TSTP Solution File: NUM458+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : NUM458+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n013.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 08:44:41 EDT 2022
% Result : Theorem 5.28s 1.89s
% Output : Proof 7.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM458+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n013.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 11:03:29 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.58/0.58 ____ _
% 0.58/0.58 ___ / __ \_____(_)___ ________ __________
% 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.58
% 0.58/0.58 A Theorem Prover for First-Order Logic
% 0.58/0.58 (ePrincess v.1.0)
% 0.58/0.58
% 0.58/0.58 (c) Philipp Rümmer, 2009-2015
% 0.58/0.58 (c) Peter Backeman, 2014-2015
% 0.58/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.58 Bug reports to peter@backeman.se
% 0.58/0.58
% 0.58/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.58
% 0.58/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.63/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.50/0.92 Prover 0: Preprocessing ...
% 2.63/1.26 Prover 0: Constructing countermodel ...
% 3.27/1.43 Prover 0: gave up
% 3.27/1.43 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.63/1.47 Prover 1: Preprocessing ...
% 3.97/1.57 Prover 1: Constructing countermodel ...
% 3.97/1.60 Prover 1: gave up
% 3.97/1.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.37/1.63 Prover 2: Preprocessing ...
% 5.11/1.79 Prover 2: Warning: ignoring some quantifiers
% 5.18/1.80 Prover 2: Constructing countermodel ...
% 5.28/1.89 Prover 2: proved (285ms)
% 5.28/1.89
% 5.28/1.89 No countermodel exists, formula is valid
% 5.28/1.89 % SZS status Theorem for theBenchmark
% 5.28/1.89
% 5.28/1.89 Generating proof ... Warning: ignoring some quantifiers
% 7.42/2.34 found it (size 39)
% 7.42/2.34
% 7.42/2.34 % SZS output start Proof for theBenchmark
% 7.42/2.34 Assumed formulas after preprocessing and simplification:
% 7.42/2.34 | (0) ? [v0] : ( ~ (v0 = 0) & ~ (sz10 = sz00) & sdtlseqdt0(xm, xm) = v0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v3, v1) = v5) | ~ (sdtasdt0(v2, v1) = v4) | ~ (sdtpldt0(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v6 & v11 = v8 & sdtasdt0(v7, v1) = v6 & sdtasdt0(v1, v7) = v8 & sdtasdt0(v1, v3) = v10 & sdtasdt0(v1, v2) = v9 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v2, v3) = v7) | ( ~ (v7 = 0) & aNaturalNumber0(v3) = v7) | ( ~ (v7 = 0) & aNaturalNumber0(v2) = v7) | ( ~ (v7 = 0) & aNaturalNumber0(v1) = v7))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ~ (sdtpldt0(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v9 & v8 = v6 & sdtasdt0(v7, v1) = v9 & sdtasdt0(v3, v1) = v11 & sdtasdt0(v2, v1) = v10 & sdtasdt0(v1, v7) = v6 & sdtpldt0(v10, v11) = v9 & sdtpldt0(v2, v3) = v7) | ( ~ (v7 = 0) & aNaturalNumber0(v3) = v7) | ( ~ (v7 = 0) & aNaturalNumber0(v2) = v7) | ( ~ (v7 = 0) & aNaturalNumber0(v1) = v7))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v3, v1) = v5) | ~ (sdtasdt0(v2, v1) = v4) | ~ (aNaturalNumber0(v1) = 0) | ? [v6] : ? [v7] : (( ~ (v7 = v6) & ~ (v5 = v4) & sdtasdt0(v1, v3) = v7 & sdtasdt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v3, v1) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ~ (aNaturalNumber0(v1) = 0) | ? [v6] : ? [v7] : (( ~ (v7 = v5) & ~ (v6 = v4) & sdtasdt0(v2, v1) = v7 & sdtasdt0(v1, v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v2, v1) = v5) | ~ (sdtasdt0(v1, v3) = v4) | ~ (aNaturalNumber0(v1) = 0) | ? [v6] : ? [v7] : (( ~ (v7 = v5) & ~ (v6 = v4) & sdtasdt0(v3, v1) = v7 & sdtasdt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v1, v3) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ~ (aNaturalNumber0(v1) = 0) | ? [v6] : ? [v7] : (( ~ (v7 = v6) & ~ (v5 = v4) & sdtasdt0(v3, v1) = v7 & sdtasdt0(v2, v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v3, v1) = v5) | ~ (sdtpldt0(v2, v1) = v4) | ? [v6] : ? [v7] : (( ~ (v7 = v6) & ~ (v5 = v4) & sdtpldt0(v1, v3) = v7 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v3, v1) = v5) | ~ (sdtpldt0(v1, v2) = v4) | ? [v6] : ? [v7] : (( ~ (v7 = v5) & ~ (v6 = v4) & sdtpldt0(v2, v1) = v7 & sdtpldt0(v1, v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v2, v1) = v5) | ~ (sdtpldt0(v1, v3) = v4) | ? [v6] : ? [v7] : (( ~ (v7 = v5) & ~ (v6 = v4) & sdtpldt0(v3, v1) = v7 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = v2 | ~ (sdtpldt0(v1, v3) = v5) | ~ (sdtpldt0(v1, v2) = v4) | ? [v6] : ? [v7] : (( ~ (v7 = v6) & ~ (v5 = v4) & sdtpldt0(v3, v1) = v7 & sdtpldt0(v2, v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, v3) = v5) | ~ (sdtasdt0(v1, v2) = v4) | ? [v6] : ? [v7] : ((v7 = v5 & sdtasdt0(v2, v3) = v6 & sdtasdt0(v1, v6) = v5) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v4, v1) = v5) | ~ (sdtpldt0(v2, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v5 & v9 = v6 & sdtasdt0(v3, v1) = v11 & sdtasdt0(v2, v1) = v10 & sdtasdt0(v1, v4) = v6 & sdtasdt0(v1, v3) = v8 & sdtasdt0(v1, v2) = v7 & sdtpldt0(v10, v11) = v5 & sdtpldt0(v7, v8) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v3) = v4) | ~ (sdtasdt0(v1, v4) = v5) | ? [v6] : ? [v7] : ((v7 = v5 & sdtasdt0(v6, v3) = v5 & sdtasdt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v1, v4) = v5) | ~ (sdtpldt0(v2, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v9 & v8 = v5 & sdtasdt0(v4, v1) = v9 & sdtasdt0(v3, v1) = v11 & sdtasdt0(v2, v1) = v10 & sdtasdt0(v1, v3) = v7 & sdtasdt0(v1, v2) = v6 & sdtpldt0(v10, v11) = v9 & sdtpldt0(v6, v7) = v5) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v4, v3) = v5) | ~ (sdtpldt0(v1, v2) = v4) | ? [v6] : ? [v7] : ((v7 = v5 & sdtpldt0(v2, v3) = v6 & sdtpldt0(v1, v6) = v5) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtpldt0(v2, v3) = v4) | ~ (sdtpldt0(v1, v4) = v5) | ? [v6] : ? [v7] : ((v7 = v5 & sdtpldt0(v6, v3) = v5 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v3) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (sdtmndt0(v2, v1) = v3) | ~ (sdtpldt0(v1, v4) = v2) | ? [v5] : (( ~ (v5 = 0) & sdtlseqdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v4) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (sdtmndt0(v2, v1) = v3) | ~ (aNaturalNumber0(v4) = 0) | ? [v5] : (( ~ (v5 = v2) & sdtpldt0(v1, v4) = v5) | ( ~ (v5 = 0) & sdtlseqdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (sdtmndt0(v2, v1) = v3) | ~ (sdtpldt0(v1, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & sdtlseqdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (sdtmndt0(v2, v1) = v3) | ~ (aNaturalNumber0(v3) = v4) | ? [v5] : (( ~ (v5 = 0) & sdtlseqdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v3, v1) = v4) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v4) & ~ (v6 = v5) & sdtasdt0(v2, v1) = v7 & sdtasdt0(v1, v3) = v6 & sdtasdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v2, v1) = v4) | ~ (aNaturalNumber0(v3) = 0) | ~ (aNaturalNumber0(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v4) & ~ (v6 = v5) & sdtasdt0(v3, v1) = v7 & sdtasdt0(v1, v3) = v6 & sdtasdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v1, v3) = v4) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v6) & ~ (v5 = v4) & sdtasdt0(v3, v1) = v7 & sdtasdt0(v2, v1) = v6 & sdtasdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | v1 = sz00 | ~ (sdtasdt0(v1, v2) = v4) | ~ (aNaturalNumber0(v3) = 0) | ~ (aNaturalNumber0(v1) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v6) & ~ (v5 = v4) & sdtasdt0(v3, v1) = v7 & sdtasdt0(v2, v1) = v6 & sdtasdt0(v1, v3) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (sdtpldt0(v3, v1) = v4) | ~ (aNaturalNumber0(v2) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v4) & ~ (v6 = v5) & sdtpldt0(v2, v1) = v7 & sdtpldt0(v1, v3) = v6 & sdtpldt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (sdtpldt0(v2, v1) = v4) | ~ (aNaturalNumber0(v3) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v4) & ~ (v6 = v5) & sdtpldt0(v3, v1) = v7 & sdtpldt0(v1, v3) = v6 & sdtpldt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (sdtpldt0(v1, v3) = v4) | ~ (aNaturalNumber0(v2) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v6) & ~ (v5 = v4) & sdtpldt0(v3, v1) = v7 & sdtpldt0(v2, v1) = v6 & sdtpldt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v3) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (sdtpldt0(v1, v2) = v4) | ~ (aNaturalNumber0(v3) = 0) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v7 = v6) & ~ (v5 = v4) & sdtpldt0(v3, v1) = v7 & sdtpldt0(v2, v1) = v6 & sdtpldt0(v1, v3) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (sdtpldt0(v1, v4) = v2) | ? [v5] : (( ~ (v5 = 0) & aNaturalNumber0(v4) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sdtlseqdt0(v1, v2) = v3) | ~ (aNaturalNumber0(v4) = 0) | ? [v5] : (( ~ (v5 = v2) & sdtpldt0(v1, v4) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtmndt0(v4, v3) = v2) | ~ (sdtmndt0(v4, v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtlseqdt0(v4, v3) = v2) | ~ (sdtlseqdt0(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] : ( ~ (sdtmndt0(v2, v1) = v3) | ~ (sdtpldt0(v1, v3) = v4) | ? [v5] : ((v5 = 0 & aNaturalNumber0(v3) = 0) | ( ~ (v5 = 0) & sdtlseqdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtmndt0(v2, v1) = v3) | ~ (aNaturalNumber0(v3) = v4) | ? [v5] : ((v5 = v2 & sdtpldt0(v1, v3) = v2) | ( ~ (v5 = 0) & sdtlseqdt0(v1, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | v1 = sz00 | ~ (aNaturalNumber0(v3) = 0) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & ~ (v5 = v4) & sdtasdt0(v3, v1) = v7 & sdtasdt0(v2, v1) = v6 & sdtasdt0(v1, v3) = v5 & sdtasdt0(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (aNaturalNumber0(v3) = 0) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & ~ (v5 = v4) & sdtpldt0(v3, v1) = v7 & sdtpldt0(v2, v1) = v6 & sdtpldt0(v1, v3) = v5 & sdtpldt0(v1, v2) = v4)) & ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (aNaturalNumber0(v3) = v2) | ~ (aNaturalNumber0(v3) = v1)) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v2, v1) = v3) | ? [v4] : ((v4 = v3 & sdtasdt0(v1, v2) = v3) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v1, v2) = v3) | ? [v4] : ((v4 = v3 & sdtasdt0(v2, v1) = v3) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtasdt0(v1, v2) = v3) | ? [v4] : ((v4 = 0 & aNaturalNumber0(v3) = 0) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v2, v1) = v3) | ? [v4] : ((v4 = v3 & sdtpldt0(v1, v2) = v3) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ((v4 = v3 & sdtpldt0(v2, v1) = v3) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtpldt0(v1, v2) = v3) | ? [v4] : ((v4 = 0 & aNaturalNumber0(v3) = 0) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v1] : ! [v2] : (v2 = sz00 | v1 = sz00 | ~ (sdtasdt0(v1, v2) = sz00) | ? [v3] : (( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : (v2 = sz00 | ~ (sdtpldt0(v1, v2) = sz00) | ? [v3] : (( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : (v1 = sz00 | ~ (sdtpldt0(v1, v2) = sz00) | ? [v3] : (( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (sdtlseqdt0(v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v2 & v4 = 0 & sdtpldt0(v1, v3) = v2 & aNaturalNumber0(v3) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (sdtlseqdt0(v1, v2) = 0) | ? [v3] : (( ~ (v3 = 0) & aNaturalNumber0(v2) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | (sdtmndt0(v2, v1) = v3 & ! [v4] : (v4 = v3 | ~ (sdtpldt0(v1, v4) = v2) | ? [v5] : ( ~ (v5 = 0) & aNaturalNumber0(v4) = v5)) & ! [v4] : (v4 = v3 | ~ (aNaturalNumber0(v4) = 0) | ? [v5] : ( ~ (v5 = v2) & sdtpldt0(v1, v4) = v5)) & ! [v4] : (v4 = v2 | ~ (sdtpldt0(v1, v3) = v4)) & ! [v4] : (v4 = 0 | ~ (aNaturalNumber0(v3) = v4)) & ! [v4] : ( ~ (sdtpldt0(v1, v3) = v4) | aNaturalNumber0(v3) = 0) & ! [v4] : ( ~ (aNaturalNumber0(v3) = v4) | sdtpldt0(v1, v3) = v2)))) & ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, sz10) = v2) | ? [v3] : ((v3 = v1 & v2 = v1 & sdtasdt0(sz10, v1) = v1) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, sz00) = v2) | ? [v3] : ((v3 = sz00 & v2 = sz00 & sdtasdt0(sz00, v1) = sz00) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (sdtasdt0(sz10, v1) = v2) | ? [v3] : ((v3 = v1 & v2 = v1 & sdtasdt0(v1, sz10) = v1) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (sdtasdt0(sz00, v1) = v2) | ? [v3] : ((v3 = sz00 & v2 = sz00 & sdtasdt0(v1, sz00) = sz00) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, sz00) = v2) | ? [v3] : ((v3 = v1 & v2 = v1 & sdtpldt0(sz00, v1) = v1) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ! [v2] : ( ~ (sdtpldt0(sz00, v1) = v2) | ? [v3] : ((v3 = v1 & v2 = v1 & sdtpldt0(v1, sz00) = v1) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3))) & ! [v1] : ( ~ (aNaturalNumber0(v1) = 0) | (sdtasdt0(v1, sz10) = v1 & sdtasdt0(sz10, v1) = v1)) & ! [v1] : ( ~ (aNaturalNumber0(v1) = 0) | (sdtasdt0(v1, sz00) = sz00 & sdtasdt0(sz00, v1) = sz00)) & ! [v1] : ( ~ (aNaturalNumber0(v1) = 0) | (sdtpldt0(v1, sz00) = v1 & sdtpldt0(sz00, v1) = v1)) & ? [v1] : ? [v2] : ? [v3] : sdtmndt0(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : sdtlseqdt0(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : sdtasdt0(v2, v1) = v3 & ? [v1] : ? [v2] : ? [v3] : sdtpldt0(v2, v1) = v3 & ? [v1] : ? [v2] : aNaturalNumber0(v1) = v2)
% 7.86/2.41 | Instantiating (0) with all_0_0_0 yields:
% 7.86/2.41 | (1) ~ (all_0_0_0 = 0) & ~ (sz10 = sz00) & sdtlseqdt0(xm, xm) = all_0_0_0 & aNaturalNumber0(xm) = 0 & aNaturalNumber0(sz10) = 0 & aNaturalNumber0(sz00) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v5 & v10 = v7 & sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v7 = v5 & sdtasdt0(v6, v0) = v8 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v4 & v8 = v5 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v9, v10) = v4 & sdtpldt0(v6, v7) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v7 = v4 & sdtasdt0(v3, v0) = v8 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v5, v6) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v2) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v1) = v3) | ~ (aNaturalNumber0(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(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] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : ((v4 = v1 & sdtpldt0(v0, v2) = v1) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | v0 = sz00 | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v2) = v4 & sdtasdt0(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3))) & ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (sdtmndt0(v1, v0) = v2 & ! [v3] : (v3 = v2 | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3] : (v3 = v2 | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4)) & ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v2) = v3)) & ! [v3] : (v3 = 0 | ~ (aNaturalNumber0(v2) = v3)) & ! [v3] : ( ~ (sdtpldt0(v0, v2) = v3) | aNaturalNumber0(v2) = 0) & ! [v3] : ( ~ (aNaturalNumber0(v2) = v3) | sdtpldt0(v0, v2) = v1)))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(sz10, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(sz00, v0) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(v0, sz10) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(v0, sz00) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(sz00, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(v0, sz00) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2))) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz10) = v0 & sdtasdt0(sz10, v0) = v0)) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz00) = sz00 & sdtasdt0(sz00, v0) = sz00)) & ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtpldt0(v0, sz00) = v0 & sdtpldt0(sz00, v0) = v0)) & ? [v0] : ? [v1] : ? [v2] : sdtmndt0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sdtlseqdt0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sdtasdt0(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : sdtpldt0(v1, v0) = v2 & ? [v0] : ? [v1] : aNaturalNumber0(v0) = v1
% 7.86/2.44 |
% 7.86/2.44 | Applying alpha-rule on (1) yields:
% 7.86/2.44 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.44 | (3) ! [v0] : ! [v1] : (v1 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.44 | (4) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz10) = v0 & sdtasdt0(sz10, v0) = v0))
% 7.86/2.44 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 7.86/2.44 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & sdtasdt0(v1, v2) = v5 & sdtasdt0(v0, v5) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.44 | (7) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtasdt0(v0, sz00) = sz00 & sdtasdt0(sz00, v0) = sz00))
% 7.86/2.44 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.44 | (9) ? [v0] : ? [v1] : aNaturalNumber0(v0) = v1
% 7.86/2.44 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5)))
% 7.86/2.44 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 7.86/2.44 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v1) = v3) | ~ (aNaturalNumber0(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.45 | (13) ? [v0] : ? [v1] : ? [v2] : sdtmndt0(v1, v0) = v2
% 7.86/2.45 | (14) ! [v0] : ! [v1] : (v0 = sz00 | ~ (sdtpldt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.45 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v1, v2) = v3) | ~ (sdtasdt0(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtasdt0(v5, v2) = v4 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.45 | (16) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | v0 = sz00 | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v2) = v4 & sdtasdt0(v0, v1) = v3))
% 7.86/2.45 | (17) ? [v0] : ? [v1] : ? [v2] : sdtlseqdt0(v1, v0) = v2
% 7.86/2.45 | (18) ~ (sz10 = sz00)
% 7.86/2.45 | (19) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz10, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(v0, sz10) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.45 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4)))
% 7.86/2.45 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.45 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v7 = v5 & sdtasdt0(v6, v0) = v8 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v6) = v5 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6)))
% 7.86/2.45 | (23) ! [v0] : ( ~ (aNaturalNumber0(v0) = 0) | (sdtpldt0(v0, sz00) = v0 & sdtpldt0(sz00, v0) = v0))
% 7.86/2.45 | (24) ? [v0] : ? [v1] : ? [v2] : sdtasdt0(v1, v0) = v2
% 7.86/2.45 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.45 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : ((v4 = v1 & sdtpldt0(v0, v2) = v1) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.45 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v4) | ~ (sdtpldt0(v0, v2) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.45 | (28) aNaturalNumber0(xm) = 0
% 7.86/2.45 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v3, v2) = v4) | ~ (sdtpldt0(v0, v1) = v3) | ? [v5] : ? [v6] : ((v6 = v4 & sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.45 | (30) ! [v0] : ! [v1] : ( ~ (sdtpldt0(sz00, v0) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(v0, sz00) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.45 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v0, v2) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.45 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0))
% 7.86/2.45 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.45 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (sdtlseqdt0(v0, v1) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.46 | (35) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz10) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtasdt0(sz10, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.46 | (36) ! [v0] : ! [v1] : ( ~ (sdtpldt0(v0, sz00) = v1) | ? [v2] : ((v2 = v0 & v1 = v0 & sdtpldt0(sz00, v0) = v0) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.46 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v2, v0) = v6 & sdtpldt0(v1, v0) = v5 & sdtpldt0(v0, v2) = v4 & sdtpldt0(v0, v1) = v3))
% 7.86/2.46 | (38) ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v1 & v3 = 0 & sdtpldt0(v0, v2) = v1 & aNaturalNumber0(v2) = 0) | ( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.46 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : ((v4 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.46 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtpldt0(v1, v0) = v6 & sdtpldt0(v0, v2) = v5 & sdtpldt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.46 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.46 | (42) ! [v0] : ! [v1] : (v1 = sz00 | v0 = sz00 | ~ (sdtasdt0(v0, v1) = sz00) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.46 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 7.86/2.46 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0))
% 7.86/2.46 | (45) ? [v0] : ? [v1] : ? [v2] : sdtpldt0(v1, v0) = v2
% 7.86/2.46 | (46) ! [v0] : ! [v1] : ( ~ (sdtasdt0(v0, sz00) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(sz00, v0) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.46 | (47) aNaturalNumber0(sz10) = 0
% 7.86/2.46 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (sdtpldt0(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v5 & v10 = v7 & sdtasdt0(v6, v0) = v5 & sdtasdt0(v0, v6) = v7 & sdtasdt0(v0, v2) = v9 & sdtasdt0(v0, v1) = v8 & sdtpldt0(v8, v9) = v7 & sdtpldt0(v1, v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v2) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v1) = v6) | ( ~ (v6 = 0) & aNaturalNumber0(v0) = v6)))
% 7.86/2.46 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4)))
% 7.86/2.46 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = 0 & aNaturalNumber0(v2) = 0) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 7.86/2.46 | (51) sdtlseqdt0(xm, xm) = all_0_0_0
% 7.86/2.46 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v3, v0) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v4 & v8 = v5 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v3) = v5 & sdtasdt0(v0, v2) = v7 & sdtasdt0(v0, v1) = v6 & sdtpldt0(v9, v10) = v4 & sdtpldt0(v6, v7) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.46 | (53) aNaturalNumber0(sz00) = 0
% 7.86/2.46 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : (( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4) | ( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.46 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtpldt0(v1, v2) = v3) | ~ (sdtpldt0(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = v4 & sdtpldt0(v5, v2) = v4 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.46 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 7.86/2.46 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v0, v1) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v1, v0) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 7.86/2.46 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v0, v2) = v4) | ~ (sdtasdt0(v0, v1) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v1, v0) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5)))
% 7.86/2.46 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : (( ~ (v4 = 0) & sdtlseqdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v0) = v4)))
% 7.86/2.46 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtpldt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtpldt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 7.86/2.46 | (61) ~ (all_0_0_0 = 0)
% 7.86/2.46 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v3) | ~ (aNaturalNumber0(v2) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v1) = v4)))
% 7.86/2.47 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v3) | ~ (aNaturalNumber0(v1) = 0) | ~ (aNaturalNumber0(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v6 = v3) & ~ (v5 = v4) & sdtasdt0(v1, v0) = v6 & sdtasdt0(v0, v2) = v5 & sdtasdt0(v0, v1) = v4) | ( ~ (v4 = 0) & aNaturalNumber0(v2) = v4)))
% 7.86/2.47 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1) | ~ (aNaturalNumber0(v2) = v0))
% 7.86/2.47 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v1, v0) = v4) | ~ (sdtasdt0(v0, v2) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v4) & ~ (v5 = v3) & sdtasdt0(v2, v0) = v6 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5)))
% 7.86/2.47 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (sdtasdt0(v0, v3) = v4) | ~ (sdtpldt0(v1, v2) = v3) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v7 = v4 & sdtasdt0(v3, v0) = v8 & sdtasdt0(v2, v0) = v10 & sdtasdt0(v1, v0) = v9 & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5 & sdtpldt0(v9, v10) = v8 & sdtpldt0(v5, v6) = v4) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.47 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | ~ (sdtpldt0(v2, v0) = v4) | ~ (sdtpldt0(v1, v0) = v3) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtpldt0(v0, v2) = v6 & sdtpldt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v0) = v5)))
% 7.86/2.47 | (68) ! [v0] : ! [v1] : ( ~ (sdtlseqdt0(v0, v1) = 0) | ? [v2] : (( ~ (v2 = 0) & aNaturalNumber0(v1) = v2) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2) | (sdtmndt0(v1, v0) = v2 & ! [v3] : (v3 = v2 | ~ (sdtpldt0(v0, v3) = v1) | ? [v4] : ( ~ (v4 = 0) & aNaturalNumber0(v3) = v4)) & ! [v3] : (v3 = v2 | ~ (aNaturalNumber0(v3) = 0) | ? [v4] : ( ~ (v4 = v1) & sdtpldt0(v0, v3) = v4)) & ! [v3] : (v3 = v1 | ~ (sdtpldt0(v0, v2) = v3)) & ! [v3] : (v3 = 0 | ~ (aNaturalNumber0(v2) = v3)) & ! [v3] : ( ~ (sdtpldt0(v0, v2) = v3) | aNaturalNumber0(v2) = 0) & ! [v3] : ( ~ (aNaturalNumber0(v2) = v3) | sdtpldt0(v0, v2) = v1))))
% 7.86/2.47 | (69) ! [v0] : ! [v1] : ( ~ (sdtasdt0(sz00, v0) = v1) | ? [v2] : ((v2 = sz00 & v1 = sz00 & sdtasdt0(v0, sz00) = sz00) | ( ~ (v2 = 0) & aNaturalNumber0(v0) = v2)))
% 7.86/2.47 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v1 | v0 = sz00 | ~ (sdtasdt0(v2, v0) = v4) | ~ (sdtasdt0(v1, v0) = v3) | ~ (aNaturalNumber0(v0) = 0) | ? [v5] : ? [v6] : (( ~ (v6 = v5) & ~ (v4 = v3) & sdtasdt0(v0, v2) = v6 & sdtasdt0(v0, v1) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v2) = v5) | ( ~ (v5 = 0) & aNaturalNumber0(v1) = v5)))
% 7.86/2.47 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (sdtasdt0(v1, v0) = v2) | ? [v3] : ((v3 = v2 & sdtasdt0(v0, v1) = v2) | ( ~ (v3 = 0) & aNaturalNumber0(v1) = v3) | ( ~ (v3 = 0) & aNaturalNumber0(v0) = v3)))
% 7.86/2.47 |
% 7.86/2.47 | Instantiating formula (23) with xm and discharging atoms aNaturalNumber0(xm) = 0, yields:
% 7.86/2.47 | (72) sdtpldt0(xm, sz00) = xm & sdtpldt0(sz00, xm) = xm
% 7.86/2.47 |
% 7.86/2.47 | Applying alpha-rule on (72) yields:
% 7.86/2.47 | (73) sdtpldt0(xm, sz00) = xm
% 7.86/2.47 | (74) sdtpldt0(sz00, xm) = xm
% 7.86/2.47 |
% 7.86/2.47 | Instantiating formula (34) with sz00, all_0_0_0, xm, xm and discharging atoms sdtlseqdt0(xm, xm) = all_0_0_0, aNaturalNumber0(sz00) = 0, yields:
% 7.86/2.47 | (75) all_0_0_0 = 0 | ? [v0] : (( ~ (v0 = xm) & sdtpldt0(xm, sz00) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0))
% 7.86/2.47 |
% 7.86/2.47 | Instantiating formula (37) with sz00, sz10, xm and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 7.86/2.47 | (76) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v0 & sdtpldt0(xm, sz00) = v1 & sdtpldt0(sz10, xm) = v2 & sdtpldt0(sz00, xm) = v3)
% 7.86/2.47 |
% 7.86/2.47 | Instantiating formula (37) with sz10, sz00, xm and discharging atoms aNaturalNumber0(xm) = 0, aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 7.86/2.47 | (77) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v1 & sdtpldt0(xm, sz00) = v0 & sdtpldt0(sz10, xm) = v3 & sdtpldt0(sz00, xm) = v2)
% 7.86/2.47 |
% 7.86/2.47 | Instantiating formula (37) with sz00, sz10, sz10 and discharging atoms aNaturalNumber0(sz10) = 0, aNaturalNumber0(sz00) = 0, yields:
% 7.86/2.47 | (78) sz10 = sz00 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v2 & sdtpldt0(sz10, sz10) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 7.86/2.47 |
% 7.86/2.47 +-Applying beta-rule and splitting (75), into two cases.
% 7.86/2.47 |-Branch one:
% 7.86/2.47 | (79) all_0_0_0 = 0
% 7.86/2.47 |
% 7.86/2.47 | Equations (79) can reduce 61 to:
% 7.86/2.47 | (80) $false
% 7.86/2.47 |
% 7.86/2.47 |-The branch is then unsatisfiable
% 7.86/2.47 |-Branch two:
% 7.86/2.47 | (61) ~ (all_0_0_0 = 0)
% 7.86/2.48 | (82) ? [v0] : (( ~ (v0 = xm) & sdtpldt0(xm, sz00) = v0) | ( ~ (v0 = 0) & aNaturalNumber0(xm) = v0))
% 7.86/2.48 |
% 7.86/2.48 | Instantiating (82) with all_23_0_15 yields:
% 7.86/2.48 | (83) ( ~ (all_23_0_15 = xm) & sdtpldt0(xm, sz00) = all_23_0_15) | ( ~ (all_23_0_15 = 0) & aNaturalNumber0(xm) = all_23_0_15)
% 7.86/2.48 |
% 7.86/2.48 +-Applying beta-rule and splitting (78), into two cases.
% 7.86/2.48 |-Branch one:
% 7.86/2.48 | (84) sz10 = sz00
% 7.86/2.48 |
% 7.86/2.48 | Equations (84) can reduce 18 to:
% 7.86/2.48 | (80) $false
% 7.86/2.48 |
% 7.86/2.48 |-The branch is then unsatisfiable
% 7.86/2.48 |-Branch two:
% 7.86/2.48 | (18) ~ (sz10 = sz00)
% 7.86/2.48 | (87) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(sz10, sz10) = v2 & sdtpldt0(sz10, sz10) = v0 & sdtpldt0(sz10, sz00) = v1 & sdtpldt0(sz00, sz10) = v3)
% 7.86/2.48 |
% 7.86/2.48 +-Applying beta-rule and splitting (76), into two cases.
% 7.86/2.48 |-Branch one:
% 7.86/2.48 | (84) sz10 = sz00
% 7.86/2.48 |
% 7.86/2.48 | Equations (84) can reduce 18 to:
% 7.86/2.48 | (80) $false
% 7.86/2.48 |
% 7.86/2.48 |-The branch is then unsatisfiable
% 7.86/2.48 |-Branch two:
% 7.86/2.48 | (18) ~ (sz10 = sz00)
% 7.86/2.48 | (91) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v0 & sdtpldt0(xm, sz00) = v1 & sdtpldt0(sz10, xm) = v2 & sdtpldt0(sz00, xm) = v3)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating (91) with all_40_0_22, all_40_1_23, all_40_2_24, all_40_3_25 yields:
% 7.86/2.48 | (92) ~ (all_40_0_22 = all_40_1_23) & ~ (all_40_2_24 = all_40_3_25) & sdtpldt0(xm, sz10) = all_40_3_25 & sdtpldt0(xm, sz00) = all_40_2_24 & sdtpldt0(sz10, xm) = all_40_1_23 & sdtpldt0(sz00, xm) = all_40_0_22
% 7.86/2.48 |
% 7.86/2.48 | Applying alpha-rule on (92) yields:
% 7.86/2.48 | (93) ~ (all_40_0_22 = all_40_1_23)
% 7.86/2.48 | (94) sdtpldt0(sz10, xm) = all_40_1_23
% 7.86/2.48 | (95) sdtpldt0(sz00, xm) = all_40_0_22
% 7.86/2.48 | (96) sdtpldt0(xm, sz10) = all_40_3_25
% 7.86/2.48 | (97) ~ (all_40_2_24 = all_40_3_25)
% 7.86/2.48 | (98) sdtpldt0(xm, sz00) = all_40_2_24
% 7.86/2.48 |
% 7.86/2.48 +-Applying beta-rule and splitting (77), into two cases.
% 7.86/2.48 |-Branch one:
% 7.86/2.48 | (84) sz10 = sz00
% 7.86/2.48 |
% 7.86/2.48 | Equations (84) can reduce 18 to:
% 7.86/2.48 | (80) $false
% 7.86/2.48 |
% 7.86/2.48 |-The branch is then unsatisfiable
% 7.86/2.48 |-Branch two:
% 7.86/2.48 | (18) ~ (sz10 = sz00)
% 7.86/2.48 | (102) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v1 = v0) & sdtpldt0(xm, sz10) = v1 & sdtpldt0(xm, sz00) = v0 & sdtpldt0(sz10, xm) = v3 & sdtpldt0(sz00, xm) = v2)
% 7.86/2.48 |
% 7.86/2.48 | Instantiating (102) with all_45_0_26, all_45_1_27, all_45_2_28, all_45_3_29 yields:
% 7.86/2.48 | (103) ~ (all_45_0_26 = all_45_1_27) & ~ (all_45_2_28 = all_45_3_29) & sdtpldt0(xm, sz10) = all_45_2_28 & sdtpldt0(xm, sz00) = all_45_3_29 & sdtpldt0(sz10, xm) = all_45_0_26 & sdtpldt0(sz00, xm) = all_45_1_27
% 7.86/2.48 |
% 7.86/2.48 | Applying alpha-rule on (103) yields:
% 7.86/2.48 | (104) ~ (all_45_0_26 = all_45_1_27)
% 7.86/2.48 | (105) sdtpldt0(sz00, xm) = all_45_1_27
% 7.86/2.48 | (106) sdtpldt0(sz10, xm) = all_45_0_26
% 7.86/2.48 | (107) sdtpldt0(xm, sz00) = all_45_3_29
% 7.86/2.48 | (108) ~ (all_45_2_28 = all_45_3_29)
% 7.86/2.48 | (109) sdtpldt0(xm, sz10) = all_45_2_28
% 7.86/2.48 |
% 7.86/2.48 +-Applying beta-rule and splitting (83), into two cases.
% 7.86/2.48 |-Branch one:
% 7.86/2.48 | (110) ~ (all_23_0_15 = xm) & sdtpldt0(xm, sz00) = all_23_0_15
% 7.86/2.48 |
% 7.86/2.48 | Applying alpha-rule on (110) yields:
% 7.86/2.48 | (111) ~ (all_23_0_15 = xm)
% 7.86/2.48 | (112) sdtpldt0(xm, sz00) = all_23_0_15
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (56) with xm, sz00, all_40_2_24, all_45_3_29 and discharging atoms sdtpldt0(xm, sz00) = all_45_3_29, sdtpldt0(xm, sz00) = all_40_2_24, yields:
% 7.86/2.48 | (113) all_45_3_29 = all_40_2_24
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (56) with xm, sz00, all_23_0_15, all_45_3_29 and discharging atoms sdtpldt0(xm, sz00) = all_45_3_29, sdtpldt0(xm, sz00) = all_23_0_15, yields:
% 7.86/2.48 | (114) all_45_3_29 = all_23_0_15
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (56) with xm, sz00, xm, all_40_2_24 and discharging atoms sdtpldt0(xm, sz00) = all_40_2_24, sdtpldt0(xm, sz00) = xm, yields:
% 7.86/2.48 | (115) all_40_2_24 = xm
% 7.86/2.48 |
% 7.86/2.48 | Combining equations (113,114) yields a new equation:
% 7.86/2.48 | (116) all_40_2_24 = all_23_0_15
% 7.86/2.48 |
% 7.86/2.48 | Simplifying 116 yields:
% 7.86/2.48 | (117) all_40_2_24 = all_23_0_15
% 7.86/2.48 |
% 7.86/2.48 | Combining equations (115,117) yields a new equation:
% 7.86/2.48 | (118) all_23_0_15 = xm
% 7.86/2.48 |
% 7.86/2.48 | Equations (118) can reduce 111 to:
% 7.86/2.48 | (80) $false
% 7.86/2.48 |
% 7.86/2.48 |-The branch is then unsatisfiable
% 7.86/2.48 |-Branch two:
% 7.86/2.48 | (120) ~ (all_23_0_15 = 0) & aNaturalNumber0(xm) = all_23_0_15
% 7.86/2.48 |
% 7.86/2.48 | Applying alpha-rule on (120) yields:
% 7.86/2.48 | (121) ~ (all_23_0_15 = 0)
% 7.86/2.48 | (122) aNaturalNumber0(xm) = all_23_0_15
% 7.86/2.48 |
% 7.86/2.48 | Instantiating formula (64) with xm, all_23_0_15, 0 and discharging atoms aNaturalNumber0(xm) = all_23_0_15, aNaturalNumber0(xm) = 0, yields:
% 7.86/2.48 | (123) all_23_0_15 = 0
% 7.86/2.48 |
% 7.86/2.48 | Equations (123) can reduce 121 to:
% 7.86/2.48 | (80) $false
% 7.86/2.48 |
% 7.86/2.48 |-The branch is then unsatisfiable
% 7.86/2.48 % SZS output end Proof for theBenchmark
% 7.86/2.48
% 7.86/2.48 1895ms
%------------------------------------------------------------------------------