TSTP Solution File: NUM471+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM471+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n004.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 08:44:50 EDT 2022
% Result : Theorem 35.68s 10.84s
% Output : Proof 57.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM471+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n004.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 : Tue Jul 5 20:17:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.70/0.97 Prover 0: Preprocessing ...
% 3.36/1.43 Prover 0: Constructing countermodel ...
% 18.97/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.06/6.01 Prover 1: Preprocessing ...
% 19.77/6.14 Prover 1: Constructing countermodel ...
% 26.14/7.63 Prover 1: gave up
% 26.14/7.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 26.14/7.67 Prover 2: Preprocessing ...
% 26.83/7.80 Prover 2: Warning: ignoring some quantifiers
% 26.99/7.81 Prover 2: Constructing countermodel ...
% 31.53/9.28 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 31.90/9.34 Prover 3: Preprocessing ...
% 31.90/9.40 Prover 3: Constructing countermodel ...
% 35.68/10.84 Prover 3: proved (1551ms)
% 35.68/10.84 Prover 2: stopped
% 35.68/10.84 Prover 0: stopped
% 35.68/10.84
% 35.68/10.84 No countermodel exists, formula is valid
% 35.68/10.84 % SZS status Theorem for theBenchmark
% 35.68/10.84
% 35.68/10.84 Generating proof ... found it (size 351)
% 57.10/21.53
% 57.10/21.53 % SZS output start Proof for theBenchmark
% 57.10/21.53 Assumed formulas after preprocessing and simplification:
% 57.10/21.53 | (0) ? [v0] : ( ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(v0, xl) = xq & sdtsldt0(xm, xl) = xp & sdtpldt0(xm, xn) = v0 & doDivides0(xl, v0) & doDivides0(xl, xm) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ sdtlseqdt0(xp, xq) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ~ (sdtpldt0(v4, v5) = v6) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (sdtasdt0(v7, v1) = v8 & sdtasdt0(v3, v1) = v10 & sdtasdt0(v2, v1) = v9 & sdtasdt0(v1, v7) = v6 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v2, v3) = v7)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | sdtlseqdt0(v4, v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v6] : ? [v7] : ( ~ (v7 = v6) & sdtasdt0(v3, v1) = v7 & sdtasdt0(v2, v1) = v6 & sdtlseqdt0(v6, v7))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v6] : ? [v7] : ( ~ (v7 = v6) & sdtasdt0(v3, v1) = v7 & sdtasdt0(v2, v1) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v1, v2) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v6] : ? [v7] : ( ~ (v7 = v6) & sdtpldt0(v3, v1) = v7 & sdtpldt0(v2, v1) = v6)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, v3) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v6] : (sdtasdt0(v2, v3) = v6 & sdtasdt0(v1, v6) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v4, v3) = v5) | ~ (sdtpldt0(v1, v2) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v6] : (sdtpldt0(v2, v3) = v6 & sdtpldt0(v1, v6) = v5)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | v1 = sz00 | ~ (sdtsldt0(v2, v1) = v3) | ~ (sdtasdt0(v1, v4) = v2) | ~ doDivides0(v1, v2) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (sdtmndt0(v2, v1) = v3) | ~ (sdtpldt0(v1, v4) = v2) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v4) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | v1 = sz00 | ~ (sdtsldt0(v2, v1) = v3) | ~ (sdtasdt0(v1, v3) = v4) | ~ doDivides0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (sdtmndt0(v2, v1) = v3) | ~ (sdtpldt0(v1, v3) = v4) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v1, v3) = v4) | ~ (sdtasdt0(v1, v2) = v4) | ~ sdtlseqdt0(v2, v3) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v1, v3) = v4) | ~ (sdtasdt0(v1, v2) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (sdtpldt0(v1, v3) = v4) | ~ (sdtpldt0(v1, v2) = v4) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtsldt0(v4, v3) = v2) | ~ (sdtsldt0(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtmndt0(v4, v3) = v2) | ~ (sdtmndt0(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtasdt0(v4, v3) = v2) | ~ (sdtasdt0(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v4, v3) = v2) | ~ (sdtpldt0(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v3) = v4) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v4) & ~ (v6 = v5) & sdtpldt0(v3, v2) = v6 & sdtpldt0(v3, v1) = v5 & sdtpldt0(v2, v3) = v7 & sdtlseqdt0(v5, v6) & sdtlseqdt0(v4, v7))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = sz00 | ~ (sdtsldt0(v2, v1) = v3) | ~ (sdtasdt0(v1, v3) = v4) | ~ doDivides0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | aNaturalNumber0(v3)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtmndt0(v2, v1) = v3) | ~ (sdtpldt0(v1, v3) = v4) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | aNaturalNumber0(v3)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ doDivides0(v1, v3) | ~ doDivides0(v1, v2) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | doDivides0(v1, v4)) & ! [v1] : ! [v2] : ! [v3] : (v1 = sz00 | ~ (sdtasdt0(v2, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | sdtlseqdt0(v2, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v1, v3) = v2) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | doDivides0(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | sdtasdt0(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | aNaturalNumber0(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v3) = v2) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | sdtlseqdt0(v1, v2)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | sdtpldt0(v2, v1) = v3) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | aNaturalNumber0(v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ doDivides0(v2, v3) | ~ doDivides0(v1, v2) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | doDivides0(v1, v3)) & ! [v1] : ! [v2] : ! [v3] : ( ~ sdtlseqdt0(v2, v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | sdtlseqdt0(v1, v3)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (sdtasdt0(sz10, v1) = v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ (sdtpldt0(sz00, v1) = v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ sdtlseqdt0(v2, v1) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : (v2 = v1 | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | iLess0(v1, v2)) & ! [v1] : ! [v2] : (v2 = sz00 | v1 = sz00 | ~ (sdtasdt0(v1, v2) = sz00) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtasdt0(sz00, v1) = v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v1, v2) = sz00) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : (v1 = sz00 | ~ (sdtpldt0(v1, v2) = sz00) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1)) & ! [v1] : ! [v2] : ( ~ (sdtasdt0(sz10, v1) = v2) | ~ aNaturalNumber0(v1) | sdtasdt0(v1, sz10) = v1) & ! [v1] : ! [v2] : ( ~ (sdtasdt0(sz00, v1) = v2) | ~ aNaturalNumber0(v1) | sdtasdt0(v1, sz00) = sz00) & ! [v1] : ! [v2] : ( ~ (sdtpldt0(sz00, v1) = v2) | ~ aNaturalNumber0(v1) | sdtpldt0(v1, sz00) = v1) & ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v3] : (sdtasdt0(v1, v3) = v2 & aNaturalNumber0(v3))) & ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ? [v3] : (sdtpldt0(v1, v3) = v2 & aNaturalNumber0(v3))) & ! [v1] : ! [v2] : ( ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | sdtlseqdt0(v2, v1) | sdtlseqdt0(v1, v2)) & ! [v1] : (v1 = sz10 | v1 = sz00 | ~ aNaturalNumber0(v1) | sdtlseqdt0(sz10, v1)) & ! [v1] : ( ~ aNaturalNumber0(v1) | sdtlseqdt0(v1, v1)))
% 57.38/21.58 | Instantiating (0) with all_0_0_0 yields:
% 57.38/21.58 | (1) ~ (xl = sz00) & ~ (sz10 = sz00) & sdtsldt0(all_0_0_0, xl) = xq & sdtsldt0(xm, xl) = xp & sdtpldt0(xm, xn) = all_0_0_0 & doDivides0(xl, all_0_0_0) & doDivides0(xl, xm) & aNaturalNumber0(xn) & aNaturalNumber0(xm) & aNaturalNumber0(xl) & aNaturalNumber0(sz10) & aNaturalNumber0(sz00) & ~ sdtlseqdt0(xp, xq) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(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] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(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] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1)) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0) & ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2))) & ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0)) & ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 57.47/21.60 |
% 57.47/21.60 | Applying alpha-rule on (1) yields:
% 57.47/21.60 | (2) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | iLess0(v0, v1))
% 57.47/21.60 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5))
% 57.47/21.60 | (4) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0))
% 57.47/21.60 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.47/21.61 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4))
% 57.47/21.61 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(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))
% 57.47/21.61 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v2))
% 57.47/21.61 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 57.47/21.61 | (10) ~ (xl = sz00)
% 57.47/21.61 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.47/21.61 | (12) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz00) = sz00)
% 57.47/21.61 | (13) sdtsldt0(xm, xl) = xp
% 57.47/21.61 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 57.47/21.61 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 57.47/21.61 | (16) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.47/21.61 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 57.47/21.61 | (18) aNaturalNumber0(xm)
% 57.47/21.61 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 57.47/21.61 | (20) ~ (sz10 = sz00)
% 57.47/21.61 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 57.47/21.61 | (22) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v0, sz10) = v0)
% 57.47/21.61 | (23) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v0, sz00) = v0)
% 57.47/21.61 | (24) ! [v0] : ! [v1] : ( ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1))
% 57.47/21.61 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtpldt0(v1, v0) = v2)
% 57.47/21.61 | (26) aNaturalNumber0(sz00)
% 57.47/21.61 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v3) = v1) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v3) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.47/21.61 | (28) ! [v0] : ! [v1] : ( ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 57.47/21.61 | (29) sdtpldt0(xm, xn) = all_0_0_0
% 57.47/21.61 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5))
% 57.47/21.61 | (31) doDivides0(xl, xm)
% 57.47/21.61 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (sdtpldt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.47/21.61 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 57.47/21.61 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0))
% 57.47/21.61 | (35) ! [v0] : ( ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 57.47/21.61 | (36) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtasdt0(sz00, v0) = v1) | ~ aNaturalNumber0(v0))
% 57.47/21.61 | (37) ! [v0] : ! [v1] : ! [v2] : (v0 = sz00 | ~ (sdtasdt0(v1, v0) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v2))
% 57.47/21.61 | (38) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.47/21.61 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v3, v4))
% 57.47/21.62 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 57.47/21.62 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : ? [v6] : ( ~ (v6 = v5) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtlseqdt0(v5, v6)))
% 57.47/21.62 | (42) aNaturalNumber0(sz10)
% 57.47/21.62 | (43) doDivides0(xl, all_0_0_0)
% 57.47/21.62 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtasdt0(v1, v0) = v2)
% 57.47/21.62 | (45) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.47/21.62 | (46) ~ sdtlseqdt0(xp, xq)
% 57.47/21.62 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ doDivides0(v0, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v3))
% 57.47/21.62 | (48) aNaturalNumber0(xn)
% 57.47/21.62 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ doDivides0(v1, v2) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v2))
% 57.47/21.62 | (50) ! [v0] : (v0 = sz10 | v0 = sz00 | ~ aNaturalNumber0(v0) | sdtlseqdt0(sz10, v0))
% 57.47/21.62 | (51) aNaturalNumber0(xl)
% 57.47/21.62 | (52) sdtsldt0(all_0_0_0, xl) = xq
% 57.47/21.62 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v1) = v5 & sdtpldt0(v2, v0) = v4 & sdtpldt0(v1, v2) = v6 & sdtlseqdt0(v4, v5) & sdtlseqdt0(v3, v6)))
% 57.47/21.62 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ sdtlseqdt0(v1, v2) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.55/21.62 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v0 = sz00 | ~ (sdtsldt0(v1, v0) = v2) | ~ (sdtasdt0(v0, v2) = v3) | ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.55/21.62 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.55/21.62 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0))
% 57.55/21.62 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v5] : (sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4))
% 57.55/21.62 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v2) = v1) | ~ aNaturalNumber0(v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v1))
% 57.55/21.62 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | aNaturalNumber0(v2))
% 57.55/21.62 | (61) ! [v0] : ! [v1] : ( ~ doDivides0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2] : (sdtasdt0(v0, v2) = v1 & aNaturalNumber0(v2)))
% 57.55/21.62 |
% 57.55/21.62 | Instantiating formula (24) with xn, xn and discharging atoms aNaturalNumber0(xn), yields:
% 57.55/21.62 | (62) sdtlseqdt0(xn, xn)
% 57.55/21.62 |
% 57.55/21.62 | Instantiating formula (25) with all_0_0_0, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_0_0, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.62 | (63) sdtpldt0(xn, xm) = all_0_0_0
% 57.55/21.62 |
% 57.55/21.62 | Instantiating formula (60) with all_0_0_0, xn, xm and discharging atoms sdtpldt0(xm, xn) = all_0_0_0, aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.62 | (64) aNaturalNumber0(all_0_0_0)
% 57.55/21.62 |
% 57.55/21.62 | Instantiating formula (61) with xm, xl and discharging atoms doDivides0(xl, xm), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 57.55/21.62 | (65) ? [v0] : (sdtasdt0(xl, v0) = xm & aNaturalNumber0(v0))
% 57.55/21.62 |
% 57.55/21.62 | Instantiating formula (24) with xm, xm and discharging atoms aNaturalNumber0(xm), yields:
% 57.55/21.62 | (66) sdtlseqdt0(xm, xm)
% 57.55/21.62 |
% 57.55/21.62 | Instantiating formula (25) with all_0_0_0, sz00, xm and discharging atoms aNaturalNumber0(xm), aNaturalNumber0(sz00), yields:
% 57.55/21.62 | (67) ~ (sdtpldt0(xm, sz00) = all_0_0_0) | sdtpldt0(sz00, xm) = all_0_0_0
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (24) with sz00, sz00 and discharging atoms aNaturalNumber0(sz00), yields:
% 57.55/21.63 | (68) sdtlseqdt0(sz00, sz00)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating (65) with all_9_0_1 yields:
% 57.55/21.63 | (69) sdtasdt0(xl, all_9_0_1) = xm & aNaturalNumber0(all_9_0_1)
% 57.55/21.63 |
% 57.55/21.63 | Applying alpha-rule on (69) yields:
% 57.55/21.63 | (70) sdtasdt0(xl, all_9_0_1) = xm
% 57.55/21.63 | (71) aNaturalNumber0(all_9_0_1)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (16) with xm, xn and discharging atoms aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.63 | (72) xn = sz00 | ~ (sdtpldt0(xn, xm) = sz00)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (19) with all_0_0_0, xm and discharging atoms aNaturalNumber0(xm), yields:
% 57.55/21.63 | (73) all_0_0_0 = xm | ~ (sdtpldt0(sz00, xm) = all_0_0_0)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (27) with all_9_0_1, xp, xm, xl and discharging atoms sdtsldt0(xm, xl) = xp, sdtasdt0(xl, all_9_0_1) = xm, doDivides0(xl, xm), aNaturalNumber0(all_9_0_1), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 57.55/21.63 | (74) all_9_0_1 = xp | xl = sz00
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (55) with xm, xq, all_0_0_0, xl and discharging atoms sdtsldt0(all_0_0_0, xl) = xq, doDivides0(xl, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 57.55/21.63 | (75) all_0_0_0 = xm | xl = sz00 | ~ (sdtasdt0(xl, xq) = xm)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (28) with xn, xn and discharging atoms sdtlseqdt0(xn, xn), aNaturalNumber0(xn), yields:
% 57.55/21.63 | (76) ? [v0] : (sdtpldt0(xn, v0) = xn & aNaturalNumber0(v0))
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (28) with xm, xm and discharging atoms sdtlseqdt0(xm, xm), aNaturalNumber0(xm), yields:
% 57.55/21.63 | (77) ? [v0] : (sdtpldt0(xm, v0) = xm & aNaturalNumber0(v0))
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (28) with sz00, sz00 and discharging atoms sdtlseqdt0(sz00, sz00), aNaturalNumber0(sz00), yields:
% 57.55/21.63 | (78) ? [v0] : (sdtpldt0(sz00, v0) = sz00 & aNaturalNumber0(v0))
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (59) with xn, all_0_0_0, xm and discharging atoms sdtpldt0(xm, xn) = all_0_0_0, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.63 | (79) sdtlseqdt0(xm, all_0_0_0)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (59) with xm, all_0_0_0, xn and discharging atoms sdtpldt0(xn, xm) = all_0_0_0, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.63 | (80) sdtlseqdt0(xn, all_0_0_0)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (61) with all_0_0_0, xl and discharging atoms doDivides0(xl, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 57.55/21.63 | (81) ? [v0] : (sdtasdt0(xl, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (24) with all_9_0_1, all_9_0_1 and discharging atoms aNaturalNumber0(all_9_0_1), yields:
% 57.55/21.63 | (82) sdtlseqdt0(all_9_0_1, all_9_0_1)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (24) with all_0_0_0, all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), yields:
% 57.55/21.63 | (83) sdtlseqdt0(all_0_0_0, all_0_0_0)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating (81) with all_17_0_2 yields:
% 57.55/21.63 | (84) sdtasdt0(xl, all_17_0_2) = all_0_0_0 & aNaturalNumber0(all_17_0_2)
% 57.55/21.63 |
% 57.55/21.63 | Applying alpha-rule on (84) yields:
% 57.55/21.63 | (85) sdtasdt0(xl, all_17_0_2) = all_0_0_0
% 57.55/21.63 | (86) aNaturalNumber0(all_17_0_2)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating (78) with all_19_0_3 yields:
% 57.55/21.63 | (87) sdtpldt0(sz00, all_19_0_3) = sz00 & aNaturalNumber0(all_19_0_3)
% 57.55/21.63 |
% 57.55/21.63 | Applying alpha-rule on (87) yields:
% 57.55/21.63 | (88) sdtpldt0(sz00, all_19_0_3) = sz00
% 57.55/21.63 | (89) aNaturalNumber0(all_19_0_3)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating (77) with all_25_0_6 yields:
% 57.55/21.63 | (90) sdtpldt0(xm, all_25_0_6) = xm & aNaturalNumber0(all_25_0_6)
% 57.55/21.63 |
% 57.55/21.63 | Applying alpha-rule on (90) yields:
% 57.55/21.63 | (91) sdtpldt0(xm, all_25_0_6) = xm
% 57.55/21.63 | (92) aNaturalNumber0(all_25_0_6)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating (76) with all_27_0_7 yields:
% 57.55/21.63 | (93) sdtpldt0(xn, all_27_0_7) = xn & aNaturalNumber0(all_27_0_7)
% 57.55/21.63 |
% 57.55/21.63 | Applying alpha-rule on (93) yields:
% 57.55/21.63 | (94) sdtpldt0(xn, all_27_0_7) = xn
% 57.55/21.63 | (95) aNaturalNumber0(all_27_0_7)
% 57.55/21.63 |
% 57.55/21.63 +-Applying beta-rule and splitting (74), into two cases.
% 57.55/21.63 |-Branch one:
% 57.55/21.63 | (96) xl = sz00
% 57.55/21.63 |
% 57.55/21.63 | Equations (96) can reduce 10 to:
% 57.55/21.63 | (97) $false
% 57.55/21.63 |
% 57.55/21.63 |-The branch is then unsatisfiable
% 57.55/21.63 |-Branch two:
% 57.55/21.63 | (10) ~ (xl = sz00)
% 57.55/21.63 | (99) all_9_0_1 = xp
% 57.55/21.63 |
% 57.55/21.63 | From (99) and (70) follows:
% 57.55/21.63 | (100) sdtasdt0(xl, xp) = xm
% 57.55/21.63 |
% 57.55/21.63 | From (99)(99) and (82) follows:
% 57.55/21.63 | (101) sdtlseqdt0(xp, xp)
% 57.55/21.63 |
% 57.55/21.63 | From (99) and (71) follows:
% 57.55/21.63 | (102) aNaturalNumber0(xp)
% 57.55/21.63 |
% 57.55/21.63 | Using (101) and (46) yields:
% 57.55/21.63 | (103) ~ (xq = xp)
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (27) with all_17_0_2, xq, all_0_0_0, xl and discharging atoms sdtsldt0(all_0_0_0, xl) = xq, sdtasdt0(xl, all_17_0_2) = all_0_0_0, doDivides0(xl, all_0_0_0), aNaturalNumber0(all_17_0_2), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 57.55/21.63 | (104) all_17_0_2 = xq | xl = sz00
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (19) with sz00, all_19_0_3 and discharging atoms sdtpldt0(sz00, all_19_0_3) = sz00, aNaturalNumber0(all_19_0_3), yields:
% 57.55/21.63 | (105) all_19_0_3 = sz00
% 57.55/21.63 |
% 57.55/21.63 | Instantiating formula (27) with xp, xq, all_0_0_0, xl and discharging atoms sdtsldt0(all_0_0_0, xl) = xq, doDivides0(xl, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 57.55/21.64 | (106) xq = xp | xl = sz00 | ~ (sdtasdt0(xl, xp) = all_0_0_0)
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (56) with xm, all_17_0_2, xp, xl and discharging atoms sdtasdt0(xl, xp) = xm, aNaturalNumber0(all_17_0_2), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 57.55/21.64 | (107) all_17_0_2 = xp | xl = sz00 | ~ (sdtasdt0(xl, all_17_0_2) = xm)
% 57.55/21.64 |
% 57.55/21.64 | From (105) and (89) follows:
% 57.55/21.64 | (26) aNaturalNumber0(sz00)
% 57.55/21.64 |
% 57.55/21.64 +-Applying beta-rule and splitting (104), into two cases.
% 57.55/21.64 |-Branch one:
% 57.55/21.64 | (96) xl = sz00
% 57.55/21.64 |
% 57.55/21.64 | Equations (96) can reduce 10 to:
% 57.55/21.64 | (97) $false
% 57.55/21.64 |
% 57.55/21.64 |-The branch is then unsatisfiable
% 57.55/21.64 |-Branch two:
% 57.55/21.64 | (10) ~ (xl = sz00)
% 57.55/21.64 | (112) all_17_0_2 = xq
% 57.55/21.64 |
% 57.55/21.64 | From (112) and (85) follows:
% 57.55/21.64 | (113) sdtasdt0(xl, xq) = all_0_0_0
% 57.55/21.64 |
% 57.55/21.64 | From (112) and (86) follows:
% 57.55/21.64 | (114) aNaturalNumber0(xq)
% 57.55/21.64 |
% 57.55/21.64 +-Applying beta-rule and splitting (107), into two cases.
% 57.55/21.64 |-Branch one:
% 57.55/21.64 | (115) ~ (sdtasdt0(xl, all_17_0_2) = xm)
% 57.55/21.64 |
% 57.55/21.64 | From (112) and (115) follows:
% 57.55/21.64 | (116) ~ (sdtasdt0(xl, xq) = xm)
% 57.55/21.64 |
% 57.55/21.64 | Using (113) and (116) yields:
% 57.55/21.64 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.64 |
% 57.55/21.64 +-Applying beta-rule and splitting (73), into two cases.
% 57.55/21.64 |-Branch one:
% 57.55/21.64 | (118) ~ (sdtpldt0(sz00, xm) = all_0_0_0)
% 57.55/21.64 |
% 57.55/21.64 +-Applying beta-rule and splitting (67), into two cases.
% 57.55/21.64 |-Branch one:
% 57.55/21.64 | (119) ~ (sdtpldt0(xm, sz00) = all_0_0_0)
% 57.55/21.64 |
% 57.55/21.64 | Using (29) and (119) yields:
% 57.55/21.64 | (120) ~ (xn = sz00)
% 57.55/21.64 |
% 57.55/21.64 +-Applying beta-rule and splitting (72), into two cases.
% 57.55/21.64 |-Branch one:
% 57.55/21.64 | (121) ~ (sdtpldt0(xn, xm) = sz00)
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (44) with all_0_0_0, sz00, xl and discharging atoms aNaturalNumber0(xl), aNaturalNumber0(sz00), yields:
% 57.55/21.64 | (122) ~ (sdtasdt0(xl, sz00) = all_0_0_0) | sdtasdt0(sz00, xl) = all_0_0_0
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (28) with all_0_0_0, all_0_0_0 and discharging atoms sdtlseqdt0(all_0_0_0, all_0_0_0), aNaturalNumber0(all_0_0_0), yields:
% 57.55/21.64 | (123) ? [v0] : (sdtpldt0(all_0_0_0, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (28) with all_0_0_0, xn and discharging atoms sdtlseqdt0(xn, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), yields:
% 57.55/21.64 | (124) ? [v0] : (sdtpldt0(xn, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (28) with all_0_0_0, xm and discharging atoms sdtlseqdt0(xm, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.64 | (125) ? [v0] : (sdtpldt0(xm, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (28) with all_0_0_0, xl and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(xl), yields:
% 57.55/21.64 | (126) ~ sdtlseqdt0(xl, all_0_0_0) | ? [v0] : (sdtpldt0(xl, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (53) with all_0_0_0, xn, all_0_0_0, xm and discharging atoms sdtpldt0(xm, xn) = all_0_0_0, sdtlseqdt0(xm, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.64 | (127) all_0_0_0 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_0_0) & ~ (v1 = v0) & sdtpldt0(all_0_0_0, xn) = v2 & sdtpldt0(xn, all_0_0_0) = v1 & sdtpldt0(xn, xm) = v0 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (37) with all_0_0_0, xl, xq and discharging atoms sdtasdt0(xl, xq) = all_0_0_0, aNaturalNumber0(xq), aNaturalNumber0(xl), yields:
% 57.55/21.64 | (128) xq = sz00 | sdtlseqdt0(xl, all_0_0_0)
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (6) with all_0_0_0, xn, xm, all_27_0_7, xn and discharging atoms sdtpldt0(xn, all_27_0_7) = xn, sdtpldt0(xn, xm) = all_0_0_0, aNaturalNumber0(all_27_0_7), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.64 | (129) ? [v0] : (sdtpldt0(all_27_0_7, xm) = v0 & sdtpldt0(xn, v0) = all_0_0_0)
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (6) with all_0_0_0, xm, xn, all_25_0_6, xm and discharging atoms sdtpldt0(xm, all_25_0_6) = xm, sdtpldt0(xm, xn) = all_0_0_0, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.64 | (130) ? [v0] : (sdtpldt0(all_25_0_6, xn) = v0 & sdtpldt0(xm, v0) = all_0_0_0)
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (6) with xn, xn, all_27_0_7, all_27_0_7, xn and discharging atoms sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(xn), yields:
% 57.55/21.64 | (131) ? [v0] : (sdtpldt0(all_27_0_7, all_27_0_7) = v0 & sdtpldt0(xn, v0) = xn)
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (25) with xn, all_27_0_7, xn and discharging atoms sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(xn), yields:
% 57.55/21.64 | (132) sdtpldt0(all_27_0_7, xn) = xn
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (53) with xm, all_25_0_6, all_0_0_0, xm and discharging atoms sdtpldt0(xm, all_25_0_6) = xm, sdtlseqdt0(xm, all_0_0_0), aNaturalNumber0(all_25_0_6), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.64 | (133) all_0_0_0 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xm) & ~ (v1 = v0) & sdtpldt0(all_25_0_6, all_0_0_0) = v1 & sdtpldt0(all_25_0_6, xm) = v0 & sdtpldt0(all_0_0_0, all_25_0_6) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (25) with xm, all_25_0_6, xm and discharging atoms sdtpldt0(xm, all_25_0_6) = xm, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xm), yields:
% 57.55/21.64 | (134) sdtpldt0(all_25_0_6, xm) = xm
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (6) with xm, xm, all_25_0_6, all_25_0_6, xm and discharging atoms sdtpldt0(xm, all_25_0_6) = xm, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xm), yields:
% 57.55/21.64 | (135) ? [v0] : (sdtpldt0(all_25_0_6, all_25_0_6) = v0 & sdtpldt0(xm, v0) = xm)
% 57.55/21.64 |
% 57.55/21.64 | Instantiating formula (24) with xp, xq and discharging atoms aNaturalNumber0(xq), aNaturalNumber0(xp), ~ sdtlseqdt0(xp, xq), yields:
% 57.55/21.64 | (136) sdtlseqdt0(xq, xp)
% 57.55/21.64 |
% 57.55/21.64 | Instantiating (131) with all_99_0_8 yields:
% 57.55/21.65 | (137) sdtpldt0(all_27_0_7, all_27_0_7) = all_99_0_8 & sdtpldt0(xn, all_99_0_8) = xn
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (137) yields:
% 57.55/21.65 | (138) sdtpldt0(all_27_0_7, all_27_0_7) = all_99_0_8
% 57.55/21.65 | (139) sdtpldt0(xn, all_99_0_8) = xn
% 57.55/21.65 |
% 57.55/21.65 | Instantiating (130) with all_103_0_10 yields:
% 57.55/21.65 | (140) sdtpldt0(all_25_0_6, xn) = all_103_0_10 & sdtpldt0(xm, all_103_0_10) = all_0_0_0
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (140) yields:
% 57.55/21.65 | (141) sdtpldt0(all_25_0_6, xn) = all_103_0_10
% 57.55/21.65 | (142) sdtpldt0(xm, all_103_0_10) = all_0_0_0
% 57.55/21.65 |
% 57.55/21.65 | Instantiating (135) with all_105_0_11 yields:
% 57.55/21.65 | (143) sdtpldt0(all_25_0_6, all_25_0_6) = all_105_0_11 & sdtpldt0(xm, all_105_0_11) = xm
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (143) yields:
% 57.55/21.65 | (144) sdtpldt0(all_25_0_6, all_25_0_6) = all_105_0_11
% 57.55/21.65 | (145) sdtpldt0(xm, all_105_0_11) = xm
% 57.55/21.65 |
% 57.55/21.65 | Instantiating (129) with all_107_0_12 yields:
% 57.55/21.65 | (146) sdtpldt0(all_27_0_7, xm) = all_107_0_12 & sdtpldt0(xn, all_107_0_12) = all_0_0_0
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (146) yields:
% 57.55/21.65 | (147) sdtpldt0(all_27_0_7, xm) = all_107_0_12
% 57.55/21.65 | (148) sdtpldt0(xn, all_107_0_12) = all_0_0_0
% 57.55/21.65 |
% 57.55/21.65 | Instantiating (125) with all_111_0_14 yields:
% 57.55/21.65 | (149) sdtpldt0(xm, all_111_0_14) = all_0_0_0 & aNaturalNumber0(all_111_0_14)
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (149) yields:
% 57.55/21.65 | (150) sdtpldt0(xm, all_111_0_14) = all_0_0_0
% 57.55/21.65 | (151) aNaturalNumber0(all_111_0_14)
% 57.55/21.65 |
% 57.55/21.65 | Instantiating (124) with all_115_0_16 yields:
% 57.55/21.65 | (152) sdtpldt0(xn, all_115_0_16) = all_0_0_0 & aNaturalNumber0(all_115_0_16)
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (152) yields:
% 57.55/21.65 | (153) sdtpldt0(xn, all_115_0_16) = all_0_0_0
% 57.55/21.65 | (154) aNaturalNumber0(all_115_0_16)
% 57.55/21.65 |
% 57.55/21.65 | Instantiating (123) with all_117_0_17 yields:
% 57.55/21.65 | (155) sdtpldt0(all_0_0_0, all_117_0_17) = all_0_0_0 & aNaturalNumber0(all_117_0_17)
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (155) yields:
% 57.55/21.65 | (156) sdtpldt0(all_0_0_0, all_117_0_17) = all_0_0_0
% 57.55/21.65 | (157) aNaturalNumber0(all_117_0_17)
% 57.55/21.65 |
% 57.55/21.65 +-Applying beta-rule and splitting (133), into two cases.
% 57.55/21.65 |-Branch one:
% 57.55/21.65 | (158) all_0_0_0 = xm
% 57.55/21.65 |
% 57.55/21.65 | Equations (158) can reduce 117 to:
% 57.55/21.65 | (97) $false
% 57.55/21.65 |
% 57.55/21.65 |-The branch is then unsatisfiable
% 57.55/21.65 |-Branch two:
% 57.55/21.65 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.65 | (161) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xm) & ~ (v1 = v0) & sdtpldt0(all_25_0_6, all_0_0_0) = v1 & sdtpldt0(all_25_0_6, xm) = v0 & sdtpldt0(all_0_0_0, all_25_0_6) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 57.55/21.65 |
% 57.55/21.65 | Instantiating (161) with all_126_0_18, all_126_1_19, all_126_2_20 yields:
% 57.55/21.65 | (162) ~ (all_126_0_18 = xm) & ~ (all_126_1_19 = all_126_2_20) & sdtpldt0(all_25_0_6, all_0_0_0) = all_126_1_19 & sdtpldt0(all_25_0_6, xm) = all_126_2_20 & sdtpldt0(all_0_0_0, all_25_0_6) = all_126_0_18 & sdtlseqdt0(all_126_2_20, all_126_1_19) & sdtlseqdt0(xm, all_126_0_18)
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (162) yields:
% 57.55/21.65 | (163) sdtpldt0(all_0_0_0, all_25_0_6) = all_126_0_18
% 57.55/21.65 | (164) sdtlseqdt0(all_126_2_20, all_126_1_19)
% 57.55/21.65 | (165) ~ (all_126_0_18 = xm)
% 57.55/21.65 | (166) sdtpldt0(all_25_0_6, xm) = all_126_2_20
% 57.55/21.65 | (167) sdtlseqdt0(xm, all_126_0_18)
% 57.55/21.65 | (168) sdtpldt0(all_25_0_6, all_0_0_0) = all_126_1_19
% 57.55/21.65 | (169) ~ (all_126_1_19 = all_126_2_20)
% 57.55/21.65 |
% 57.55/21.65 +-Applying beta-rule and splitting (127), into two cases.
% 57.55/21.65 |-Branch one:
% 57.55/21.65 | (158) all_0_0_0 = xm
% 57.55/21.65 |
% 57.55/21.65 | Equations (158) can reduce 117 to:
% 57.55/21.65 | (97) $false
% 57.55/21.65 |
% 57.55/21.65 |-The branch is then unsatisfiable
% 57.55/21.65 |-Branch two:
% 57.55/21.65 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.65 | (173) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_0_0) & ~ (v1 = v0) & sdtpldt0(all_0_0_0, xn) = v2 & sdtpldt0(xn, all_0_0_0) = v1 & sdtpldt0(xn, xm) = v0 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 57.55/21.65 |
% 57.55/21.65 | Instantiating (173) with all_140_0_22, all_140_1_23, all_140_2_24 yields:
% 57.55/21.65 | (174) ~ (all_140_0_22 = all_0_0_0) & ~ (all_140_1_23 = all_140_2_24) & sdtpldt0(all_0_0_0, xn) = all_140_0_22 & sdtpldt0(xn, all_0_0_0) = all_140_1_23 & sdtpldt0(xn, xm) = all_140_2_24 & sdtlseqdt0(all_140_2_24, all_140_1_23) & sdtlseqdt0(all_0_0_0, all_140_0_22)
% 57.55/21.65 |
% 57.55/21.65 | Applying alpha-rule on (174) yields:
% 57.55/21.65 | (175) sdtpldt0(all_0_0_0, xn) = all_140_0_22
% 57.55/21.65 | (176) sdtpldt0(xn, all_0_0_0) = all_140_1_23
% 57.55/21.65 | (177) ~ (all_140_1_23 = all_140_2_24)
% 57.55/21.65 | (178) ~ (all_140_0_22 = all_0_0_0)
% 57.55/21.65 | (179) sdtlseqdt0(all_140_2_24, all_140_1_23)
% 57.55/21.65 | (180) sdtlseqdt0(all_0_0_0, all_140_0_22)
% 57.55/21.65 | (181) sdtpldt0(xn, xm) = all_140_2_24
% 57.55/21.65 |
% 57.55/21.65 | Instantiating formula (36) with all_0_0_0, xl and discharging atoms aNaturalNumber0(xl), yields:
% 57.55/21.65 | (182) all_0_0_0 = sz00 | ~ (sdtasdt0(sz00, xl) = all_0_0_0)
% 57.55/21.65 |
% 57.55/21.65 | Instantiating formula (17) with all_25_0_6, xm, all_126_2_20, all_107_0_12 and discharging atoms sdtpldt0(all_25_0_6, xm) = all_126_2_20, yields:
% 57.55/21.65 | (183) all_126_2_20 = all_107_0_12 | ~ (sdtpldt0(all_25_0_6, xm) = all_107_0_12)
% 57.55/21.65 |
% 57.55/21.65 | Instantiating formula (17) with all_25_0_6, xm, xm, all_126_2_20 and discharging atoms sdtpldt0(all_25_0_6, xm) = all_126_2_20, sdtpldt0(all_25_0_6, xm) = xm, yields:
% 57.55/21.65 | (184) all_126_2_20 = xm
% 57.55/21.65 |
% 57.55/21.65 | Instantiating formula (32) with xn, all_27_0_7, all_25_0_6, xn and discharging atoms sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), yields:
% 57.55/21.65 | (185) all_27_0_7 = all_25_0_6 | ~ (sdtpldt0(xn, all_25_0_6) = xn)
% 57.55/21.65 |
% 57.55/21.65 | Instantiating formula (17) with xn, xm, all_140_2_24, all_0_0_0 and discharging atoms sdtpldt0(xn, xm) = all_140_2_24, sdtpldt0(xn, xm) = all_0_0_0, yields:
% 57.55/21.65 | (186) all_140_2_24 = all_0_0_0
% 57.55/21.65 |
% 57.55/21.66 | Using (181) and (121) yields:
% 57.55/21.66 | (187) ~ (all_140_2_24 = sz00)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (32) with xn, all_27_0_7, all_99_0_8, xn and discharging atoms sdtpldt0(xn, all_99_0_8) = xn, sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(xn), yields:
% 57.55/21.66 | (188) all_99_0_8 = all_27_0_7 | ~ aNaturalNumber0(all_99_0_8)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (32) with all_0_0_0, xm, all_115_0_16, xn and discharging atoms sdtpldt0(xn, all_115_0_16) = all_0_0_0, sdtpldt0(xn, xm) = all_0_0_0, aNaturalNumber0(all_115_0_16), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.66 | (189) all_115_0_16 = xm
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (32) with xm, all_25_0_6, all_105_0_11, xm and discharging atoms sdtpldt0(xm, all_105_0_11) = xm, sdtpldt0(xm, all_25_0_6) = xm, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xm), yields:
% 57.55/21.66 | (190) all_105_0_11 = all_25_0_6 | ~ aNaturalNumber0(all_105_0_11)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (32) with all_0_0_0, xn, all_111_0_14, xm and discharging atoms sdtpldt0(xm, all_111_0_14) = all_0_0_0, sdtpldt0(xm, xn) = all_0_0_0, aNaturalNumber0(all_111_0_14), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.66 | (191) all_111_0_14 = xn
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (32) with all_0_0_0, all_111_0_14, all_103_0_10, xm and discharging atoms sdtpldt0(xm, all_111_0_14) = all_0_0_0, sdtpldt0(xm, all_103_0_10) = all_0_0_0, aNaturalNumber0(all_111_0_14), aNaturalNumber0(xm), yields:
% 57.55/21.66 | (192) all_111_0_14 = all_103_0_10 | ~ aNaturalNumber0(all_103_0_10)
% 57.55/21.66 |
% 57.55/21.66 | Equations (186) can reduce 187 to:
% 57.55/21.66 | (193) ~ (all_0_0_0 = sz00)
% 57.55/21.66 |
% 57.55/21.66 | From (184) and (166) follows:
% 57.55/21.66 | (134) sdtpldt0(all_25_0_6, xm) = xm
% 57.55/21.66 |
% 57.55/21.66 | From (189) and (154) follows:
% 57.55/21.66 | (18) aNaturalNumber0(xm)
% 57.55/21.66 |
% 57.55/21.66 | From (191) and (151) follows:
% 57.55/21.66 | (48) aNaturalNumber0(xn)
% 57.55/21.66 |
% 57.55/21.66 +-Applying beta-rule and splitting (182), into two cases.
% 57.55/21.66 |-Branch one:
% 57.55/21.66 | (197) ~ (sdtasdt0(sz00, xl) = all_0_0_0)
% 57.55/21.66 |
% 57.55/21.66 +-Applying beta-rule and splitting (122), into two cases.
% 57.55/21.66 |-Branch one:
% 57.55/21.66 | (198) ~ (sdtasdt0(xl, sz00) = all_0_0_0)
% 57.55/21.66 |
% 57.55/21.66 | Using (113) and (198) yields:
% 57.55/21.66 | (199) ~ (xq = sz00)
% 57.55/21.66 |
% 57.55/21.66 +-Applying beta-rule and splitting (128), into two cases.
% 57.55/21.66 |-Branch one:
% 57.55/21.66 | (200) sdtlseqdt0(xl, all_0_0_0)
% 57.55/21.66 |
% 57.55/21.66 +-Applying beta-rule and splitting (126), into two cases.
% 57.55/21.66 |-Branch one:
% 57.55/21.66 | (201) ~ sdtlseqdt0(xl, all_0_0_0)
% 57.55/21.66 |
% 57.55/21.66 | Using (200) and (201) yields:
% 57.55/21.66 | (202) $false
% 57.55/21.66 |
% 57.55/21.66 |-The branch is then unsatisfiable
% 57.55/21.66 |-Branch two:
% 57.55/21.66 | (200) sdtlseqdt0(xl, all_0_0_0)
% 57.55/21.66 | (204) ? [v0] : (sdtpldt0(xl, v0) = all_0_0_0 & aNaturalNumber0(v0))
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (60) with all_99_0_8, all_27_0_7, all_27_0_7 and discharging atoms sdtpldt0(all_27_0_7, all_27_0_7) = all_99_0_8, aNaturalNumber0(all_27_0_7), yields:
% 57.55/21.66 | (205) aNaturalNumber0(all_99_0_8)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (60) with all_107_0_12, xm, all_27_0_7 and discharging atoms sdtpldt0(all_27_0_7, xm) = all_107_0_12, aNaturalNumber0(all_27_0_7), aNaturalNumber0(xm), yields:
% 57.55/21.66 | (206) aNaturalNumber0(all_107_0_12)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (60) with all_105_0_11, all_25_0_6, all_25_0_6 and discharging atoms sdtpldt0(all_25_0_6, all_25_0_6) = all_105_0_11, aNaturalNumber0(all_25_0_6), yields:
% 57.55/21.66 | (207) aNaturalNumber0(all_105_0_11)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (25) with all_103_0_10, xn, all_25_0_6 and discharging atoms sdtpldt0(all_25_0_6, xn) = all_103_0_10, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), yields:
% 57.55/21.66 | (208) sdtpldt0(xn, all_25_0_6) = all_103_0_10
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (60) with all_103_0_10, xn, all_25_0_6 and discharging atoms sdtpldt0(all_25_0_6, xn) = all_103_0_10, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), yields:
% 57.55/21.66 | (209) aNaturalNumber0(all_103_0_10)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (6) with xm, xm, all_27_0_7, xm, all_25_0_6 and discharging atoms sdtpldt0(all_25_0_6, xm) = xm, aNaturalNumber0(all_27_0_7), aNaturalNumber0(all_25_0_6), aNaturalNumber0(xm), yields:
% 57.55/21.66 | (210) ~ (sdtpldt0(xm, all_27_0_7) = xm) | ? [v0] : (sdtpldt0(all_25_0_6, v0) = xm & sdtpldt0(xm, all_27_0_7) = v0)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (3) with xn, xn, all_27_0_7, all_25_0_6, xn and discharging atoms sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), yields:
% 57.55/21.66 | (211) all_27_0_7 = all_25_0_6 | ~ (sdtpldt0(xn, all_25_0_6) = xn) | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_27_0_7, xn) = v1 & sdtpldt0(all_25_0_6, xn) = v0)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (3) with xn, xn, all_25_0_6, all_27_0_7, xn and discharging atoms sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), yields:
% 57.55/21.66 | (212) all_27_0_7 = all_25_0_6 | ~ (sdtpldt0(xn, all_25_0_6) = xn) | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_27_0_7, xn) = v0 & sdtpldt0(all_25_0_6, xn) = v1)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (6) with xn, xn, all_25_0_6, all_27_0_7, xn and discharging atoms sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), yields:
% 57.55/21.66 | (213) ~ (sdtpldt0(xn, all_25_0_6) = xn) | ? [v0] : (sdtpldt0(all_27_0_7, all_25_0_6) = v0 & sdtpldt0(xn, v0) = xn)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (6) with xn, xn, all_27_0_7, all_25_0_6, xn and discharging atoms sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), yields:
% 57.55/21.66 | (214) ~ (sdtpldt0(xn, all_25_0_6) = xn) | ? [v0] : (sdtpldt0(all_25_0_6, all_27_0_7) = v0 & sdtpldt0(xn, v0) = xn)
% 57.55/21.66 |
% 57.55/21.66 | Instantiating formula (53) with xm, all_27_0_7, all_0_0_0, xm and discharging atoms sdtlseqdt0(xm, all_0_0_0), aNaturalNumber0(all_27_0_7), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.66 | (215) all_0_0_0 = xm | ~ (sdtpldt0(xm, all_27_0_7) = xm) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xm) & ~ (v1 = v0) & sdtpldt0(all_27_0_7, all_0_0_0) = v1 & sdtpldt0(all_27_0_7, xm) = v0 & sdtpldt0(all_0_0_0, all_27_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (53) with all_126_0_18, all_25_0_6, xm, all_0_0_0 and discharging atoms sdtpldt0(all_0_0_0, all_25_0_6) = all_126_0_18, aNaturalNumber0(all_25_0_6), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.67 | (216) all_0_0_0 = xm | ~ sdtlseqdt0(all_0_0_0, xm) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_126_0_18) & ~ (v1 = v0) & sdtpldt0(all_25_0_6, all_0_0_0) = v0 & sdtpldt0(all_25_0_6, xm) = v1 & sdtpldt0(xm, all_25_0_6) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_126_0_18, v2))
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (8) with xm, all_0_0_0, xn and discharging atoms sdtlseqdt0(xn, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.67 | (217) ~ sdtlseqdt0(all_0_0_0, xm) | sdtlseqdt0(xn, xm)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (2) with xm, all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.67 | (218) all_0_0_0 = xm | ~ sdtlseqdt0(all_0_0_0, xm) | iLess0(all_0_0_0, xm)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (28) with xm, all_0_0_0 and discharging atoms aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.67 | (219) ~ sdtlseqdt0(all_0_0_0, xm) | ? [v0] : (sdtpldt0(all_0_0_0, v0) = xm & aNaturalNumber0(v0))
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (53) with all_140_0_22, xn, xm, all_0_0_0 and discharging atoms sdtpldt0(all_0_0_0, xn) = all_140_0_22, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), aNaturalNumber0(xm), yields:
% 57.55/21.67 | (220) all_0_0_0 = xm | ~ sdtlseqdt0(all_0_0_0, xm) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_140_0_22) & ~ (v1 = v0) & sdtpldt0(xn, all_0_0_0) = v0 & sdtpldt0(xn, xm) = v1 & sdtpldt0(xm, xn) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_140_0_22, v2))
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (39) with xm, all_0_0_0, xp, xq, xl and discharging atoms sdtasdt0(xl, xq) = all_0_0_0, sdtasdt0(xl, xp) = xm, sdtlseqdt0(xq, xp), aNaturalNumber0(xq), aNaturalNumber0(xp), aNaturalNumber0(xl), yields:
% 57.55/21.67 | (221) xq = xp | xl = sz00 | sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (8) with xm, all_0_0_0, xl and discharging atoms sdtlseqdt0(xl, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), aNaturalNumber0(xl), yields:
% 57.55/21.67 | (222) ~ sdtlseqdt0(all_0_0_0, xm) | sdtlseqdt0(xl, xm)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (6) with all_126_0_18, all_0_0_0, all_25_0_6, all_107_0_12, xn and discharging atoms sdtpldt0(all_0_0_0, all_25_0_6) = all_126_0_18, sdtpldt0(xn, all_107_0_12) = all_0_0_0, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xn), yields:
% 57.55/21.67 | (223) ~ aNaturalNumber0(all_107_0_12) | ? [v0] : (sdtpldt0(all_107_0_12, all_25_0_6) = v0 & sdtpldt0(xn, v0) = all_126_0_18)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (6) with all_126_0_18, all_0_0_0, all_25_0_6, all_103_0_10, xm and discharging atoms sdtpldt0(all_0_0_0, all_25_0_6) = all_126_0_18, sdtpldt0(xm, all_103_0_10) = all_0_0_0, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xm), yields:
% 57.55/21.67 | (224) ~ aNaturalNumber0(all_103_0_10) | ? [v0] : (sdtpldt0(all_103_0_10, all_25_0_6) = v0 & sdtpldt0(xm, v0) = all_126_0_18)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (6) with all_140_0_22, all_0_0_0, xn, all_107_0_12, xn and discharging atoms sdtpldt0(all_0_0_0, xn) = all_140_0_22, sdtpldt0(xn, all_107_0_12) = all_0_0_0, aNaturalNumber0(xn), yields:
% 57.55/21.67 | (225) ~ aNaturalNumber0(all_107_0_12) | ? [v0] : (sdtpldt0(all_107_0_12, xn) = v0 & sdtpldt0(xn, v0) = all_140_0_22)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (6) with all_0_0_0, xn, all_107_0_12, all_27_0_7, xn and discharging atoms sdtpldt0(xn, all_107_0_12) = all_0_0_0, sdtpldt0(xn, all_27_0_7) = xn, aNaturalNumber0(all_27_0_7), aNaturalNumber0(xn), yields:
% 57.55/21.67 | (226) ~ aNaturalNumber0(all_107_0_12) | ? [v0] : (sdtpldt0(all_27_0_7, all_107_0_12) = v0 & sdtpldt0(xn, v0) = all_0_0_0)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (6) with all_0_0_0, xn, all_107_0_12, xn, all_27_0_7 and discharging atoms sdtpldt0(all_27_0_7, xn) = xn, sdtpldt0(xn, all_107_0_12) = all_0_0_0, aNaturalNumber0(all_27_0_7), aNaturalNumber0(xn), yields:
% 57.55/21.67 | (227) ~ aNaturalNumber0(all_107_0_12) | ? [v0] : (sdtpldt0(all_27_0_7, v0) = all_0_0_0 & sdtpldt0(xn, all_107_0_12) = v0)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (3) with all_0_0_0, all_140_1_23, all_107_0_12, all_0_0_0, xn and discharging atoms sdtpldt0(xn, all_107_0_12) = all_0_0_0, sdtpldt0(xn, all_0_0_0) = all_140_1_23, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), yields:
% 57.55/21.67 | (228) all_107_0_12 = all_0_0_0 | ~ aNaturalNumber0(all_107_0_12) | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_107_0_12, xn) = v1 & sdtpldt0(all_0_0_0, xn) = v0)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (3) with all_140_1_23, all_0_0_0, all_0_0_0, all_107_0_12, xn and discharging atoms sdtpldt0(xn, all_107_0_12) = all_0_0_0, sdtpldt0(xn, all_0_0_0) = all_140_1_23, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), yields:
% 57.55/21.67 | (229) all_107_0_12 = all_0_0_0 | ~ aNaturalNumber0(all_107_0_12) | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_107_0_12, xn) = v0 & sdtpldt0(all_0_0_0, xn) = v1)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (6) with all_140_1_23, xn, all_0_0_0, all_99_0_8, xn and discharging atoms sdtpldt0(xn, all_99_0_8) = xn, sdtpldt0(xn, all_0_0_0) = all_140_1_23, aNaturalNumber0(all_0_0_0), aNaturalNumber0(xn), yields:
% 57.55/21.67 | (230) ~ aNaturalNumber0(all_99_0_8) | ? [v0] : (sdtpldt0(all_99_0_8, all_0_0_0) = v0 & sdtpldt0(xn, v0) = all_140_1_23)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (6) with xm, xm, all_105_0_11, all_25_0_6, xm and discharging atoms sdtpldt0(xm, all_105_0_11) = xm, sdtpldt0(xm, all_25_0_6) = xm, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xm), yields:
% 57.55/21.67 | (231) ~ aNaturalNumber0(all_105_0_11) | ? [v0] : (sdtpldt0(all_25_0_6, all_105_0_11) = v0 & sdtpldt0(xm, v0) = xm)
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (53) with xm, all_105_0_11, all_0_0_0, xm and discharging atoms sdtpldt0(xm, all_105_0_11) = xm, sdtlseqdt0(xm, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.67 | (232) all_0_0_0 = xm | ~ aNaturalNumber0(all_105_0_11) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xm) & ~ (v1 = v0) & sdtpldt0(all_105_0_11, all_0_0_0) = v1 & sdtpldt0(all_105_0_11, xm) = v0 & sdtpldt0(all_0_0_0, all_105_0_11) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 57.55/21.67 |
% 57.55/21.67 | Instantiating formula (25) with xm, all_105_0_11, xm and discharging atoms sdtpldt0(xm, all_105_0_11) = xm, aNaturalNumber0(xm), yields:
% 57.55/21.67 | (233) ~ aNaturalNumber0(all_105_0_11) | sdtpldt0(all_105_0_11, xm) = xm
% 57.55/21.68 |
% 57.55/21.68 | Instantiating formula (3) with all_0_0_0, xm, all_103_0_10, all_25_0_6, xm and discharging atoms sdtpldt0(xm, all_103_0_10) = all_0_0_0, sdtpldt0(xm, all_25_0_6) = xm, aNaturalNumber0(all_25_0_6), aNaturalNumber0(xm), yields:
% 57.55/21.68 | (234) all_103_0_10 = all_25_0_6 | ~ aNaturalNumber0(all_103_0_10) | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_103_0_10, xm) = v1 & sdtpldt0(all_25_0_6, xm) = v0)
% 57.55/21.68 |
% 57.55/21.68 | Instantiating formula (53) with all_0_0_0, all_103_0_10, all_0_0_0, xm and discharging atoms sdtpldt0(xm, all_103_0_10) = all_0_0_0, sdtlseqdt0(xm, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.68 | (235) all_0_0_0 = xm | ~ aNaturalNumber0(all_103_0_10) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_0_0) & ~ (v1 = v0) & sdtpldt0(all_103_0_10, all_0_0_0) = v1 & sdtpldt0(all_103_0_10, xm) = v0 & sdtpldt0(all_0_0_0, all_103_0_10) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 57.55/21.68 |
% 57.55/21.68 | Instantiating formula (25) with all_0_0_0, all_103_0_10, xm and discharging atoms sdtpldt0(xm, all_103_0_10) = all_0_0_0, aNaturalNumber0(xm), yields:
% 57.55/21.68 | (236) ~ aNaturalNumber0(all_103_0_10) | sdtpldt0(all_103_0_10, xm) = all_0_0_0
% 57.55/21.68 |
% 57.55/21.68 | Instantiating formula (6) with all_0_0_0, all_0_0_0, all_117_0_17, all_107_0_12, xn and discharging atoms sdtpldt0(all_0_0_0, all_117_0_17) = all_0_0_0, sdtpldt0(xn, all_107_0_12) = all_0_0_0, aNaturalNumber0(all_117_0_17), aNaturalNumber0(xn), yields:
% 57.55/21.68 | (237) ~ aNaturalNumber0(all_107_0_12) | ? [v0] : (sdtpldt0(all_107_0_12, all_117_0_17) = v0 & sdtpldt0(xn, v0) = all_0_0_0)
% 57.55/21.68 |
% 57.55/21.68 | Instantiating formula (6) with all_0_0_0, all_0_0_0, all_117_0_17, all_103_0_10, xm and discharging atoms sdtpldt0(all_0_0_0, all_117_0_17) = all_0_0_0, sdtpldt0(xm, all_103_0_10) = all_0_0_0, aNaturalNumber0(all_117_0_17), aNaturalNumber0(xm), yields:
% 57.55/21.68 | (238) ~ aNaturalNumber0(all_103_0_10) | ? [v0] : (sdtpldt0(all_103_0_10, all_117_0_17) = v0 & sdtpldt0(xm, v0) = all_0_0_0)
% 57.55/21.68 |
% 57.55/21.68 | Instantiating formula (53) with all_0_0_0, all_117_0_17, xm, all_0_0_0 and discharging atoms sdtpldt0(all_0_0_0, all_117_0_17) = all_0_0_0, aNaturalNumber0(all_117_0_17), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.68 | (239) all_0_0_0 = xm | ~ sdtlseqdt0(all_0_0_0, xm) | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_0_0) & ~ (v1 = v0) & sdtpldt0(all_117_0_17, all_0_0_0) = v0 & sdtpldt0(all_117_0_17, xm) = v1 & sdtpldt0(xm, all_117_0_17) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 57.55/21.68 |
% 57.55/21.68 +-Applying beta-rule and splitting (236), into two cases.
% 57.55/21.68 |-Branch one:
% 57.55/21.68 | (240) ~ aNaturalNumber0(all_103_0_10)
% 57.55/21.68 |
% 57.55/21.68 | Using (209) and (240) yields:
% 57.55/21.68 | (202) $false
% 57.55/21.68 |
% 57.55/21.68 |-The branch is then unsatisfiable
% 57.55/21.68 |-Branch two:
% 57.55/21.68 | (209) aNaturalNumber0(all_103_0_10)
% 57.55/21.68 | (243) sdtpldt0(all_103_0_10, xm) = all_0_0_0
% 57.55/21.68 |
% 57.55/21.68 +-Applying beta-rule and splitting (237), into two cases.
% 57.55/21.68 |-Branch one:
% 57.55/21.68 | (244) ~ aNaturalNumber0(all_107_0_12)
% 57.55/21.68 |
% 57.55/21.68 | Using (206) and (244) yields:
% 57.55/21.68 | (202) $false
% 57.55/21.68 |
% 57.55/21.68 |-The branch is then unsatisfiable
% 57.55/21.68 |-Branch two:
% 57.55/21.68 | (206) aNaturalNumber0(all_107_0_12)
% 57.55/21.68 | (247) ? [v0] : (sdtpldt0(all_107_0_12, all_117_0_17) = v0 & sdtpldt0(xn, v0) = all_0_0_0)
% 57.55/21.68 |
% 57.55/21.68 +-Applying beta-rule and splitting (238), into two cases.
% 57.55/21.68 |-Branch one:
% 57.55/21.68 | (240) ~ aNaturalNumber0(all_103_0_10)
% 57.55/21.68 |
% 57.55/21.68 | Using (209) and (240) yields:
% 57.55/21.68 | (202) $false
% 57.55/21.68 |
% 57.55/21.68 |-The branch is then unsatisfiable
% 57.55/21.68 |-Branch two:
% 57.55/21.68 | (209) aNaturalNumber0(all_103_0_10)
% 57.55/21.68 | (251) ? [v0] : (sdtpldt0(all_103_0_10, all_117_0_17) = v0 & sdtpldt0(xm, v0) = all_0_0_0)
% 57.55/21.68 |
% 57.55/21.68 +-Applying beta-rule and splitting (223), into two cases.
% 57.55/21.68 |-Branch one:
% 57.55/21.68 | (244) ~ aNaturalNumber0(all_107_0_12)
% 57.55/21.68 |
% 57.55/21.68 | Using (206) and (244) yields:
% 57.55/21.68 | (202) $false
% 57.55/21.68 |
% 57.55/21.68 |-The branch is then unsatisfiable
% 57.55/21.68 |-Branch two:
% 57.55/21.68 | (206) aNaturalNumber0(all_107_0_12)
% 57.55/21.68 | (255) ? [v0] : (sdtpldt0(all_107_0_12, all_25_0_6) = v0 & sdtpldt0(xn, v0) = all_126_0_18)
% 57.55/21.68 |
% 57.55/21.68 +-Applying beta-rule and splitting (224), into two cases.
% 57.55/21.68 |-Branch one:
% 57.55/21.68 | (240) ~ aNaturalNumber0(all_103_0_10)
% 57.55/21.68 |
% 57.55/21.68 | Using (209) and (240) yields:
% 57.55/21.68 | (202) $false
% 57.55/21.68 |
% 57.55/21.68 |-The branch is then unsatisfiable
% 57.55/21.68 |-Branch two:
% 57.55/21.68 | (209) aNaturalNumber0(all_103_0_10)
% 57.55/21.68 | (259) ? [v0] : (sdtpldt0(all_103_0_10, all_25_0_6) = v0 & sdtpldt0(xm, v0) = all_126_0_18)
% 57.55/21.68 |
% 57.55/21.68 +-Applying beta-rule and splitting (192), into two cases.
% 57.55/21.68 |-Branch one:
% 57.55/21.68 | (240) ~ aNaturalNumber0(all_103_0_10)
% 57.55/21.68 |
% 57.55/21.68 | Using (209) and (240) yields:
% 57.55/21.68 | (202) $false
% 57.55/21.68 |
% 57.55/21.68 |-The branch is then unsatisfiable
% 57.55/21.68 |-Branch two:
% 57.55/21.68 | (209) aNaturalNumber0(all_103_0_10)
% 57.55/21.68 | (263) all_111_0_14 = all_103_0_10
% 57.55/21.68 |
% 57.55/21.68 | Combining equations (263,191) yields a new equation:
% 57.55/21.68 | (264) all_103_0_10 = xn
% 57.55/21.68 |
% 57.55/21.68 | Simplifying 264 yields:
% 57.55/21.68 | (265) all_103_0_10 = xn
% 57.55/21.68 |
% 57.55/21.68 | From (265) and (208) follows:
% 57.55/21.68 | (266) sdtpldt0(xn, all_25_0_6) = xn
% 57.55/21.68 |
% 57.55/21.68 | From (265) and (209) follows:
% 57.55/21.68 | (48) aNaturalNumber0(xn)
% 57.55/21.68 |
% 57.55/21.68 +-Applying beta-rule and splitting (211), into two cases.
% 57.55/21.68 |-Branch one:
% 57.55/21.68 | (268) ~ (sdtpldt0(xn, all_25_0_6) = xn)
% 57.55/21.68 |
% 57.55/21.68 | Using (266) and (268) yields:
% 57.55/21.68 | (202) $false
% 57.55/21.68 |
% 57.55/21.68 |-The branch is then unsatisfiable
% 57.55/21.68 |-Branch two:
% 57.55/21.68 | (266) sdtpldt0(xn, all_25_0_6) = xn
% 57.55/21.68 | (271) all_27_0_7 = all_25_0_6 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_27_0_7, xn) = v1 & sdtpldt0(all_25_0_6, xn) = v0)
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (212), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (268) ~ (sdtpldt0(xn, all_25_0_6) = xn)
% 57.55/21.69 |
% 57.55/21.69 | Using (266) and (268) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (266) sdtpldt0(xn, all_25_0_6) = xn
% 57.55/21.69 | (275) all_27_0_7 = all_25_0_6 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_27_0_7, xn) = v0 & sdtpldt0(all_25_0_6, xn) = v1)
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (214), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (268) ~ (sdtpldt0(xn, all_25_0_6) = xn)
% 57.55/21.69 |
% 57.55/21.69 | Using (266) and (268) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (266) sdtpldt0(xn, all_25_0_6) = xn
% 57.55/21.69 | (279) ? [v0] : (sdtpldt0(all_25_0_6, all_27_0_7) = v0 & sdtpldt0(xn, v0) = xn)
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (275), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (280) all_27_0_7 = all_25_0_6
% 57.55/21.69 |
% 57.55/21.69 | From (280) and (147) follows:
% 57.55/21.69 | (281) sdtpldt0(all_25_0_6, xm) = all_107_0_12
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (233), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (282) ~ aNaturalNumber0(all_105_0_11)
% 57.55/21.69 |
% 57.55/21.69 | Using (207) and (282) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (207) aNaturalNumber0(all_105_0_11)
% 57.55/21.69 | (285) sdtpldt0(all_105_0_11, xm) = xm
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (183), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (286) ~ (sdtpldt0(all_25_0_6, xm) = all_107_0_12)
% 57.55/21.69 |
% 57.55/21.69 | Using (281) and (286) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (281) sdtpldt0(all_25_0_6, xm) = all_107_0_12
% 57.55/21.69 | (289) all_126_2_20 = all_107_0_12
% 57.55/21.69 |
% 57.55/21.69 | Combining equations (289,184) yields a new equation:
% 57.55/21.69 | (290) all_107_0_12 = xm
% 57.55/21.69 |
% 57.55/21.69 | Simplifying 290 yields:
% 57.55/21.69 | (291) all_107_0_12 = xm
% 57.55/21.69 |
% 57.55/21.69 | From (291) and (206) follows:
% 57.55/21.69 | (18) aNaturalNumber0(xm)
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (234), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (240) ~ aNaturalNumber0(all_103_0_10)
% 57.55/21.69 |
% 57.55/21.69 | From (265) and (240) follows:
% 57.55/21.69 | (294) ~ aNaturalNumber0(xn)
% 57.55/21.69 |
% 57.55/21.69 | Using (48) and (294) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (209) aNaturalNumber0(all_103_0_10)
% 57.55/21.69 | (297) all_103_0_10 = all_25_0_6 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_103_0_10, xm) = v1 & sdtpldt0(all_25_0_6, xm) = v0)
% 57.55/21.69 |
% 57.55/21.69 | From (265) and (209) follows:
% 57.55/21.69 | (48) aNaturalNumber0(xn)
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (231), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (282) ~ aNaturalNumber0(all_105_0_11)
% 57.55/21.69 |
% 57.55/21.69 | Using (207) and (282) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (207) aNaturalNumber0(all_105_0_11)
% 57.55/21.69 | (302) ? [v0] : (sdtpldt0(all_25_0_6, all_105_0_11) = v0 & sdtpldt0(xm, v0) = xm)
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (230), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (303) ~ aNaturalNumber0(all_99_0_8)
% 57.55/21.69 |
% 57.55/21.69 | Using (205) and (303) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (205) aNaturalNumber0(all_99_0_8)
% 57.55/21.69 | (306) ? [v0] : (sdtpldt0(all_99_0_8, all_0_0_0) = v0 & sdtpldt0(xn, v0) = all_140_1_23)
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (190), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (282) ~ aNaturalNumber0(all_105_0_11)
% 57.55/21.69 |
% 57.55/21.69 | Using (207) and (282) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (207) aNaturalNumber0(all_105_0_11)
% 57.55/21.69 | (310) all_105_0_11 = all_25_0_6
% 57.55/21.69 |
% 57.55/21.69 | From (310) and (145) follows:
% 57.55/21.69 | (91) sdtpldt0(xm, all_25_0_6) = xm
% 57.55/21.69 |
% 57.55/21.69 +-Applying beta-rule and splitting (225), into two cases.
% 57.55/21.69 |-Branch one:
% 57.55/21.69 | (244) ~ aNaturalNumber0(all_107_0_12)
% 57.55/21.69 |
% 57.55/21.69 | From (291) and (244) follows:
% 57.55/21.69 | (313) ~ aNaturalNumber0(xm)
% 57.55/21.69 |
% 57.55/21.69 | Using (18) and (313) yields:
% 57.55/21.69 | (202) $false
% 57.55/21.69 |
% 57.55/21.69 |-The branch is then unsatisfiable
% 57.55/21.69 |-Branch two:
% 57.55/21.69 | (206) aNaturalNumber0(all_107_0_12)
% 57.55/21.69 | (316) ? [v0] : (sdtpldt0(all_107_0_12, xn) = v0 & sdtpldt0(xn, v0) = all_140_0_22)
% 57.55/21.69 |
% 57.55/21.69 | From (291) and (206) follows:
% 57.55/21.69 | (18) aNaturalNumber0(xm)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (188), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (303) ~ aNaturalNumber0(all_99_0_8)
% 57.55/21.70 |
% 57.55/21.70 | Using (205) and (303) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (205) aNaturalNumber0(all_99_0_8)
% 57.55/21.70 | (321) all_99_0_8 = all_27_0_7
% 57.55/21.70 |
% 57.55/21.70 | Combining equations (280,321) yields a new equation:
% 57.55/21.70 | (322) all_99_0_8 = all_25_0_6
% 57.55/21.70 |
% 57.55/21.70 | From (322) and (205) follows:
% 57.55/21.70 | (92) aNaturalNumber0(all_25_0_6)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (232), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (282) ~ aNaturalNumber0(all_105_0_11)
% 57.55/21.70 |
% 57.55/21.70 | From (310) and (282) follows:
% 57.55/21.70 | (325) ~ aNaturalNumber0(all_25_0_6)
% 57.55/21.70 |
% 57.55/21.70 | Using (92) and (325) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (207) aNaturalNumber0(all_105_0_11)
% 57.55/21.70 | (328) all_0_0_0 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xm) & ~ (v1 = v0) & sdtpldt0(all_105_0_11, all_0_0_0) = v1 & sdtpldt0(all_105_0_11, xm) = v0 & sdtpldt0(all_0_0_0, all_105_0_11) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (235), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (240) ~ aNaturalNumber0(all_103_0_10)
% 57.55/21.70 |
% 57.55/21.70 | From (265) and (240) follows:
% 57.55/21.70 | (294) ~ aNaturalNumber0(xn)
% 57.55/21.70 |
% 57.55/21.70 | Using (48) and (294) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (209) aNaturalNumber0(all_103_0_10)
% 57.55/21.70 | (333) all_0_0_0 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_0_0) & ~ (v1 = v0) & sdtpldt0(all_103_0_10, all_0_0_0) = v1 & sdtpldt0(all_103_0_10, xm) = v0 & sdtpldt0(all_0_0_0, all_103_0_10) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (221), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (334) sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (218), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (335) ~ sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (334) and (335) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (334) sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 | (338) all_0_0_0 = xm | iLess0(all_0_0_0, xm)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (333), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (158) all_0_0_0 = xm
% 57.55/21.70 |
% 57.55/21.70 | Equations (158) can reduce 117 to:
% 57.55/21.70 | (97) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.70 | (342) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_0_0) & ~ (v1 = v0) & sdtpldt0(all_103_0_10, all_0_0_0) = v1 & sdtpldt0(all_103_0_10, xm) = v0 & sdtpldt0(all_0_0_0, all_103_0_10) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (219), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (335) ~ sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (334) and (335) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (334) sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 | (346) ? [v0] : (sdtpldt0(all_0_0_0, v0) = xm & aNaturalNumber0(v0))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (239), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (335) ~ sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (334) and (335) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (334) sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 | (350) all_0_0_0 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_0_0) & ~ (v1 = v0) & sdtpldt0(all_117_0_17, all_0_0_0) = v0 & sdtpldt0(all_117_0_17, xm) = v1 & sdtpldt0(xm, all_117_0_17) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (350), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (158) all_0_0_0 = xm
% 57.55/21.70 |
% 57.55/21.70 | Equations (158) can reduce 117 to:
% 57.55/21.70 | (97) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.70 | (354) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_0_0_0) & ~ (v1 = v0) & sdtpldt0(all_117_0_17, all_0_0_0) = v0 & sdtpldt0(all_117_0_17, xm) = v1 & sdtpldt0(xm, all_117_0_17) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_0_0_0, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (328), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (158) all_0_0_0 = xm
% 57.55/21.70 |
% 57.55/21.70 | Equations (158) can reduce 117 to:
% 57.55/21.70 | (97) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.70 | (358) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xm) & ~ (v1 = v0) & sdtpldt0(all_105_0_11, all_0_0_0) = v1 & sdtpldt0(all_105_0_11, xm) = v0 & sdtpldt0(all_0_0_0, all_105_0_11) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (210), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (359) ~ (sdtpldt0(xm, all_27_0_7) = xm)
% 57.55/21.70 |
% 57.55/21.70 | From (280) and (359) follows:
% 57.55/21.70 | (360) ~ (sdtpldt0(xm, all_25_0_6) = xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (91) and (360) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (362) sdtpldt0(xm, all_27_0_7) = xm
% 57.55/21.70 | (363) ? [v0] : (sdtpldt0(all_25_0_6, v0) = xm & sdtpldt0(xm, all_27_0_7) = v0)
% 57.55/21.70 |
% 57.55/21.70 | From (280) and (362) follows:
% 57.55/21.70 | (91) sdtpldt0(xm, all_25_0_6) = xm
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (226), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (244) ~ aNaturalNumber0(all_107_0_12)
% 57.55/21.70 |
% 57.55/21.70 | From (291) and (244) follows:
% 57.55/21.70 | (313) ~ aNaturalNumber0(xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (18) and (313) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (206) aNaturalNumber0(all_107_0_12)
% 57.55/21.70 | (369) ? [v0] : (sdtpldt0(all_27_0_7, all_107_0_12) = v0 & sdtpldt0(xn, v0) = all_0_0_0)
% 57.55/21.70 |
% 57.55/21.70 | From (291) and (206) follows:
% 57.55/21.70 | (18) aNaturalNumber0(xm)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (215), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (359) ~ (sdtpldt0(xm, all_27_0_7) = xm)
% 57.55/21.70 |
% 57.55/21.70 | From (280) and (359) follows:
% 57.55/21.70 | (360) ~ (sdtpldt0(xm, all_25_0_6) = xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (91) and (360) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (362) sdtpldt0(xm, all_27_0_7) = xm
% 57.55/21.70 | (375) all_0_0_0 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xm) & ~ (v1 = v0) & sdtpldt0(all_27_0_7, all_0_0_0) = v1 & sdtpldt0(all_27_0_7, xm) = v0 & sdtpldt0(all_0_0_0, all_27_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (375), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (158) all_0_0_0 = xm
% 57.55/21.70 |
% 57.55/21.70 | Equations (158) can reduce 117 to:
% 57.55/21.70 | (97) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.70 | (379) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = xm) & ~ (v1 = v0) & sdtpldt0(all_27_0_7, all_0_0_0) = v1 & sdtpldt0(all_27_0_7, xm) = v0 & sdtpldt0(all_0_0_0, all_27_0_7) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(xm, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (229), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (244) ~ aNaturalNumber0(all_107_0_12)
% 57.55/21.70 |
% 57.55/21.70 | From (291) and (244) follows:
% 57.55/21.70 | (313) ~ aNaturalNumber0(xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (18) and (313) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (206) aNaturalNumber0(all_107_0_12)
% 57.55/21.70 | (384) all_107_0_12 = all_0_0_0 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_107_0_12, xn) = v0 & sdtpldt0(all_0_0_0, xn) = v1)
% 57.55/21.70 |
% 57.55/21.70 | From (291) and (206) follows:
% 57.55/21.70 | (18) aNaturalNumber0(xm)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (384), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (386) all_107_0_12 = all_0_0_0
% 57.55/21.70 |
% 57.55/21.70 | Combining equations (291,386) yields a new equation:
% 57.55/21.70 | (158) all_0_0_0 = xm
% 57.55/21.70 |
% 57.55/21.70 | Equations (158) can reduce 117 to:
% 57.55/21.70 | (97) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (389) ~ (all_107_0_12 = all_0_0_0)
% 57.55/21.70 | (390) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_107_0_12, xn) = v0 & sdtpldt0(all_0_0_0, xn) = v1)
% 57.55/21.70 |
% 57.55/21.70 | Equations (291) can reduce 389 to:
% 57.55/21.70 | (391) ~ (all_0_0_0 = xm)
% 57.55/21.70 |
% 57.55/21.70 | Simplifying 391 yields:
% 57.55/21.70 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (216), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (335) ~ sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (334) and (335) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (334) sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 | (396) all_0_0_0 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_126_0_18) & ~ (v1 = v0) & sdtpldt0(all_25_0_6, all_0_0_0) = v0 & sdtpldt0(all_25_0_6, xm) = v1 & sdtpldt0(xm, all_25_0_6) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_126_0_18, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (217), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (335) ~ sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (334) and (335) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (334) sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.70 | (400) sdtlseqdt0(xn, xm)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (227), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (244) ~ aNaturalNumber0(all_107_0_12)
% 57.55/21.70 |
% 57.55/21.70 | From (291) and (244) follows:
% 57.55/21.70 | (313) ~ aNaturalNumber0(xm)
% 57.55/21.70 |
% 57.55/21.70 | Using (18) and (313) yields:
% 57.55/21.70 | (202) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (206) aNaturalNumber0(all_107_0_12)
% 57.55/21.70 | (405) ? [v0] : (sdtpldt0(all_27_0_7, v0) = all_0_0_0 & sdtpldt0(xn, all_107_0_12) = v0)
% 57.55/21.70 |
% 57.55/21.70 | From (291) and (206) follows:
% 57.55/21.70 | (18) aNaturalNumber0(xm)
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (396), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (158) all_0_0_0 = xm
% 57.55/21.70 |
% 57.55/21.70 | Equations (158) can reduce 117 to:
% 57.55/21.70 | (97) $false
% 57.55/21.70 |
% 57.55/21.70 |-The branch is then unsatisfiable
% 57.55/21.70 |-Branch two:
% 57.55/21.70 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.70 | (410) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_126_0_18) & ~ (v1 = v0) & sdtpldt0(all_25_0_6, all_0_0_0) = v0 & sdtpldt0(all_25_0_6, xm) = v1 & sdtpldt0(xm, all_25_0_6) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_126_0_18, v2))
% 57.55/21.70 |
% 57.55/21.70 +-Applying beta-rule and splitting (220), into two cases.
% 57.55/21.70 |-Branch one:
% 57.55/21.70 | (335) ~ sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.71 |
% 57.55/21.71 | Using (334) and (335) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (334) sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.71 | (414) all_0_0_0 = xm | ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_140_0_22) & ~ (v1 = v0) & sdtpldt0(xn, all_0_0_0) = v0 & sdtpldt0(xn, xm) = v1 & sdtpldt0(xm, xn) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_140_0_22, v2))
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (222), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (335) ~ sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.71 |
% 57.55/21.71 | Using (334) and (335) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (334) sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.71 | (418) sdtlseqdt0(xl, xm)
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (414), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (158) all_0_0_0 = xm
% 57.55/21.71 |
% 57.55/21.71 | Equations (158) can reduce 117 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.71 | (422) ? [v0] : ? [v1] : ? [v2] : ( ~ (v2 = all_140_0_22) & ~ (v1 = v0) & sdtpldt0(xn, all_0_0_0) = v0 & sdtpldt0(xn, xm) = v1 & sdtpldt0(xm, xn) = v2 & sdtlseqdt0(v0, v1) & sdtlseqdt0(all_140_0_22, v2))
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (228), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (244) ~ aNaturalNumber0(all_107_0_12)
% 57.55/21.71 |
% 57.55/21.71 | From (291) and (244) follows:
% 57.55/21.71 | (313) ~ aNaturalNumber0(xm)
% 57.55/21.71 |
% 57.55/21.71 | Using (18) and (313) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (206) aNaturalNumber0(all_107_0_12)
% 57.55/21.71 | (427) all_107_0_12 = all_0_0_0 | ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_107_0_12, xn) = v1 & sdtpldt0(all_0_0_0, xn) = v0)
% 57.55/21.71 |
% 57.55/21.71 | From (291) and (206) follows:
% 57.55/21.71 | (18) aNaturalNumber0(xm)
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (427), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (386) all_107_0_12 = all_0_0_0
% 57.55/21.71 |
% 57.55/21.71 | Combining equations (291,386) yields a new equation:
% 57.55/21.71 | (158) all_0_0_0 = xm
% 57.55/21.71 |
% 57.55/21.71 | Equations (158) can reduce 117 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (389) ~ (all_107_0_12 = all_0_0_0)
% 57.55/21.71 | (433) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_107_0_12, xn) = v1 & sdtpldt0(all_0_0_0, xn) = v0)
% 57.55/21.71 |
% 57.55/21.71 | Equations (291) can reduce 389 to:
% 57.55/21.71 | (391) ~ (all_0_0_0 = xm)
% 57.55/21.71 |
% 57.55/21.71 | Simplifying 391 yields:
% 57.55/21.71 | (117) ~ (all_0_0_0 = xm)
% 57.55/21.71 |
% 57.55/21.71 | Instantiating formula (5) with all_0_0_0, xm and discharging atoms sdtlseqdt0(all_0_0_0, xm), sdtlseqdt0(xm, all_0_0_0), aNaturalNumber0(all_0_0_0), aNaturalNumber0(xm), yields:
% 57.55/21.71 | (158) all_0_0_0 = xm
% 57.55/21.71 |
% 57.55/21.71 | Equations (158) can reduce 117 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (335) ~ sdtlseqdt0(all_0_0_0, xm)
% 57.55/21.71 | (439) xq = xp | xl = sz00
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (439), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (96) xl = sz00
% 57.55/21.71 |
% 57.55/21.71 | Equations (96) can reduce 10 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (10) ~ (xl = sz00)
% 57.55/21.71 | (443) xq = xp
% 57.55/21.71 |
% 57.55/21.71 | Equations (443) can reduce 103 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (445) ~ (all_27_0_7 = all_25_0_6)
% 57.55/21.71 | (446) ? [v0] : ? [v1] : ( ~ (v1 = v0) & sdtpldt0(all_27_0_7, xn) = v0 & sdtpldt0(all_25_0_6, xn) = v1)
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (213), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (268) ~ (sdtpldt0(xn, all_25_0_6) = xn)
% 57.55/21.71 |
% 57.55/21.71 | Using (266) and (268) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (266) sdtpldt0(xn, all_25_0_6) = xn
% 57.55/21.71 | (450) ? [v0] : (sdtpldt0(all_27_0_7, all_25_0_6) = v0 & sdtpldt0(xn, v0) = xn)
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (185), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (268) ~ (sdtpldt0(xn, all_25_0_6) = xn)
% 57.55/21.71 |
% 57.55/21.71 | Using (266) and (268) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (266) sdtpldt0(xn, all_25_0_6) = xn
% 57.55/21.71 | (280) all_27_0_7 = all_25_0_6
% 57.55/21.71 |
% 57.55/21.71 | Equations (280) can reduce 445 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (201) ~ sdtlseqdt0(xl, all_0_0_0)
% 57.55/21.71 | (457) xq = sz00
% 57.55/21.71 |
% 57.55/21.71 | Equations (457) can reduce 199 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (459) sdtasdt0(xl, sz00) = all_0_0_0
% 57.55/21.71 | (460) sdtasdt0(sz00, xl) = all_0_0_0
% 57.55/21.71 |
% 57.55/21.71 | Using (460) and (197) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (460) sdtasdt0(sz00, xl) = all_0_0_0
% 57.55/21.71 | (463) all_0_0_0 = sz00
% 57.55/21.71 |
% 57.55/21.71 | Equations (463) can reduce 193 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (465) sdtpldt0(xn, xm) = sz00
% 57.55/21.71 | (466) xn = sz00
% 57.55/21.71 |
% 57.55/21.71 | Equations (466) can reduce 120 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (468) sdtpldt0(xm, sz00) = all_0_0_0
% 57.55/21.71 | (469) sdtpldt0(sz00, xm) = all_0_0_0
% 57.55/21.71 |
% 57.55/21.71 | Using (469) and (118) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (469) sdtpldt0(sz00, xm) = all_0_0_0
% 57.55/21.71 | (158) all_0_0_0 = xm
% 57.55/21.71 |
% 57.55/21.71 | Equations (158) can reduce 117 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (474) sdtasdt0(xl, all_17_0_2) = xm
% 57.55/21.71 | (475) all_17_0_2 = xp | xl = sz00
% 57.55/21.71 |
% 57.55/21.71 | From (112) and (474) follows:
% 57.55/21.71 | (476) sdtasdt0(xl, xq) = xm
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (75), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (116) ~ (sdtasdt0(xl, xq) = xm)
% 57.55/21.71 |
% 57.55/21.71 | Using (476) and (116) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (476) sdtasdt0(xl, xq) = xm
% 57.55/21.71 | (480) all_0_0_0 = xm | xl = sz00
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (480), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (96) xl = sz00
% 57.55/21.71 |
% 57.55/21.71 | Equations (96) can reduce 10 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (10) ~ (xl = sz00)
% 57.55/21.71 | (158) all_0_0_0 = xm
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (106), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (485) ~ (sdtasdt0(xl, xp) = all_0_0_0)
% 57.55/21.71 |
% 57.55/21.71 | From (158) and (485) follows:
% 57.55/21.71 | (486) ~ (sdtasdt0(xl, xp) = xm)
% 57.55/21.71 |
% 57.55/21.71 | Using (100) and (486) yields:
% 57.55/21.71 | (202) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (488) sdtasdt0(xl, xp) = all_0_0_0
% 57.55/21.71 | (439) xq = xp | xl = sz00
% 57.55/21.71 |
% 57.55/21.71 +-Applying beta-rule and splitting (439), into two cases.
% 57.55/21.71 |-Branch one:
% 57.55/21.71 | (96) xl = sz00
% 57.55/21.71 |
% 57.55/21.71 | Equations (96) can reduce 10 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 |-Branch two:
% 57.55/21.71 | (10) ~ (xl = sz00)
% 57.55/21.71 | (443) xq = xp
% 57.55/21.71 |
% 57.55/21.71 | Equations (443) can reduce 103 to:
% 57.55/21.71 | (97) $false
% 57.55/21.71 |
% 57.55/21.71 |-The branch is then unsatisfiable
% 57.55/21.71 % SZS output end Proof for theBenchmark
% 57.55/21.71
% 57.55/21.71 21123ms
%------------------------------------------------------------------------------