(v2, v0) = v9 & sdtasdt0(v1, v0) = v8 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v5, v6) = v4))
% 9.51/2.84 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 9.51/2.84 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2))
% 9.51/2.84 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElementOf0(v1, xJ) | ~ aElementOf0(v0, xJ) | aElementOf0(v2, xJ))
% 9.51/2.84 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt1(v3, v2) = v1) | ~ (sdtpldt1(v3, v2) = v0))
% 9.51/2.84 | (35) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aElement0(v1) | ~ aElement0(v0))
% 9.51/2.85 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5))
% 9.51/2.85 | (37) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aElement0(v0))
% 9.51/2.85 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6))
% 9.51/2.85 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtpldt0(v1, v0) = v2)
% 9.51/2.85 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ aSet0(v1) | ~ aSet0(v0) | aSet0(v2))
% 9.51/2.85 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | sdtpldt0(v0, v1) = v2)
% 9.51/2.85 | (42) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aElement0(v0) | sdtpldt0(v0, sz00) = v0)
% 9.51/2.85 | (43) ! [v0] : ( ~ aElementOf0(v0, all_0_3_3) | ? [v1] : ? [v2] : (sdtpldt0(v1, v2) = v0 & aElementOf0(v2, xJ) & aElementOf0(v1, xI)))
% 9.51/2.85 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aElementOf0(v0, xI) | ~ aElement0(v1) | aElementOf0(v2, xI))
% 9.51/2.85 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasasdt0(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | aElementOf0(v3, v1))
% 9.51/2.85 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 9.51/2.85 | (47) ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aElement0(v0) | (sdtasdt0(v0, all_0_4_4) = v1 & sdtasdt0(all_0_4_4, v0) = v1))
% 9.51/2.85 | (48) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ~ aElement0(v0) | sdtasdt0(sz10, v0) = v0)
% 9.51/2.85 | (49) ! [v0] : ( ~ aSet0(v0) | aIdeal0(v0) | ? [v1] : ? [v2] : ? [v3] : (aElementOf0(v1, v0) & ((sdtasdt0(v2, v1) = v3 & aElement0(v2) & ~ aElementOf0(v3, v0)) | (sdtpldt0(v1, v2) = v3 & aElementOf0(v2, v0) & ~ aElementOf0(v3, v0)))))
% 9.51/2.85 | (50) ! [v0] : ! [v1] : ( ~ (smndt0(v0) = v1) | ~ aElement0(v0) | aElement0(v1))
% 9.51/2.85 | (51) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(v0, sz10) = v1) | ~ aElement0(v0))
% 9.51/2.85 | (52) ! [v0] : ! [v1] : (v1 = v0 | ~ aSet0(v1) | ~ aSet0(v0) | ? [v2] : ((aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)) | (aElementOf0(v2, v0) & ~ aElementOf0(v2, v1))))
% 9.51/2.85 | (53) aIdeal0(xJ)
% 9.51/2.85 | (54) aElementOf0(all_0_2_2, all_0_3_3)
% 9.51/2.85 | (55) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ~ aElement0(v0) | sdtpldt0(sz00, v0) = v0)
% 9.51/2.85 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5))
% 9.51/2.85 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ~ aElementOf0(v0, xJ) | ~ aElement0(v1) | aElementOf0(v2, xJ))
% 9.51/2.85 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v0, v1) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0))
% 9.51/2.85 | (59) aIdeal0(xI)
% 9.51/2.85 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, v1) = v3) | ~ aIdeal0(v0) | ~ aElementOf0(v1, v0) | ~ aElement0(v2) | aElementOf0(v3, v0))
% 9.51/2.85 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0) | sdtpldt0(v1, v0) = sz00)
% 9.51/2.85 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtasasdt0(v0, v1) = v2) | ~ aSet0(v3) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : (( ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v1) | ~ aElementOf0(v4, v0)) & (aElementOf0(v4, v3) | (aElementOf0(v4, v1) & aElementOf0(v4, v0)))))
% 9.51/2.85 | (63) ! [v0] : ! [v1] : ( ~ aElementOf0(v1, v0) | ~ aSet0(v0) | aElement0(v1))
% 9.51/2.85 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasasdt0(v3, v2) = v1) | ~ (sdtasasdt0(v3, v2) = v0))
% 9.51/2.85 | (65) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(v0, sz00) = v1) | ~ aElement0(v0))
% 9.51/2.85 | (66) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aElement0(v0))
% 9.51/2.85 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4))
% 9.51/2.85 | (68) aSet0(xJ)
% 9.51/2.85 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0) | sdtpldt0(v0, v1) = sz00)
% 9.51/2.85 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aElement0(v2) | ~ aElement0(v1) | ~ aElement0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4))
% 9.51/2.85 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aElement0(v1) | ~ aElement0(v0) | aElement0(v2))
% 9.51/2.85 | (72) (sdtasdt0(all_0_1_1, all_0_2_2) = all_0_0_0 & aElement0(all_0_1_1) & ~ aElementOf0(all_0_0_0, all_0_3_3)) | (sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0 & aElementOf0(all_0_1_1, all_0_3_3) & ~ aElementOf0(all_0_0_0, all_0_3_3))
% 9.51/2.86 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v1, v0) = v2) | ~ (smndt0(v0) = v1) | ~ aElement0(v0))
% 9.51/2.86 | (74) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(v0, sz00) = v1) | ~ aElement0(v0))
% 9.51/2.86 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt1(v0, v1) = v2) | ~ aElementOf0(v3, v2) | ~ aSet0(v1) | ~ aSet0(v0) | ? [v4] : ? [v5] : (sdtpldt0(v4, v5) = v3 & aElementOf0(v5, v1) & aElementOf0(v4, v0)))
% 9.51/2.86 |
% 9.51/2.86 | Instantiating formula (63) with all_0_2_2, all_0_3_3 and discharging atoms aElementOf0(all_0_2_2, all_0_3_3), aSet0(all_0_3_3), yields:
% 9.51/2.86 | (76) aElement0(all_0_2_2)
% 9.51/2.86 |
% 9.51/2.86 | Instantiating formula (75) with all_0_2_2, all_0_3_3, xJ, xI and discharging atoms sdtpldt1(xI, xJ) = all_0_3_3, aElementOf0(all_0_2_2, all_0_3_3), aSet0(xJ), aSet0(xI), yields:
% 9.51/2.86 | (77) ? [v0] : ? [v1] : (sdtpldt0(v0, v1) = all_0_2_2 & aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 9.51/2.86 |
% 9.51/2.86 | Instantiating (77) with all_13_0_9, all_13_1_10 yields:
% 9.51/2.86 | (78) sdtpldt0(all_13_1_10, all_13_0_9) = all_0_2_2 & aElementOf0(all_13_0_9, xJ) & aElementOf0(all_13_1_10, xI)
% 9.51/2.86 |
% 9.51/2.86 | Applying alpha-rule on (78) yields:
% 9.51/2.86 | (79) sdtpldt0(all_13_1_10, all_13_0_9) = all_0_2_2
% 9.51/2.86 | (80) aElementOf0(all_13_0_9, xJ)
% 9.51/2.86 | (81) aElementOf0(all_13_1_10, xI)
% 9.51/2.86 |
% 9.51/2.86 | Instantiating formula (63) with all_13_0_9, xJ and discharging atoms aElementOf0(all_13_0_9, xJ), aSet0(xJ), yields:
% 9.51/2.86 | (82) aElement0(all_13_0_9)
% 9.51/2.86 |
% 9.51/2.86 | Instantiating formula (63) with all_13_1_10, xI and discharging atoms aElementOf0(all_13_1_10, xI), aSet0(xI), yields:
% 9.51/2.86 | (83) aElement0(all_13_1_10)
% 9.51/2.86 |
% 9.51/2.86 | Instantiating formula (41) with all_0_2_2, all_13_1_10, all_13_0_9 and discharging atoms sdtpldt0(all_13_1_10, all_13_0_9) = all_0_2_2, aElement0(all_13_0_9), aElement0(all_13_1_10), yields:
% 9.51/2.86 | (84) sdtpldt0(all_13_0_9, all_13_1_10) = all_0_2_2
% 9.51/2.86 |
% 9.51/2.86 +-Applying beta-rule and splitting (72), into two cases.
% 9.51/2.86 |-Branch one:
% 9.51/2.86 | (85) sdtasdt0(all_0_1_1, all_0_2_2) = all_0_0_0 & aElement0(all_0_1_1) & ~ aElementOf0(all_0_0_0, all_0_3_3)
% 9.51/2.86 |
% 9.51/2.86 | Applying alpha-rule on (85) yields:
% 9.51/2.86 | (86) sdtasdt0(all_0_1_1, all_0_2_2) = all_0_0_0
% 9.51/2.86 | (87) aElement0(all_0_1_1)
% 9.51/2.86 | (88) ~ aElementOf0(all_0_0_0, all_0_3_3)
% 9.51/2.86 |
% 9.51/2.86 | Instantiating formula (30) with all_0_0_0, all_0_2_2, all_13_1_10, all_13_0_9, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, all_0_2_2) = all_0_0_0, sdtpldt0(all_13_0_9, all_13_1_10) = all_0_2_2, aElement0(all_13_0_9), aElement0(all_13_1_10), aElement0(all_0_1_1), yields:
% 9.51/2.86 | (89) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_13_0_9, all_0_1_1) = v3 & sdtasdt0(all_13_1_10, all_0_1_1) = v4 & sdtasdt0(all_0_1_1, all_13_0_9) = v0 & sdtasdt0(all_0_1_1, all_13_1_10) = v1 & sdtasdt0(all_0_2_2, all_0_1_1) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_0_0)
% 9.51/2.86 |
% 9.51/2.86 | Instantiating formula (30) with all_0_0_0, all_0_2_2, all_13_0_9, all_13_1_10, all_0_1_1 and discharging atoms sdtasdt0(all_0_1_1, all_0_2_2) = all_0_0_0, sdtpldt0(all_13_1_10, all_13_0_9) = all_0_2_2, aElement0(all_13_0_9), aElement0(all_13_1_10), aElement0(all_0_1_1), yields:
% 9.51/2.86 | (90) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (sdtasdt0(all_13_0_9, all_0_1_1) = v4 & sdtasdt0(all_13_1_10, all_0_1_1) = v3 & sdtasdt0(all_0_1_1, all_13_0_9) = v1 & sdtasdt0(all_0_1_1, all_13_1_10) = v0 & sdtasdt0(all_0_2_2, all_0_1_1) = v2 & sdtpldt0(v3, v4) = v2 & sdtpldt0(v0, v1) = all_0_0_0)
% 9.51/2.86 |
% 9.51/2.86 | Instantiating formula (6) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms sdtasdt0(all_0_1_1, all_0_2_2) = all_0_0_0, aElement0(all_0_1_1), aElement0(all_0_2_2), yields:
% 9.51/2.86 | (91) sdtasdt0(all_0_2_2, all_0_1_1) = all_0_0_0
% 9.51/2.86 |
% 9.51/2.86 | Instantiating (90) with all_56_0_15, all_56_1_16, all_56_2_17, all_56_3_18, all_56_4_19 yields:
% 9.51/2.86 | (92) sdtasdt0(all_13_0_9, all_0_1_1) = all_56_0_15 & sdtasdt0(all_13_1_10, all_0_1_1) = all_56_1_16 & sdtasdt0(all_0_1_1, all_13_0_9) = all_56_3_18 & sdtasdt0(all_0_1_1, all_13_1_10) = all_56_4_19 & sdtasdt0(all_0_2_2, all_0_1_1) = all_56_2_17 & sdtpldt0(all_56_1_16, all_56_0_15) = all_56_2_17 & sdtpldt0(all_56_4_19, all_56_3_18) = all_0_0_0
% 9.51/2.86 |
% 9.51/2.86 | Applying alpha-rule on (92) yields:
% 9.51/2.86 | (93) sdtasdt0(all_0_1_1, all_13_1_10) = all_56_4_19
% 9.51/2.86 | (94) sdtasdt0(all_13_1_10, all_0_1_1) = all_56_1_16
% 9.51/2.86 | (95) sdtasdt0(all_0_1_1, all_13_0_9) = all_56_3_18
% 9.51/2.86 | (96) sdtasdt0(all_0_2_2, all_0_1_1) = all_56_2_17
% 9.51/2.86 | (97) sdtasdt0(all_13_0_9, all_0_1_1) = all_56_0_15
% 9.51/2.86 | (98) sdtpldt0(all_56_1_16, all_56_0_15) = all_56_2_17
% 9.51/2.86 | (99) sdtpldt0(all_56_4_19, all_56_3_18) = all_0_0_0
% 9.51/2.86 |
% 9.51/2.86 | Instantiating (89) with all_58_0_20, all_58_1_21, all_58_2_22, all_58_3_23, all_58_4_24 yields:
% 9.51/2.86 | (100) sdtasdt0(all_13_0_9, all_0_1_1) = all_58_1_21 & sdtasdt0(all_13_1_10, all_0_1_1) = all_58_0_20 & sdtasdt0(all_0_1_1, all_13_0_9) = all_58_4_24 & sdtasdt0(all_0_1_1, all_13_1_10) = all_58_3_23 & sdtasdt0(all_0_2_2, all_0_1_1) = all_58_2_22 & sdtpldt0(all_58_1_21, all_58_0_20) = all_58_2_22 & sdtpldt0(all_58_4_24, all_58_3_23) = all_0_0_0
% 9.51/2.86 |
% 9.51/2.86 | Applying alpha-rule on (100) yields:
% 9.51/2.86 | (101) sdtpldt0(all_58_4_24, all_58_3_23) = all_0_0_0
% 9.51/2.86 | (102) sdtasdt0(all_13_0_9, all_0_1_1) = all_58_1_21
% 9.51/2.86 | (103) sdtasdt0(all_0_1_1, all_13_0_9) = all_58_4_24
% 9.51/2.86 | (104) sdtasdt0(all_13_1_10, all_0_1_1) = all_58_0_20
% 9.51/2.86 | (105) sdtpldt0(all_58_1_21, all_58_0_20) = all_58_2_22
% 9.51/2.86 | (106) sdtasdt0(all_0_2_2, all_0_1_1) = all_58_2_22
% 9.51/2.87 | (107) sdtasdt0(all_0_1_1, all_13_1_10) = all_58_3_23
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (31) with all_13_0_9, all_0_1_1, all_56_0_15, all_58_1_21 and discharging atoms sdtasdt0(all_13_0_9, all_0_1_1) = all_58_1_21, sdtasdt0(all_13_0_9, all_0_1_1) = all_56_0_15, yields:
% 9.51/2.87 | (108) all_58_1_21 = all_56_0_15
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (31) with all_13_1_10, all_0_1_1, all_56_1_16, all_58_0_20 and discharging atoms sdtasdt0(all_13_1_10, all_0_1_1) = all_58_0_20, sdtasdt0(all_13_1_10, all_0_1_1) = all_56_1_16, yields:
% 9.51/2.87 | (109) all_58_0_20 = all_56_1_16
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (31) with all_0_1_1, all_13_0_9, all_56_3_18, all_58_4_24 and discharging atoms sdtasdt0(all_0_1_1, all_13_0_9) = all_58_4_24, sdtasdt0(all_0_1_1, all_13_0_9) = all_56_3_18, yields:
% 9.51/2.87 | (110) all_58_4_24 = all_56_3_18
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (31) with all_0_1_1, all_13_1_10, all_56_4_19, all_58_3_23 and discharging atoms sdtasdt0(all_0_1_1, all_13_1_10) = all_58_3_23, sdtasdt0(all_0_1_1, all_13_1_10) = all_56_4_19, yields:
% 9.51/2.87 | (111) all_58_3_23 = all_56_4_19
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (31) with all_0_2_2, all_0_1_1, all_56_2_17, all_58_2_22 and discharging atoms sdtasdt0(all_0_2_2, all_0_1_1) = all_58_2_22, sdtasdt0(all_0_2_2, all_0_1_1) = all_56_2_17, yields:
% 9.51/2.87 | (112) all_58_2_22 = all_56_2_17
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (31) with all_0_2_2, all_0_1_1, all_0_0_0, all_58_2_22 and discharging atoms sdtasdt0(all_0_2_2, all_0_1_1) = all_58_2_22, sdtasdt0(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 9.51/2.87 | (113) all_58_2_22 = all_0_0_0
% 9.51/2.87 |
% 9.51/2.87 | Combining equations (113,112) yields a new equation:
% 9.51/2.87 | (114) all_56_2_17 = all_0_0_0
% 9.51/2.87 |
% 9.51/2.87 | From (108) and (102) follows:
% 9.51/2.87 | (97) sdtasdt0(all_13_0_9, all_0_1_1) = all_56_0_15
% 9.51/2.87 |
% 9.51/2.87 | From (109) and (104) follows:
% 9.51/2.87 | (94) sdtasdt0(all_13_1_10, all_0_1_1) = all_56_1_16
% 9.51/2.87 |
% 9.51/2.87 | From (110) and (103) follows:
% 9.51/2.87 | (95) sdtasdt0(all_0_1_1, all_13_0_9) = all_56_3_18
% 9.51/2.87 |
% 9.51/2.87 | From (111) and (107) follows:
% 9.51/2.87 | (93) sdtasdt0(all_0_1_1, all_13_1_10) = all_56_4_19
% 9.51/2.87 |
% 9.51/2.87 | From (114) and (98) follows:
% 9.51/2.87 | (119) sdtpldt0(all_56_1_16, all_56_0_15) = all_0_0_0
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (6) with all_56_0_15, all_13_0_9, all_0_1_1 and discharging atoms sdtasdt0(all_13_0_9, all_0_1_1) = all_56_0_15, aElement0(all_13_0_9), aElement0(all_0_1_1), yields:
% 9.51/2.87 | (120) sdtasdt0(all_0_1_1, all_13_0_9) = all_56_0_15
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (6) with all_56_1_16, all_13_1_10, all_0_1_1 and discharging atoms sdtasdt0(all_13_1_10, all_0_1_1) = all_56_1_16, aElement0(all_13_1_10), aElement0(all_0_1_1), yields:
% 9.51/2.87 | (121) sdtasdt0(all_0_1_1, all_13_1_10) = all_56_1_16
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (57) with all_56_3_18, all_0_1_1, all_13_0_9 and discharging atoms sdtasdt0(all_0_1_1, all_13_0_9) = all_56_3_18, aElementOf0(all_13_0_9, xJ), aElement0(all_0_1_1), yields:
% 9.51/2.87 | (122) aElementOf0(all_56_3_18, xJ)
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (44) with all_56_4_19, all_0_1_1, all_13_1_10 and discharging atoms sdtasdt0(all_0_1_1, all_13_1_10) = all_56_4_19, aElementOf0(all_13_1_10, xI), aElement0(all_0_1_1), yields:
% 9.51/2.87 | (123) aElementOf0(all_56_4_19, xI)
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (31) with all_0_1_1, all_13_0_9, all_56_0_15, all_56_3_18 and discharging atoms sdtasdt0(all_0_1_1, all_13_0_9) = all_56_0_15, sdtasdt0(all_0_1_1, all_13_0_9) = all_56_3_18, yields:
% 9.51/2.87 | (124) all_56_0_15 = all_56_3_18
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (31) with all_0_1_1, all_13_1_10, all_56_1_16, all_56_4_19 and discharging atoms sdtasdt0(all_0_1_1, all_13_1_10) = all_56_1_16, sdtasdt0(all_0_1_1, all_13_1_10) = all_56_4_19, yields:
% 9.51/2.87 | (125) all_56_1_16 = all_56_4_19
% 9.51/2.87 |
% 9.51/2.87 | From (125)(124) and (119) follows:
% 9.51/2.87 | (99) sdtpldt0(all_56_4_19, all_56_3_18) = all_0_0_0
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (3) with all_56_3_18, all_56_4_19, all_0_0_0, all_0_3_3, xJ, xI and discharging atoms sdtpldt1(xI, xJ) = all_0_3_3, sdtpldt0(all_56_4_19, all_56_3_18) = all_0_0_0, aElementOf0(all_56_3_18, xJ), aElementOf0(all_56_4_19, xI), aSet0(xJ), aSet0(xI), ~ aElementOf0(all_0_0_0, all_0_3_3), yields:
% 9.51/2.87 | (127) $false
% 9.51/2.87 |
% 9.51/2.87 |-The branch is then unsatisfiable
% 9.51/2.87 |-Branch two:
% 9.51/2.87 | (128) sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0 & aElementOf0(all_0_1_1, all_0_3_3) & ~ aElementOf0(all_0_0_0, all_0_3_3)
% 9.51/2.87 |
% 9.51/2.87 | Applying alpha-rule on (128) yields:
% 9.51/2.87 | (129) sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0
% 9.51/2.87 | (130) aElementOf0(all_0_1_1, all_0_3_3)
% 9.51/2.87 | (88) ~ aElementOf0(all_0_0_0, all_0_3_3)
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (63) with all_0_1_1, all_0_3_3 and discharging atoms aElementOf0(all_0_1_1, all_0_3_3), aSet0(all_0_3_3), yields:
% 9.51/2.87 | (87) aElement0(all_0_1_1)
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (43) with all_0_1_1 and discharging atoms aElementOf0(all_0_1_1, all_0_3_3), yields:
% 9.51/2.87 | (133) ? [v0] : ? [v1] : (sdtpldt0(v0, v1) = all_0_1_1 & aElementOf0(v1, xJ) & aElementOf0(v0, xI))
% 9.51/2.87 |
% 9.51/2.87 | Instantiating (133) with all_56_0_25, all_56_1_26 yields:
% 9.51/2.87 | (134) sdtpldt0(all_56_1_26, all_56_0_25) = all_0_1_1 & aElementOf0(all_56_0_25, xJ) & aElementOf0(all_56_1_26, xI)
% 9.51/2.87 |
% 9.51/2.87 | Applying alpha-rule on (134) yields:
% 9.51/2.87 | (135) sdtpldt0(all_56_1_26, all_56_0_25) = all_0_1_1
% 9.51/2.87 | (136) aElementOf0(all_56_0_25, xJ)
% 9.51/2.87 | (137) aElementOf0(all_56_1_26, xI)
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (63) with all_56_0_25, xJ and discharging atoms aElementOf0(all_56_0_25, xJ), aSet0(xJ), yields:
% 9.51/2.87 | (138) aElement0(all_56_0_25)
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (63) with all_56_1_26, xI and discharging atoms aElementOf0(all_56_1_26, xI), aSet0(xI), yields:
% 9.51/2.87 | (139) aElement0(all_56_1_26)
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (70) with all_0_0_0, all_0_2_2, all_0_1_1, all_13_1_10, all_13_0_9 and discharging atoms sdtpldt0(all_13_0_9, all_13_1_10) = all_0_2_2, sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0, aElement0(all_13_0_9), aElement0(all_13_1_10), aElement0(all_0_1_1), yields:
% 9.51/2.87 | (140) ? [v0] : (sdtpldt0(all_13_0_9, v0) = all_0_0_0 & sdtpldt0(all_13_1_10, all_0_1_1) = v0)
% 9.51/2.87 |
% 9.51/2.87 | Instantiating formula (70) with all_0_0_0, all_0_2_2, all_0_1_1, all_13_0_9, all_13_1_10 and discharging atoms sdtpldt0(all_13_1_10, all_13_0_9) = all_0_2_2, sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0, aElement0(all_13_0_9), aElement0(all_13_1_10), aElement0(all_0_1_1), yields:
% 9.51/2.88 | (141) ? [v0] : (sdtpldt0(all_13_0_9, all_0_1_1) = v0 & sdtpldt0(all_13_1_10, v0) = all_0_0_0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (41) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0, aElement0(all_0_1_1), aElement0(all_0_2_2), yields:
% 9.51/2.88 | (142) sdtpldt0(all_0_1_1, all_0_2_2) = all_0_0_0
% 9.51/2.88 |
% 9.51/2.88 | Instantiating (141) with all_64_0_27 yields:
% 9.51/2.88 | (143) sdtpldt0(all_13_0_9, all_0_1_1) = all_64_0_27 & sdtpldt0(all_13_1_10, all_64_0_27) = all_0_0_0
% 9.51/2.88 |
% 9.51/2.88 | Applying alpha-rule on (143) yields:
% 9.51/2.88 | (144) sdtpldt0(all_13_0_9, all_0_1_1) = all_64_0_27
% 9.51/2.88 | (145) sdtpldt0(all_13_1_10, all_64_0_27) = all_0_0_0
% 9.51/2.88 |
% 9.51/2.88 | Instantiating (140) with all_66_0_28 yields:
% 9.51/2.88 | (146) sdtpldt0(all_13_0_9, all_66_0_28) = all_0_0_0 & sdtpldt0(all_13_1_10, all_0_1_1) = all_66_0_28
% 9.51/2.88 |
% 9.51/2.88 | Applying alpha-rule on (146) yields:
% 9.51/2.88 | (147) sdtpldt0(all_13_0_9, all_66_0_28) = all_0_0_0
% 9.51/2.88 | (148) sdtpldt0(all_13_1_10, all_0_1_1) = all_66_0_28
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (41) with all_64_0_27, all_13_0_9, all_0_1_1 and discharging atoms sdtpldt0(all_13_0_9, all_0_1_1) = all_64_0_27, aElement0(all_13_0_9), aElement0(all_0_1_1), yields:
% 9.51/2.88 | (149) sdtpldt0(all_0_1_1, all_13_0_9) = all_64_0_27
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (41) with all_66_0_28, all_13_1_10, all_0_1_1 and discharging atoms sdtpldt0(all_13_1_10, all_0_1_1) = all_66_0_28, aElement0(all_13_1_10), aElement0(all_0_1_1), yields:
% 9.51/2.88 | (150) sdtpldt0(all_0_1_1, all_13_1_10) = all_66_0_28
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (56) with all_0_0_0, all_0_2_2, all_13_1_10, all_13_0_9, all_0_1_1 and discharging atoms sdtpldt0(all_13_0_9, all_13_1_10) = all_0_2_2, sdtpldt0(all_0_1_1, all_0_2_2) = all_0_0_0, aElement0(all_13_0_9), aElement0(all_13_1_10), aElement0(all_0_1_1), yields:
% 9.51/2.88 | (151) ? [v0] : (sdtpldt0(v0, all_13_1_10) = all_0_0_0 & sdtpldt0(all_0_1_1, all_13_0_9) = v0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (56) with all_0_0_0, all_0_2_2, all_13_0_9, all_13_1_10, all_0_1_1 and discharging atoms sdtpldt0(all_13_1_10, all_13_0_9) = all_0_2_2, sdtpldt0(all_0_1_1, all_0_2_2) = all_0_0_0, aElement0(all_13_0_9), aElement0(all_13_1_10), aElement0(all_0_1_1), yields:
% 9.51/2.88 | (152) ? [v0] : (sdtpldt0(v0, all_13_0_9) = all_0_0_0 & sdtpldt0(all_0_1_1, all_13_1_10) = v0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (56) with all_0_0_0, all_0_1_1, all_56_0_25, all_56_1_26, all_0_2_2 and discharging atoms sdtpldt0(all_56_1_26, all_56_0_25) = all_0_1_1, sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_0_2_2), yields:
% 9.51/2.88 | (153) ? [v0] : (sdtpldt0(v0, all_56_0_25) = all_0_0_0 & sdtpldt0(all_0_2_2, all_56_1_26) = v0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (56) with all_64_0_27, all_0_1_1, all_56_0_25, all_56_1_26, all_13_0_9 and discharging atoms sdtpldt0(all_56_1_26, all_56_0_25) = all_0_1_1, sdtpldt0(all_13_0_9, all_0_1_1) = all_64_0_27, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_13_0_9), yields:
% 9.51/2.88 | (154) ? [v0] : (sdtpldt0(v0, all_56_0_25) = all_64_0_27 & sdtpldt0(all_13_0_9, all_56_1_26) = v0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (56) with all_66_0_28, all_0_1_1, all_56_0_25, all_56_1_26, all_13_1_10 and discharging atoms sdtpldt0(all_56_1_26, all_56_0_25) = all_0_1_1, sdtpldt0(all_13_1_10, all_0_1_1) = all_66_0_28, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_13_1_10), yields:
% 9.51/2.88 | (155) ? [v0] : (sdtpldt0(v0, all_56_0_25) = all_66_0_28 & sdtpldt0(all_13_1_10, all_56_1_26) = v0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (41) with all_0_1_1, all_56_1_26, all_56_0_25 and discharging atoms sdtpldt0(all_56_1_26, all_56_0_25) = all_0_1_1, aElement0(all_56_0_25), aElement0(all_56_1_26), yields:
% 9.51/2.88 | (156) sdtpldt0(all_56_0_25, all_56_1_26) = all_0_1_1
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (70) with all_0_0_0, all_0_1_1, all_0_2_2, all_56_0_25, all_56_1_26 and discharging atoms sdtpldt0(all_56_1_26, all_56_0_25) = all_0_1_1, sdtpldt0(all_0_1_1, all_0_2_2) = all_0_0_0, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_0_2_2), yields:
% 9.51/2.88 | (157) ? [v0] : (sdtpldt0(all_56_0_25, all_0_2_2) = v0 & sdtpldt0(all_56_1_26, v0) = all_0_0_0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating (155) with all_74_0_29 yields:
% 9.51/2.88 | (158) sdtpldt0(all_74_0_29, all_56_0_25) = all_66_0_28 & sdtpldt0(all_13_1_10, all_56_1_26) = all_74_0_29
% 9.51/2.88 |
% 9.51/2.88 | Applying alpha-rule on (158) yields:
% 9.51/2.88 | (159) sdtpldt0(all_74_0_29, all_56_0_25) = all_66_0_28
% 9.51/2.88 | (160) sdtpldt0(all_13_1_10, all_56_1_26) = all_74_0_29
% 9.51/2.88 |
% 9.51/2.88 | Instantiating (157) with all_76_0_30 yields:
% 9.51/2.88 | (161) sdtpldt0(all_56_0_25, all_0_2_2) = all_76_0_30 & sdtpldt0(all_56_1_26, all_76_0_30) = all_0_0_0
% 9.51/2.88 |
% 9.51/2.88 | Applying alpha-rule on (161) yields:
% 9.51/2.88 | (162) sdtpldt0(all_56_0_25, all_0_2_2) = all_76_0_30
% 9.51/2.88 | (163) sdtpldt0(all_56_1_26, all_76_0_30) = all_0_0_0
% 9.51/2.88 |
% 9.51/2.88 | Instantiating (154) with all_78_0_31 yields:
% 9.51/2.88 | (164) sdtpldt0(all_78_0_31, all_56_0_25) = all_64_0_27 & sdtpldt0(all_13_0_9, all_56_1_26) = all_78_0_31
% 9.51/2.88 |
% 9.51/2.88 | Applying alpha-rule on (164) yields:
% 9.51/2.88 | (165) sdtpldt0(all_78_0_31, all_56_0_25) = all_64_0_27
% 9.51/2.88 | (166) sdtpldt0(all_13_0_9, all_56_1_26) = all_78_0_31
% 9.51/2.88 |
% 9.51/2.88 | Instantiating (152) with all_80_0_32 yields:
% 9.51/2.88 | (167) sdtpldt0(all_80_0_32, all_13_0_9) = all_0_0_0 & sdtpldt0(all_0_1_1, all_13_1_10) = all_80_0_32
% 9.51/2.88 |
% 9.51/2.88 | Applying alpha-rule on (167) yields:
% 9.51/2.88 | (168) sdtpldt0(all_80_0_32, all_13_0_9) = all_0_0_0
% 9.51/2.88 | (169) sdtpldt0(all_0_1_1, all_13_1_10) = all_80_0_32
% 9.51/2.88 |
% 9.51/2.88 | Instantiating (151) with all_82_0_33 yields:
% 9.51/2.88 | (170) sdtpldt0(all_82_0_33, all_13_1_10) = all_0_0_0 & sdtpldt0(all_0_1_1, all_13_0_9) = all_82_0_33
% 9.51/2.88 |
% 9.51/2.88 | Applying alpha-rule on (170) yields:
% 9.51/2.88 | (171) sdtpldt0(all_82_0_33, all_13_1_10) = all_0_0_0
% 9.51/2.88 | (172) sdtpldt0(all_0_1_1, all_13_0_9) = all_82_0_33
% 9.51/2.88 |
% 9.51/2.88 | Instantiating (153) with all_84_0_34 yields:
% 9.51/2.88 | (173) sdtpldt0(all_84_0_34, all_56_0_25) = all_0_0_0 & sdtpldt0(all_0_2_2, all_56_1_26) = all_84_0_34
% 9.51/2.88 |
% 9.51/2.88 | Applying alpha-rule on (173) yields:
% 9.51/2.88 | (174) sdtpldt0(all_84_0_34, all_56_0_25) = all_0_0_0
% 9.51/2.88 | (175) sdtpldt0(all_0_2_2, all_56_1_26) = all_84_0_34
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (46) with all_0_1_1, all_13_0_9, all_64_0_27, all_82_0_33 and discharging atoms sdtpldt0(all_0_1_1, all_13_0_9) = all_82_0_33, sdtpldt0(all_0_1_1, all_13_0_9) = all_64_0_27, yields:
% 9.51/2.88 | (176) all_82_0_33 = all_64_0_27
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (46) with all_0_1_1, all_13_1_10, all_66_0_28, all_80_0_32 and discharging atoms sdtpldt0(all_0_1_1, all_13_1_10) = all_80_0_32, sdtpldt0(all_0_1_1, all_13_1_10) = all_66_0_28, yields:
% 9.51/2.88 | (177) all_80_0_32 = all_66_0_28
% 9.51/2.88 |
% 9.51/2.88 | From (177) and (168) follows:
% 9.51/2.88 | (178) sdtpldt0(all_66_0_28, all_13_0_9) = all_0_0_0
% 9.51/2.88 |
% 9.51/2.88 | From (176) and (172) follows:
% 9.51/2.88 | (149) sdtpldt0(all_0_1_1, all_13_0_9) = all_64_0_27
% 9.51/2.88 |
% 9.51/2.88 | From (177) and (169) follows:
% 9.51/2.88 | (150) sdtpldt0(all_0_1_1, all_13_1_10) = all_66_0_28
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (56) with all_64_0_27, all_0_1_1, all_56_1_26, all_56_0_25, all_13_0_9 and discharging atoms sdtpldt0(all_56_0_25, all_56_1_26) = all_0_1_1, sdtpldt0(all_13_0_9, all_0_1_1) = all_64_0_27, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_13_0_9), yields:
% 9.51/2.88 | (181) ? [v0] : (sdtpldt0(v0, all_56_1_26) = all_64_0_27 & sdtpldt0(all_13_0_9, all_56_0_25) = v0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (70) with all_0_0_0, all_0_1_1, all_0_2_2, all_56_1_26, all_56_0_25 and discharging atoms sdtpldt0(all_56_0_25, all_56_1_26) = all_0_1_1, sdtpldt0(all_0_1_1, all_0_2_2) = all_0_0_0, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_0_2_2), yields:
% 9.51/2.88 | (182) ? [v0] : (sdtpldt0(all_56_0_25, v0) = all_0_0_0 & sdtpldt0(all_56_1_26, all_0_2_2) = v0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (56) with all_0_0_0, all_0_1_1, all_56_1_26, all_56_0_25, all_0_2_2 and discharging atoms sdtpldt0(all_56_0_25, all_56_1_26) = all_0_1_1, sdtpldt0(all_0_2_2, all_0_1_1) = all_0_0_0, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_0_2_2), yields:
% 9.51/2.88 | (183) ? [v0] : (sdtpldt0(v0, all_56_1_26) = all_0_0_0 & sdtpldt0(all_0_2_2, all_56_0_25) = v0)
% 9.51/2.88 |
% 9.51/2.88 | Instantiating formula (56) with all_76_0_30, all_0_2_2, all_13_1_10, all_13_0_9, all_56_0_25 and discharging atoms sdtpldt0(all_56_0_25, all_0_2_2) = all_76_0_30, sdtpldt0(all_13_0_9, all_13_1_10) = all_0_2_2, aElement0(all_56_0_25), aElement0(all_13_0_9), aElement0(all_13_1_10), yields:
% 9.51/2.89 | (184) ? [v0] : (sdtpldt0(v0, all_13_1_10) = all_76_0_30 & sdtpldt0(all_56_0_25, all_13_0_9) = v0)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (41) with all_76_0_30, all_56_0_25, all_0_2_2 and discharging atoms sdtpldt0(all_56_0_25, all_0_2_2) = all_76_0_30, aElement0(all_56_0_25), aElement0(all_0_2_2), yields:
% 9.51/2.89 | (185) sdtpldt0(all_0_2_2, all_56_0_25) = all_76_0_30
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (39) with all_78_0_31, all_56_1_26, all_13_0_9 and discharging atoms sdtpldt0(all_13_0_9, all_56_1_26) = all_78_0_31, aElement0(all_56_1_26), aElement0(all_13_0_9), yields:
% 9.51/2.89 | (186) sdtpldt0(all_56_1_26, all_13_0_9) = all_78_0_31
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (39) with all_74_0_29, all_56_1_26, all_13_1_10 and discharging atoms sdtpldt0(all_13_1_10, all_56_1_26) = all_74_0_29, aElement0(all_56_1_26), aElement0(all_13_1_10), yields:
% 9.51/2.89 | (187) sdtpldt0(all_56_1_26, all_13_1_10) = all_74_0_29
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (32) with all_74_0_29, all_56_1_26, all_13_1_10 and discharging atoms sdtpldt0(all_13_1_10, all_56_1_26) = all_74_0_29, aElement0(all_56_1_26), aElement0(all_13_1_10), yields:
% 9.51/2.89 | (188) aElement0(all_74_0_29)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (19) with all_74_0_29, all_56_1_26, all_13_1_10 and discharging atoms sdtpldt0(all_13_1_10, all_56_1_26) = all_74_0_29, aElementOf0(all_56_1_26, xI), aElementOf0(all_13_1_10, xI), yields:
% 9.51/2.89 | (189) aElementOf0(all_74_0_29, xI)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (70) with all_64_0_27, all_0_1_1, all_13_0_9, all_56_0_25, all_56_1_26 and discharging atoms sdtpldt0(all_56_1_26, all_56_0_25) = all_0_1_1, sdtpldt0(all_0_1_1, all_13_0_9) = all_64_0_27, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_13_0_9), yields:
% 9.51/2.89 | (190) ? [v0] : (sdtpldt0(all_56_0_25, all_13_0_9) = v0 & sdtpldt0(all_56_1_26, v0) = all_64_0_27)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (70) with all_64_0_27, all_0_1_1, all_13_0_9, all_56_1_26, all_56_0_25 and discharging atoms sdtpldt0(all_56_0_25, all_56_1_26) = all_0_1_1, sdtpldt0(all_0_1_1, all_13_0_9) = all_64_0_27, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_13_0_9), yields:
% 9.51/2.89 | (191) ? [v0] : (sdtpldt0(all_56_0_25, v0) = all_64_0_27 & sdtpldt0(all_56_1_26, all_13_0_9) = v0)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (70) with all_66_0_28, all_0_1_1, all_13_1_10, all_56_1_26, all_56_0_25 and discharging atoms sdtpldt0(all_56_0_25, all_56_1_26) = all_0_1_1, sdtpldt0(all_0_1_1, all_13_1_10) = all_66_0_28, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_13_1_10), yields:
% 9.51/2.89 | (192) ? [v0] : (sdtpldt0(all_56_0_25, v0) = all_66_0_28 & sdtpldt0(all_56_1_26, all_13_1_10) = v0)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (70) with all_84_0_34, all_0_2_2, all_56_1_26, all_13_1_10, all_13_0_9 and discharging atoms sdtpldt0(all_13_0_9, all_13_1_10) = all_0_2_2, sdtpldt0(all_0_2_2, all_56_1_26) = all_84_0_34, aElement0(all_56_1_26), aElement0(all_13_0_9), aElement0(all_13_1_10), yields:
% 9.51/2.89 | (193) ? [v0] : (sdtpldt0(all_13_0_9, v0) = all_84_0_34 & sdtpldt0(all_13_1_10, all_56_1_26) = v0)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (70) with all_84_0_34, all_0_2_2, all_56_1_26, all_13_0_9, all_13_1_10 and discharging atoms sdtpldt0(all_13_1_10, all_13_0_9) = all_0_2_2, sdtpldt0(all_0_2_2, all_56_1_26) = all_84_0_34, aElement0(all_56_1_26), aElement0(all_13_0_9), aElement0(all_13_1_10), yields:
% 9.51/2.89 | (194) ? [v0] : (sdtpldt0(all_13_0_9, all_56_1_26) = v0 & sdtpldt0(all_13_1_10, v0) = all_84_0_34)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (39) with all_84_0_34, all_56_1_26, all_0_2_2 and discharging atoms sdtpldt0(all_0_2_2, all_56_1_26) = all_84_0_34, aElement0(all_56_1_26), aElement0(all_0_2_2), yields:
% 9.51/2.89 | (195) sdtpldt0(all_56_1_26, all_0_2_2) = all_84_0_34
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (193) with all_96_0_35 yields:
% 9.51/2.89 | (196) sdtpldt0(all_13_0_9, all_96_0_35) = all_84_0_34 & sdtpldt0(all_13_1_10, all_56_1_26) = all_96_0_35
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (196) yields:
% 9.51/2.89 | (197) sdtpldt0(all_13_0_9, all_96_0_35) = all_84_0_34
% 9.51/2.89 | (198) sdtpldt0(all_13_1_10, all_56_1_26) = all_96_0_35
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (192) with all_98_0_36 yields:
% 9.51/2.89 | (199) sdtpldt0(all_56_0_25, all_98_0_36) = all_66_0_28 & sdtpldt0(all_56_1_26, all_13_1_10) = all_98_0_36
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (199) yields:
% 9.51/2.89 | (200) sdtpldt0(all_56_0_25, all_98_0_36) = all_66_0_28
% 9.51/2.89 | (201) sdtpldt0(all_56_1_26, all_13_1_10) = all_98_0_36
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (183) with all_100_0_37 yields:
% 9.51/2.89 | (202) sdtpldt0(all_100_0_37, all_56_1_26) = all_0_0_0 & sdtpldt0(all_0_2_2, all_56_0_25) = all_100_0_37
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (202) yields:
% 9.51/2.89 | (203) sdtpldt0(all_100_0_37, all_56_1_26) = all_0_0_0
% 9.51/2.89 | (204) sdtpldt0(all_0_2_2, all_56_0_25) = all_100_0_37
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (182) with all_102_0_38 yields:
% 9.51/2.89 | (205) sdtpldt0(all_56_0_25, all_102_0_38) = all_0_0_0 & sdtpldt0(all_56_1_26, all_0_2_2) = all_102_0_38
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (205) yields:
% 9.51/2.89 | (206) sdtpldt0(all_56_0_25, all_102_0_38) = all_0_0_0
% 9.51/2.89 | (207) sdtpldt0(all_56_1_26, all_0_2_2) = all_102_0_38
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (190) with all_104_0_39 yields:
% 9.51/2.89 | (208) sdtpldt0(all_56_0_25, all_13_0_9) = all_104_0_39 & sdtpldt0(all_56_1_26, all_104_0_39) = all_64_0_27
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (208) yields:
% 9.51/2.89 | (209) sdtpldt0(all_56_0_25, all_13_0_9) = all_104_0_39
% 9.51/2.89 | (210) sdtpldt0(all_56_1_26, all_104_0_39) = all_64_0_27
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (181) with all_108_0_41 yields:
% 9.51/2.89 | (211) sdtpldt0(all_108_0_41, all_56_1_26) = all_64_0_27 & sdtpldt0(all_13_0_9, all_56_0_25) = all_108_0_41
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (211) yields:
% 9.51/2.89 | (212) sdtpldt0(all_108_0_41, all_56_1_26) = all_64_0_27
% 9.51/2.89 | (213) sdtpldt0(all_13_0_9, all_56_0_25) = all_108_0_41
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (184) with all_114_0_44 yields:
% 9.51/2.89 | (214) sdtpldt0(all_114_0_44, all_13_1_10) = all_76_0_30 & sdtpldt0(all_56_0_25, all_13_0_9) = all_114_0_44
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (214) yields:
% 9.51/2.89 | (215) sdtpldt0(all_114_0_44, all_13_1_10) = all_76_0_30
% 9.51/2.89 | (216) sdtpldt0(all_56_0_25, all_13_0_9) = all_114_0_44
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (191) with all_116_0_45 yields:
% 9.51/2.89 | (217) sdtpldt0(all_56_0_25, all_116_0_45) = all_64_0_27 & sdtpldt0(all_56_1_26, all_13_0_9) = all_116_0_45
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (217) yields:
% 9.51/2.89 | (218) sdtpldt0(all_56_0_25, all_116_0_45) = all_64_0_27
% 9.51/2.89 | (219) sdtpldt0(all_56_1_26, all_13_0_9) = all_116_0_45
% 9.51/2.89 |
% 9.51/2.89 | Instantiating (194) with all_118_0_46 yields:
% 9.51/2.89 | (220) sdtpldt0(all_13_0_9, all_56_1_26) = all_118_0_46 & sdtpldt0(all_13_1_10, all_118_0_46) = all_84_0_34
% 9.51/2.89 |
% 9.51/2.89 | Applying alpha-rule on (220) yields:
% 9.51/2.89 | (221) sdtpldt0(all_13_0_9, all_56_1_26) = all_118_0_46
% 9.51/2.89 | (222) sdtpldt0(all_13_1_10, all_118_0_46) = all_84_0_34
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (46) with all_56_0_25, all_13_0_9, all_104_0_39, all_114_0_44 and discharging atoms sdtpldt0(all_56_0_25, all_13_0_9) = all_114_0_44, sdtpldt0(all_56_0_25, all_13_0_9) = all_104_0_39, yields:
% 9.51/2.89 | (223) all_114_0_44 = all_104_0_39
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (46) with all_56_1_26, all_13_0_9, all_78_0_31, all_116_0_45 and discharging atoms sdtpldt0(all_56_1_26, all_13_0_9) = all_116_0_45, sdtpldt0(all_56_1_26, all_13_0_9) = all_78_0_31, yields:
% 9.51/2.89 | (224) all_116_0_45 = all_78_0_31
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (46) with all_56_1_26, all_13_1_10, all_74_0_29, all_98_0_36 and discharging atoms sdtpldt0(all_56_1_26, all_13_1_10) = all_98_0_36, sdtpldt0(all_56_1_26, all_13_1_10) = all_74_0_29, yields:
% 9.51/2.89 | (225) all_98_0_36 = all_74_0_29
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (46) with all_56_1_26, all_0_2_2, all_84_0_34, all_102_0_38 and discharging atoms sdtpldt0(all_56_1_26, all_0_2_2) = all_102_0_38, sdtpldt0(all_56_1_26, all_0_2_2) = all_84_0_34, yields:
% 9.51/2.89 | (226) all_102_0_38 = all_84_0_34
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (46) with all_13_0_9, all_56_1_26, all_118_0_46, all_78_0_31 and discharging atoms sdtpldt0(all_13_0_9, all_56_1_26) = all_118_0_46, sdtpldt0(all_13_0_9, all_56_1_26) = all_78_0_31, yields:
% 9.51/2.89 | (227) all_118_0_46 = all_78_0_31
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (46) with all_13_1_10, all_56_1_26, all_96_0_35, all_74_0_29 and discharging atoms sdtpldt0(all_13_1_10, all_56_1_26) = all_96_0_35, sdtpldt0(all_13_1_10, all_56_1_26) = all_74_0_29, yields:
% 9.51/2.89 | (228) all_96_0_35 = all_74_0_29
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (46) with all_0_2_2, all_56_0_25, all_76_0_30, all_100_0_37 and discharging atoms sdtpldt0(all_0_2_2, all_56_0_25) = all_100_0_37, sdtpldt0(all_0_2_2, all_56_0_25) = all_76_0_30, yields:
% 9.51/2.89 | (229) all_100_0_37 = all_76_0_30
% 9.51/2.89 |
% 9.51/2.89 | From (224) and (218) follows:
% 9.51/2.89 | (230) sdtpldt0(all_56_0_25, all_78_0_31) = all_64_0_27
% 9.51/2.89 |
% 9.51/2.89 | From (226) and (206) follows:
% 9.51/2.89 | (231) sdtpldt0(all_56_0_25, all_84_0_34) = all_0_0_0
% 9.51/2.89 |
% 9.51/2.89 | From (225) and (200) follows:
% 9.51/2.89 | (232) sdtpldt0(all_56_0_25, all_74_0_29) = all_66_0_28
% 9.51/2.89 |
% 9.51/2.89 | From (223) and (216) follows:
% 9.51/2.89 | (209) sdtpldt0(all_56_0_25, all_13_0_9) = all_104_0_39
% 9.51/2.89 |
% 9.51/2.89 | From (224) and (219) follows:
% 9.51/2.89 | (186) sdtpldt0(all_56_1_26, all_13_0_9) = all_78_0_31
% 9.51/2.89 |
% 9.51/2.89 | From (228) and (197) follows:
% 9.51/2.89 | (235) sdtpldt0(all_13_0_9, all_74_0_29) = all_84_0_34
% 9.51/2.89 |
% 9.51/2.89 | From (227) and (221) follows:
% 9.51/2.89 | (166) sdtpldt0(all_13_0_9, all_56_1_26) = all_78_0_31
% 9.51/2.89 |
% 9.51/2.89 | From (229) and (204) follows:
% 9.51/2.89 | (185) sdtpldt0(all_0_2_2, all_56_0_25) = all_76_0_30
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (56) with all_64_0_27, all_78_0_31, all_56_1_26, all_13_0_9, all_56_0_25 and discharging atoms sdtpldt0(all_56_0_25, all_78_0_31) = all_64_0_27, sdtpldt0(all_13_0_9, all_56_1_26) = all_78_0_31, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_13_0_9), yields:
% 9.51/2.89 | (238) ? [v0] : (sdtpldt0(v0, all_56_1_26) = all_64_0_27 & sdtpldt0(all_56_0_25, all_13_0_9) = v0)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (41) with all_104_0_39, all_56_0_25, all_13_0_9 and discharging atoms sdtpldt0(all_56_0_25, all_13_0_9) = all_104_0_39, aElement0(all_56_0_25), aElement0(all_13_0_9), yields:
% 9.51/2.89 | (239) sdtpldt0(all_13_0_9, all_56_0_25) = all_104_0_39
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (70) with all_64_0_27, all_78_0_31, all_56_0_25, all_13_0_9, all_56_1_26 and discharging atoms sdtpldt0(all_78_0_31, all_56_0_25) = all_64_0_27, sdtpldt0(all_56_1_26, all_13_0_9) = all_78_0_31, aElement0(all_56_0_25), aElement0(all_56_1_26), aElement0(all_13_0_9), yields:
% 9.51/2.89 | (240) ? [v0] : (sdtpldt0(all_56_1_26, v0) = all_64_0_27 & sdtpldt0(all_13_0_9, all_56_0_25) = v0)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (39) with all_108_0_41, all_56_0_25, all_13_0_9 and discharging atoms sdtpldt0(all_13_0_9, all_56_0_25) = all_108_0_41, aElement0(all_56_0_25), aElement0(all_13_0_9), yields:
% 9.51/2.89 | (241) sdtpldt0(all_56_0_25, all_13_0_9) = all_108_0_41
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (33) with all_108_0_41, all_56_0_25, all_13_0_9 and discharging atoms sdtpldt0(all_13_0_9, all_56_0_25) = all_108_0_41, aElementOf0(all_56_0_25, xJ), aElementOf0(all_13_0_9, xJ), yields:
% 9.51/2.89 | (242) aElementOf0(all_108_0_41, xJ)
% 9.51/2.89 |
% 9.51/2.89 | Instantiating formula (70) with all_76_0_30, all_0_2_2, all_56_0_25, all_13_0_9, all_13_1_10 and discharging atoms sdtpldt0(all_13_1_10, all_13_0_9) = all_0_2_2, sdtpldt0(all_0_2_2, all_56_0_25) = all_76_0_30, aElement0(all_56_0_25), aElement0(all_13_0_9), aElement0(all_13_1_10), yields:
% 9.51/2.90 | (243) ? [v0] : (sdtpldt0(all_13_0_9, all_56_0_25) = v0 & sdtpldt0(all_13_1_10, v0) = all_76_0_30)
% 9.51/2.90 |
% 9.51/2.90 | Instantiating formula (70) with all_0_0_0, all_66_0_28, all_13_0_9, all_56_0_25, all_74_0_29 and discharging atoms sdtpldt0(all_74_0_29, all_56_0_25) = all_66_0_28, sdtpldt0(all_66_0_28, all_13_0_9) = all_0_0_0, aElement0(all_74_0_29), aElement0(all_56_0_25), aElement0(all_13_0_9), yields:
% 9.51/2.90 | (244) ? [v0] : (sdtpldt0(all_74_0_29, v0) = all_0_0_0 & sdtpldt0(all_56_0_25, all_13_0_9) = v0)
% 9.51/2.90 |
% 9.51/2.90 | Instantiating formula (56) with all_0_0_0, all_66_0_28, all_74_0_29, all_56_0_25, all_13_0_9 and discharging atoms sdtpldt0(all_56_0_25, all_74_0_29) = all_66_0_28, sdtpldt0(all_13_0_9, all_66_0_28) = all_0_0_0, aElement0(all_74_0_29), aElement0(all_56_0_25), aElement0(all_13_0_9), yields:
% 9.51/2.90 | (245) ? [v0] : (sdtpldt0(v0, all_74_0_29) = all_0_0_0 & sdtpldt0(all_13_0_9, all_56_0_25) = v0)
% 9.51/2.90 |
% 9.51/2.90 | Instantiating formula (56) with all_0_0_0, all_84_0_34, all_74_0_29, all_13_0_9, all_56_0_25 and discharging atoms sdtpldt0(all_56_0_25, all_84_0_34) = all_0_0_0, sdtpldt0(all_13_0_9, all_74_0_29) = all_84_0_34, aElement0(all_74_0_29), aElement0(all_56_0_25), aElement0(all_13_0_9), yields:
% 9.51/2.90 | (246) ? [v0] : (sdtpldt0(v0, all_74_0_29) = all_0_0_0 & sdtpldt0(all_56_0_25, all_13_0_9) = v0)
% 9.51/2.90 |
% 9.51/2.90 | Instantiating (245) with all_134_0_49 yields:
% 9.51/2.90 | (247) sdtpldt0(all_134_0_49, all_74_0_29) = all_0_0_0 & sdtpldt0(all_13_0_9, all_56_0_25) = all_134_0_49
% 9.51/2.90 |
% 9.51/2.90 | Applying alpha-rule on (247) yields:
% 9.51/2.90 | (248) sdtpldt0(all_134_0_49, all_74_0_29) = all_0_0_0
% 9.51/2.90 | (249) sdtpldt0(all_13_0_9, all_56_0_25) = all_134_0_49
% 9.51/2.90 |
% 9.51/2.90 | Instantiating (246) with all_142_0_53 yields:
% 9.51/2.90 | (250) sdtpldt0(all_142_0_53, all_74_0_29) = all_0_0_0 & sdtpldt0(all_56_0_25, all_13_0_9) = all_142_0_53
% 9.51/2.90 |
% 9.51/2.90 | Applying alpha-rule on (250) yields:
% 9.51/2.90 | (251) sdtpldt0(all_142_0_53, all_74_0_29) = all_0_0_0
% 9.51/2.90 | (252) sdtpldt0(all_56_0_25, all_13_0_9) = all_142_0_53
% 9.51/2.90 |
% 9.51/2.90 | Instantiating (244) with all_144_0_54 yields:
% 9.51/2.90 | (253) sdtpldt0(all_74_0_29, all_144_0_54) = all_0_0_0 & sdtpldt0(all_56_0_25, all_13_0_9) = all_144_0_54
% 9.51/2.90 |
% 9.51/2.90 | Applying alpha-rule on (253) yields:
% 9.51/2.90 | (254) sdtpldt0(all_74_0_29, all_144_0_54) = all_0_0_0
% 9.51/2.90 | (255) sdtpldt0(all_56_0_25, all_13_0_9) = all_144_0_54
% 9.51/2.90 |
% 9.51/2.90 | Instantiating (238) with all_148_0_56 yields:
% 9.51/2.90 | (256) sdtpldt0(all_148_0_56, all_56_1_26) = all_64_0_27 & sdtpldt0(all_56_0_25, all_13_0_9) = all_148_0_56
% 9.51/2.90 |
% 9.51/2.90 | Applying alpha-rule on (256) yields:
% 9.51/2.90 | (257) sdtpldt0(all_148_0_56, all_56_1_26) = all_64_0_27
% 9.51/2.90 | (258) sdtpldt0(all_56_0_25, all_13_0_9) = all_148_0_56
% 9.51/2.90 |
% 9.51/2.90 | Instantiating (243) with all_160_0_62 yields:
% 9.51/2.90 | (259) sdtpldt0(all_13_0_9, all_56_0_25) = all_160_0_62 & sdtpldt0(all_13_1_10, all_160_0_62) = all_76_0_30
% 9.51/2.90 |
% 9.94/2.90 | Applying alpha-rule on (259) yields:
% 9.94/2.90 | (260) sdtpldt0(all_13_0_9, all_56_0_25) = all_160_0_62
% 9.94/2.90 | (261) sdtpldt0(all_13_1_10, all_160_0_62) = all_76_0_30
% 9.94/2.90 |
% 9.94/2.90 | Instantiating (240) with all_162_0_63 yields:
% 9.94/2.90 | (262) sdtpldt0(all_56_1_26, all_162_0_63) = all_64_0_27 & sdtpldt0(all_13_0_9, all_56_0_25) = all_162_0_63
% 9.94/2.90 |
% 9.94/2.90 | Applying alpha-rule on (262) yields:
% 9.94/2.90 | (263) sdtpldt0(all_56_1_26, all_162_0_63) = all_64_0_27
% 9.94/2.90 | (264) sdtpldt0(all_13_0_9, all_56_0_25) = all_162_0_63
% 9.94/2.90 |
% 9.94/2.90 | Instantiating formula (46) with all_56_0_25, all_13_0_9, all_144_0_54, all_148_0_56 and discharging atoms sdtpldt0(all_56_0_25, all_13_0_9) = all_148_0_56, sdtpldt0(all_56_0_25, all_13_0_9) = all_144_0_54, yields:
% 9.94/2.90 | (265) all_148_0_56 = all_144_0_54
% 9.94/2.90 |
% 9.94/2.90 | Instantiating formula (46) with all_56_0_25, all_13_0_9, all_142_0_53, all_144_0_54 and discharging atoms sdtpldt0(all_56_0_25, all_13_0_9) = all_144_0_54, sdtpldt0(all_56_0_25, all_13_0_9) = all_142_0_53, yields:
% 9.94/2.90 | (266) all_144_0_54 = all_142_0_53
% 9.94/2.90 |
% 9.94/2.90 | Instantiating formula (46) with all_56_0_25, all_13_0_9, all_108_0_41, all_148_0_56 and discharging atoms sdtpldt0(all_56_0_25, all_13_0_9) = all_148_0_56, sdtpldt0(all_56_0_25, all_13_0_9) = all_108_0_41, yields:
% 9.94/2.90 | (267) all_148_0_56 = all_108_0_41
% 9.94/2.90 |
% 9.94/2.90 | Instantiating formula (46) with all_13_0_9, all_56_0_25, all_160_0_62, all_108_0_41 and discharging atoms sdtpldt0(all_13_0_9, all_56_0_25) = all_160_0_62, sdtpldt0(all_13_0_9, all_56_0_25) = all_108_0_41, yields:
% 9.94/2.90 | (268) all_160_0_62 = all_108_0_41
% 9.94/2.90 |
% 9.94/2.90 | Instantiating formula (46) with all_13_0_9, all_56_0_25, all_160_0_62, all_162_0_63 and discharging atoms sdtpldt0(all_13_0_9, all_56_0_25) = all_162_0_63, sdtpldt0(all_13_0_9, all_56_0_25) = all_160_0_62, yields:
% 9.94/2.90 | (269) all_162_0_63 = all_160_0_62
% 9.94/2.90 |
% 9.94/2.90 | Instantiating formula (46) with all_13_0_9, all_56_0_25, all_134_0_49, all_162_0_63 and discharging atoms sdtpldt0(all_13_0_9, all_56_0_25) = all_162_0_63, sdtpldt0(all_13_0_9, all_56_0_25) = all_134_0_49, yields:
% 9.94/2.90 | (270) all_162_0_63 = all_134_0_49
% 9.94/2.90 |
% 9.94/2.90 | Instantiating formula (46) with all_13_0_9, all_56_0_25, all_104_0_39, all_160_0_62 and discharging atoms sdtpldt0(all_13_0_9, all_56_0_25) = all_160_0_62, sdtpldt0(all_13_0_9, all_56_0_25) = all_104_0_39, yields:
% 9.94/2.90 | (271) all_160_0_62 = all_104_0_39
% 9.94/2.90 |
% 9.94/2.90 | Combining equations (269,270) yields a new equation:
% 9.94/2.90 | (272) all_160_0_62 = all_134_0_49
% 9.94/2.90 |
% 9.94/2.90 | Simplifying 272 yields:
% 9.94/2.90 | (273) all_160_0_62 = all_134_0_49
% 9.94/2.90 |
% 9.94/2.90 | Combining equations (271,273) yields a new equation:
% 9.94/2.90 | (274) all_134_0_49 = all_104_0_39
% 9.94/2.90 |
% 9.94/2.90 | Combining equations (268,273) yields a new equation:
% 9.94/2.90 | (275) all_134_0_49 = all_108_0_41
% 9.94/2.90 |
% 9.94/2.90 | Combining equations (265,267) yields a new equation:
% 9.94/2.90 | (276) all_144_0_54 = all_108_0_41
% 9.94/2.90 |
% 9.94/2.90 | Simplifying 276 yields:
% 9.94/2.90 | (277) all_144_0_54 = all_108_0_41
% 9.94/2.90 |
% 9.94/2.90 | Combining equations (277,266) yields a new equation:
% 9.94/2.90 | (278) all_142_0_53 = all_108_0_41
% 9.94/2.90 |
% 9.94/2.90 | Combining equations (275,274) yields a new equation:
% 9.94/2.90 | (279) all_108_0_41 = all_104_0_39
% 9.94/2.90 |
% 9.94/2.90 | Simplifying 279 yields:
% 9.94/2.90 | (280) all_108_0_41 = all_104_0_39
% 9.94/2.90 |
% 9.94/2.90 | Combining equations (280,278) yields a new equation:
% 9.94/2.90 | (281) all_142_0_53 = all_104_0_39
% 9.94/2.90 |
% 9.94/2.90 | Combining equations (281,266) yields a new equation:
% 9.94/2.90 | (282) all_144_0_54 = all_104_0_39
% 9.94/2.90 |
% 9.94/2.90 | From (282) and (254) follows:
% 9.94/2.90 | (283) sdtpldt0(all_74_0_29, all_104_0_39) = all_0_0_0
% 9.94/2.90 |
% 9.94/2.90 | From (280) and (242) follows:
% 9.94/2.90 | (284) aElementOf0(all_104_0_39, xJ)
% 9.94/2.90 |
% 9.94/2.90 | Instantiating formula (3) with all_104_0_39, all_74_0_29, all_0_0_0, all_0_3_3, xJ, xI and discharging atoms sdtpldt1(xI, xJ) = all_0_3_3, sdtpldt0(all_74_0_29, all_104_0_39) = all_0_0_0, aElementOf0(all_104_0_39, xJ), aElementOf0(all_74_0_29, xI), aSet0(xJ), aSet0(xI), ~ aElementOf0(all_0_0_0, all_0_3_3), yields:
% 9.94/2.90 | (127) $false
% 9.94/2.90 |
% 9.94/2.90 |-The branch is then unsatisfiable
% 9.94/2.90 % SZS output end Proof for theBenchmark
% 9.94/2.90
% 9.94/2.90 2295ms
%------------------------------------------------------------------------------